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A lič o - § * * * *g, * º - tº. ~ *. g sº x- ar; . º: .* w r * - —------ …—-- - - - -------------—-----. ld 1.jūj;1ji !!!!!! 2) TSS7 ! ! * * . ºº: Ipºſ: #| Tº ------, - ... . . . . . * r § §ARTz; Sitnºrº...º.º. - #. . . . . . y | ---- º: VEsºxº • * **, * * * * : # IIBRARYºğºof THE # iniWERSITYOFMićiliciº F# tººlſings f, = i ** i Fºr * * * Y- ! -- º i #!º #SS - Słºcurºsºci * * *::::::::::::::: s * º #ºsºsº; wº --mms + t i 5 %. * | *. * * R I I) AN * AIN H RIT. § Tº º ºn tº % § 3. (). RD NA * § rection o CLARKE, R.E. F.R.A.S. under the di S XANDER ROS % .3% AL S. R.I § & º L. H. JAME § % # "O LONE tº ºwn, * * * tº tº nº § % Tºr ș * ģš § § { 3. 1 sportswoopſ º wº Yºr, , ANI) s § ºwº sº ... tº ſº In ºr tº º § 3. ºn 1 Nº. w * - i § & Q TO THE RIGHT HON ORABLE SECRETARY OF STATE FOR WAR . "THIS WORK IS WITH PERMISS (ON, RE SPECTFULLY DEIDICATED BY HENRY JAMES, I. : CO I, ONE I., R.E. SUPERINTEN 1) ENT OF THE ORI) NAN C E SUlt VEY. ºd w of pn Anct surve Y offict. So UTHAM PTON - 2'- FEB 1 i 85 8. * * * * * *. * PREFACE. THE Principal Tiangulation of the United Kingdom, which was commenced in 1783, under General Roy, for the more immediate purpose of connecting the Observatories of º Greenwich and Paris, and determining the difference of longitude between; them, has been gradually extended, under the successive direction of Colonel Williams, General Mudge, General Colby, Colonel Hall, and myself over the entire United Kingdom, to form. the basis of the National Survey; it is now finished, and an account of all the operations connected with the work is given in this volume. - But the details of the measurement of the bases, with a full description of the instru- ments employed for taking the angles between the Trigonometrical Stations and the Astro- nomical Observations, and a full account of the successive steps which have been taken in the . progress of the work, will be found in the previously published works of the Survey, a list of which is subjoined. - - . . . * * * * * + * , - , * . . . .."-- # *... * I have also given a list of the names of all the Officers and Non-commissioned Officer , ºr - who have been Personally engaged either in the measurement of the Bases or in taking sº * * * * * , * ~ * . . . * * * *, * * -, * “. . ." the Trigonometrical or Astronomical Observations, and I deeply regret that the late gº ; : « Major-General Colby, who for twenty-seven years held the office of Superintendent of . º the Survey, and under whose able direction the Triangulation was extended over the whole of Ireland and the far greater portion of Great Britain, did not survive to see the º results of this great work given to the public. l The voluminous computations connected with the reduction of the observations have been made by Lieutenant-Colonel Yolland, Captain Cameron, and Captain Alexander Clarke, tl, * # PREFACE. assisted by Quartermaster Young and Mr. O'Farrell, and a great number of computers; but the chief and most important portion of the work, including all the calculations connected with the determination of the Tigure, Dimensions, and Mean Specific Gravity of the Earth, has been performed by Captain Clarke. w * * * * * * * * ~ * *-*. - r ºr... . . . ... ... . . . I gladly avail myself of this opportunity of expressing my best thanks to G. B. Airy, Esq., the Astronomer Royal, for the valuable advice and assistance which we have uniformly ** received from him during the progress of the work. . . . . . . . . . . . . . .” . . . . . . . . . . . . HENRY JAMES, .* ‘. * * * * - s’ . . . & - + . . . º - - i * > ORDNANCE SURVEY OFFICE, . . . . . Lieut.-Colonel R.E., and Colonel. 2nd February 1858. . . . . . . . . . . . . . . . g - r - - - - - - * * . . - -- - r . . . . - * . .' . :- * * 4 k. º . . . ~ * * * º tº- + º' {{#s •. 1 * * # ~. * : * * **, $ º gº h •r • sº * * . * * † * * * vº •. : , , r e r º f ** * * *.* -- * # * * * ºf ~~~ •wrº * cº- k * | rº *}. - * r + * * *... -- ** * , - i I iſ m * * * * * *-* - * * *s * * - ‘. . . * * **::::, # * , > * * " * . * * º * * * .* r -- ** __ ºf r # * *: # --- .* *s- #-k s} ºf ''," *s * * : f : 1..? • * ": *...* s * ** * ºr º ** * * . ~~ * + ºr * ‘. . . . ; : - - - * Fºr , ºr f . º +. *- ** * * * ** r: . . . . . . . . . . . . . . . • * * * * * * * * * * * • - - - - - - - - - - - tº ſº tº º º ſº tº Method of observing with the Theodolite................................ * * * * . . . . . . . . . . * * * * . . . * * * * * , - * 6 tº º º ſº tº C tº $ & 8 º' is tº e g º is © C C C C & 52. - j, * . . . . » - for Azimuth......................................... - tº º º ſº. 56 P*ription of the Zenith Sector ................................................. • . . . . . . . . . . . . . . . 59 Method of observing with the Zenith Sector ............................... * * * * * * , * i. - - . e e º e s tº a C & 62 SECTION III–Reduction of Observations e e s e º e º e e s e s e e o e o e o 'o e º 'º e s e e º 'º e s s .. ....... * * * * * * . . Reduction of Horizontal Angles .............................................. * tº e º 'º º º 67 “. . . . . . . Corrections to Azimuthal Observations “................................ - * ~ 3 - * * * * * : . . . SECTION IV.-Obse - - * * * * • * * * * * * * * : . . . . . . . - a . - - * - …“ 71 rvations, Terrestrial and Astronomical ................... * * * * - ſº - e e s e s e e s e s e º e º 'º e º e º 'º e º 'º' 72 Horizontal Angles observed at the different stations ~ - . . . . . . . . . . . . . . . . . 67 * * * * . . . ; Azimuthal 9bservations............................. “…...........…” à. ious *esults of Observations made with the Zenith Sectors for the Latitudes of var . I98 : . " " ' " ' " . . . . . . . . . . points in the Triangulation ~~~~ • 4 t . V-Measurement of Base Lines.... * * * * t , : SECTION. *. 2OO * * * † - - tº C C, C © C Q Q & © & Q & Q Q D & © & -- -- - & Q & © tº 0 & 0 & & G & © tº 0 & 9 º C & © tº 6 c e º 'º º e º c tº tº e º O L Q is tº tº - - - - - º - * → 2OO "Compensation Bars..... * * * * * * * * * * * * * * * - ... . . . . . . . . . . . . . . . . . . . 293 Standards “.......................................................................... ~~~~ 2O4. Comparisons of Standards ~~~~ .............. 206 - * “” “… Hounslow Heath Base, tº: 2 IO - Salisbury Plain and Misterton Carr Bases ..............................“ ... . . . . . . . 2 II * . ...... Rhuddlan Marsh *º 213 : “......... Lough **:::::::::::::::::::::..................................…” *** * + . . . . ~ e c e s e e o 'º e º s e s tº e º 'º e º 'º 9 º' " 2I4. Remeasurement of Salisbury Plain Base IIl 1849.................. º, º º ... ſº º - b º * * * * ~ * X CONTENTS. - s I’age SECTION VI.-Principles of Calculation • * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *'. . . . . . . . . . . . . . . . . . . . . . . 228 Coordinates in the Meridian Flane, Radius of Curvature, &c. .............................. 228 Of the mutual relations of two points on a Spheroidal Surface .............................. 230 Dalby's Theorem.......” “........................................... 235 Of Spheroidal Triangles. Legendre's Theorem ................................................ 237 Latitudes, Longitudes, and Azimuths ............................................................ 246 ... ... Combination of Observations. Theory of most probable. Corrections....................... .255. Meridian Arcs....” “.................................................................. 264 * . . . M. º. - + ºf + = # * * ... Logarithms........:” “..............................................:::::::::............ 268. - º 7 * * * * * * * , # 2 g º º sº, sº ºn s - * +: * * * * * sº : : * * , ^i, + x- * * * * * * ** } # #: * . . . . . . . . . ; * * * * . . . * * * * * * * * * * ~ * * * * * * * * v- * * * * - * * * * * * * * . . . . . . * . . . . . . . . . - - ... " . . . . . . +*ā- ºr ºf .- : * ~ *r -, ...” - # * - - # * * - * i # -: * * == -F - VII.-Reducti he Tri lati f SECTION II, Re alction O the rtangu ation e e s e e o 'º e s e o 'º e º e s e e s is e º 'º e º 'º e º 'º e º 'º º e º 'º 6 s 6 tº e º 'º e o e º e s tº e º 'º e 27I ×r - . . . * * x , * , ºf ... -- > * # . . . tº t . . . . . . . . * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * . . . . . . . . . . . . . .. * . * * * * : * ~ * : * ' * * * * * * , , - . . . *-* * * - . ... ', ". - -- r * * r * : * . . . . . . . . . . . . .......Division of Triangulation into Figures............................ “. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 ... ... .... ... Method.of Calculation.exemplified in Figure I'..................…......... 278 ... ... . . . . Geometrical Equations for the whole Triangulation.….......................................... 307 ... . . .....I'esulting Algebraic Equations of Condition, between the Corrections, to the observed * * * * * * * * r * * * * * * * Bearings........................................................“....... 327 Values of Corrections finally deduced ............................................................ 372 .............Connection of Special Points with the Triangulation ..........…............................: 394 Base Line Extremities .................................…“… 394 to 4oo ` Zenith Sector Stations and Observatories..........................….: .......... 401 to 411 ``'Connection of the points Mordington and Burnswark......................................... 412 Tables showing Mean Amounts of the Corrections ............................................. 414 : s * * * # * * * * * * * * * * * * * * -- * * * * = * * * * * º -: * - ". . . . + “. . ." * * * * I * * * * * * * * . . . . . . . . * * * * * * * * *. * v -, * * * * * * .* * * • . . . . . . . . . • , , * * * * * ~. . . . . . -- : * * * * * * *- : * > . . ; r & f . . . - * + - a . * * ** " .." -- *** *. : * * * * * * - -- # * . . . - # * * **s * * * * * * w tº sº. " ft. * * f # * ** • - * J. + * ... * -a - : # * * * * * * * * * *, *, * > * * * * * * * * * * * * * * * , ". . * -, - " .. # F -º , ºr -r, & : - , , ' ". . . ..” * : ... tº . . . - w * * * t # * * “r - - - - -- - , . - SE º III ſº i. cº- -- ºr r * *... . ; : * ‘VIII.-Triangles. and JDistances , - . . . . . . * : * - i : ſº {} ſº i. § e e o se e s e s e s e e s so e o e s e e s e e º 'o e o e º e o e º e º e º 'º 9 ° 9 ° 9 °.9 ° 0.9 ° 9 • * * * * * * * * * * - *g *- 3. -- * * * * r * * * * • * f .*. - - r * * f : . * -: * . . . } * * * * * = s. * -- - * * * - - - • , w - § - * * * # * tº ** - ** * * * # * i. • . . * *. f * ... I * , , - • , “” . . . . . . . .” 3 * * : * , , • * * * . .4 * * r r * = < * , , r * * , " . , --- " - r" | Y. r & º , “ . . ." • * - * *** - * . * : * * * * * * * * ~ * * : * ~ * ... • * * - ‘. . . . . . . •' . . , i . . . . . . # * # a "w . # # sº t - - - * + æ à & #. * * * * * * * * * * * * • *::, ... : : F. º . . . . . . . . . . * . . . tº º Comparisóñ. of Băses sº º, , , . . . . º, º tº . . . . . . . . . . . . . . . . . . . . . . . . . . “. . . . . . . . ū ū ſº tº ſº tº g º ºr g g g g g ſº 422 IPrincipal Triangles “..........................................“ 426 to 495 -- . . . . . . . . . . . .” -- tº * § * i tº * : * wº . . ++’. ºr -y * * * : * * * * * -. * * Determination of the Meridional. Distances of Hensbarrow and Ben Hutig, Dunnose:::::: - º > * * * nd Saxavord 6 ** ~ -- ... . . . . ..........” * * * * * * * * * * * : * , ,'...”.” “... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .';***::::::::'''''''''''''''''“ - ." - ". . ." •'. ' , " ... * Her * * * * * * * * * * * * * * * > . * * * * * *, * = . . . . . . ….'.S.' ... . . . # * * * * * * * * * * * * * ** * * * * º ** sº • * * a s is A & 8 a. s. s r. ºr 4 + + a s = m. s. * * # * * * * * * * * * * * * * * * * * * . . . . . . . . . . . . . * * * * * * . . . . . . . . . . . , t → • * * * * * * * * * * * * ~ * * * * * * * * * * * * * * * * * * * . . . . . . " " -- " . . . . - * * * • * * * * * * * * * * * * * * * * * * * * : * ~ * ~ * * * * * . . . . . . . . . . . . . . . . sº • 2. : # , * . . . * ... •,•.” * * * ** - - * - f --- - * * * * * * * * > . . . . . . . . . . . . . . . . . . * *** * * * * * *.” ". . . .” -- tº tº ºr." < **** - cº- - - - * * * - - 3. nº {. * ſº * iº * * if ºr * *r ECTION IX—Terrestrial Zenith Distances and Altitudes...........:::::::::::::::::.. O º 6S--- so sº. S. . . . . sºº's sº *** * * * * * * * * * * * * * * * * * * * 9 s: • * * - : r. * , , , ;", ". . . . * * * gº dº ** * * * * • * * * *** § ~ * * * * * * * * * * § t is ºr ºr ºr * * * * * * * * * * * * * * * * * * * * * * * * > . . . . . . . . . . . . . . . . . . ; ; º: . # :* -...-: ~ ::::" . . . . . . . ; , , r: • Y w w w ... . . . . . . ** º * * * * * * * > . . . * * * ...’, ... . . . . . . . . . . . . . . . . . . . . . . . . . . . * * § -- -- - & # * i. ** aſsº 3. -- K. + - ſº tº * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ~ *, * • * : * * * * * * : ... - r * { crºr... . . . Obsérvations “”, “ . . . . . . . . . . . . ......................................: 514 to 539 Coefficient of Refraction. .........::::::::::::::: , , -, * : *, *, *, '.' . . . .--, * *** * * * * * * * * > . . . . . . . . . . . . . . . . . . . . . . * * * * * * * * * * * * * * * * * 542 * r * * * * - r * * * * * * -, - - # º sh +. 1. * * * * : * : * * * ºf * * * * tº f * * * * > * > ... . . " •' . . º . . . ., " :"...", .. “. . . . . . . . . . . ; st g º 'º fºx, sº º º ºf m + º- + - * . . . . . . . . . Tablé of Altitudés of Stations above the mean Lével of the 'Séâ:::::...; 558 > - * *- & e º e º e º e º e s tº e º 'º e º ºs º º 'º e º º e º 'º f - *-* CONTENTs. ºxi ‘....:"; - - Page SE º - . . . . . ** a tº ºr - tº - * - * ~ * * r º - - - *** * * °TION X-Connection of Geodetical and Astronomical Observations........................... 560 ". sº * * * * * * * * * • s ** * * - i. * * * -- - - - +. * ~ * * * * * * * * * * * . . . * ~ * * * . . . . .''. * * . . . . ' ' ' - .. . “. . . *. *. … … ". . . s “. . . * # *.S. - ... Remarks on the original Arc Dunnose to Clifton................................................ 563 '- º º Oñ the Deflection at Tunnose, as inferred from the Latitudes of the Stations selected rº. " " : in its immediate neighbourhood by Lieut.-Colónel Yolland, R.E......................... 569 ... “….. Theory. of the Astronomer. Royal as to the extent.of Local, Attractions..................... 572 “….....“On the ºpeflections produced by given masses................................................... 575 * * * * * * ‘’’ ‘’’ ‘‘..Of the Disturbance produced by a compact and very dense mass below the Surface ... 585 ”9f the Disturbance produced by an elongated and very dense mass below the Surface. 591 ' ' ' ' ' ' " . . . . . . . . . . . 9bservations for the Determination of the Attraction of Mountains........................ 597 Of the Attraction of Arthur's Seat, Edinburgh................................................... 599. * Resulting Value of the mean Density of the Earth ............................................. 609 ‘’’’’’’ ‘’’. ‘On-the-Influence, of Irregularities, in the Mathematical Surface of the Earth on the " # * r *. *Parison of Astronomical and Geodetical Observations................................. 609. * +. - * * * * * * * , * + - -" * * * * * * * * * * * * • * , , f * * * * * * * * * * * * * * * * * * * * * * * * > . . . . . . . . . . . tion *I-Determination of the. Amount of Local Attraction at various Astronomical * - - - - :: ' , , , ; ; Stations in the Triangulation. .. • * * * * * •. se “. . . . . . . . . . e's • . . . . . . . • . . . . . . . . . . . . . . . . . . 625 * * * * Jº * * * * * > ... 3. *' t + ... * { fºr * * - .*, . . * * * * * * *- : * * * * . ; * * * ... " - * * * * * * * * * * * w y if t w x * * * * *... • T. r. - r - + - -- - * : * * , , . " * *-*. * ** * * * * --- * * * * * * - * * * * * *, * * * *- & + * * * * * *- * * * * * * - - - iº -- -- $ *ºr rº sle of Wi ht St 4 * * * * * ~ * : * * * * **-* , , ** * * * * * * . . . . " . . * * *r, ' ' ' - # * * * * * * * * * : * ~ * : * * * * * . . . 62 * * * * ** * - ... ** - - - - * *... . . . .", * . * * g &l 1011S • * * * * * * * * * * * * * * * * * * * * * * * * tº e º e º e º 'º e s e e s is e º s e º e º & C & E & 0 e º e s is a c e s e e s ∈ e º 'º e s sº e º 'º e º º - * - . . . . . . . . * * * * * : *-* * * * d i. * * * * ** … - º - * - r " * : * * +. * - --- - * * * * * ... ." . . * * . . . . . . . . . . . . .” -- . . . . . . . . . . . . . . . . . - . . . " • • * : * > . ‘. . . . . . . . * r-, -: * - ºr - ' - - - - . . . . . . - * * * ~ * - * * * - - #. * * tº e º 'º tº *** ****** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * - * * * * * : * . . . . § . . . . . . . ; : - * - - -- O # Tle r -- : ' ". . . . . * + - - * > - * , , " ' ". . -- -, *, . * * * * • *, * * * - * ~ * . - * * * º - -, tº Ul 1ſ l OOI".. * * - F- - * º tº e e s p → • * * g e º 'º e º e º 0 & º 'º º 4. & * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * tº º º & Q ſº tº * * * * * * , , - * w - a- 4. ‘’’’ ‘’Calton. *inburgh...….…................................................................. 643 Lough Foyle “..............................................i.............................“ 645 ** ~~~~…~~~~ 647 Monach “.........................................................…. 649 Hungry Hill “....................................................................“ 65% Forth “…~~~~ 654 * “…~ * *~…~~~ 658 ** “…~ * Cowhythe ****** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 662 ºr ºr +. - * * * * * *** ****** - *-*-* - ~ *-* * -----------.... . *-** **, *, *s . .” --- a SEC - {} • ‘’ - - -* - ſº TION XII—Determination of the Spheroid most nearly representing the Surface of Great Britain and Ireland........................................................“ 665 ** Observations made with Ramsden's Zenith Sector.................................... 666 Calculation of Latitudes, Longitudes, &c., on approximate Spheroid........................ 674 Calculation of Equations of Condition .................................................…” ‘’” *** Pauations................................................…~ 695 "* …~"… ſº b 2 xii º ‘CONTENTs. SECTION XIII.-Of the Length of the Degree, &c.—Latitudes and Longitudes and Directions of the Meridian at the different Stations........................... Table showing the Lengths of Degrees, Minutes, and Seconds in Great Britain ......... * Table for converting Distances on and perpendicular to the Meridian into Seconds of Arc “"“”''''''''''“. . . . . . . . . ..................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Latitudes and Longitudes of the Stations • . . . Positions of Observatories........................................................................... * Comparisons of observed Azimuths ............................................................... “. . . Tinal Distances between the Parallels of different Astronomical Points .................. * e s e º e º e o 'º e e s e o e s e e s e e s e s et e º 'º e º sº e º e º 'º e s tº e o e º e s p → • e s e e * * * * * * * * * : * . . SECTION XIV.—Figure of the Parth..............................................................“ f f : * * * * * = . . Distance of Parallels of Greenwich and Dunkirk..............................................., -- . . . . . . . Equation for determining the most probable Values of the three Constants entering into the Equation of the Meridian............................................................... . . . . . . . . . . . . Resulting System of Corrections to observed Latitudes ....................................... Determination of the Ellipse most nearly representing the measured Meridian Arcs ... . . . . . . . . . ... Corresponding System of Corrections to the observed Latitudes ........................... … ºxamination of the preceding Results ............................................................ Data of the Problem “............................................................................” Page 717 721 722 723 728 728 732 733 736 743 745 760 * * * * * * ſº # . . . r f # wº- - 4. * * * & ſº " " - - - - - - - - - - - . . . . . . . * * * * * * * * . * * * * * * * * ~ * . . . . . . . . . ! . . . . . . . * * * * * * * * * * * * * * > . . . . . . . . . . . . . . . . * : * * * * : - - - - . . . . . . . , * d * * * * * * * ... + s * * * * * * * : * : . . . . . . . . . ** * * * * * * * w a . . . . . * * * * * * * " " " " - * * * . . . . . tº # * $ * * * * * * * * * * * * * * t * r #º * ' ' ' ' ' ' ' ' ' ' ' ' ' . . . . . . . . . . . . . . . . * . . " * - + + * f : 3. * * * * * * * * : . . . . . . . . . . . . . . . . # *. * *r-w * wr-º-º-º-ºr-wºrwºr-r ** * A * **** * - +º, + º +. * £ 4 & * * * * * * * * * . . . . . •ºr * rº * sº * * * * - - - † -º º & . - - †. • * * * * * * * * r * t * • *. * * 764 766 77o '772 INTRODUCTION. *-*. The National or Parl ... • ºr iamentary Standard Yard having been destroyed in the fire which standard of º °nsumed the Houses - * * tº " * tº º e - - * * * ... Length. Astronoma, D --> of Parliament in 1834, a commission was issued to G. B. Airy, Esq., gth: * Royal, Rev. R. Sheepshanks, and Francis Baily, Esq., to make a new National tandard of Length from the data derived from the previous comparisons which had been ..made between the old Standard Yard and several existing standards, such as the two belonging to the Ordnance Survey, the Royal Astronomical Society's Standard, and others. * - The Wºw Standard Yard (of which two copies—one of bronze, No. 29, and the other i. "ought iron, No. 55—have been sent to me by the Astronomer Royal) is a bar 38 inches º: and 1 inch square in section, with wells at either. extremity drilled out to the depth O & “ . . . . . . * * . * * * * . . . . . - º ºnal at the bottom of these wells transverse lines are drawn on platina, the istance between Which, at the temperature engraved on the bar, is one yard. ... * ; , , The Commissioners have very properly not given the length of the new Standard as *mpared with any other Standard; they have restored the Standard with the greatest - possible accuracy, and the lengths of all others must be found from it by comparison. . The lengths of all the bases and the distances between the Trigonometrical Stations © • tº " & º * • " . . . . - * are given in this volume are in terms of the Io-feet Standard O, , which is the Standard O s . . - º • • - -- - - - - * - 9f the Ordnance Survey; but it is obviously necessary that the length of O, and of the • *ometical distances should be given in terms of the National Ståndard of Length. of I have therefore had a Standard I O * (Intermediate Ordnance) made, on which 3; lengths * the Standard Yard have been set off, and the 10 feet thus obtained has been sºmned with the lo-feet Standard O, . A detailed account of the comparisons will be given in a separate volume; but to obtain the lengths and distances in this volume in terms * the National Standard. of Length, we must add to the log. distances the correction -- tº oooooo 5 (ap * * * Proximate). The amount of difference in Io feet is .oOo.14 inches, and in a mile ‘OZ5, inches. . . . . . . . . 4. -- . . . . . . . . . . . . . . . . . . . . xiv INTRODUCTION. Base Measure- The base-lines from which all the trigonometrical distances have been computed are ***" those which were measured on Salisbury Plain, and on the shore of Lough Foyle in Ireland: they are respectively 6: 93 and 7.89 miles long, and were measured with General Colby's Compensations Bars. The difference between the measured lengths and their lengths as computed through the Triangulation is + o-4178 feet, or about 5 inches. Mean Base. This difference has been divided in proportion to the square roots of the lengths of - the measured bases, from which we have obtained the Mean Base which has been used in the Triangulation; there is, therefore, a difference of + or – o 2 feet, or 2; inches, between the measured and computed length of these bases. - Four other base-lines were measured with Ramsden's 100-feet Steel Chains,—one of Hounslow Heath, one at Misterton Carr near Doncaster, and one at Belhelvie in Aberdeenshire, and the greatest difference between the measured lengths and the computed lengths of these bases from the mean base does not amount to 3 inches. The fourth base was measured in an unfavourable position on Rhuddlan Marsh in North Wales, and the difference between the measured and computed length in this case is I. 596 feet. - HorizontalAngles: The Horizontal Angles, as well as the Azimuthal Bearings of the Stations were principally obtained from observations with Ramsden's great 3-feet Theodolites; and the perfection of these instruments may be judged of from the fact, that the sum of the angles in the triangles rarely differed 3”.4 from the true sum. Correction of To correct the discrepancies thence arising by the theory of probabilities, so as to render the Triangulation consistent in itself, and as perfect {lS possible, has been a work of immense labour; but we should not have done justice to a great national work of this kind if we had failed to render it as perfect as possible before giving it to the public. Lengths of the . The sum of all the distances or sides in the Principal Triangulation is about 206,710,000 jº feet, or, in round numbers, exactly ten times the radius of the Earth (radius of the Earth = 20,890,000). The mean length of a side is 35.4 miles. There are 37 lines whose lengths are between 80 and 90 miles; 18 between 90 and 100 miles in length; and 11 exceeding Ioo miles in length. The longest side in the Triângulation is III miles, viz. that from Slieve Donard to Sca Fell. * * . --- XV INTRODUCTION. r - , , . " " --- 1 - e, 1 sden's Zenith Sector The latitudes of 32 of the stations have been º *: and with Airy's of 8 feet radius, which was destroyed in the fire at ". º From the very close Zenith Sector of 20:5 inches radius, by Troughton an • º º instrument, and the "PProximation of the observed zenith distances of the stars w ~~~ :- ºr 6- . calculated on Airy's The longitudes of the different Stations were m the º º º the observed Figure of the Earth, by using the observed intinue o h º the distances to each azimuth of the meridian mark, and transferring this azimut º are then used to Station in *ccession; the observed latitudes and the º latitude and azimuth ; the determine Corrections to Airy's Figure, and the Greenwic º * corrections. longitudes and latitudes then received their necessary * . - * . . . nsmission of chrono- The longitudes were also determined chronometrically by º º in this way between - . . - º LIIl *ters, and by transit observations; the difference of longitude obtai CIne Q º º r lentia including an al’C th &t points viz Greenwich and Feaghmaan in the Island of Wa 3. 3. ë - W of about ten degree in the position of found to correspond to a difference of 461 feet in th p S, Was foun the Station, as determined geodetically . * * istance from - • ſº T t in the distance It will be observed that there is a difference of about 170 fee iſ . ſº : this great error was unnose to Clifton as given in this volume and that previously published; g detected when the detailed Triangulati ID º - istrict. on was extended over the same dist Latitudesº - . tº itudes, f W tº y actual levelling with Alti he altitudes lany e Stations have been determined by act tical * * iverpool; but the vel a spirit level, and are all referred to the mean tidal level at Liver p ith the ~~ : *-o-º-º: observed with angles, or *enith distances of the Stations, were also reciprocally theodolites. - * : * * a height t - - '... * * * ** Ben Macdui, the heig Since the printing of the computed height (at *...*. º the western side the * that hill has been determined by spirit levelling. By leveling º, side the result was *ight was found ºn 4-95.70 feet, and by *** º also with the computed 4295 76 feet. The agreements of these results with one anothe and - height, 4295.6 feet, are very remarkable. -, - The refraction Was found to . refraction is +. - - • ſº ean refraction is #, the *gles subtended by the Stations from the centre of the Earth; the m - * - * fraction. * - *~!-- ~~~~ ſº # to #: of Re * * * 4-n + r.' re-ſ: '41. A . sphere from F. UO 57. in n . 1 state of the atmo Vary. In a norma ºxvi INTRODUCTION. Figure and Dimensions of the Earth. ‘Density of the Earth. Local Attraction. but we have cases in which the refraction reaches i. and others in which there is no refraction, 2 and a few in which the refraction was actually negative. The great amount of refraction in the morning, its diminution towards the middle of the day, and its increase again towards evening, is obviously caused by the greater amount of aqueous vapour in the lower portion of the atmosphere in the morning and evening, as compared with the amount in the middle of the day. In Airy's Figure of the Earth, the equatorial radius is 20,923,713 feet, and the polar radius is 20,853,810 feet, giving an ellipticity of ; ; but from the Ordnance and other more recent surveys abroad, the axes are found to be 20,926,500 feet and 20,855,400 feet, and the ellipticity about ; ; but the results are slightly dependent on the results to be obtained from the measurement of the Russian arc of meridian, which will probably modify them in some degree; the account of the measurement of the Russian arc is not yet published. The result obtained from pendulum observations gives an ellipticity of . The mean density of the Earth, as determined from the observations at Arthur's Seat, is 5.316. I cannot help regretting that a series of Stations in plains, and in localities where, from the geological structure of the country, we might infer that little or no deflection of the plumb-line could exist, had not been selected for the express purpose of measuring an arc of meridian. The summits of mountains were necessarily selected for the connecting points in the Triangulation; but, from the want of symmetry in the mountains themselves, the irregular manner in which other mountain masses surround the Stations, the diversity in their geological structure, and the unknown distance to which the igneous rocks especially extend below or around, must always leave a doubt upon the determination of the latitudes of such Stations. The minor Triangulation for the detailed survey of the kingdom is now rapidly extending, and I think it not improbable that we shall be able at no distant period to select such a series of Stations as I have described, and thus obtain other arcs of meridians more free from the probability of error than those in the Principal Triangulation. When I directed the observations for the investigation of the amount of the local attraction at Arthur's Seat to be made, we had not only a perfectly contoured plan from which the distribution and quantity of matter in the hills and mountains round it was accurately known, but we knew also the exact geological structure of the country and the specific gravity INTRODUCTION. xvii of the rock, and º * latitudes º º is a discrepancy of 2"...o between the observed and the computed obtain better result s for. I am not satisfied with this result, and believe we should ults if the course I have indicated had been followed. The lat requested º: º when engaged on the Geological Survey of Scotland, was made for dºmi n view the intention of the late General Colby to have observations point out Such m ng the mean density of the Earth, and Dr. M'Culloch was requested to *respondence co Ountains as he thought well suited for the purpose; and I find in the mountains, i nnected with this subject, that he recommended Ben Stack and Seul Wein in the South West of Sutherlandshire, as well suited for the purpose. I ha º . . . . àre jº. the geological structure of the district in which these mountains Geological the old red Sandston º º great series of quartzose micaceous stratified rocks, on which Structure. Series bands of li e of Caithness rests unconformably, and which has at the base of the of limestone and pure white quartz strata. These white quartz strata rest unconform ably upon a coarse red congl & ſº º eiss. glomerate, which again rests unconformably upon the º * º * mountain I have ever examined; it is composed of Seul Wein. * monument of the gre º strata, and stands out by itself on a plain of gneiss, it is about 1500 º high egulation of the * of the Earth in former geological periods: large; and as I fear * verial sides, but the mass of the mountain is not taken near it, I do not º * great inequality in the refraction if observations were determining the mean an ore, consider it well suited for the purpose of observations for -: C y of the Earth. No º ** * - the º º º: º º well mited for the purpose; this mountain is composed of Ben St" hot large, and it h ata resting on the gneiss, and although its form is good, its mass is - th ge, an t it has other mountains round it, and a great range at but a short distance on & northern side, all of which would affect the observations. I sti º º gravit still think we ought to have further observations for determining the , mean specific l { q \ }• g *" of T y of the Earth, and I proposed last year to send a party for this purpose to the Peak CIler º •- - riffe, and I now purpose, as soon as the detailed survey reaches Ben Nevis, to have obs º º º *Vations taken at this the highest mountain in Great Britain. H. JAMES, - , … ………… ;---&- & + … ►►|-）*------***************************«f „...„...„…„…-… * * * *~~~~=+） ***** S E C T I O N I. D E S C R IB TI () N 0 F STATION S. ACKLAM WoLD, 1842, is a large moor in Yorkshire, about I mile east of the village of Acklam, and 3 miles north of the village of Kirby Underdale, and on the left-hand side of the road leading from the latter place to Malton. The station is on the South-eastern rise of the most easterly of two barrows, distant from each other 293 feet, and is marked by a piece of white limestone with a hole in it, placed 1.8 feet. below the surface. ARBURY Hill, 1843, is an insulated eminence in a field belonging to Righton Farm, in the parish of Badby, Northamptonshire, about 1.5 miles west of the village. The hill was visited in 1799 and 1800, and again in 1843, with the Ordnance 3-foot theodolite; but of the point from which the earlier observations were made, no trace is to be found. The station of 1843 is marked by a stone 18 inches square, With a hole to denote the centre, and the words “Arbury Hill, 1843,” cut into it, and sunk 3.8 feet below the general surface. In the bottom of the hole in the Stone, a fourpenny-piece of the present reign, dated 1841, was inserted, but when the stone was examined in 1850 it had been removed. A pole 19 feet high has been erected over the stone. By comparison of the old and new angles, the site of the earlier station is supposed to have been about 5 or 6 feet due east of the new station. *H, 1842. This station is on the highest part of a hill, about 2.25 miles south-west from Buxton, and about a quarter of a mile to the west of the road from Buxton to Leek, in the county of Derby. Observations were taken from the hill in 1807 and in 1842 with the great instruments, but the old station is altogether lost. A pile 17 feet high, built of stone to the height of 4.5 feet, and the remainder of turf, denotes the station of 1842, the centre of which is marked by a stone with a * in it, and inscribed with a broad arrow and the letters “B.O. 1842." The *ce of the stone is about 1 inch below the tops of the pickets of the frame on Which the instrument rested, which were left in the ground. The frame consisted of four upright posts or pickets, 5 feet long, mortised into the corners of a square frame, and strongly braced together. Baconsthorpe ToweR, 1843. This station is in the centre of the top of the tower of the Parish church of Baconsthorpe, in the county of Norfolk, about 4 miles south-east of the town of Holt. -27 A. 2. PRINCIPAL TRIANGULATION. BALLycREEN, 1852. This station is on a sharp-topped mountain, known in its neighbour- hood by the name of Mottee, three quarters of a mile from the fifth milestone on the road from Rathdrum to Baltinglass, in the county of Wicklow. The station point is marked by a hole 1.5 inches deep and I inch in diameter, in a sandstone measuring 12 inches by II, and 9 inches deep, which is jammed between two pieces of rock, and its upper surface level with the general surface of the ground. The frame which supported the instrument in 1852 was left in position, and a pile of turf, 60 feet in circumference at the base and Io. 75 feet high, built over it. BALSIIAM ToweR, 1844. This tower is that of the parish church of Balsham in Cambridge- shire, situated about 6 miles east of Babraham and about 12 miles south-east of Cambridge. tº BALTA, 1817, 1847. This station is situated in the small island of Balta, which lies to the cast of the island of Unst, one of the Shetland Isles. The island is rather more than one mile in length from north to south, and about half a mile in breadth at the broadest part, forming an excellent natural breakwater to Balta Sound. The station is on the highest part of the south end of the island, and is marked by a hole bored in a stone sunk about 2 feet below the natural surface of the ground, and by a pile of earth and stones, 6 feet high, erected over it. Trom this station the zenith-sector station on Balta is distant 215.5 feet, and bears 90° II' from the south. It is marked by a hole in a stone, sunk about 2 feet below the surface. BANSTEAD, 1848. The stations at Banstead, in the county of Surrey, are about half a mile west of the parish church, in a grass field called Tumble Field, on the west side of the road leading from Sutton to Reigate, and opposite the Black Boy Beer-house. The new station of 1848 is 748 feet from the chimney of the house or cottage at the entrance of the field, and is in a line with the chimney and Banstead Church spire: it is marked by a piece of freestone about 12 inches square, with a hole 3 inches deep in the centre, placed 3.2 feet under the surface. The old station of 1792 is 6.2 feet north of the former, and is well marked with a stone, about 6 inches diameter, shaped like a truncated cone, placed with its large end downwards, and about 24 inches below the surface. BARDON HILL, 1842, is in Leicestershire, nearly equidistant from the towns of Leicester, Loughboro’, and Ashby-de-la-Zouch; the turnpike road from Leicester to Ashby-de- la-Zouch passing about half a mile from and on the south side of the hill, at a distance of 9 miles from the former town. The station is situated on a rock near the western side of the summit, and 273-7 feet distant, in a west-by-north direction, from a summer-house on the top of the hill. There have been two sets of observations taken from this hill, both from the same site. A pile was erected, at the conclusion of the first series, above a centre mark bored in the solid rock. This centre was found DESCRIPTION OF STATIONS. 3 and the instrument was placed above it for the observations of 1842, and the site Was also marked by four holes excavated in the rock for the pickets of the frame of the instrument. These pickets were each about 4 feet long, and after being tightly *ged, were run in with lead and well braced together. The pile was restored. BARRow Hill, 1845. This station is situated in a field called “Inner Mill Field,” belonging to Boro' Tarm, in the parish of Chivelstone, in the southern part of Devonshire, and about 8 miles south-east of Kingsbridge. The station is marked by a stone, with a hole drilled in it 2 inches deep, denoting the exact spot from which the obscrvations Wºre made, and sunk 16 inches below the surface of the ground. BAURTREGAUM, 1831. The station is on the western head of a large hill or mountain, about 8 miles South-west of Tralee, and on the left side of the road leading from Tralee to Dingle through Blenerville. Curraheen Chapel is on the Dingle and Tralee road; and a person intending to visit Baurtregaum station from Tralee should leave the Dingle road at this chapel, and pursue the course of a stream upwards for about 2.5 or 3 -o miles. This stream leads to Caum Brack Lough, which is about 1.5 miles east of the station; the passage from Curraheen Chapel to Caum Brack Lough is of easy ascent, * remainder is difficult. The station is marked by a large pile of stones, within Which will be found the centre stone, an irregular piece of sandstone, level with the 8°neral surface, and marked with a hole. * Heap, 1845. This headland in the English Channel is in the parish of Eastbourne, °9"ty of Sussex, about 2 miles south of the town. Observations were taken on the *" in 1793 with the Ordnance 3-foot theodolite, and in 1845 with the 18-inch theodolite; but the sites from whence the angles were taken are not identical, though both are adjacent to the houses occupied by the Coast Guard. The site of the earlier station was marked by an old gun with its breech imbedded in the soil, and its muzzle about 2 or 3 feet above the surface; but when the place was visited in 1842 it had been removed, and a signal-house to which the site was referred had also been pulled down; no vestige therefore of the site could be found, though careful search was "made. In 1844 renewed attempts were made to find some indication of the site, but these being unsuccessful, a point about 105 ſect north-east of the well in the rear of * guard's buildings, was selected as a site for the new station, and marked with a * Stone, measuring 13 inches by 11, with a hole 2 inches deep, and a broad arrow * on the top, over which a pile of turf was erected. The 18-inch theodolite was Placed above this centre stone in 1845. BEACON Hill, 1849. The station on Beacon Hill, in the parish of Bulford near Amesbury, in the county of Wilts, is about 3 miles east-south-east of Amesbury, and about a quarter of a mile north of the Amesbury and Andover road. The station, being the north-east end of the base line measured in 1794 on Salisbury plain, was marked by an iron cannon with its muzzle 8 or Io inches above A 2 .-l.n PRINCIPAL TRIANGULATION. the surface. The calibre of the gun is a little more than 4 inches, and its centre was in the observations of 1849 adopted as the observing station. BEAcon HILL, TREscow, I850. The station so called is situated on the highest part of Beacon Hill, in the island of Trescow, one of the Scilly Isles, and is about 1.5 miles from Old Grimsby. The station is about 60 feet from an old watchlouse. BEN CHEILT, 1819, is a large mountain in the county of Caithness. The station was on BEN BEN the north-western end of the highest part of the hill, which is about a foot higher than the station, and about 400 yards south-east of it. The peat moss, which was about 2 feet deep, was dug out in a circular pit of 8 feet in diameter, which being filled in with clay, the pickets for the instrument were driven into it and braced together. Large stones were laid upon and round the braces to steady them, so that the station is easily discovered, even if the pile which surrounds the staff were removed. - CLEUGH, 1848. This station is situated on the most northerly and one of the most prominent points of the Ochill Hills, in the county of Clackmannan, about 2 miles north of the village of Tillicoultry, and 4 miles north-east of the small town or village of Alva. The station is distinguished by a stone pile, 13 feet high and 36 feet in circumference, erected around the frame on which the instrument stood. The centre of the station is marked by a large flat stone, with a hole in its centre about 4 inches i deep, placed 3 feet below the general surface of the top of the mountain, and by a similar stone placed level with the surface and within the wooden frame or stand which supported the instrument. There is no permanent mark or object near the station from which measurements can be given, but there are several protruding pieces of rock only a few yards distant. The best and easiest way of ascending this hill is from Alva by the Blackforde Horse path, which passes about I mile west of the station. CLIBRIG, 1839. This mountain is situated in the exact centre of Sutherlandshire. With the exception of Ben More in Assynt, which exceeds it by about 70 feet, it is the highest in that county. It lies to the right of the high road from Golspie (through Lairg) to Tongue, and its summit is distant in a south-easterly direction about 4 miles from the inn of Ault-ma-harrow. The top of the hill as seen from the north has a ridge falling gently to the east, but abruptly to the west. The station was not quite at the top of the hill, but at an angle of the ridge, where there was a knoll with a few large stones projecting from the earth. The highest of these stones is from 3 to 4 feet above the centre mark of the pile which was erected on the site of the station. On taking down the old pile, the centre mark was found. The pickets on which the frame of the theodolite rested, were placed in four holes, 6 or 8 inches deep and 4 inches square, drilled in the solid rock. These pickets were about 18 inches DESCRIPTION OF STATIONS. 5 long, and after being tightly wedged were run in with lead. The pile was rebuilt 18 feet high and about 16 feet in diameter. BEN HEYNish, 1822, is an isolated hill in the island of Tiree, one of the Western Isles of BEN BEN BEN Scotland. The hill is composed entirely of gneiss and is flat-topped, but furrowed by shallow ravines dividing it into several points, that on which the station is situate being rather the highest and, by calculation, 462 feet above the mean level of the sea. The centre of the station is marked by a hole bored in the solid rock to the depth of 4 or 5 inches, four other holes of a similar description were also made, into which Wooden pickets were driven for the feet of the large theodolite to rest on; these holes, and a large angular block of gneiss Io or 12 feet high, about 57.5 feet distant from the station in the direction of Canna, will serve to identify the spot. The trigono- *trical point is identical with the zenith-sector point. HUTIG, 18 38, is a large mountain situated near the centre of the north coast of Sutherlandshire. Its summit is about a mile from the edge of the coast on the north, * about 3 miles south-east from the Whiten Head. From the village and inn at *irkiboll by the Moin House the distance to the top is about 11 miles, and from Hailaim Inn on Loch Eriboll by the Moin House it is Io miles. The route by the Moin House is the best way for carriage of heavy articles to the !"; but by crossing the moor from the Tongue or Hope ferties the distance will be less by a mile or two, but it is rougher walking. There is a good road also ſom Tongue Ferry by Talmin, round to a river and bay called the “Strath,” which is at the foot of the hill on the east side within about 2 miles. * - The top of the hill is rocky and rugged, and has two ridges running north-east and *west; the station was on the highest part of the rock on the western ridge, and had a very large block of stone a few feet to the north of it. The old pile put up in 1819 was found undisturbed, but no centre mark was discovered. The centre Was, however, taken accurately by a tape as soon as the pile was cleared away, and a hole 5 inches deep and I inch in diameter was jumped to mark the spot. * = & * 1844 observations for latitude were made with Airy's zenith sector, the position which it occupied being identical with the trigonometrical station above described. *Wºns, 1850. This mountain is in Perthshire, and lies 5 miles north-west of Loch Tay and about 8 miles north-east of Killin in that county. The station is on a mass of rock at the western extremity and highest point of the ridge, which runs east and "*; it is marked by a hole bored in the rock, and the frame which supported the *nt, over which is a pile of stones 12.5 feet high and 15 feet in diameter. *wo series of observations were made at this station, the first in 1841 and the second in 1850. LoMond, 1818, is a large mountain in Stirlingshire. The station is 52.4 feet south- "ast by east of the cliff at the western end of the summit of the mountain. It is on 6 PRINCIPAL TRIANGULATION. the broadest part of the summit, and a little lower than the narrow flat above the western cliff, which was not sufficiently large to hold the observation tent. The site is marked by a wooden picket having a hole bored in it, and by the pickets on which the instrument rested in 1818. The mountain is composed almost entirely of micaceous schist and quartz rock; the ascent is by no means difficult, and the prospect from it on a clear day is not only very extensive, but extremely beautiful and magnificent, The point on which Airy's zenith sector was placed is identical with this station. BEN MACDUI, 1847. Ben Macdui is the highest of the Grampian Hills, and is about 12 miles north-west of Castleton of Braemar, in the county of Aberdeen. The station is on the southernmost summit above Glen Lui-beg, and near the united boundaries of the counties of Inverness, Banff, and Aberdeen. The site is marked by a hole about 6 inches deep, in an enormous stone, over which a large pile, about 22 feet high, was erected. The pile was circular, but not of a shape similar to those generally erected to denote trigonometrical stations; it is perpendicular for a few feet, and then reduced in circumference. BEN MoRE, MULL, 1822. This mountain is in the island of Mull, one of the Western Islands of Scotland. . The station is situated on the highest and most salient point, about 30 feet from the edge of the precipice. The rock on the summit was found so splintery and frangible that the station could not be prepared in the usual manner, by securing pickets into the rock. A strong framework of wood was therefore constructed, and buried in the soil, resting upon the solid rock. This, when tightly rammed, was found perfectly free from vibration. The framework was left to mark the station, and a stone 18 inches in diameter, with a hole in it 2 inches deep, was placed in the centre; above these a pile of stones 13 feet in diameter was erected. BEN MoRE, S. UIST, 1851. The mountain of Ben More, in the island of South Uist, is on the eastern coast, and not far from the centre of the island; it is about 2 miles north of Loch Eymort, and about 5 miles east of Howmore in that island. The top of the mountain consists of two ridges meeting at an angle: the lower ridge is very rocky, sharp, and abrupt; the higher ridge has a rather flat top about 200 yards wide, with an immense precipice along the north side. The station is on the highest part of the latter ridge, and at the junction of the ridges close to the precipice. The stations of 1840–1 and 1851 are identical, and the site was marked in 1851 by a pile of stone 49 feet in circumference at the base, and 14.5 feet high; the centre is denoted by a hole pierced in the rock 2.7 feet below the surface of the ground beneath the pile. BEN TARTEvil, 1822, is a large hill situated in the parish of Portnahaven, in the island of Islay. The station is on the summit, and is rendered permanent by the holes bored DESCRIPTION OF STATIONS. 7 in the rock for the pickets of the theodolite. A wooden centre mark was also left, "d the whole covered by a pile 14 feet in diameter, the lower part of stone, and the remainder of turf. The station was examined in 1841, and a centre stone was placed above the wooden °ntre, without disturbing it or the pickets, and the pile raised to the height of 2O feet. The road from Skiba to Portnahaven passes about 1 mile east of the station. BEN Nevis, 1848. This mountain, the roughest and highest in Scotland, is in the parish of Kilmanivaig, in the county of Inverness, and about 7 miles east of Fort William. The top of the mountain has a flat rugged surface, of considerable extent. The station, which is upon the highest part of the mountain, and within a few yards of a precipice of about 1500 feet, is marked by a hole in a very large stone *ting on a rock about level with the surface, and by a similar stone about 3 feet above the surface, and within and level with the frame which supported the instrument. The ſame of the instrument and centre marks, are protected by a stone pile 60 feet in circumference and 25 feet high. * BEN Wyvis, 1819. The station on this mountain, in the county of Ross-shire, is marked by * Pile enclosing a pole and centre stone about 2.5 feet square and 6 inches thick, Weighing about 3.5 cwt., with a hole in the centre 4 inches deep. BENconn, 18 3o. This station is about 9 miles east of the town of Clifden, in the county * Galway, and is on the summit of one of the Twelve Pins of Connemara. The Centre stone measures 32 inches by 20 inches, with a hole in its centre, not very deep, but sufficiently defined. The length of the stone is in an east-north-east and a west- South-west direction. The pile is 8 feet high. BERKIIAMPSTEAD, 1823. The station at Berkhampstead, in Hertfordshire, is on the gazebo or observatory tower belonging to Mr. W. Stratton, of Little Berkhampstead. The tower is circular, and about 100 feet high; the instrument was placed about II inches °ºstward of the centre of the tower. BLACK Comm, 1841, is a large rocky hill in the parish of Whitbeck, in the county of °umberland. The station is on the top of the hill, and is marked by a pile of stones 14: 5 feet high and 50 feet in circumference, erected above a centre stone with a hole in it 4 inches deep and an inch in diameter. The station was restored in 1852. BLACKDown, I848–9. This is a large hill in the parish of Portisham, in Dorsetshire, about miles west-south-west of Dorchester, and I .75 miles south of the village of Winter- Olll'Ile. A column was erected here in 1845 in honour of the late Admiral Sir Thomas Hardy. It is an octagonal tower, 71.25 feet high, ascended by a winding stair of 120 8 PRINCIPAL TRIANGULATION. stone steps, the newel of which in the centre of the tower corresponds with the centres of the stations observed from in 1797 and 1848–9, and is identical with the zenith-sector station in 1842–3. A hole was drilled in the centre of the topmost stone of the newel, and run in with lead, to mark the station. BLAckIIEDDON, 1846. This station is situated on the highest point of Blackheddon Hill, in the county of Northumberland, about 5 miles north-west of the town of Belford, 3 miles east of Lowick, and Io miles south of Berwick-on-Tweed. Two piles, about 3o feet distant from each other, mark the sites on which the instruments were placed during the observations of 1809 and 1846, the smaller pile denoting the former or old station, and the larger pile, built of stone 18 feet high, distinguishing the latter or new station. The new station is marked by a hole in a large stone 3.5 feet below the surface. The hill commands views of the sea to the north-east and east, and the Cheviot and Lammermuir Mountains. BLUE HILL, I814. This station is about 4 miles from Aberdeen, and half a mile on the right of the road from Aberdeen to Stonehaven, by the stone bridge over the Dee; it is situated on a low barren place partially covered with heath, and planted with fir very stunted in its growth. The site is marked by a centre stone sunk below the general surface, and a well-built pile of stones 16 feet high, with a diameter of 13 feet, erected above it. Boniface Down, 1846. The trigonometrical station on Boniface Down, in the Isle of Wight, is identical with the station from which the observations with Airy's zenith sector were made in 1846. The station is in the centre of an apparently artificial mound of decayed vegetable matter on the Down, about 100 yards south-west of, and about Io feet lower than its highest part, which is due south of Dunnose station. A point 2237 feet eastwards from the second and principal junction of the roads from Ventnor and Wroxhall to Shanklin, measured along the road, is in line between this station and the station on Dunnose; the formerlying about 60 yards to the south of this point. The station is marked by a centre stone with a hole bored in it, sunk 2 feet below the surface. - Boston ToweR, 1842, is the tower of the parish church of Boston, in the county of Lincoln; it is of an octagonal form, with 16 pinnacles, viz., a large pinnacle at each angle, and a smaller pinnacle between the larger ones. In consequence of the obstruction which they presented to the field of the instrument, it was placed upon two different points, the first being 5-8 feet south of the centre of the tower, and the other 2.8 feet north of the centre: the first is the trigonometrical station. Borron HEAD, 1840, is a large hill about 3 miles south-east of the village of Ingleby- green-hoe, in the northern part of Yorkshire. The station is situated on the south- DESCRIPTION OF STATIONS. tº 9 West edge of a large barrow, and is 4 feet south and 12 feet west of the southern edge ºf a deep indentation or hollow, extending from the north edge of the barrow southwards. It is marked by a hole in a stone, sunk about 1.75 feet below the Surface. BRANDon Down, 18 53. This Down separates the villages of East and West Brandon, in the County of Durham, from the former of which it is about a mile distant ; and the lane between the two villages passes close to the hill. The station is upon the flattest part of the highest point of the Down at the western extremity of a sharp ridge, which appears to have been thrown up from a quarry near it many years ago. BRANDon, 1845. This station is in the parish of Brandon, in the county of Suffolk; it is situated on the highest part of the ground, in a large rabbit warren, called Wangford Rabbit Warren. A small house, called Shaker's Lodge, inhabited by the keepers, is 22 chains eastward of the station, which is marked by a centre stone with a hole in it, Placed 8 feet below the surface in consequence of the ground being very fine sand, and to afford proper foundation and support for the pole, 44 feet long, which was erected above it. The plantations of Brandon Park obstructing the view in the north and cast direction, and another plantation obstructing the view on the south-east side of the station, it was necessary to erect a stage for the 2-foot theodolite, which was 39 feet high. *Andon. This station is on the summit of a well-known hill, about 8 miles due north of the town of Dingle, in the west of the county of Kerry. The station is marked by an excellent stone pile 14 feet high. The centre is marked by a hole in a piece ºf sandstone, level with the surface. Forty links north of the station there is a Small grave-like excavation, having its sides and eastern end rudely lined with stones, and opposite the west cnd is a small upright flagstone, presenting the appearance of a grave or headstone; this is called by some the chapel, and by others St. Bran- don's bed. About 6o links north-north-west of it there is a small well. Bºassa, 1821. This station is so called from its being situated in Brassa, one of the Shetland Isles. On the top of the Wart Hill, where the instrument was fixed, are two *ds that appear to be the ruins of ancient watch-towers and furnaces. Similar remains are found on the top of every hill in Zetland and Orkney bearing the name of Wart or Ward; such hills, as the term implies, having in ancient times been selected º *y the inhabitants on account of their commanding situations to descry their enemies at a distance, and spread the intelligence of their approach. The western of the two mounds upon Wart Hill, Brassa, was selected as the station, and was marked by a * sunk in the ground to denote the centre. A pole and a stone pile were erected Over the station. Pantuond or Bnesſes STATION, 1817, is about 6 miles north-west of New Aberdeen and *bout 1 mile west of New Hills Kirk, and is situated on a low heathy mountain, B IO º PRINCIPAL TRIANGULATION. cultivated to within three quarters of a mile of the top on its south side. The station is marked by a pile of turf and stone 23 fect in height, and 53 feet in circumference. The centre is denoted by a stone hammer weighing about three pounds, with a handle about a foot long, thrust through the old centre picket of the frame of the instrument; a large flagstone more than 2 feet wide was laid on the hammer, and on this flagstone a piece of fir about 4 feet long was erected as a guide to the centre. Broadway Tower, 1850. This is an hexagonal tower with 3 turrets, one at each alternate angle, situated on a prominent hill in the parish of Broadway, Worcestershire, about. 1 mile to the east of Broadway New Church Tower, and 2.5 miles to the south of Campden Church Tower. The station is upon the top of the tower, and its site is marked by a copper nail driven in the lead near the centre of the tower. Brown WILLY, I 849, is a high and rugged topped hill, about 5 miles south-east of Camelford, in the county of Cornwall. The station was upon a barrow of loose stones on the summit of the hill, and was marked by a flat stone with a hole through it, placed in the earth level with the general surface of the hill. A pile of stones, 11 feet high and Io feet in diameter at the base, was erected above the centre stone. Bunwell Tower, 1844. The tower of the parish church of Bunwell in the county of Norfolk is the site of this station. The instrument was placed exactly over the centre of the tower, and the frame on which the instrument was fixed rested on the battle- ments. Buniergii Moon, 1806, is in the North Riding of Yorkshire, about a mile and a half south- east of Kirkleatham, and a mile north-west of Upleatham. The station is close to a bend in a stone wall and is marked by a pole 30 feet high. Butsen HILL, 1845, is an eminence in the parish of East Meon, in the county of Hants, about 2.5 miles west of Petersfield, and about three-quarters of a mile west of the road from Petersfield to Portsmouth. The station is marked by the pickets on which the instrument rested, cut off about 18 inches below the surface, and a stone measuring 2.7 feet by 1.4 feet, and about 6 inches thick, with a hole in it denoting the centre, placed between the pickets 2-4 feet below the surface. A pile 14 feet high and II feet in diameter was erected over the site. Capen IDRIs, 1844. This station is situated on the highest point of Cader Idris mountain, 6 miles south of Dolgelly, and 8 miles cast of Barmouth in North Wales. It is about 2914 feet above the level of the sea, and 92 feet south of a small hut built near the mountain top as a place of shelter to tourists. CAmendannagh STATION, 1832, is situated on a mountain about 6 miles west of the town of Mill Street, and about I mile south of an old road leading from Mill Street to DESCRIPTION OF STATIONS. * II *illarney. The surface of the entire mountain is bog 2 or 3 feet deep, and parti- *ly so about the station, which is marked by a turf pile 7 feet high, enclosing a smaller pile of stones. The centre stone is a piece of clay slate measuring 28 inches by 17 inches, and 3 feet below the general surface of the mountain; the length of the * is in a north and south direction. CARN GALVER, 18 50. The station called Carn Galver is situated on the top of Morvah- look-out-Hill near Penzance, in the county of Cornwall, from which town it is about 7 miles north-west, and about 2 miles north-east of the village of Morvah, and * 5 miles south-west of Zennor. The station is marked by a centre stone sunk about 2 feet below the top of the barrow. The point known as Carn Galver by the country People is about o'75 of a mile castward of the station. CARRIGFADDA, 18 32. This station, in the south of the county of Cork, is situated on the * summit of a small hill about 8 miles south-south-east of the town of Dunma- mivay, and about 4. 5 miles north-north-west of Roscarberry. From Dunmanivay there is a cart road, by the club house and Lough Thariv, skirting the foot of the hill on the north side; the hill is of easy ascent, and covered with heath on the top. The °ntre stone, which measures 27 inches by 17 inches, is level with the surface, and marked by a cross cut in its upper surface. The pile is about 7 feet high. * 1846. This station is on the summit of the Cheviot. The ground is flat and very boggy, but a gravelly soil was found at a depth of 9 feet. A triangular frame was sunk 2 feet into the gravel, and uprights mortised into each corner, and well braced together, for the feet of the instrument to rest upon. When the observatory was first set up, it sank into the ground at the rate of half an inch per diem, and at length *sted upon the framework supporting the instrument. A number of piles II feet long were therefore procured and driven into the ground, and their tops connected by two cross beams, upon which the observatory was raised by means of levers. *oup, 1848. This station is in a field near Epping in Essex. It is 13.54 feet from * Centre of Greenwich north meridian mark, 9.67 feet from the south-west corner, "d to 12 feet from the south-east corner, of the base of the obelisk; and is marked by **ound hole bored in a square stone, the upper surface of which is level with the *face of the ground. This station is identical with that used by Captain Kater. CLEISILAM, 1840. This, the highest mountain in the Hebrides, is in that part of the º of Lewis which is in the county of Inverness. It is near the south and west shore O Loch Seaforth, and, being the most conspicuous object in that part, cannot easily be mistaken. - The huts nearest to the mountain are at Marvig, from which it is distant º 3 or 4 miles. West Tarbert, a small village on the south side of the hill, is about. * 7 miles distant. On account of the accommodation which the observing party" IB 2 I 2 PRINCIPAL TRIANGULATION. 1840 required, the men and stores were landed at a farm house and shooting lodge at Mole-na-harig, about 6 miles south-west from the hill. The station is upon the highest point of the mountain. A pile 18 feet high occupied the site of the station previous to the preparation of the ground for the reception of the frame of the instru- ment in 1840, but on taking it down no centre mark was found. The centre of the pile was therefore ascertained by careful measurement, and the instrument placed over it. On quitting the station the wooden pickets were left in the rock, a large stone with a centre hole in it was placed even with the surface, and a stone pile 2 I feet on slope, and 18 or 19 feet in diameter, erected. A few feet from the pile is a large rock. CLIFTON BEACON, 1842. This station is about a quarter of a mile south-by-west of the village of Clifton, which is 1.5 mile south by east of Conisboro’, a small town half way between the towns of Rotherham and Doncaster in Yorkshire. The station is in an arable field close to and on the south side of a hedge, across one field from a lane leading out of the village of Clifton in a westerly direction. In 1842, when additional observations were made at the station, two centre stones were left, one at the depth of 4 feet 6 inches below the surface, and the other at the surface; the beacon pole was replaced, and a stone pile built round it, II 5 feet high and 30 feet in circumference. From this point the zenith sector station is 3.5 feet distant, bearing due south. CNoc GIIIUBHAIs, 1838, is a low round hill about 17 miles west of Ben Hutig, and 2.75 miles south-east from Cape Wrath Lighthouse. The road from Durness to the Lighthouse passes near it, the nearest point of the road across the moor being about I 25 miles. The station is at the top of the hill, and is marked by a pile 15 feet in diameter and I5 feet high, erected above a centre stone and the four pickets on which the table of the instrument rested, which were wedged into holes bored in the rock and run in with lead. CoLLIER LAW, 1851. On this hill, in the parish of Stanhope, in the county of Durham, there are two stations, about 247 feet distant from each other, and called respectively Collier Law Old, and Collier Law New, stations. They are situated on the top of the mountain, about 4.5 miles north-east of Stanhope, and about 5 miles north of Frosterley; and are marked by two piles, each 14 feet in circumference and 15 feet high. The western pile marking the old station has a pole of 13 feet in its centre, braced to the pickets left by the instrument; the other pile marking the new station has a centre stone and a short pole. The easiest ascent of the mountain is from Frottesley. Comingdon, 1845. This station is upon a hill about 2 miles north of the village of Swanage, and an equal distance south-west of Studland, in the county of Dorset, and is nearly 3.5 miles east of Corfe Castle, in the island of Purbeck, I 3 DESCRIPTION OF STATIONS. arishes of Studland and The remains of an old fence, the reputed boundary i. º in a south-east Swanage, may be traced over the hill fiom . º The station is marked by direction, and passes the station 50 feet to the * mºre d about a foot below * turf pile, about 6 feet high, built above a centre n Oł1C orted the instrument. the general Surface, and the piles and bracings which supp º .. tlach. Banffshire. The Connyhannib, 1850. This hill is situated in the . of * and south-west, *ntain has a long flat or ridge-like top, exten º, covered with vegetable consisting of loose fragments of ..". * i. about 2 miles south º º matter. The station is on the highest par t’s Cairn, and is indicated by a Rinnes Kirk, and about 1. 5 miles south-east of Cook's º *. The centre is stone pile 13 feet high and 46 feet in º º a hole 4 inches deep and *ked by a large flat block of quartz, of about 4 cwt., wi º rted the instrument *5 inches in diameter bored in it, and by the frame which supported being left in position. able field, upon a hill CowHYTHE, 1847. This station is situate on the north edge of * three-eighths of in the parish of F ordyce, county of Banff; it is about one q e mile east of the village a mile from the edge of the cliff above the Sea, and about O]] of Portsoy, where the hill is called “ Cairn Rankee. d, in 1846, about 30 inches below The original centre mark of the station was º the upper part with a strong * surface; it consisted of a wooden picket, mounte i. decayed, but the iron hoop iron hoop, 4.2 5 inches in diameter; the wood was quite yed, b W* firmly set in the earth. ***** *** ne, 20 inches by The º Was replaced without disturbing the Iron º º º º picket, its *4 inches, with a hole I ‘75 inches deep bored IIl it. WàS #. stone and the piles on CCntre *Sponding with the centre of the iron ring. * ile º wº enclosed in a pile. which the instrument stood in 1846, with their bracings, &c., are of stones and turf 9 feet high. ſº et due north of the The site on which Airy's zenith sector was placed º ** been used for *trical station, and is identical with that state ickets were found that Ramº Zenith sector in 1813; but no centre mark or p * indicate it had ever been used as a station. it levelling on the 25th August The altitude of Cowhythe, as obtained by spirit levelling *3, is 272-75 feet above low water. tri º country people in its CRADLE, 1843, or Pen Cader Fawr, or, as it is usually º *... ; . town of neighbourhood, “the Cader,” is situated about 8 miles of the Black Mountains. - Crickhowell, in Brecknockshire, South Wales, in the º appearance of a trun- * steep mound, which when viewed from a distance º º at the top is the **ted cone, forms the summit, on the north side i W hole in it to mark the Station. A Stone, 2.5 feet long and 2 feet wide, with a - I4 PRINCIPAL TRIANGULATION. centre of the station, was left 2.5 feet below the surface, and a stone pile, 19 feet high and 18 feet in diameter, was built over it. CRIFFEL, 1841. This station is on the top and close to the south-west edge of “Douglas Cairn,” which is on the highest part of the well-known mountain named Criffel, Io miles south of Dumfries, and 3 miles south of the village of New Abbey. It is marked by a hole in the solid rock, in the centre of a square formed by four pickets on which rested the instrument. A wall runs over the top of the mountain in a north-east and south-west direction, forming an angle near the station, which is 80 feet due east from the nearest point of the wall. * CROGILAN, 1828, is on the highest pinnacle of Croghan Mountain, about 8 miles west of Arklow, in the county of Wicklow. The station is either on or close to the line separating the county of Wexford from the county of Wicklow, and is well marked by a stone measuring 26 inches by Io inches, having a good centre hole bored in it. The centre stone is level with the surface, and is covered by a small pile. CRoss FELL, 1841, is a remarkable mountain, about 9 miles south of Alston, in Cumber- land. The station is on its summit, and may be discovered by means of the stones placed around the staff. CROWLE BEAcon, 1806. This station was situated on a barrow where once stood a windmill, nearly 150 feet east of a mill. The station was 36.9 feet from the corner of the hedge next the road and 43.9 feet from the road; the barrow has, however, lately been removed, and with it every trace of the old station. CUILCAGII, 1828. This mountain which is in the counties of Fermanagh and Cavan, is about 4 miles west of Swanlinbar, and 12 miles south-west of Enniskillen. It is ridge- formed, exhibiting two precipices, one to the north and the other to the east, the former in the direction of the dip; the station is on an ancient carn near the north- eastern angle formed by the junction of these precipices. A pile and staff were first placed on the mountain by Major-General Colby's direction in 1825. As a station Cuilcagh is of the first order, commanding a vast number of churches and other points connected with the district triangulation, and thereby assisting to furnish bases for the surveys of about 20 counties, CyßN-y-BRAIN, 1852. This station is on the most westerly of two headlands nearly half a mile apart, forming a saddle-top to the broad moorish mountain of this name. It is about 1857 feet above the level of the sea; and the ascent to it from Llangollen, through a dreary journey of 5 or 6 miles, is neither steep nor difficult. There is an old round tower, about 25 feet high, within 50 feet of the station; and though it is on ground several feet lower than the base of the small pile built over it, this tower is very liable JDESCRIPTION OF STATIONS. I5 to be observed from any distant point instead of the station pile. It seems not "Probable that this tower has been built with the stones described in the third volume ºf the “Account of the Trigonometrical Survey,” as forming a large cairn about 3° yards north-west of the station. This cairn is not now in existence, but there is a large heap of stones on the eastern summit. DANBURY CHURCH SPIRE, 1844. This church is in the parish of Danbury, in the county of Essex, about 5 miles distant from the towns of Chelmsford and Maldon, on the high *ad between them. The station is above the centre at the top of the spire. The instrument was supported on a scaffold erected from the top of the tower, and the observatory was supported by another scaffold similar in plan and construction; both rested on the walls of the tower, and were similarly cross braced, that bearing the instrument had its four uprights resting on the middle of the walls, and the other bearing the observatory rested on the angles. The spire of Danbury Church is built of wood, and was considered a much less stable structure for the instrument than the Scaffold here described. - *N, 1846. This bold headland is in the parish of Gorran, about 2.5 miles south of the parish church, in the county of Cornwall. The station is in the north-east corner of * Small field, and is marked by a small stone pile, 8 feet high, erected over the pickets * Which the instrument stood; which were left in the ground, and a centre stone, With a small hole in it, sunk 1 foot below the common surface. * Hill, 1850. This hill is in the parish of Dean, in the county of Wilts. The station **out 1.25 miles south-west of the village of Dean, and nearly the same distance north-north-east of the village of Whiteparish. It is in the north-west corner of a "ge field, bounded on the north by a plantation of mixed trees. A circular block of sandstone, with its upper surface smooth, and about 20 inches in diameter, having * hole in it 3.75 inches deep and about 1 inch in diameter, marks the centre of the station. The stone is imbedded in the ground about 20 inches below the surface. DEERNEss, 1821, is a large hill in the Mainland, island of Orkney. The station was upon * Small mound on the highest part of the mountain, and was marked by a centre stone and pile with a pole in it. DELAMERE, 1842. This station is in Delamere Forest, near Tarporley. The station from which the observations of 1805 were taken is described in the observation book to have been 22. 7 feet west of a hedge running north and south over the top of the hill, and 129 feet south of another hedge, running at right angles from the former. In 1840 the station was visited for the purpose of restoration, but no Picket, or other remains serving to point out its site, could be found. By means, how- ***, of observations taken with a small theodolite, the observer was enabled to fix I6 PRINCIPAL TRIANGULATION. upon a point very near the old station. This was marked by a stone, 1.25 feet long by I foot wide, with a hole cut in it, placed about 18 inches below the surface of the ground. A pole 25 feet long was erected over the centre. From a combination of the 3-foot theodolite angles taken in 1805 with those taken in 1842 over the point selected in 1840, and marked as here described, the position of the old station appears to be 3.7 feet from the new station, and to bear 201° 1' 16" from the south, reckoning by the west and north, Doolieve STATION, 1832, is situated on a low dark-coloured hill, about 9 miles south of the city of Cork, and about 4 miles south-east of the small village of Ballinhassig, which is on the old road from Cork to Kinsale. The station occupies the summit of a very small mound on the western extremity of the hill, and is marked by an irregular piece of clay slate level with the surface, about 36 or 40 inches in length, and pointed at both ends, the greatest breadth not exceeding 14 inches, and having a small hole bored in it about three quarters of an inch deep. The length of the stone is in a north-east and south-west direction, and it is covered by a pile of stones about 8 feet high. DITCHLING, 1844. This station is at Ditchling, in the county of Sussex, and about 6 miles from Brighton. It is in the middle of a small rising, which has the appearance of having once been a barrow, and is marked by a hole in a stone sunk 2.5 feet below the general surface. Divis, 1825. This station is on the summit of a well-known mountain of the same name, about 3.5 miles west of the Exchange Buildings, in the town of Belfast. It may be approached by the Shanklin Road for rather more than a mile, then by a bye-road skirting the mountain on the cast side. The station is marked by a pile of large coarse stones, having a diameter at base of 16 feet and raised to a height of about 5 feet; this truncated section of a pile has a small quantity of bog turf on its top. The centre stone has a smooth upper surface, with a well-formed hole in it, 2 inches deep and 2 inches in diameter. It is level with the surface of the mountain. Divis Station is about 140 links due south of a fence which crosses the mountain in an east and west direction. *. DUDwick, 1816. Dudwick Hill, in the parish of Ellon, Aberdeenshire, is the site of this station, which is distant about 6 miles north-north-east of Ellon, and about 1 mile to the left of the road from Ellon to Peterhead. The station is marked by a pile 20 feet high. - DUNKERY BEACON, 1844. This well-known hill, in the parish of Luckham, Somersetshire, is about 3.5 miles south of Porlock, I - 5 mile south-south-east of the village of Stoke Pero, and 2 miles south-south-west of Luckham. There are three barrows on the hill, composed of stone, touching each other at their bases. The station of 1844 is upon the south top of the central or most eastern barrow, and is marked by a centre stone, DESCRIPTION OF STATIONS. 17 with a hole jumped in it, and sunk about 2 feet below the surface of the barrow. A pile 19 feet high and 53 feet in circumference was erected over it. DUNNET *AD, 1838. The station on this remarkable headland, on the north coast of the **y of Caithness, is on the highest point of the rising ground in the rear of the *ighthouse, from which it is distant 1273 feet in a south-easterly direction. Four holes Wºre jumped in the rock, at a depth of 7 feet below the surface, to receive the feet of the posts, which were wedged in and run with lead. The framework was left, and Pºle of stone II feet in diameter and Io feet high built over it. DUNNose, 1844. This station is situated about 30 yards north-west of the summit of Shanklin Down, 1.5 mile south-west of the village of Shanklin, in the Isle of Wight. The centre is marked by a large gun imbedded in the soil, the top being nearly level With the natural surface of the ground. In 1846 observations were made with Airy's Zenith sector at this point. DUNRICH, 1850. This station is about 7 miles south of the town of Peebles, and 7 miles West of the village of Traquair in Selkirkshire; it is on the summit of the hill called by the inhabitants Gumscleugh, and is named Dunrich, after the peak of the mountain immediately north of the observing station. The old centre-mark, and framework used for the instrument in 1816, were refound in 1841, and covered with a Well-made pile. " *59, when additional observations were taken from this station, the pile was taken down, and the instrument placed on the original centre, as near as possible in the position indicated to have been occupied by the instrument at the previous observations. The framework which supported the instrument on this occasion was left in position, ***ound of turf and mud erected above it to the height of 15 feet, having a piece of deal, 4 inches by 3 inches and 12 feet long, standing on the centre stone. At a *nce of 435.5 feet eastward from the station, will be found a stone weighing about 4 or 5 cwt., placed by Major-General Colby in the Meridian of Edinburgh Castle, having a centre mark and the letters “E.M. 1816.” DUNSTABLE, 1843. This station is upon Dunstable Down, in the county of Bedford, and is marked by a pile erected over a block of Portland stone weighing 17 cwt. Two sets of observations have been taken at this station, one in 1823 and the other in 1843. * 95 feet from the centre stone in a south-east direction will be found Kensworth *tation, which is marked by a centre stone. ºasington, 1846. The station is in the south-west corner of a cultivated field, about a mile north of the village of Easington, in Yorkshire. It is on the highest ground, close to the cliff, about twenty yards from the ruins of an old house, and marked in the usual manner by a centre stone and a pile, C I8 PRINCIPAL TRIANGULATION, EAST LoMond STATION, 1818, is situated on the mountain of that name in Fifeshire, and about I mile South-south-west from the town of Falkland. In 1818 the site of the station was marked by a stone 4 feet long and 13 inches square sunk in the ground, with the date “1818” and the letters “T. S." cut on its upper surface. This stone was refound in 1841, but the letters were obliterated. A hole was bored in it, and a pile of turf 12 feet high, with a diameter of 16 feet, was raised above it. ELY MINSTER STATION, 1842–3, is in the centre of the octagon top of the western tower. EASTON ToweR, 1843. This station is on the tower of Easton church, about 2 miles south- west of Stamford. The instrument was supported on a scaffold erected over the centre of the tower, and just high enough to enable the observer to obtain a clear view over the parapet and staircase. EPPING Cupola, 1844. The cupola on which this station is situated, and from which it is named, is that of the Union workhouse at Epping, in the county of Essex. The cupola is about the centre of the middle building, and is surmounted by a ball; the centre of the instrument was made to coincide with the centre of this ball, but should the ball be removed, the station may be found by bisecting the ridge of the central building, which runs north and south. FAIR ISLE, 1821. This station is upon the highest part of Wart Hill, in Fair Isle, on the north coast of Scotland, nearly equidistant between the Shetland and Orkney Isles. The hill is the highest in the island, and lies near its north-west extremity. A large stone 4 feet in length, with 3 holes in it, marks the station; the central hole denotes the point over which the instrument was fixed, and in the other two were inserted pickets for the feet of the instrument. A staff was erected over the stone, and a pile 14 feet in diameter and about 16 feet high built round the staff. FAIRLIGHT, 1844. This station is on Fairlight Down, in the county of Sussex. The site on which the instrument was in position is about 81.75 feet from the centre of the octagonal tower of Fairlight Windmill, and is marked by a pole or beacon 3o. 6 feet high. - FASHVEN, 1838, is a mountain on the north coast of Sutherlandshire, about 1.25 miles south from the sixth milestone on the road between Durness and Cape Wrath Light- house. It rises very abruptly on three sides, and on the fourth in a long slope from the south to the north, terminating in a kind of saddle-top. The station was not on the highest point, but on a more convenient spot, 343 feet from the highest pro- jecting piece of rock at the north extremity. Four holes will be found in the rock, covered by a pile, Io feet in diameter and 12 feet high. FEAGIIMAAN, 1832, or Geokaun, is about 2.5 miles west of the ferryhouse opposite Reenard, and three quarters of a mile south of Reenardrolaun Point, in the island of Valencia, DESCRIPTION OF STATIONS. 19 county of Kerry, Ireland. The station is on the highest part of the hill, immediately above the slate quarries. * i. º tº i. tº i. * º º * jº The zenith sector station is identical with the trigonometrical station, and is marked by a centre stone, sunk about I foot under the surface, which by calculation is 884 feet above the mean level of the sea. ** 1821. This station is on the top of Word, the highest hill in the island of Petlar, one of the Shetland Isles. The top of the hill is flat to a considerable extent, and on the north side there is a large mass of stones, apparently the ruins of some ancient building, from which the station lics about 150 yards south. On the west side of the top of the hill is another mass of stones, which appears to be the remains of one of the rude ſurnaces used in former times as signals of alarm; from this the station is between 70 and 80 yards south-east. The pickets on which the instrument stood were left in the ground, and a large flat stone, with a hole 3 inches decp bored in it, marks the centre of the station, over which a plank was crected, and * stone pile, 12 feet in diameter and 15 feet high. "Try Hill, 1821. The station on the top of this hill, in the island of Westray, one of the lmost northerly of the Orkney Islands, is on a mound of earth and stones, called by the inhabitants “the Watchhouses.” The mound is consolidated by time, and forms one mass with the hill. The pickets on which the instrument stood were left in the ground; a large stone with a hole in it 3 inches deep, corresponding to the centre of the instrument, was sunk in the ground to mark the station, and a stone pile with a Pole in it was crected above them. * Fonth Mountain, 1829, 1843. On the top of this mountain, which is about 4 miles south- West of the town of Wexford, there are several large projecting rocks, called the Carrickadee Rocks, on the summit of the highest of which is the station. Tho centre s marked by a hole, rather more than 4 inches deep and about an inch and a half in diameter, in the north-north-west slope of the rock. The holes made for the stand of the zenith sector will also be found in the rock. The station is covered by a large *one pile, 14.5 feet in diameter at the base and about 1o feet high. ** 1821. This station is on the top of Smood Hill, Foula, one of the Shetland Isles. It is marked by a large stone with a hole in the centre, which corresponded to the °ntre of the instrument. The pickets on which the instrument rested were left II] Position, and a pile of stones, I 3 feet in diameter and 17 feet high, with a pole rest”8 * the central stone, was erected above them. Tour Milº Stone, 1850. The station so called is on the summit of a small hill in the Parish of South Newton, in the county of Wilts, and about 3.75 miles from Salisburi. y *nd a little to the west of the road from Salisbury to Devizes. The cent” of the C 2 2O PRINCIPAL TRIANGULATION. station is marked by a rough picce of black flint stone, with a natural tapering hole in its upper surface of about I 5 inches deep, and about the same diameter at the top. The stone is placed 20 inches below the general surface. GADs HILL, 1845. This hill is near Chatham, in the county of Kent. The station is 250 feet north-west of the obelisk upon the hill. GARFontiI CLIFF, 1842. The station on Garforth Cliff, in the parish of Garforth in York- shire, is about 8 miles east of Leeds, and about 315 feet north of the road from Leeds to Selby, through Whitkirk, in a line nearly with the churches of Kippax and Gar- forth. The frame on which the instrument rested was left in the ground, the top of the pickets being about 9 inches above the surface. The centre stone is 2.25 feet under the common surface. GERTH OF SCAw, 1847. This station is situated a short distance to the west of the neck of land that connects Lambaness with the mainland of Unst, one of the Shetland Islands, which neck is occasionally in very stormy weather, with the wind from the north-west, washed over by the sea. The site of the station is marked by a stone, with a hole in its centre, placed about 2 feet below the surface, with a small pile of stones and turf above it. GLASHMEAL, 1841. This station is on the highest and western summit of the mountain of this name, in the junction of the three counties, Perth, Forfar, and Aberdeen, about 8 miles south from Braemar, and 3 miles eastward of the road leading from Braemar to Glenshee. It is marked by a hole 2.5 inches deep in a centre stone, and built over by a pile of stones 20 feet high and 45 feet in circumference at base. GoAT FELL, 1852. This station is marked by a hole 1.5 inches in diameter, and 3 inches deep, cut in the rock on the highest point of Goat Fell Mountain, 5 miles north- west of Brodick village in the Isle of Arran. It is the centre of a square formed by four pickets, on which the theodolite was supported. These pickets are wedged into the rock, and are covered by a pile of stone and turf Io. 5 feet high, and 30 feet in circumference. The road to it by Brodick and the mill-dam is very rough, but not steep till within 2 chains of the top. GooNHILLY, 1846. This station is situated on a bleak moor known by the name of Goon- hilly Downs, about 6 miles south-east from the town of Helston, and 1.75 miles nearly due south of St. Martin's, in the county of Cornwall. The site of the station is a small mound, from which the undefined boundaries between the estates of different proprietors diverge. The point on the mound from which these boundaries radiate is marked by a beacon placed over the site of that which has obtained the local name of the “Dry Tree;” and it is now marked in addition by a stone having a hole bored in it, and placed 3 feet under the surface, and the beacon re-erected thereon is 2 I DESCRIPTION OF STATIONS. ºf pile. This point is *PPorted by three braces, cach 12 feet long, and a small ºt * in *:: *al with that from which the zenith sector observations were m º • al- > county of Goulbston Cºuncil ToweR, 1843. The station at Gorleston Church, in the y Norfolk, is in the centre of the top of the tower. tº n in the GnRAT STIRLING STATION, 1850, is about 1 mile south-west of the sº º point Parish of Peterhead and county of Aberdeen. It is 25 feet º º to . the of the hill, on which a large hole has been bored in the protru . I i. of the sector base of a flagstaff. This rock is about 4.5 feet higher º i. d Windmill near *tion, and, being used as a sea mark in conjunction wº l iº, approached **terhead, is not permitted to be removed. T he quarrymen . bored in the rock. *in 27 feet of it. The centre of the station is marked by a hole gº * untain, a few GREAT WHERNSIDE, 1840. This station is on the top of a * II.10 3. miles west from New Malton in the North Riding of Yorkshire. * : º ſº ar Gainsborough in GRINGLEy. Joining the east end of Gringley-on-the-Hill, a village near G * is barrow wº • * i º * * tº * * * * * a "º º row. The centre of this b +incolnshire, is a field in which is a ve y large barrow marks the station. GALTYMoRE. The station is about 8 miles south of the town of TIpperary º: - on the summit of the Galtymore, which is the highest point . mound well *ge of mountains. About the middle of the summit there m º the mountain. Covered with moss, and rising 4 or 5 feet above the ordinary SUll'itlCC lomerate rock, 9m the summit of this mound is the station, marked by a piece of º centre hole *"PPer surface of which measures about 24 inches by 17 inches. * •- tremendous is 2 inches deep and well formed. On the north of Galtymore there is a precipice. - tº º * * * * * er Hill, near HANGER HILL ToweR, 1848, is a slight square brick-built º º º TO of Ealing, in the county of Middlesex. The station was upon the c .. º Happisburgh, on HAPPISBUngu, 1843. This station is on the tower of the pºlish º º º top . 'the the north-eastern coast of the county of Norfolk. The º i. thaº the tower. *oof, the centre of the theodolite being made to correspond wi tº {- i. f the town of HART FELL, 1847, is a mountain in Dumfriesshire, about 6 miles i. by a pile, Moffatt; the station is on the highest part of the mountain, º the height of 3 feet, *4 feet in diameter at base and 16 feet high, built of stones O as in position is and the remainder of turf. The site on which the instrument W ed a halfpcnny *oted by a centre stone with a hole drilled in it, in which is inser date 1806). tº ‘k somewhat ( It may i. well to remark that there is the appearance of a station marl º º all holes * : ~4:-- ~~ a circle of 8 sma lower and to the Westward of the true station, consisting of round a centre one. 22 PRINCIPAL TRIANGULATION. HENSBARRow, 1845. The trigonometrical station on this large and well-known barrow near Roche, in the county of Cornwall, is 17.9 feet due south from a stone denoting the boundary of two estates, and is marked by a stone with a hole borcd in its centre, placed I foot below the surface. The zenith sector station is 72 feet south of this point. HIGH Pont CLIFF, 1846, is on the highest and most easterly of two headlands between Ventnor and Bonchurch in the Isle of Wight. The cliff consists of a chalky marl, and rises perpendicularly from the sea to the height of about 130 ſect. The station was 9 fect from the edge of the cliff at an angle projecting southwards, and 6 and 13 feet respectively from two re-entering angles on the west and east sides; but, from the crumbling nature of the soil, the site will probably be ſound nearer the cdge of the cliff than as above mentioned. The station on which Airy's zenith scctor was placed in Port Valley is in the bottom of the valley, 263 feet on the north side of the High Port Cliff Station, and in a line with it and the south-east station on Boniface Down. HIGH Wilhays, 1845. This station is on the rock of the same name in the parish of Oakhampton, in the county of Devon, from which town it is distant about 5 miles South, and is about I mile south of a well known rock called “Yes Tor,” which may be seen from the common called Oakhampton Park. The site is marked by a good stone pile, 20 feet high, erected above the centre mark of the station, which is a hole, 3.5 inches deep, drilled into the solid rock. The pickets on which the instrument rested were left in position, and being of hard wood, and let into the rock and fixed with lead, are likely to remain some time. HILL of HowTH. This station is on the highest of a series of peaks and ridges of nearly equal altitude in the promontory of Howth, in the county of Dublin, and close to the eastern edge of a quarry. It was marked by a centre stone with a wooden plug driven into it, and the posts (about 1.5 feet long) which supported the instrument left in the ground. A pole, with pile surrounding it, was left over the station. HINGHAM Tower, 1843. This station is over the centre of the tower of Hingham parish church, in Norfolk. The tower is a plain stone building, about 12o ſect high, without pinnacles, and the instrument was supported on three uprights let into two strong joists, which were let into the walls of the tower a few feet below the roof. Holste Moss, 1841. This station is on the highest part of a large broad-topped moorish hill south-west of Holmfirth, and crossed by the road leading from Further to Hudders. field. About 9 feet of the soil at Holme Moss is soft black turf or moss, good for fuel. The station is marked by a pile, which at an examination in 1841 was found to have been erected over the framework on which the instrument was placed. DESCRIPTION OF STATIONS. 23 Hungny Hill, 1832, 1843, is in the parish of Adrigole, about 5 miles north-east from Castletown, Bantry Bay, county of Cork. The hill has two summits, about three quarters of a mile apart. The station is on the higher and more northern one. The site is marked by a hole bored in the rock, which is within I ſoot of the surface, and the pickets which supported the instrument; the whole is covered by a pile. The zenith sector and trigonometrical stations are identical. INGLEBonough, 1807. This station is on the top of the mountain of this name, 5 miles east of Ingleton Village, in the West Riding of Yorkshire; it is about 60 yards from the highest part of an old building towards the north-east, which building is on the nearest brink of Ingleborough from the station south-westward. INKPEN BEAcon, 1844. This station is situated on or near the highest point of a cultivated field known by that name, about 2 miles south-east of the village of Inkpen and I mile north of the village of Coombe, in the county of Wilts. The stone marking the centre of the station is imbedded in the soil at a depth of 4 feet. r There are no measurements for refinding this point, as there were no permanent objects in the vicinity to which it might be referred. JURA, Nonth PAP, 1847. The station thus denominated is situated on the summit of the *ountain called Beinn-an-oir, the highest and most northerly of three hills at the solith- west extremity of Jura in Argyleshire. A pile, 16 feet high and 17 feet in diameter, * Crected over the centre stone, Kambonellis. This hill is situated in the parish of Wendron, in the county of Cornwall. The station is on a flat, between two eminences on the top of the hill, and is marked by a round hole cut in a stone, with a pile of stone 15 feet high and 38 feet in cir- *ence at base erected over it. A new stone fence has lately been built 51 - 5 feet south of the station. KARNMINNis, 1845. This station is in the parish of Towednack, in the county of Cornwall, *bout 3 miles south-west of St. Ives, and about a quarter of a mile south of the road *ing from St. Ives to Zennor Churchtown. The site of the station is a bare rock, °lose on the south-west side of an old ill-defined cairn (the summit of the cairn is about 8 feet higher than the station), from which the station is separated by an old fence, which at this place is the boundary of the parishes of Towednack and Zennor. A turf pile indicates the site, and as the centre mark of the station a hole 2 inches *P was drilled in the rock beneath the pile. The piles which supported the instrument were let into the rock with lead and left in position enclosed in the pile. KEEPER, 1830. This station is on the top of the Keeper Mountain, about 6 miles º: north-east of the village of Newport, in the county of Tipperary, and 3 miles east of " 24 PRINCIPAL TRIANGULATION. chapel and national school-house of Killascully. On the north-north-east summit of the hill is a large cairn of stones, on the top of which is the station. The centre stone, which is level with the surface, measures 31 inches by 20 inches, and has a hole 2 inches deep drilled in its upper surface. This, with the pickets of the great instrument frame, is covered by a pile 6 feet high, or Io ſect above the general surface. About one chain south-south-west of the station there is a collec- tion of stones resembling that upon which the station is, but not so high or so well formed. KELLIE LAW, 1847. This station is about 4 miles north-west of Anstruther, in Fifeshire, on a hill of the same name, and is 30 feet north-west from the centre of a large barrow. It is marked by a hole 4 inches deep in the centre of a stone measuring 2.5 feet by I. 3 feet, and placed 3.3 feet below the surface of the ground. There is a stout pole 30 feet long, with a cross on its top, resting on the centre stone, and a small pile built around it. From this point the zenith sector station is distant 210. I feet, bearing 302°53' from the south. KEYSOE SPIRE, 1843. This station is coincident with the centre of Keysoe Church Spire, in a small village near Kimbolton, in Huntingdonshire. The spire is tall and slender, and to obtain a bearing for the instrument, about 20 feet of the top was removed, and a simple frame of joisting was laid on the base of the soundholes below, on which the feet of the instrument stood, just high enough to give a clear view over the wall top, and with barely sufficient room for the observer, also inside of the spire, to move round the instrument. KIPPURE, 1829. This station is on the summit of the mountain of this name in the county of Wicklow, Io miles south of Dublin, and about the same distance west of Bray. It is marked by the frame on which the instrument rested, left in the ground, and by two centre stones; the original one, which is large, is sunk 4 feet below the surface, and marked by a deeply-cut cross; the other is smaller, and rests between the upper ends of the posts. Three shallow cup-like holes are in line north of the true centre hole. A pile 18 feet in diameter, the lower part of stones, the upper of Sods,--is erected over the station. A small pole is supported in the centre of the pile. KNOCKALONGY, 1828. This mountain is the highest of the Ox mountains in the county of Sligo, 14 miles west-south-west of the town of Sligo, and 4 miles south-south-west of Skreen. The station, which is on the summit, is marked. by a cross cut on a large stone. The top of the mountain is covered with soft bog about 8 feet deep. KNoCKANAFFRIN, 1829. This station is on the summit of the mountain of this name in the parish of Rathcormac, in the county of Waterford. It is marked by a hole I - 5 inches in depth and I inch in diameter, drilled in a stone, and covered with a stone pile 12 feet high, and 35.5 feet in circumference at base. There is a large piece of rock 8 feet north-west of the station, 25 DESCRIPTION OF STATIONS. Jº In º to the depth of nearly Io * of the mountain is covered "...i . * extent, ºd º º: *y parts this turf has º . A large hole was dug. .. : this framc * º: thus º º: made to rest on the .º th bottom of º ... . a very weighty i. º station. the hole; another stone was placed under the pole ------e | W * fl l ld Tip º 54 º * th-west of bout 15 miles sou º tº Clogheen, and a * boundary ‘m nºxy .. 4 3 miles south of c º be found, a É. it wº in 1852 no trace of the station º the station. & l - º * º the top of the mountain having been construc f the town of Cahirciveen, 8 This station is about 6 miles north-east o KnockNADonet, I 4O. This C. º igh mountain, highest point of a hig º º ‘ry, and on the highes r ion is marked in the south of the county of Kerry, !-- ~ 7. The station º north base of which forms the south coast of Dingle Bay * imbedded in º * ne slightly imbe by a stone Pile 7 feet high, within which is a small centre sto Sº, r Sºo - the gravel or common surface. KnockNAskAG Rathcor the e * tº 4 th-west of ‘k, is about 3 miles sou “º ty of Cork, is a tation is on - in the north of the coun - w º' ‘mov. The sta II, º: intº on the road from Cork to º in a south-west . º of the mountain, which slopes away º the immediate vicinity of lir º ". extends to a distance of about 3 miles. º but without any heath. tºº. the mountain has a thin covering of peat º al out three quarters of an º * tre stone is a piece of sandstone, having a hole inches under the surface, in deep in its smooth upper surface, and placed º à cookhouse are about . K} º ‘emains of the ino a little tu for it . º ut 8 feet high. The 1 º there being OW º It is d º º station s and from the circumstance : f bject yards north-east o ; : in a permanent o * or heath where it was built, it is likely to remain a p | * * º Q ty * of this arish, in the COUIIl T ER, I 843 The station Oil the church hi 2 AWSHALL CHURCH OWER, I sº p vo li rawn from Of Suff :--4----~~~4; two lines drawn f Suffolk. ; the top of the tower, and at the intersection of Ulffolk, is on th º º the corners of the parapet inside the tower. ish church of * tower of the paris * {} ignated is upon the f the tower. Axtir * • The station so designa tº ſº ſº •e of the top o *º º of Suffolk. The station is in the centre o *Xfield in the county * * LA Ahmay ‘n terminus of the N * • * * * e northern teri HILL, 1817, is situated in Aberdeenshire. It formed th YTON HILL, /? identified, as the ..: not be identi Belhelvie B red in 1817, but the exact station cam - - °lhelvie Base measure - ivy º ated. *nd about it has been reclaimed and cultiv LEITH HILL, 18 Sussex. from it. º º ** Dorking, in - ith Hill Tower, neal ; c. 44. This station is on the centre of Leith F ; and is 78. 17 feet distant th. station of 1822 bears from this º : i. i.e. distant. •c or 7° {tl|Cl I tº The station of 1795 bears 2O7 º 3. 26 PRINCIPAL TRIANGULATION, LINCOLN MINSTER, 1842. The station at Lincoln Minster was on the great tower about 4.2 feet to the north and 6. 25 feet eastward of the centre of the tower. LITTLE STIRLING, 1814. This station is in the parish of Cruden, Aberdeenshire, about 28 miles north of Aberdeen, 5 miles south of Peterhead, and about 1.5 miles to the left of a new road leading from Aberdeen to Peterhead. The four pickets which Supported the instrument frame, and a centre picket, with a hole in it 9 inches deep, were left at the station; a centre stone was also placed over the centre picket, and a pile of turf, 18 feet high, with a circumference at base of 45 feet, erected around them. Lough FoylE BASE, North END. This station is situated in the townland of Ballymul- holland, parish of Magilligan, in the county of Londonderry, about 2.75 miles south of the martello tower on Magilligan Point at the entrance of Lough Foyle. The ground between this station and Mount Sandy is composed of low sand hills, and is much broken and very rugged. Lough FoxLE BASE, South END. This station is on a small rising ground called Sheep Hill, about a quarter of a mile south-east from Ballykelly Church, in the townland of Drummond, parish of Tamlaght, and county of Londonderry. These stations are marked by dots made with the point of a needle in platina wires, 35th of an inch in diameter, run with lead into holes I. 5 inch in diameter and 6 inches deep, bored into blocks of Dungiven sandstone, 4 feet square and 20 inches deep. These blocks are laid in cement above other and similar blocks roughly chiselled, and placed on beds of solid masonry. The whole at each station is enclosed in a chamber of masonry 6 feet square, with walls 2 feet thick and 3 feet deep, covered over with a lid of flagstone, with bolts and rings passing through them, by which they may be removed with safety to the dots. On the upper surface of the flags cross lines are drawn, with the crosses vertically over the dots. This masonry is covered over with a tumulus of earth; and a circular wall 2 feet thick, with eight internal buttresses, is built as a base for an iron railing 4.5 feet high, enclosing a space 30 feet in diameter. The zenith sector station is in the same field with the south end of the base, from which point it is distant 559 feet due east. Af LoNGMOUNT Pole, 1843. The station so denominated is situated on the range called the Long Mynd, and is about 2 miles in a westerly direction from the town of Church Stretton in Shropshire. On the completion of the observations in 1843, a stone 2 feet by 18 inches and 3 inches thick, with a hole jumped in it to mark the centre of the station, was placed two feet and a half below the surface of the ground. On the upper surface of the stone are cut the words “Longmount Pole Station, 1843.” A pole, standing 42 feet above the surface, was erected over the centre of the station, and a pile 18. 5 feet high and 17.5 feet in diameter built around it. 27 DESCRIPTION OF STATIONS. h • ** to the ºn side of the entrance LUMSDEN, 1846, is a hill in Berwickshire, close to the southern º: a short distance from Firth of Forth iout 4 miles west of Coldingham, º lf a mile from Lumsden the Edinburgh ind Berwick Road. The station is about ha º it is marked by the Farmhouse and about 50 yards south-west of a large º the observations in Centre picket which supported the frame of the instrumen d ºil and a pile of turf 1809. A Stone, with a hole cut in it 3 inches deep, is place i. and aros in its centre, 18 feet high and 54 feet in circumference, surmounted by a po is erected above the centre stone. º ſº he - tº .. hannel, is in t LUNDy ISLAND 1845. The station on Lundy Island, in º Ann; me outline Celltro Of . ruin, said to have been formerly a chapel º i is 14t .25 feet due west of the walls is ye. visible. The lighthouse on Lundy Islan tº º an be ſ tº ored in it, and c * the station, which is marked by a centre stone, with a hole bor 3. Cºl. } easily found. rev Friars tower at LYNN Old *Well, 1843. This station is upon the top of ..". flagstaff in its Lynn, in the county of Norfolk. The tower is . ange The instrument “entre, and a staircase, turret, and vane at its most no t . the flagstaff stands. Xº Placed nearly in the centre of the tower, in the º . at the conclusion of the The flagstaff stood originally 3 feet further south, Ult, & *tions it was fixed above the site of the station. & ‘ch of sº tº of the parish churc MAKER CHURCH Towell, 1846. This station is upon º º * placed in the Maker, near Plymouth, in the county of Devon. The in °ontre of the tower. MALVERN, 1844. T f W •. Two & - k orcester. This station is at Great Malvern, in the county o Sets of observ º is place, viz., in *tions have been taken with the great instrument º: is not to be 18o3 and 1844. The site upon which the carlier º º the centre stone by found. The Present station is within a mile i. the . Great Malvern station, e - r inscribe C !-- ~ +-- t 'hich it was mark was 2 feet by 1.5 feet, an & ſº ich the instrumen * W i. º mº in the soil, and the framework on which *od was also left beneath the pile. MA * ‘ders of the 'counties of Ross and MSUIL, 1848. The mountain of Mamºuſ º O]] the º h º: iodge in Glen Affaric, Inverness, about 7 miles north-west of Captain Inge is on the highest point of the *nd 20 miles west of Invercannich. The station º 6o feet in circumference *9tuntain, and is marked by a stone pile 23 feet high * : the tl. c. b * c instrument was fixed ; t th ase, crected a ove the frame upon which the instrume + 2 - b ſ frame WàS IO feet high. ntain threc inn is a nilo alºnet, a Inoll * bject near the station is a pile on C 5 The only permanent object net - * º º I'll] CC: to º * , ring a similar appea Quarters of a mile north, and about the height of and having - Mamsuil. D 4 28 PRINCIPAL TRIANGULATION. MENDIP, 1844. This station is on the Mendip Hills, in the south-east corner of a field in Oak Hill, Somersetshire, near the junction of four roads leading respectively to 3ristol, Frome, Shepton Mallet, and Wells. The site is about 161 : 5 feet north-west from the finger-post at the junction of the roads, and about 94 feet north of the mile- stone. A centre stone is placed 18 inches below the surface. MERRICK, 1852. This mountain is in Kirkcudbrightshire, about 4 miles east of Polgowan Farmhouse, 12 miles north of Newton Stewart, and about 5 miles east of the road leading from that place to Ayr. The whole of the northern side of the mountain is bounded by a steep cliff, from the highest point of which a sharp narrow ridge extends towards the north, connecting the mountain with an adjoining hill called Shalloch of Menach. The station is about Io yards from the point where the ridge joins the top of the mountain, and in the angle formed by two fences. The frame of the instrument was left in position, and a substantial stone pile, 48 feet in circumference at the base and 16 feet high, was erected above it. The dimensions of the centre stone are 2 feet by 1.4 feet, and 5 inches thick; the hole marking the centre is 2 inches deep. MICKFIELD CHURCII ToweR, 1845. This church is near Debenham, in the ‘county of Suffolk. It has a square tower, and the station is nearly in the centre, being 8... I feet distant from the north parapet wall, 7. I feet from the south wall, 8.8 feet from the east wall, and 7.5 feet from the west wall. The instrument was raised by scaffolding about 30 feet above the parapet. * MILR HILL, 1850. This hill, also known as Alton Hill, is in the parish of Stanton, in Wiltshire, about 2 miles north of Honey-street wharf. The station on this hill is in a cultivated field, about 877 links west from an artificial pond or reservoir, sur- rounded with a thorn hedge, and about a mile and a quarter cast of a house on the summit of St. Ann's Hill. A coarse stone, with a small hole in its centre, is placed 2 feet below the ordinary surface, to denote the precise spot from which the obser- vations were made. - MonACH, 1839, is a saddle-backed hill, in the parish of Stornoway, in the northern part of the island of Lewis. The surface of the ground is 813.8 feet above the mean level of the sea, as obtained by spirit levelling; but from the fact of the hill rising from an extensive flat moor, with no other high ground in its vicinity, it is a very conspicuous object from every direction, and cannot be mistaken. It has two summits, lying east and west of each other; the station, which has also been adopted as a sector station, is on the highest part of the eastern summit. The ground surrounding the station being all soft and peaty, and the instrument when in position not being insulated, a slight tremor was detected on closely watching the bubble of the level when any jumping or concussion of the ground on the outside took place; otherwise the instrument was firm and steady. A pile, 14 feet high and 57 ſect in circumference, marks the station. DESCRIPTION OF STATIONS. 29 MoUNT BATTock, 1847, is a high mountain at the eastern extremity of the Grampian Hills, and in the county of Kincardine, about 4 miles west of the “Muckle Stane” of Clachnabane, which nearly overhangs the high road from Kincardine O'Neil to Fetter- *irn, and about 9 miles west of the bridge of Dye on the road leading from Ban- chory to "ettercairn. The station on this mountain is marked by a pile of stone, 16 feet high with a diameter of 15 feet. The framework which supported the Instrument during the observations in 1847 was left in the ground, and the centre from Which these observations were made is marked by a stone, with a hole I. 5 inches *p, placed level with the surface in the centre of the four piles on which the instru- * stood, and level with their tops in the true vertical line of the original centre- *k, which was removed. MoRMONTH, *47. The hill on which this station is situate is called Mormond, and is * 3.5 miles north-east of the village of Mormonth, otherwise known as Strichen, in the parish of Rathen, in Aberdeenshire. The station is on the south-east summit of the hill, but there is no permanent object near it by which its position could be pointed out. It is, however, marked by a stone with a hole 1. 5 inches deep, placed 5-75 feet below the surface of the ground, in the centre of the frame on which the instrument was fixed, which was left in position. A pile of turf, 16 feet high and '5 feet in diameter at the base, was erected above the station. Mount *INSTER station is on the summit of the mountain known by this name, about 5 *iles north-north-west of the village of Kiltealy, and about an equal distance **uth-west of the town of Newtown Barry. The station is marked by a large and irregular Pile of stones, having a circumference at base of about 70 feet. The *tre stone, which is a piece of granite measuring 32 inches by 12 inches, having a good hole in its Centre, with four other holes round it, each about a quarter of an inch deep, is in the Cºntre of the pile, about 6 feet above the general surface of the ground. Mowcott, 18 51. Mowcopt is the highest of a range of hills, extending in a south-west and *9th-east direction in the county of Cheshire. The station on this hill is situated *bout a mile and three quarters north of Newchapel, and about 3 miles south-west of Biddulph 9hurch tower. The site of the station is marked by a well-defined hole bored in a large stone, the upper surface of which is placed about 8 inches below the general Surface of the ground, and is about 24 feet Io inches south-east of a large cut Picket or cross on the edge of a precipice. A pole 21.5 feet high was set up over the * *d a stone pile 41 feet in circumference at base and 7 feet high erected around it. 4. - º & . º * † r * º NASEBy "owth, 1842. This station is over the centre of Naseby Church tower in North *Pºonshire. The tower is free from pinnacles, and the instrument was raised on a scaffold just sufficiently high to enable the observer to isolate the instrument from the *oof of the tower. 3O * PRINCIPAL TRIANGULATION. NAUGHToN CIIURCII ToweR, 1845. The station on this church tower, in the county of Suffolk, is in the centre of the roof of the tower. The instrument was placed over the centre of the tower on a platform about 14.5 feet high. The station was not free from motion. NoDES BEACON, 1845. This hill is in the parish of Freshwater, Isle of Wight, about 6 miles south-west of the town of Yarmouth. On the highest part of this well-known spot, and about 1.5 miles from the lighthouse on the Needles Point, there is a large barrow on which there is a beacon about 40 feet high. The station commands an open view of the sca between St. Catherine's Point and St. Alban's Head. The station is on the northern side of the barrow, about 32.75 feet from the centre of the beacon, therefore no object was erected over the site. A large stone, with a hole in its centre, was sunk 3 feet below the surface to denote the station. NonTH RoNA, 1850. This station is on the south-east and highest point of the island of this name, about 47 miles north-north-east of the Butt of Lewis. The hill is 355.2 feet above the level of the sea, and is very precipitous on the east side, but sloping gently towards the west. The zenith sector station of the same name is 24 ſect north-north- west of the trigonometrical station, and both are marked by holes bored in the rock. Norwich Spine, 1844. This station is on the top of the spire of the cathedral church of the city of Norwich in the county of Norfolk. The vane and the upright stone were removed, and the instrument placed on the flat stone composing the leaves of the finial, the centre of the instrument coinciding with the centre of the vane. The observatory was supported by a scaffolding built round the spire, and connected at various heights with its inside frame-work to within 30 feet of the top, above which height the scaffolding supported itself quite independently. The height of the scaffolding was 81 feet, and the instrument was 299 feet above the ground. Nonwood, 1844. This station is near the north-west, corner of a cultivated field on the east side of the road leading from Sheerness through East Church in the Isle of Sheppey. It is marked by a well cut square stone with a hole bored in its centre, and the letters B.O. and a broad arrow cut on it. The stone is about 3 feet under the surface. The instrument was raised on a stage 31 feet above the ground for the purpose of obtaining a clear view over various trees in its immediate vicinity on the west side. Old Lodge, 1849. This station is in Old Lodge Farm, in the parish of Lower Wallop, Hampshire, about 3 miles west of Lower Wallop Church. The site of the station is in a plantation about 40 chains north-east of Old Lodge farmhouse, and is marked by a square stone, with a hole in it I'5 inches deep, placed 15 inches below the general surface. DESCRIPTION OF STATIONS, 3 I OLD SAnuyſ 9astLB, 1849. This station is on the highest part of the north-west side of the inner ring of Old Sarum Castle, in Wiltshire. The station is marked by a piece of green sandstone sunk 2.8 feet below the surface. **one has a hole drica'ini to the depth of about 1.5 inches, which was after- * filled in with lead around a piece of copper wire, which projects about an * of inch above the surface of the lead; the piece of wire marks very accurately - * Point above which the instrument was placed in 1849. Old SARUM Gun, 1849. This station is the south-west end of the base line measured on Salisbury Plain during the summer of 1794, and was then marked by an iron cannon imbedded in the ground, with its muzzle projecting about 12 inches above the *ace. It is situated on the right hand side of the road from Salisbury to Ames- *y, and 617 links on the Salisbury side of the second milestone on that road, and *out 25 feet east of the boundary of the road. The centre of the bore at the muzzle "* adopted as the centre of the station of 1849. A piece of hard wood driven into the bore, and having a needle inserted in its centre, denotes the precise Station, and the extremity of the base line. ORFond 9astiſ, 1843, is in the town of Orford, on the east coast of Suffolk. The instrument was placed exactly above the centre of the spot occupied by the *gstaff, which was cut down for the purpose, but afterwards replaced. Should the flagstaff at any time be removed, the station may readily be found from the circum- *nce of the heel of the staff having rested on the newel of the stone staircase. Papoleswoman, 1844. This station is situated in a grass field near Paddlesworth Church, in the *nty of Kent, and not far from the highest ground. It is about 726 feet *south-east of a circular fir plantation, and marked by a large stone, having the Words “Station of I844” cut on it, with a hole 3 inches deep to mark the centre, sunk I '75 feet below the surface. A pole 34 feet high was also erected over the centre. PanAcosme, 1845. The station at Paracombe, on the summit of a high hill in the north- ***st of Devonshire, is about 2 miles south-east of the village of that name, and about 1.2 5 miles west of Longstone Bar. The hill forms part of the Exmoor *8°, and has several barrows on its top, and a stone wall running along it. The * was upon the third barrow from Paracombe, and about 23 feet from the Wall. sº PENDLE * 1841. There is a round conical barrow about 10 feet diameter upon the hill. The centre of the barrow is the station, and is marked by a stone, measuring 30 inclies by 18, with a hole jumped in it. A. PENINNis, 1850, is in the Isle of St. Mary's, one of the Scilly isles. The station is upon the top of the windmill, and in the centre. 32 PRINCIPAL TRIANGULATION. Pentinney, 1845. This station is on a low round hill about 2.5 miles south-south-east of the village of St. Just in Cornwall, and about half a mile west of the road leading from St. Just to Sancreed Church. The station is within the ruins of an old fort and near the north-west side; it is marked by a stone having a hole drilled in it 2 inches deep and placed level with the surface. The pickets on which the instrument rested were left in the ground, and a pile of stones raised above them to the height of 12 feet, with a diameter at the base of 9 feet. Pillesdon, 1845. This station is on the hill known as Pillesdon Pen, in the county of Dorset, about 2 miles north of the village of Pillesdon, 3 miles south-west of Broad- winsor, and 7 miles north-west of Bridport. Two series of angles have been taken from the hill, the first in 1795, and the latter in 1845, on both occasions with the Ordnance 3-foot theodolite. The present station is on the south-east point of the remains of an ancient fortification on the top of the hill, about 40 perches to the right of the road leading from Broadwinsor to Axminster. A stone with a small hole in it to denote the centre of the station, placed 18 inches below the general surface, marks the precise position over which the instrument was placed in 1845. In 1850 a pole was erected above the centre stone. PLYNLIMMON, 1805. The station on this celebrated mountain in Wales is 9 feet north of the centre cairn on the top of the hill, and marked by a stone pile. PRECELLY, 1842. This station is on Precelly mountain about 14 miles from Haverford- west, in Pembrokeshire, South Wales, and in a north-easterly direction from it. It is about 2 miles north-east of the New Inn, and about half way on the high road between the towns of Haverfordwest and Cardigan. The mountain is of a conical shape, and has two small barrows on its summit; on the centre of the South-western barrow is the station. On completing the observations in 1842, a centre stone 2 fect 6 inches long, I foot 9 inches broad, and I foot 4 inches thick, with a hole in it, was left to mark the site, the upper surface of the stone being about 18 inches below the surface of the ground. In attempting to place the stone in the hole, it fell with the side in which the hole had been jumped undermost, and as its great weight rendered it very difficult to move it, a fresh hole was jumped in the upper surface of the stone, and marks the centre of the station. RoNAs, 1821, is a large flat-topped hill in the north-west of the Mainland, one of the Shet- land Isles. The hill is covered with blocks or boulders, and the débris of granite. The station is on the highest part of the hill, about 45 yards north-west-by-north of the ruins of an ancient watchhouse, and is marked by an oblong stone about 5 feet long, with a hole bored in it to mark the centre. The wooden centre, and the pickets on which the stand of the instrument was fixed, were also left in the ground, and a large pile of stone 13 feet in diameter and 16 feet high, was erected around a staff placed over the centre stone. * DESCRIPTION OF STATIONS. 33 *** 1848. This station is on the highest ground about Rue Rea Head in Ross-shire. * * *bout 10 miles north-west of Poolewe, about 5 miles west of Inveransdale, *ut 1.5 miles north from Melvaig, and about 2 miles south-east from the extreme headland forming the entrance to Loch Ewe. The ground for some miles about the station is of a very soft and boggy nature, so much so that it is a difficult matter to approach the station in wet weather; but the station itself is on a bed of firm and sandy ground. A turf pile, 45 feet in circumference at the base and I5 • *et high, indicates the position of the station, which is also marked by a hole in a large stone placed about 2.5 feet below the surface, and within the frame on which the instrument stood; the top of the frame is level with the general surface. There is not a mark of any description near the pile that could be taken for it from any direction. - RYDER's Hill, 1845, is a flathill situated about 6 miles west-by-north of Buckfastleigh Church **out 4 miles from the small village of Holne, and nearly an equal distance from *Two Bridges Inn in Devonshire. The station is on the summit of the hill, and is well known by the name of “Peter on the Mount,” by the inhabitants of the South Dartmoor. About iz feet south from the station stands a stone with the letter H rudely cut on it, to mark the limit of the parish of Holne in this direction; the Parochial authorities in their annual perambulation describe the stone by the name Peter on the Mount. The entire framework used in the support of the great instru- *W* left in position, and a stone, with a small hole 2 inches deep to mark the Centre, was also placed on the gravel within the frame; the interior of the frame is filled up with stones level with the surface, and a turf pile, 12 feet in diameter and I 3 feet high, was erected above it. St. AGNes *Arios, 1850, is situated 219 feet to the north-east of the lighthouse in the Parish and island of St. Agnes, one of the Scilly Islands. It is close to the road Which passes the lighthouse and the church, on a small common used as a playground by the children attending the parish school. The centre is marked by a hole in a * sunk 2 feet below the surface. * St. ANN's HILL, 1792. This station is upon St. Ann's Hill, in the county of Surrey; * is about 20 feet below the top of the hill, and on being revisited and identified IIl 1844 was marked by a centre stone and a pole. In consequence of some obstructions ° the view a new station was prepared on the top, about 285.5 feet from the old * but no observations were made from it. St. MARTIN's HEAD, 1850. This is a station on St. Martin's Island, one of the Scilly Isles, * the coast of Cornwall. The site of the station is about 50.6 feet from a large beacon known as St. Martin's Daymark. * - - , * * E tº - 34 PRINCIPAL TRIANGULATION. St. Paul's, 1848. This station is on the centre of the top of the cross on St. Paul's Cathedral. A cradle to fit the cross was constructed of scantling, on which the instrument stood, and a scaffold was erected from the golden gallery to the same level, and on the floor of this scaffold the observatory rested. St. PETER’s CHURCH ToweR; 1844. This church tower is that of the parish church of St. Peter's, in the Isle of Thanet, Kent. - The station is on the centre of the tower above a signal house on the top of the tower, formerly used for telegraphic despatches. The stage on which the instrument was fixed was erected around the original house upon the same base, but was otherwise perfectly isolated from it. SAweL, 1827, is situated 7 miles south-west from Dungiven and 2 miles from Learmont, in the county of Derry; its summit is round and covered with bog to the depth of 6 feet. The sub-stratum is mica slate, varying much in hardness. A centre stone, 3 feet long, 2.75 feet wide, and nearly I foot thick, and marked with a hole, rests between the tops of the frameposts, is wedged tightly with stones, and further secured by mortar; on this was erected a staff, and around it a pile of stones and turf 15 feet high and of rather greater diameter, was built. SAYRs LAW, 1846, is the highest point of the Lammermuir Hills, in Haddingtonshire, about Io miles south-east of the town of Haddington, and 7 miles east of the village of Gifford. There is no permanent object near the station, except a pile on West Hopes Hill, about 1 mile west. The site of the station is marked by a pile of turf, 20 feet high and about 58 feet in circumference at base, erected above a large stone about 2 feet long and Io inches wide with a hole through it, under which is an oaken picket. The frame upon which the instrument was fixed was left in position over the centre stone and picket. x ... • SAxAvond, 1817. This station is on the hill of that name in the parish and island of Unst, the most northerly of the Shetland Isles; it is an isolated hill at the northern extremity of the island, and rises abruptly from the sea to the east of the north extremity of a range of hills, extending from the north-west point of the island at Hermaness to the south-east point at Mouness; the hill sloping off rather more suddenly to the north than towards the Söuth. The station is marked by a stone with a hole in its centre placed about two feet, below the surface, and a small pile of stones about 8 feet in height above the general surface, which is by calculation 937 feet above the mean level of the sea. Observations were taken from this station with Airy's zenith sector. ScA FELL PIKE, 1841. This hill lies between Eskdale and Wastdale, in the county of Cumberland; its summit is about three quarters of a mile north-east of Sca Fell, from which it is separated by a deep chasm called the Mickle Door. The station is DESCRIPTION OF STATIONS. 35 marked by a pile, 21 feet high and 18 feet in diameter, beneath which the frame on which the instrument stood, and a centre stone with a hole in it marking the exact * of the station, will be found. The nearest houses are at Wastdale Head, * whence the station is best-approached. SCARADIN, *39, in the county of Caithness, is situated about 4 miles left of the road between Berriedale and Dunleath, both on the mail-coach road from Inverness to Thurso. The nearest houses to the foot of Scarabin are at Braemar, about 2 miles * The top of the hill is covered with loose stones. The central and highest summit, upon which is the station, has rather a flat surface just below the highest ridge, * the pile denoting the station is a little to the left of it. * Pile constructed at the conclusion of the observations in 18 39 was of stone, *9 feet in diameter and 20 feet on slope. Scourtnalapich, 1846, is a high mountain in the north-west of the county of Inverness, close to the borders of Ross-shire. The site of the station of 1846 is about roo feet West-south-west of the highest peak of the mountain, and is covered by a pile of Stones 22 feet high and about 16 feet in diameter, raised above the frame and platform * Which the instrument rested. * *. sº * Piles of the framework were not driven into the soil, but were mortised into &l *quare frame, which was placed on the natural surface of the mountain, and built *ound with stones to the height of 3 feet, forming a foundation for the platform of the observatory. In the centre of the 4 piles, a stone with a hole drilled in it about ** deep, was inserted to mark the centre of the station. .* route to the station is by Struy Bridge to Invercannich Bridge and the head of Loch Molardich. " - SEVERNDRoog Tower, 1848. The statién so called is the centre of the north-west turret of *ndroog Castle on shooters Hill, in the parish of Eltham, county of Kent. º From this point which is the station of 1822 and 1848, General Roy's station of *79% is Io. 73 inches distant, and hears 157° 30' from the south. SLIEve Posaub, 1846. This station is on the top of the highest of the Mourne mountains, in the county of Down, in Ireland. It is marked by a hole bored in the centre of a Square stone, measuring 3.5 by 3.5 feet, and by a pile of stones built over it. Sieve LEAGUE, 182 8, is a high mountain, about 12 miles west of Killybegs, in the county of Pomegal, and forms the extreme south-west promontorv of the county in which it is situated. The hill has three not very conspicuous surnimits; on the western of º * the station. On the eastern brow,-close to the cliff-of the western summit, a p C of stones, 3o feet in diameter and 4 feet high, indicates the spot where the great instrument was once in position on the wildest headland probably in Great º º Treland. The centre stone is a piece of mica slate, measuring 1.67 feet by I .5 ce E 2 36 PRINCIPAL TRLANGULATION. imbedded in gravel and small stones, having a hole an inch and a half deep in its centre; the hole cannot be called a well formed one, being a little too wide at the opening, but still sufficiently defined for its use. About I mile east of the station, and probably I,000 feet below its level, is a limestone quarry. SLIEVE MORE, 1831, is an isolated hill in the north end of the island of Achill, in the county Mayo. Its length is in an east and west direction, and the pile denoting the station is about 2 chains west of the eastern extremity of its summit. It is marked by a hole in a piece of mica slate, measuring 24 inches by 14 inches, level with the surface, and having its length in a north and south direction. The centre hole in the stone is an ill-shaped one, being nearly 3 inches in diameter, and scarcely 1.5 inches deep. Slieve More station is about 2.5 miles north-west of the chapel Dukenella, and 3 miles north-north-east of the village of Keel. It would be difficult to ascend the mountain from any side except the west. # SLIEVE SNAGHT, 1827. This mountain is in the parish of Carnadongh, in the county of Donegal. The station, which is on the highest part of the mountain at the east end, is marked by a stone about 2 feet square, having a hole 2 inches deep drilled in its centre, with a pile of stone, 14 feet high and 50 feet in circumference at base, erected over it. SNOWDON, 1842. The station on this celebrated mountain in North Wales is upon the highest peak, and is marked by a pile 20 feet in diameter, beneath which a hole is bored in the rock to denote the centre. * * º - SouTHAMPTON STATION. This station was over the chimney of the west wing of the Ordnance Map Office, 4 inches south from a broad arrow cut on the south edge of the partition between the two central funnels. , Trom this station the zenith sector station is distant io9. O feet, and bears 285°53' from the south. * South BERULE, 1840, forms one of a range of hills running north-east and south-west throughout the Isle of Man; it is about 7 miles north-east of Castletown, and 6 miles South-south-east from Peel. - * The station is close to the south edge of the hill, and nearly in the centre of the diameter of a semicircular wall, distant about 200 yards from the station, which wall is supposed to have been the boundary of an ancient Danish camp, and is so called at the present time. A large slate stone with a hole bored in it, sunk 3 feet below the surface of the ground, marks the station. The sector station of 1842 is identical with this station, but that of 1845 is 74 feet due south, and about 16 feet lower. - SouTH LOPHAM ToweR, 1844. This is the parish church of South Lopham, in the county of Norfolk. The instrument was placed above the centre of the top of the tower, upon a platform 19.25 feet above the battlements. DESCRIPTION OF STATIONS. 37 SouTH RoNALDSHAY, 1821. The station on the island of South Ronaldshay, one of the Orkney islands, is upon the top of the Wart Hill, where a mound of turf and stone marks the situation of an ancient watch-house. The instrument was placed on the top of the *und; a centre stone was sunk in the ground, and a pole and pile erected *Veit to mark the site. Southwold Towen, 1844. This station is on the centre of the square tower of Southwold °hurch, on the east coast of Suffolk. The instrument was raised 23 feet above the top of the tower by scaffoldings. { Stoke Tower, 1844. This station is on the church tower of the parish of Stoke, in the *ty of Suffolk. The instrument was placed in the centre of the roof. StoRn, 1847. This station is on the top of Storr Head, a remarkably rocky and precipitous *lountain, near the village of Rig, on the east coast of the Isle of Skye. STRONsay, 1821. The station on Stronsay, one of the Orkney Isles, is on the highest ground ºf the island, and near the Burgh Head. It is marked by a centre stone With a hole in it, and by a pile of stone and turf. * SWAFFHAM, 1843. Swaffham church spire, in the county of Norfolk, was selected for a station in the month of September 1843, to correct the triangles of Cambridgeshire * those of the north and east of Norfolk. The station was on the north-east Corner of the tower, and the instrument was placed on a stage which raised it within 19 feet of the top of the spire, which was sufficient for the purpose of observing all * Principal stations that had taken the spire. º - * Swyne BARRow, *45. This station is on the west side of an artificial mound raised about 70 or 80 years ago by the proprietor, Mr. Pitt, on Swyre Head, about 1 mile west of Encombe *ouse, the seat of Lord Eldon, and about 2 miles north-west of St. Alban's Head, and nearly an equal distance south-east of the small village of Kimeridge, on the **oast of Dorsetshire. A block of stone weighing about 1.5 cwt., with a hole " * Placed 4 inches under the ordinary surface, marks the station. In the centre of the hole is a piece of rod iron (a quarter of an inch in diameter) run in with lead * Prºjecting 1 inch above the surface of the stone; the centre of this piece of " * the precise centre from which the observations were made. The four Piles on which the instrument rested were left in the ground. The ground about the station is the property of the Earl of Lldon, and, as it is used as a preserve for game, the station may remain a long time undisturbed. * º 1829, is about 3 miles north-east of the town of Gorey, in the county of Wex- Ol'Oi - ; it is a rough rocky hill, and in an ordinary sized carn of stones in its summit is . station; it is marked by a centre stone, having a good round hole in it I-5 inches eep, level with the surface of the mountain, and a stone pile above it 12 feet high. J 38 PRINCIPAL TRIANGULATION. TARBATHY, 1817. This station is situated on Tarbathy Hill, on the coast of Aberdeen- shire, and was the southern extremity of the Belhelvie Base. No trace of the exact site of the station is now in existence. TAUR, 1834. This hill is about 7 miles north-east of King William's T own, on the confines of Cork and Kerry. The station is on the summit of the hill, which is flat or rather concave about the station; in the centre of this concavity there is a small mound of stones, and the centre of this mound is the station. The pile is about 6 feet high, and the centre stone will be found 4.5 feet under the surface,—an irregular shaped stone weighing between 80 and 90 pounds. The top of Taur hill is covered quite close to the station with good peat moss. There are no stones on the hill, with the exception of those about the station. TAWNAGHMORE, 1843, is a long narrow-topped hill in the county of Mayo, Ireland, about 2 miles from the coast guard station at Belderg. The station, which is identical with the zenith sector station, is on the highest point of the hill, and is marked by the frame on which the zenith sector rested, which was left in the ground. TELEGRAPH ToweR, 1850, is a station so called after the telegraph tower on which it is situated, in the island of St. Mary's, one of the Scilly Isles. The station is in the centre of the top of the tower. THARFIELD, 1843. This station is on the high land eastward of the village of Buckland, in Hertfordshire. ºr \ THAXTED CHURCH SPIRE, 1844. This station is immediately over the centre of the coping- stone of Thaxted church spire. The instrument was supported by a scaffold erected from about the middle of the spire, and the observatory was supported by another scaffold erected from the top of the tower at the base of the spire. TILTON, 1843. This station is situated in a pasture field, which is the second from and on the north side of the road leading from Tilton village towards Oakham, in Rutland, and at a distance of nearly 2 miles from the former. It is marked by a centre stone of irregular shape, measuring about 18 inches by 16 inches, having a hole, 3 inches in depth and I inch in diameter, bored in its centre, sunk 3.5 ſeet below the general surface of the hill. The square wooden frame on which the instrument rested was left in the ground, the top being nearly level with the surface; and a pile of turf, 12 feet in diameter and Io feet in height, has been erected over it. Torts ToweR, 1845. This tower is that of the parish church of Tofts, in the county of Norfolk. The station is in the centre of the roof of the tower. \ t TREvoSE HEAD, 1846. The station on this headland in the Bristol Channel, about 5 miles north-west of Padstow, in the county of Cornwall, is on the most prominent part, and 917 links east-south-east of the centre of the lighthouse, - ſ DESCRIPTION OF STATIONS. 39 ** 1827. This mountain is in the county of Antrim, 6 miles south-west of Cush- *all. The station is on the top of the mountain, and is marked by a pile of turf I 5 , feet in height, and 50 feet in circumference at base. The top of the mountain is long and flat, and exceedingly boggy and wet. - Upcot Down, 1850. This station is situated in a cultivated field on Upcot Hill, in the northern part of Wiltshire, about 1.25 miles east of the church tower of Broad Hinton, and about 5 miles south of Swindon church tower. The site of the station is marked by a piece of freestone, measuring 15 inches by 12 inches and 6 inches thick, with a * I inch in diameter and 2 inches deep, bored in it. The upper part of the stone is about 1.3 feet below the general surface of the ground. A pole, 12 feet long, Was placed Perpendicularly over the station. , Vicans CARN, 1827, is on a cultivated hill, about 4 miles south-south-east of the city of *gh. The station is on the summitofa large carn of small stones known by this name. It is about 24 feet in diameter at the top, and its height above the general ***bout to feet. The station is a little to the south-south-west of the present Centre of the carn; and the centre stone, which has a well-cut hole, is 6 feet below the surface of the top of the carn, and rests on a bed of small stones. Walpole St. Peter's, 1843. This station was upon the church tower of Walpole St. Peter's, in the county of Norfolk. The tower is square, strongly built, and has | * *y high roof, out of which rises a massive vane post covered with lead. This Pºº" Was taken down, and the theodolite placed exactly in the centre of the tower. WALTON Tower 1844. This station is on the centre of Walton church tower, on the east Coast of Essex. t * i WATER CRAG, 1852. This is a barren mountain in the North Riding of Yorkshire. The station is a boundary mark between Arkengarth Dale and Swale Dale, and is situated 1.5 miles south-east of William Gill Houses, 5 miles west of Arkengarth Dale, and 7 miles *th-by-cast of Muker. There is not an object on the hill from which measurements * be taken, but the station is well known to the inhabitants for miles around. The site of the station is marked by a pile of stone 14 feet high, and 36 feet m Circumference at base. º WEEK Down, I846. The trigonometrical station on Week Down, on the south side of the * of Wight, is identical with that from which the observations were made with *iny's zenith sector. The Down is about three quarters of a mile north-north-east of the village of St. Lawrence, and has several tumuli upon its summit. Three of - these tumuli lie nearly north and south of each other; on the central and largest of them, called “The Frenchman's Grave,” is the station: it is marked by a centre stone, having a hole bored in it, placed 2 feet below the surface. PRINCIPAL TRIANGUIATION. WESTBURY Down, 1850. The station on Westbury Down in Wiltshire is about 2 miles north-east of Westbury church, and I mile south-west of Bratton church, and about 200 yards south of Bratton Castle. The site is on the side of the road leading from Bratton to Warminster over the Down, and near the junction of several small mounds which run at right angles, and serve as boundaries to the several farms. A stone, with a hole 4 inches deep, and 1.75 in diameter, is placed 1.6 feet below the surface; and, a pile 9 feet high, with a pole 21.7 feet long, was erected above the stone. WHITEHORSE HILL, 1844, is in the county of Berkshire, on a range of hills running east and west between Wantage and Lambourn. The station is on the outer edge of a bank, apparently that of a fortified encamp- ment on the east-south-east extremity of the hill; it is 12 feet from the edge of the bank, and 20 feet west of the path leading from Farringdon to Lambourne. The stone placed to mark the centre of the station is nearly level with the surface, and has a hole jumped in its centre, and the year 1799 inscribed upon it. WHITTLE HILL, 1841, or as it is better locally known, Whittle Pike or Skelp Moor, is in Lancashire, 2 miles east of the village of Edenfield, 6 miles from Bury, 7 miles from Rochdale, and about half a mile from Knoll Moor, which is higher than Whittle Hill, and bounds about 90° of the view to the north-east. The station was on the highest point of the hill, and is marked by a pile chiefly built of turf. The wooden frame on which the instrument stood, was left in the pile, together with a centre stone, having a hole in it, and marked with a broad arrow, and the date of the year “ 1841.” WINGREEN, 1844. Two series of observations have been taken from the top of Wingreen Hill, situated about 2 miles south-east of the village of Charlton, in Dorsetshire, and about 5 miles south-east of the town of Shaftesbury. The observations taken in 1794 were from a point now distinguished as Wingreen Old Station, and those of 1844 from a spot called Wingreen New Station. The stations are about 17.5 feet apart, the , new station being about 50 yards in a south-easterly and perpendicular direction from the road which passes over the hill, and 185.9 feet south-south-west of an old tree in a small circular plantation of stunted birch trees. The old station is 203. 3 feet also south-south-west from the old tree. Both sites are marked by centre stones with holes in them, in each of which was placed a halfpenny of the reign of George III. The stone marking the new station is sunk 3 feet below the surface, that at the old station Io inches. ~ WISP, 1809, 1816. This station is on the top of Wisp Hill, 2 miles south-west of Mosspaul Inn, between the counties of Roxburgh and Dumfries. The centre is covered with a turf pile. WoRDESLow, 1846. The station is about a mile and a quarter north-east of Houghton-le- Spring, in the county of Durham; it is 94 feet from the highest point of the hill, in line with the middle range of houses in the village of Houghton-le-Spring. DESCRIPTION OF STATIONS. 4.I WRoTHAM, 1844. This station is in the southern corner of a field called “The Plains" *P* Wrotham Hill, in the county of Kent. * 1821. This station is in the Island of Yell, one of the Shetland Isles; it is on the top of Comb Hill, or the “Long Cairn” as it is termed by the inhabitants, to the north of two piles on the same hill, and nearly on the same level. One of the piles is of turf, and the other of stone; from the former it is about a quarter of a mile, * from the latter half a mile. A stone sunk into the ground, and having a hole bored in it to the depth of 3 inches, marks the centre. A pole 20 feet long and 6 inches in diameter, supported by a pile of stone and turf, was erected over the site. York MINSTER, 1846. This station is on the centre of the great tower whence it is llamed, S E C T I O N II. DES C RIPTION OT INSTRUMENTS, THE perfection of the results of geodetical, operations, and the degree of importance to be attached to them, must be proportioned to the excellence of the individual observations, or to the mean error of an observation, which depends not only on the skill and carefulness of the observer, but on the perfection of his instruments. It is therefore desirable in a collection of such results to have descriptions of the instruments with which the observations were made; but, inasmuch as minute descriptions of all the chief instruments that have been used on the Ordnance Survey have been already published in the previous volumes of the Survey, it will not be necessary here to give more than a general description of each, Description of Theodolites. (1.) The Principal Triangulation for the Ordnance Survey of Great Britain and Ireland has been effected with four large theodolites, namely, two of 3 feet in diameter, one of 2 feet in diameter, and a fourth of 18 inches diameter. Besides these, however, Subsidiary use has been made in a few cases, and for short distances only, of smaller instruments, having diameters of 12, 9, and 7 inches. The two first-mentioned instruments, measuring 3 feet in diameter, were constructed by the celebrated Ramsden, at the close of the last century. One belongs to the Honourable Board of Ordnance, the other is the property of the Royal Society. The only difference between these instruments is, that the horizontal circle of the former is divided to ten minutes, and read by three micro- scopes; while in the latter the circle is divided to quarter degrees, or parts of fifteen minutes, and is read by five microscopes: the respective advantage in each case being coun- terbalanced by the corresponding comparative disadvantage. Each instrument has an extra microscope not generally used, being one of the original pair at 180° from one another. They have, therefore, respectively four and six microscopes. The following general description, written with reference to the Ordnance theodolite, of which an engraving will be found in Plate I, is applicable, with the exceptions just mentioned, to the other instrument. (2.) The Great Theodolite.—The instrument consists of three distingt principal parts, not including its stand, which is a strong circular four-legged mahogany table, firmly braced. The lower part consists of, and connects rigidly, the feet of the instrument, the vertical axis, and the microscopes for reading the horizontal circle. 43 DESCRIPTION OF INSTRUMENTS. The next hollow vertical telescope. - The third The instru united at the p *etal, about ei this cy - tº sº tº attached. q ists of the telescope, its axis, and the vºnial º: | are firmly part COllSIStS O 'ee fect, provided with levelling screws, V linder of bell- º º º * jº. a strong º i. * From tléC Wller i. e ...] ... 10 - º ght inches high and seven in º º of the instrument, wº linder, and Very strongly connected with it. h, having a bell-metal base, and term º * of steel, conical in form, and about two feet hº m the upper part of the º *ing in a cast-steel pivot with sloping checks. º, microscopes for ºrding: e project three *S, carrying at their extremities * et of the instrument. These arm S horizontal circle; each microscope is over one of t f m instrument, so that the º * Strongly braced to one another and to the feet o º d its axis, is as nearly as pºliº i between the *icroscope, the feet of the instrument, º t microscopes, there is a fourth rigid and "erable. Besides these three equidis {{Il icroscope, with that one which bisecting the angle of 120° made by one pair. This tº: the other two having is 180° distant from it, were the original pair of º W wºn in perfect adjustment, been subsequently applied. One revolution of i. º wire over the space º is º to ". minute, ten º: . into 6o parts, so º *... º d two dots. The micrometer hea º ividing mentally the space, º: indicated, * tenths of seconds can be estimated y º º y f twentieth of an inch, between two divisions of the . divided by dots into spaces o The horizontal circle, of brass, is 3 feet in diame ..". the hollow brass exterior º ten minutes, and COnnected ". º º º º: hº high, 5.5 º º: . by ten hollow *ical radii. The exterior axi ... ." . his hollow ax º º and 2.5 inches in diameter at the top. Within º º º, steel axis: the . * steel is strongly driven, fitting exactly the º sloping checks fitting º end is terminated interiorly in a thick bell-metal plate, s rior axis and circle, when place On to the *tremity of the steel axis. Thus the .. smoothness, and without any "Pon the interior axis, revolve with the greatest º top of the axis it is easy . shake, By means of an arrangement of screws on ner, and consequently the º: WI1 *egulate the Pressure of the outcr axis upon the in º axis and circle are let OW it revolution. When the instrument is travelling, the º not be used for observing, º º completely "Pon the inner axis. In this state "...". hand, could the in sºme, 8. Would require force to move the circle; nor, on i. s in that case there would º used for observing if the pressure were made too ligli 'º. degree of pressure or *: Shake at the °ºntre from want of sufficient cºntact ... but me limits are not wide. becil *volution must therefore be regulated by the obset º of the instrument, and has hich *cellent method of Centering is one of the best º inmense wear and tear to W *uch admired. Probably no other could have stoo F 2 44 PRINCIPAL TRIANGULATION. these instruments have been subjected, not only from constant use, but from travelling, necessarily in the roughest manner, and exposure to weather on the summits of the wildest mountains. A horizontal flat bar 2 feet long, and projecting 1 foot on each side of the centre of the instrument, extends across the top of the outer axis. On its extremities are raised the Y’s for the support of the pivots of the telescope. It is supported and made perfectly rigid by two ladder-formed braces springing from the lower part of the outer axis. The Y’s are of such a height as to permit a circle of 6 inches radius attached to the axis of the transit to pass freely, and consequently the telescope to be directed to the stars at high elevation, not including of course the zenith. The focal length of the telescope is 36 inches, aperture 2.5 inches, and the generally used magnifying power 54. In the focus of the eye-piece are the cross wires, with the usual apparatus for adjustment in collimation. Two of the wires intersect in an acute vertical angle; the third is horizontal. By means of a small screw, this horizontal wire has a vertical motion, and is intended for measuring small vertical angles, the amount being indicated by the revolutions and parts of revolutions of the screw. In astronomical observations the wires are illuminated as in ordinary transit instruments, and a reflecting eye-piece used. Concentric with the hollow axis of the telescope, are two vertical circles, similarly placed on each side of the telescope, their planes about 2 inches and a half apart. The diameter of each divided circle is Io. 5 inches. They are read by two long horizontal micrometer microscopes passing through the short vertical arms carrying the Y’s, each division of the micrometer head being equal to 3 seconds. The perfect adjustment of the micrometers as to distinct vision and runs is very tedious, and can only be effected after much practice. The runs of the micrometer are easily altered, particularly by travelling. In this adjustment, however, as is also the case with others, if the precise amount of error is known, it is all that is necessary; for if Io-Hºn. revolutions of the micrometer go to Io minutes, or the space between two dots, then m being known by, observation, the values of a revolution and division become known. The instrument has two long levels; one of them, 21 inches long, hangs by brackets at the extremities of the horizontal arm, when required in that position, and is also used for levelling the telescope. The other is the striding level, 24 inches long, for levelling the pivots of the telescope in astronomical observations: one division of this level is assumed as cqual to one second, which is true only for moderate temperatures. The whole body of the instrument admits of a small horizontal motion in any direction on its table, which is perforated in the centre. This motion, which is commu- nicated by horizontal screws acting on the raised edge of the mahogany table or stand, is used only for the final adjustment of the centre of the instrument vertically over the centre- mark of the station. The weight of the whole instrument is about 200 lbs. ; it is carried, when travelling, in a four-wheeled spring-van, j. 45 DESCRIPTION OF INSTRUMENTS. tº •on: ly the msden. It is of precise (3) The Eighteen-inch Theodolite was * by Ral ior hollow axis. t &d * ſº * : * rºº ſº * *9 general construction as the tWO º to the base of the º inch at the sº The circle is attached * º º inches in diameter at º iº the Y’s º This conical axis is 12 º C horizontai bar which supports º is braced to the lower pai top '. º *h is º The bar is 12.5 inches long, and lass receiving the te escope { } * e object g as of the axis. he telescope is 19.5 inches, the . **. º 1S The focal length º "... power 30. To the º centre of the telescope 2 inches, and the ordinary ; it is placed about 4 inches from ise at the other extremity. Connected the vertical cº C i of the axis, having a º: , three verniers. The and 2 inches from one º nches; it is read to Io seconds hº is read by three The diameter of this circle *: ided by lines to every five m entS. horizontal circle, which º º manner as in the large insti º mahogany, being º lillcromotor microscopes 111 til C upon a thick hexagonal plate ce screws passing through Tho whole. instrument *...". is levelled by º nº of the three-legged Connected with it as Its base. :ut in metal bosses in the upper º, the same level, this plate and acting in gº º nºt As in the 3-foot IIMS horizontal arm carrying *ool forming the stand of the º either the telescope or the used for astronomical I2 inches long, is º for * tº. A striding level is also w the Y's, hanging in each cas is a instruments, i ſº large instru as in the b ti the value of one division of this level, observation; . Second. & t the d Simms a Messrs. Troughton an n’s - ºri,..., , # Theodolite was made by Messrs t onstruction from º . (4.) The Two-foo º voy. It is of a different c t, with a repeating table, i. º of the * º º and azimuth instrument, dii to theodolites, and more s rictly † ical radii to - r ith six conica which has been seldom used. • * * * and connected with ical and of steel, izontal circle is 2 feet in diameter a This axis is conical an den's The horizonta c 'nal axis of the instrument. w ion as the axes of Rams º Vertical º: iº, but is not so long in proportio (2S *ut 2:5 inches in diam 2 {º ical microscope * . º * º six vertica .43 instruments. f metal, about 8 inches in º upon the vertical º .. metal, t * - i. S t A cylindical º o . arms, and an interior hollow axis, º pressure is regulated as * . ached by co nical ra ul º mi revolves smoothly round it r surface of the drum ſº Interior axis Just . From a metal plate on the uppe The pillars are of º º { 's Ollt CS: C. ithout ill º º the Y’s for the pivots of the º in a vertical plane, With . | Illal'S º º to revolve freely on its ax It is *Clght to allow the ** a ... f the drum. •e 2. 125 inches. °ming in contact with the º º 7 inches, and the º º together º CSCODC ſº * *n\{W SC .. The focal length º . . I5 inches º º: The horizonta * 'O VC1'tlCall C * * , O l ed º: º concentric with the axis of rotation °onnecting bars, t att plac 46 PRINCIPAL TRIANGULATION. and both vertical circles are divided by lines, on silver inlaid into brass, to every 5 minutes; the former is read by the vertical microscopes attached to the radii proceeding from the drum, and the latter by horizontal microscopes passing through the pillars supporting the telescope. As in the Royal Society's theodolite, five of the microscopes are equidistant, or 72° apart, while the sixth bisects one of these spaces. It will be seen that this instrument differs entirely from Ramsden's, in this respect, that the microscopes for reading the horizontal circle move round with the telescope, while the circle itself remains clamped; in Ramsden's theodolites, on the contrary, the horizontal circle moves round with the telescope, while the microscopes are fixed to the lower part of the instrument. A full description of the instrument will be found in the “Account of . the Measurement of the Lough Toyle Base,” pp. Io9 and Io9. (5.) The stores generally accompanying an observing party are as follows:– 1 Waggon for Instrument. 15 Brass rings for heliostats. I Observatory. 7 Pocket telescopes. 2 Wooden houses. I Chronometer. II Five-inch theodolites. I Mountain barometer. 13 Large heliostats. II Pocket compasses. II Portable heliostats. To Mcasuring tapes. &c. &c. &c. with all the necessaries for camp life, and full supplies of stationery, carpenters' tools, mathe- matical instruments, and any books that may be of use to the observer. The strength of the party varies from 6 to Io men. (6.) The portable observatories used for the theodolites are hexagonal in plan, with a pyramidal skeleton roof, canvas covered. The wooden sides or panels are 5 feet high (4 feet for the 18-inch theodolite), a space of 2 feet, canvas covered, being left between their upper cdge and the horizontal rafters of the roof, for the unobstructed use of the telescope. The six iron rods supporting the roof and resting on the tops of the six uprights at the corners of the hexagoń, are so formed, being double, that by revolving round a vertical axis, any one of them can be twisted out of the line of sight of the telescope, should it be necessary. Framed wooden huts, having canvas covers to their tops, have now been many years in general use for the partics employed on the Ordnance Survey with the large theodolites and with the zenith sector. The experiment was first tried in 1840, on the recommendation of Major Robinson, R.E., who was then in charge of the Ordnance 3-foot theodolite, in the north of Scotland, and they have been found to be not only much more comfortable for the officers and men employed on this arduous and, at times, disagreeable duty, but also more cconomical than marquees and tents. They vary in size from 8 feet square to 9 feet by 12, and being constructed in parts they are casily packed or carried by piccos to the tops of mountains. (7.) Heliostats are used for reflecting the sui's rays to distant stations. The smallest size is 5 inches in diameter, being merely a plane mirror set in brass, with a stand or handle DESCRIPTION OF INSTRUMENTS, 47 terminated in a spike for sticking in the ground. The next size is 12 inches in diameter. The larger heliostats are rectangular; the largest measures 20 inches by 16. The surface of the mirror, in each case, can be moved with ease to follow the sun. The exact position * * surface is determined by throwing its light through a ring placed in the line between the heliostat, or the reflecting station, and the station reflected to. The ring, which lies in "..." plane perpendicular to the line joining the two stations, and at a convenient distance from the heliostat, is placed in its true position by means of a small theodolite, Method of placing the Instrument in Position. (8.) In placing the theodolite over a station to be observed from, the first point to be *nded to, and which has always been considered of the greatest importance, is that it shall rest upon a perfectly solid foundation. The method of obtaining this desideratum must " each case depend entirely on the nature of the ground. While at some stations the instrument has rested almost upon the solid rock; at others some difficulty has been Cxperienced in getting a steady foundation, as for instance at the station on Holme Moss, where it was found that the bog extended to a depth of 9 feet, and below it was a layer of Sand 6 fect thick, all of which had to be removed to a total depth of 15 feet before a solid foundation could be obtained, from which to build a strong scaffolding up to the ordinary surface of the ground. Even on the tops of mountains some trouble has occasionally been found in obtaining a firm foundation for the instrument to rest upon. In one or two instances the instrument has been sunk in the ground, so that the telescope only grazed the top of the hill; the excavation also served as a protection against storms. This method would of course be very objectionable if the surface of the hill were flat and of considerable extent. * The following description from the observation-book of the station on Ben Hutig, II] Sutherlandshire, will serve to give a general idea of the method of preparing the station When the foundation is rocky:—Four holes were jumped in the rock, about 6 inches deep and 5 inches by 3 in length and breadth, at equal distances of 1.75 feet from the centre mark of the station, to receive four pieces of wood scantling, upon the heads of which the feet of the table for the instrument were to be screwed. These holes were run with lead, the toPs of the scantling cut off and levelled accurately, and further secured against shaking by four *ontal braces mailed near the tops, and also two diagonal ones. Their tops were cut oft at the level of the highest piece of the rock on which a corner of the observatory rested, * Were thus also on a level with the lower edges of the six panels forming the sides of the observatory. The panels were supported by piling up stones so as to form a level all round with that of the top of the rock. A space of about 4 ſect square Wils left in. the Centre of the flooring, by which the instrument and its stand were insulated, and not liable ***ken by any motion above or around it. The flooring was laid upon joists, 6 inchº above the level of the top of the posts. A batten of wood was nailed upon the extremity of the flooring round the centre space, to keep the feet of the observer from touching the legs of the table of the theodolite. 48 PRINCIPAL TRIANGUIATION. . When the station is on ground of a soft and boggy nature, a hole of a sufficient diameter is sunk until a bed of gravelly carth is reached, which is levelled and firmly rammed. A strongly braced framework of wood of sufficient height, is then placed in the excavation, which is afterwards filled up with stones. Thus the instrument being also isolated from the flooring of the observatory, is rendered as nearly as possible perfectly free from any source of unsteadiness. In order also that the centre of the station may not be lost, four pickets are driven into the ground previous to the commencement of the excava- tion, in such positions that the intersection of diagonal lines joining them shall coincide exactly with the centre-mark of the station. In exposed situations on the tops of mountains a wall of stone is generally built close round the lower part of the observatory, a precaution which at the station on Fashven saved the great instrument from certain destruction, as on the 11th of October 1838 a storm levelled all the marquees and tents, and moved the observatory from its true position, although thus protected by a wall 2 feet thick. In some cases it has been necessary to raise the instrument above the surface, in order to obtain observations of distant points, not visible from the ground. The high stage used for the great instruments is 32 feet high, but has been only used in cases of absolute necessity. At the south end of the Base-line on Salisbury Plain this stage only barely sufficed to make the two extremities of the line mutually visible. Many instances of high scaffolding occurred in the triangulation of the Eastern Counties, where, the country being flat, the stations were over church-towers. One of the most remarkable was the station on Thaxted Church. The tower of this edifice is 79 feet high, and is surmounted by a spire of 93 feet, making a total height of 172 feet from the ground to the top of the spire. The scaffold for the observatory was carried from the base to the top of the spire; the scaffold for the supporting the instrument, which was interior to the other, was raised from a point of the spire 139 feet above the ground, having its bearing upon timbers passing through the spire at that height. Thus the instrument, at the height of 178 feet above ground, was insulated, and not affected by the movements of the observer, or the action of the wind upon the observatory. This was the 18-inch theodolite. The station, as will be seen on reference to the diagram, was indispensable to the connexion of the triangulation. In placing the framework for receiving the feet of the instrument, every care has always becm taken to have it as nearly concentric with the station as possible: the legs of the table of the instrument are then screwed to the framework. The circular mahogany tray upon which the instrument immediately rests, is then placed on the table, and accurately brought over the centre mark by means of a plumb line suspended from the orifice in its centre, and the motion communicated by horizontal screws acting on the edge of the table, as before explained. º (9.) The Referring Object.—The next step after the placing of the instrument in position is to select a spot for the referring-object; an object which from its position should be visible under all circumstances, and to which all other objects are to be referred as to their bearings. * DESCRIPTION OF INSTRUMENTS. 49 The referring-object, or, as it is usually written in abbreviation, the R.O., generally used **in stations, consists of two similar and equal rectangular plates of metal, A. A. —*— in the same vertical plane, and with parallel edges, sliding upon horizontal - cross-pieces B. B. This being placed against the sky, a fine vertical line of | light of any required breadth is obtained. When the opening cannot be backed by the sky, the same effect is easily produced by a plane mirror placed behind the opening, and inclined at an angle of 45°. The angular —H- breadth of the opening generally adopted, and found most convenient for —l perfect bisection, is about Io". ſº In the placing of the referring-object, two points have to be attended to; namely, that it must be as nearly as possible on the same level as the observer, and that it must not be either too close or too distant. If too close, it will not be visible to perfection without altering the focus of the telescope, which is to be avoided; and if too far off, it may be hidden, when required, by mist. The ordinary distance is between one and two miles; but *P** top of a mountain it is obvious that a selection cannot always be made, and the best position that offers must be taken. In some cases the distance has been as small as half a mile, and the effect of the proximity of the referring-object then tells with disadvan- tage upon the observations of the elongations of circumpolar stars for absolute azimuth. "these observations a lamp is placed behind the referring-object. A. A. Method of Observing with the Theodolite. (Io.) All the adjustments of the theodolite are more or less liable to be deranged by travelling, and consequently the first operation at a station is to correct any deficiencies of this nature. In general, however, the mode of observing is calculated to eliminate * much as possible the effects of slight errors of adjustment. - The general adjustment consists in this: that the line of collimation of the telescope should be perpendicular to its axis of rotation, this axis perpendicular to the revolving axis * the instrument, and the latter perpendicular to the plane of the horizon. The runs of *micrometers should also agree with the divisions on the limb. The observations then proceed as follows: the instrument being perfectly levelled, and the lower part or body firmly clamped to the table, the observer directs his telescope "Pon the referring-object, and having carefully clamped the upper limb, brings the inter. *ction of the crosshairs, by the motion of the tangent screw, to bisect the vertical line of light in the referring-object. He then reads the degrees, minutes, and seconds gº” by * divided circle and each of the micrometer microscopes. The upper limb is then unclamped, and the telescope directed on the next point to be observed, which is bisected, and the readings recorded. Similarly, all the other points to be observed, and then finally - the referring-object is bisected and read again. The agreement of this last reading with G. So PRINCIPAL TRIANGULATION. that at the commencement of the series is some test of the care of the observer and the steadiness of the instrument. Each such series is called an “arc” and they are numbered consecutively from the commencement to the close of the station. The first arc being completed, the telescope is reversed in its Y’s, the horizontal circle turned through 180°, and the levels adjusted, if necessary: the second arc is then proceeded with, precisely in the same manner as the first, closing as well as commencing with the referring-object. * The second arc being completed, the lower limb of the instrument is moved through a small angle, 20° or 30°, and clamped, so as to get readings on another part of the circle ; and in this position the third are is taken. The third arc being completed, the telescope and horizontal circle are reversed as in the second arc; and so on. - It has generally been the custom to read both horizontal and vertical circles for each bisection of a point, but the vertical angles have not, perhaps, been measured with such care as the horizontal; and the readings of the vertical circles for the true level position of the telescope have not generally been observed at the close of each arc, although its variation during the time of observation of a complete arc is liable to be larger than the change in the readings of the referring-object. All observations, when received in the office, are considered of equal weight, unless a remark of the observer against any observation condemns it as to be rejected. Observations under favourable circumstances are doubtless more valuable than observations under less favourable circumstances; but how to assign their relative numerical value is a question that admits of no general solution. Observations are seldom taken under decidedly unfavourable circumstances, if it can be avoided. “It appears that the longer time one is compelled to bestow, and does bestow, upon observations, under less favourable circumstances, in a great measure compensates external disadvantages, and that causes of errors of observation of which the observer himself has not been conscious often influence him no less than those which obtrude themselves upon him.”—(Bessel: Gradmessung in Ostpreussen.) It has indeed been often noticed, that an observation to which the observer has attached a remark to the effect that the bisection was unsatisfactory, or that the light was bad, or any other expression of doubt, has been found to agree with singular precision with the general mean or probable truth. The mode of observing described above does not strictly apply to the observations from the commencement of the survey until the year 1839, for the referring-object was first instituted in 1840 by Lieutenant-Colonel (then Captain) Yolland, both for the sake of con- venienceandof accuracy. Otherwise the method followed was much the same as that described above. The method of “arcs" has been always followed; though in the earlier operations an arc contained a smaller number of points. It has never becn the practice to observe single and independent angles, as in the Indian and other geodetical operations. DESCRIPTION OF INSTRUMENTs. 5 I (II.) As the readings of the microscopes at each observation are read out by the observer, ** they are recorded by the booker—invariably in ink—in the observation book. The following is the form :- Lººm------ Royal Society's Theodolite. IBEN INEVIS. 11th November 1846. Degrees Seconds of Microscopes. * - $. Means. Arc 141. Bar' 25".466 Ther; attº 40°. and Call i tº Minutes. A. IB | C D | E Readings of Vert. Circles correspond- ing to Telescope Level, A o'o. 2” C I} o? o' o”. Q f f/ A/ f/ A/ A/ // l ; : º } R. O. . i. * * † • I2 I 22 || 21 19 15 21%| 20% I9'4o Observer. Pilo Scournalapich * . 164 || 54 24 || 25 | 19 | 18 23#| 21.90 "...sº "dep. A 359°35'42" D 359°35' 39” Booker, } Pile Ben Wyvis i. . 182 || 23 || 57 | 53 46 48 5o 50.8o Timo 7% A.M. Gd dop. A 359° 28' 51" I, 359°28' 49” * in diº, * Ben Macdui . . . . . 56 50 | 54, 55; 47 |47 ||34 || 51.70 Cillſ in di º O ~ 2. / - , // So - ~/ - . . - ºn. ... ºp. A 359°39'14" | 359°39'14" ..] 8 IBen Wyvis, and Pile 5o miles * g 49 24 16 | 16%| 7 || Io 14 | 12:8o Glashmeal tº mis G. d Ç V - A/ O º // * ſº “vi 5 * • A 2. ty in direction of op. A 359° 23' 7” B 359° 23' 5 #ºn Tuire, Ben | Pile Ben Amhlair. C. * T • | 74 26 || 45 || 43 || 35 | 35 | 41 || 39.8o artevil, B Gºlden. 9 o of n rººf ° 32' 21” More South U. dep. A 359°32'25" B 359°32'21 l • QO * Storr, and on | Pile Ben Lawers . º º Io? 56 44 || 43 || 35 | 35 | 39%. 39.3 all low hills. G"dep. A 359°39'57" B 359°39' 54” Pile Ben Dornish . i. i. . I61 G"dep. A 359° 21'5" is 359° 21' 2" Pile Ben More in Cowal (v.h.)” . 169 || 38 || 35 | 35}| 26 26 || 32 || 30-90 | G"dep. A 359° 18' 6" B 359° 18' o” Pile Ben More in Mull (v.h.) • 44 || 38 || 65 || 65 62 || 65|| 65|| 64.5o G" dep. A 359° 28′ 16” B 359° 28 13.” Pile Creachbheinn tº tº G"dep. A 359° 1' 30” B 359° 1' 27’’ R. O. for Elongations . * wº G"dep. A 357° 26' 32” B 3.57° 26'28" R. O. . : . I º º • 121 2. 45 || 41 || 35 | 32 || 38 || 38:20 23.70 5 O 4. 3 2. 2. 2 4. 2 4. # 2. 3 # 24 % 69 49 || 36||38|| 55 55 56; 56.19 | 21 | 20 | 16 || 21 | 20 | 19.60 2 2. fº T-- =ºmsºmº- The column of means is not supplied by the observer; it is filled in in the º ***, and each mean corrected if necessary for the runs of the microscopes, the values o which are 9°casionally observed and recorded. The original record of the observations is retained by the observer until the book is filled. A copy of the day's work is made every T- * This, -** = º tº a ſº - any atmospheric together with some other similar abbreviations, as (m.m.) (f) are used to º tiny ſ *cumstance peculiar to the observation, as very hazy, much motion, faint. G 2 52 PRINCIPAL TRIANGULATION. evening, and being carefully compared by the observer with the original, is transmitted to the head quarter office every two or three days, or in very remote stations as opportunities offer. In the later operations of the principal triangulation the observer has generally been furnished with a list of bearings of the principal points or heliostats that he is expected to observe, in order that no time or opportunities may be lost. When there is doubt as to whether any of these principal points may not be too low or too distant to be observed, the approximate depression is also given to the observer, so that on a fine day he may be able, by the observed depression of the furthest ground visible in the direction of the given point, to ascertain whether it is entirely cut off by this intervening ground, or whether it may not under peculiar atmospheric circumstances be visible. (12.) A watch is always kept in the camp for distant heliostats. The first man that calls out “heliostat,” when one of these star-like points shows itself, receives a shilling for his vigilance. In order also to incite watchfulness in the man directing the heliostat to the observing station, and that he might miss no gleam of sunshine, a pecuniary reward was proposed in 1840 by Captain Robinson, R.E., and sanctioned by Major General Colby, Superintendent of the Survey. The amount varied with the distance, being 6 pence for each time the heliostat was observed for a distance less than 10 miles, one shilling for a distance between Io and 20 miles, and so on; whilst for a distance between 90 and Ioo miles the allowance was I5 shillings, and for a distance over Ioo miles, a guinea. But, subsequently to the cstablishment of this rule, the size of the heliostats used for long distances was increased, whereby the chances of observation were also increased; the allowance was therefore reduced, and for long distances half allowance was given for the second arc, a-third allowance for the third arc, and a shilling each for every subsequent observation on the same day. The propriety of this allowance will be readily admitted when it is remembered that as long a period as a month has very frequently occurred between consecutive observations of very distant points. The value of an observation under such circumstances becomes very great. (13.) Observations for Absolute Azimuth.-The determination of the direction of the meridian at various points in the triangulation has in all cases been effected by observations of the elongations of the following circumpolar Stars:– o, Ursae Minoris. 8 Ursae Minoris. s Ursae Minoris. 7. Ursae Minoris. 5I Cephei. In the earlier observations the polar star alone was used. The time of the elongation was calculated, and the instrument carefully levelled for the observation. When the time arrived, the angle between the star and the referring lamp was taken ; the telescope was then immediately taken out of its Y’s, the horizontal circle turned through 180°, and the telescope replaced in a reversed position as regards its pivots and the collimation: the angle was then re-observed. DESCRIPTION OF INSTRUMENTS. 53 In subsequent observations, however, the exact error and rate of the chronometer have generally been *known, as special observations for time were seldom made. The approximate time was then all that the observer had to assist him, and therefore the observation of the * Was commenced about a quarter of an hour before the elongation, and continued until about ten minutes Past the elongation, as judged by the motion in azimuth of the star. The instrument was kept carefully levelled, and the telescope and horizontal circle reversed at the apparent *9ment of elongation. The reading of the referring lamp was observed both before and after the clongation, in reversed positions of the telescope. In the year 1844, at the suggestion of the Astronomer Royal, who had visited one of the observing Parties, and made himself acquainted with the mode of observation, the instru- ºnents were fitted with striding or pivot levels, and the reversal of the horizontal circle at the elongation discontinued, as well as any attempts to eliminate mechanically the collima- * error; the observed level error and the observed collimation error were thereafter recorded, * the observations corrected accordingly. The method of observation since then is as *llows: the instrument being levelled, the referring lamp is first bisected; the telescope * then reversed in its Y’s, and the lamp again bisected; the telescope is then directed * the star, which is observed every three or four minutes, and the readings of the circle and of the chronometer recorded at each bisection. When the star is stationary the telescope is *Versed, and the observations of the star continued until about ten minutes past the clongation; the referring lamp is then again observed in two positions of the telescope. The error of collimation is inferred from the readings of the lamp. The striding level ** read and recorded six times previous to the elongation, in reversed positions, to eliminate the °rror of the level, and as many times immediately after the elongation. º It is necessary, even when the readings of a pivot level are recorded, to have the *nstrument as nearly level as possible, for the value in seconds of a division of the level is * Very variable quantity, varying very sensibly with the temperature, which alters the * of the glass tube of the level. In some levels an increase of temperature in- *ases the value of a division; in others it diminishes it. By experiments upon the level of the 3-feet theodolite, it was ascertained, that though at the ordinary temperature of 66 the value of a division was very nearly one scCond, yet at the temperature of 32” the value **ased to 5 seconds. It is therefore necessary that very little should depend upon * readings of the level, or that the instrument should be as nearly as possible level *ing the observations. This, unfortunately, has not always been attended to by thc *Vers, and is doubtless the cause of many discrepancies otherwise unaccountable in the *sults of azimuthal observations. "the observations taken at Ben More, South Uist, in 1851, the reversal of the telescope during the observations of the star was discontinued, as also in the few observations that have been made at other stations since that date. The weight of the telescope, and the danger of °ommunicating a move to the circle during the reversal, make that practice º "his species of observation is very difficult and delicate, and discrepancies in lC *ts, unavoidable even with the best observers, have been observed in all cou" 54 PRINCIPAL TRIANGULATION. They necessarily increase with the latitude, and are probably due to some lurking level error and instrumental defects. - The terrestrial object observed in connexion with the star is generally a lamp placed behind the opening in the referring object before described, and detriment to the observa- tions has doubtless often occurred by the necessity of having it too near the observer on the tops of mountains. -- (14.) Probable error of an Observation.—The probable error of an observation is dependent upon the circumstances of the observation as much as on the excellence of the instrument or the eye of the observer, and still more on the nature of the object to be observed, or, as it is technically termed, bisected. With a view to test the power of the telescope, and to determine what accuracy of observation might be expected on a fine object at a short distance, the following experiment was made :-A wooden framework was set up at a distance of about two miles and a quarter from the Ordnance theodolite when at Ben More, South Uist. It was so arranged that being placed against the sky, a fine vertical line of light, of which the breadth was regulated by the sliding of a board, was shown to the observer. The breadth of this opening was varied by half inches, from half an inch to six inches, during the observations, which are recorded as follows:— BEN MoRE, SouTH UIST. Ordnance 3-ft. Theodolite . . . 14th August 1855. Observations made to an opening in a frame with a sliding board, fixed near the pile on Hecla. No. Width. sº IReadings of Microscopes. Mean. Opening. A IB C I 6.o Left 27.5 29.o 27.5 28.oo Right - || 36.5 39-o 37.o 37.5o 2. 5-5 Left * 28.o 3O.O 27.5 28.5o Right 36.5 38.5 36.o 37.Oo 3 5.o Left * 29.o 3I.O 27.5 29-16 Right . 36.5 39'o 36.o 37. 16 4. 4-5 Left • 3O.O 3 I-5 29-o 3o. 16 Right 36.5 38.5 35-o 36.66 5 4-o Left 30.5 32-O 29.o 30.5o Right 37.o 38.5 36.o 37. I6 6 || 3:5 ſºft, 31.5 335 | 39.5 31.16 Right 37.o 38.5 || 35-5 37.oo 7 3-o | Left | 33-o 34.5 || 30-5 32.66 Right 37.o 38.o 35-5 36.83 8 2.5 | Left, 34.0 | 35-o 31.5 33.5o Right | 37.5 38.0 35-5 36.83 9 2-o Left 34.5 35-o 32-o 33.83 Right | 37.o 39'o 35°o 37-oo IO I'5 Left 36.o 37.5 33-o 35.5o Right 37.5 39-o 35-o 37. I6 DESCRIPTION OF INSTRUMENTS. 55 “The light of an inch opening and of half an inch opening are visible, but not sufficiently defined for observation. {{ The centres of the spaces are bisected in the following observations:— Readings of Microscopes. No. Width. Mean. A. IB C I 1-0 37-5 38.o 35-5. 37-oo 2 I-5 37.o 37.5 34°o 36. 16 3 Q - O 36.o 37.5 33'5 35-66 4. 2.5 36.O 37'5 33°o 35.5o 5 3.o 35-5 37.o 33°o 35. 16 6 3-5 35-O 36-5 33-O 34.83 . . 4-O 35-o 35-5 32°5 34°33 8 4-5 33-5 35°o 32-o 33'50 9 5-O 33'5 35°o 3 I-5 33-33 IO 5°5 33°5 35°o 3 I-o 33. I6 II 6.o 33'5 35°o 3I -o 33. IG “ Ti - - - 16 •vrn 4; - º º the ni *servations were made under very favourable circumstances; the object was well defined, and **ir clear of motion.” W. J.ENKINS, Corp., R.S.M. ºf from the first set of these observations we would determine the most probable angular Vil * º * * ſº lue of an opening of one inch, we should have the following equations, where r is the angular value required, 6 a – 9.5o = o 3.5 a - 5.84 = o 5-5 a -8.5o = o 3 a -4. I7 = o 5 r – 8-oo = o 2.5 a - 3.33 = o 4-5 a - 6.5o = o 2 a. – 3-17 = o 4a – 6.66 = o 1.5 + – 1.66 = o Multiplying each equation by its co-efficient of r, and adding, there results 161.25 a - 249.74 = o º ... a = I’’-55 Wow the individual values of a as derived from the observations are (1) . . . . I-58 (6) . . . . . 1.67 (2) . . . . . 1.56 (7) . . . . I-39 (3) . . . . 1.60 (8) . . . . 1.33 (4) . . . . I-44 (9) . . . . 1.58 i A d (5) * º ſº q I.67 (Io) i. º • • I • II . l * the true value of r as determined from the distance of the observed object, * I2462 feet, is a = 1”. 38 56 PRINCIPAL TRIANGULATION. It appears, then, that the opening as deduced by observation is, as might be expected, rather greater than its real value; the difference, however, is extremely small. When compared with the true angular value of the aperture in each case, the observa- tions show the following errors :- (1) . . . . + I’’.22 (6) . . . . -- 1:01 (2) . . . . 4 o'91 (7) . . . . 4- og (3) e e is " + I • IO (8) tº ſº º tº - * I 2 (4) • e º * + o-29 (9) tº g º º + 4 I (5) e e º 'º' + I. I.4. (Io) * . . . . . . . - 41 giving a mean error of o'-79, or a probable error of o”. 53, for each observation of the angle. Now the observed value of the angle depends upon two equally good single observations; therefore the probable error of a single observation is the above probable error divided by the square root of 2, or = o' 38. In the second set of observations if 37"--w" be the reading of the right edge of the opening, then a will be found to be r=+ 12, and the resulting corrections to the bisections of the spaces will be, (1) . . . . —o".57 (6) . . . . – 12 (2) tº º 'º º —-o? (7) tº g º º + og (3) . . . . + -ob (8) . . . . ---52 (4) tº ſº tº ſº. - • IO (9) tº dº ſº tº + 34 (5) tº tº ſº º —-11 (Io) tº e º 'º + 17 (II) * * * * * — .18 giving a mean error of o”:27, or a probable error of o”. 18. It is therefore clear that a streak of light can be bisected with extreme precision; the probable error of this species of observation being, as far as can be determined from these observations, about half that of the bisection of a dark edge against a strong light. Description of the Zenith-Sector. (15.) The instrument used for the determination of the latitudes of points fixed in the triangulation of Great Britain and Ireland, from the commencement of the survey up to the year 1836, was the zenith-sector constructed by Ramsden, described in the second volume of the “Account of the Trigonometrical Survey,” and destroyed by fire in the Tower of London. -E This instrument consisted of an arc of about I 54°with a radius of 8 feet, divided into spaces of 5’ each by dots on the heads of gold pins, and having a micrometrical division, by which quantities of about a tenth of a second could be judged. The focal length of the telescope was about 8 feet, and the diameter of the object-glass 4 inches, showing distinctly stars of the 3rd magnitude during daylight in clear weather. The instrument was read off by means of a plumb-line; and the apparatus for placing it truly vertical, for reversing its position, and DESCRIPTION OF INSTRUMENTS. 57 for bringing the plumb-line over the centre of the instrument, were all very perfect. But, notwithstanding the general excellence of the instrument, it was not, from the complexity of its construction and the number of its parts, well adapted to constant transport from station to station; the necessary reversal of the instrument on successive nights, and the Consequent delay during bad weather, was also a source of considerable inconvenience. * “onsequence of these deficiencies, an application was made to the Astronomer Royal by Major General Colby for a design for a new zenith-sector, by which the obser- Vations of a single fine night might give an accurate determination of the latitude. The design Was furnished; and eventually the construction of the instrument superintended by Mr. Airy. The first principle in this instrument, now known as Airy's Zenith-Sector, was the *rangement for making successive observations in two positions of the instrument, face ** face west at the same transit. The second principle was the substitution of a level or *}stem of levels for the usual plumb-line. The third principle was the casting in * piece, as far as practicable, of each of the different parts of the instrument, in order to avoid the 8"at number of screws and fastenings with which most instruments are hampered, and to secure, if possible, perfect rigidity. tº . The lower part of this instrument, which is represented in outline in Plate 1 is a *ectangular tray of cast-iron, which is screwed, if required, to the pier or framework on which the instrument may rest, by means of ears projecting from the plane of its base. Within this tray is placed a rectangular thin plate of iron, whose breadth is two inches less than that of the tray, and length one inch less. This plate has three bosses on its upper *e, one at the centre of one extremity of the rectangle, the other two at the other extremity • These bosses are cut to receive the footscrews of the instrument; and imme- diately °9′responding to them on the lower surface are three other bosses, on which the plate Tests, and by means of which the weight of the instrument is immediately transferred to the tray. By means of screws passing horizontally through the sides of the tray, #111 azimuthal **on is communicated to the plate, and by them also it is retained in the required plane of azimuth. The instrument is in three parts; the Framework, the Revolving Frame, and the Telescope Frame. The Framework is cast in four pieces; the lower part, an inverted rectangular tray with levelling footscrews; two uprights, with broad bearing pieces, very firmly screwed to the inverted tray; and a cross bar uniting the tops of these uprights, whose ends are cut £1S SCreWS. Through the centre of this bar passes downwards a screw with a conical point, which together with the vertex of a cone rising from the centre' of the inverted rectan- º tray, determine the axis of revolution, and form the bearings of the Revolving 'rame. The Revolvin tray, S In th º ſº * ſº º * of {l g Frame is cast of gun-metal, in one piece. It is also in the º tion i. º sº Fºº º - O trongly ribbed at the back, having four lappets or ears acting as stops in the º: **ntre of the front of this frame is a raised ring of about nine inches diameter, Sº, H 58 # PRINCIPAL TRIANGULATION. the bearing plate of the Telescope Frame. Concentric with this ring at each end of the frame are the divided limbs, which have a radius of 20.5 inches, and are divided on silver to. every five minutes; the divisions are numbered from o' to 360°, interrupted by the portions of the circle which are wanting. There is also at each end a raised clamping-limb, roughly divided, to which the clamp for securing the Telescope Frame at the required zenith distance is attached; the graduation furnishing zenith distances on both sides of the zenith, and also circle readings corresponding with those of the divisions of the limb, the pointer-reading being given by a small index attached to the clamp. On the reverse side of the Revolving Frame are mounted three levels, the divisions of which are numbered from right to left. The Telescope Frame revolves in a vertical plane by a horizontal axis or pivot, of 3 inches diameter, passing through a correspotiding cylindrical hole in the Revolving Frame. Cast in one piece with the Telescope Frame, are, the ring for holding the object-glass-cell of the telescope, the four micrometer microscopes, which are afterwards bored through the metal, and the eye-piece. The micrometers are of the usual construction, the wires inter- sect in an acute angle, and have a range of about Io minutes on the divided limb. The value of a division of the micrometers reading the limb is approximately a quarter of a second. º In the eye-piece of the telescope are five meridional wires carried by a fixed plate, and a single wire at right angles to them, moved by a micrometer-screw. The range of the screw admits of the wire being carried completely across the field of view: one division of the telescope micrometer is equal to o'-43096. The tube of the telescope is merely a protection from dust, and carries no essential part of the instrument except a simple apparatus for regulating the amount of light illuminating the wires, which, by the turning of a screw, increases or diminishes the orifice through which the light enters. The focal length of the telescope is 46 inches, the diameter of the object-glass 3.75 inches, and the magnifying power usually employed, about 70. The cast-iron tray, forming the stand of the instrument, generally rests when in use on strong pickets or piles driven into the ground, or secured to the rock by jumper-holes. In some instances a strong rectangular frame of wood has been sunk into the ground; and this method of preparing the station is found the most expeditious and convenient, the frame being carried about with the observatory and stores. - The Revolving Frame is generally reversed in its position with regard to the pivots, once at each station, so that the reading of the zenith point as given by the pointer at the lower end of the telescope is for one part of the observations about 12°30', and for the other part about 192°30'. Method of observing with the Zenith-Sector. (16.) The deviation of the plane of the instrument from the meridian, which is generally very small, being carefully aheerlained by observations of the transits of northerly DESCRIPTION OF INSTRUMENTS. - 59 and southerly stars, and the axis being as nearly as possible vertical, the observer sets the Telescope IP "ame at the approximate zenith distance of the star to be observed, and clamps it. He then, before the star enters the field, reads the four micrometer microscopes, *"ediately after them the levels on the reverse side of the Revolving Frame. He is then teady to observe the star, which is done by bringing the micrometer wire in the ey e-piece of the telescope to bisect the star on one of the wires, the name of the wire being recorded with the reading of the telescope micrometer. This completes a single observation. The Telescope Frame is then immediately unclamped, and the Revolving Frame TCVersed by turning it through 180° on its vertical axis, so that the face which * was east is now west. The Telescope Frame is quickly set to the approximate *mith distance, and clamped, and the star again bisected by the telescope micrometer on * of the wires; generally the same one on which it was previously observed. The five *ometers are then read, and the levels on the reverse side. This completes the double observation. b The method of reduction is then, for each position of the instrument, to add together, the pointer reading, the mean of the readings of the microscopes, the correction for their uns. the reading of the telescope micrometer, and the mean indication of the three levels, * the correction for azimuthal deviation, and for the wire on which the star is *d. This sum is called the corrected instrumental reading. The mean of thc Corrected instrumental readings for the same star observed face cast and face west is the quantity corresponding to an observation of the zenith, and is called the zenith point. The *enith points must, when the instrument is carefully used, agree with great exactness, and therefore * Comparison of their values affords a test of the accuracy of the observations. "he amount of the azimuthal deviation is ascertained by comparing the differences of theo Served transits of northerly and southerly stars with the truc differences of their meridian transits, or differences of right ascension. If A be the excess of the difference of **scension of two stars over the observed difference of time of their transits, 3 º' their º Polar distances, and a the latitude of the instrument, then a, the azimuthal devi" lon, is, *. O. = A sin 6 sin 6' T cos x sin (6 – 3') The °orrection to the zenith distance 2, on account of this deviation, is, L sin “o sin 2 cos 2. T Tsin 5 sin 27 Where 3 is the north polar distance of the star. * r º * * * * r; * y nich The correction for the equatorial interval i from the meridian, of the Wire on wl the star is observed, is, in seconds, *2 + tº cot 6 sin I" re * the upper sign applying to south stars, the lower sign to north stars. H 2 6o PRINCIPAL TRIANGULATION. TABLE SHOWING THE STATIONs visitED witH AIRY's ZENITH-SECTOR. + Number Year. Stations. Oſficer or N; C. o. in charge of the sº of Nº. Orl cºol. Instrument. Party. Observations servations. were made. 1842–3 Blackdown. Lieuts. Hornby and Gosset, R.E. . 7 2O 1087 1843 | Precclly iº Lieuts. Hornby and Luykin, R.E. . 5 17 674 1843 Forth Mountain . Lieut. IIornby, R.E. ". . . 7 I 2. 659 1843 || Hungry Hill 3} 33 7 9 295 1843 | Feaghmaan 33 33 7 9 395 1843 Taunaghmore . * 25 33 2. 7 2.94 1843 S. end of L. Foyle Base 2s 33 2. 6 335 1844 Monach tº . Lieut. Gosset, R.E. 5 IO I8o 1844 Ben Hulig. 33 35 6 IO 48o 1845 Hensbarrow Corp. Steel, R.S.M. sº º 4. 6 290 1842 | South Berule Lieuts. Hornby and Gosset, R.E. 6 2. II3 1845 | South Berule Corp. Steel, R.S.M. tº ſº 3 2. II.4. 1845 Ben Lomond Corp. Steel, R.S.M. 4. I I 635 1845 Ben Heynish j} 33 4. IO 267 1846 Week Down 33 35 4 I I 556 1846 | Dunnosc 3 y 33 4. I3 643 1846 | Boniface Down . 23. 32 4. 7 356 1846 | Port Valley 5 y 22 4. IO 4.II 1846–7. Saxavord 2} 33 4. 2O 566 1847 Gerth of Scaw 33 32 4. 2. I 581 1847 | Balta. 55 35 4. 2O 732 1847 Cowhythe . 33 53 . . . . 4. I8 64I 1847–8, Southampton Serg, Steel & Corp. Jenkins, R.S.M. 2. I8o 8730 1850 | St. Agnes . . Serg, Steel, R.S.M. tº º 4. II 4.18 1850 | Goonhilly Down. 33 23 \ 4. 9 442 1850 | North Rona 33 35 4. 5 428 1850 Great Stirling 3} 33 4. 9 439 Three of the stations whose latitudes were determined with Ramsden's Zenith-Sector have been re-determined with Airy's Zenith-Sector. The comparisons are as follows: Stations, Airy. Ramsden." Dif. O º f/ # C f f/ f / Dunnose 5o 37 6.98 || 5o 37 7.09 O ~ I I Balta . 6o 45 I-68 6o 45 2.31 o.63 *... Cowhythe 57 4. I 9-58 57 41 9.74 o. I6 1 The latitudes here given are as published in the volume of the Ordnance Survey entitled “Astronomical Observations made with Ramsden's Zenith-Sector.” In the present volume the resulting latitudes are slightly altercd, according to the method of reduction explained in the note at page 199. DESCRIPTION OF INSTRUMENTS. - 6I • The latitude of Balta, given by Ramsden's Zenith-Sector, was deduced by amplitudes with Dunnose after an interval of 1 5 years, the observations at Dunnose having been made * 1802, those at Balta in 181 7. But the latitude of Balta, deduced from all the observa- º then made, would have been 60° 45' 1". 59, and similarly the latitude of Cowhythe, *d from all the observations made in 1813, would have been 57° 41' 9". 47, both of Which are more nearly equal to the results obtained from Airy's Zenith-Sector. There is no appreciable difference in the results given by the instrument in the two positions of the revolving frame. Thus, the latitude of Southampton with the pointer teading from o' to 25°, by 1384 Observations of stars north of the zenith, is 50° 54' 46”.81 & I 196 33 35 south 33 tº º º º 46”.68 and with the pointer reading from 180° to 205°, 1944 Observations of stars north of the zenith give 50° 54' 46”.8o 749 33 53 south 46”-55 tº For a detailed description of this instrument, and the method of observing, together * all the observations that have been made with it, the reader is referred to the last Published volume of the Ordnance Survey, entitled “Astronomical Observations made With Airy's Zenith-Sector.” 55 SECTION III. REDUCTION OF OBSERVATIONS. (1.) Until the year 1840 the mean results from the observation books were abstracted in the form of “included angles;” thus, supposing cº, 3, 2, 0, . . . . . . . o, B, to be the reading of two objects A B, upon n different arcs, then the angle between A and B was taken as, i 9, - a, + 3, − x, -- . . . . . + 3 − x, 72. In consequence, however, of the imperfection of this method, and the great labour involved in it, it was abandoned by Captain Yolland, and the more perfect solution of the question of most probable bearings by the theory of probabilities substituted in its stead. (2.) The theory of the reduction of the observed to the most probable mean bearings is as follows: Let the bearings of the objects observed, reckoned from the referring-object, be A B C . . . . these being the most probable values to be determined, and let the first arc give the readings m, mº mº m? . . . . . m, corresponding to the arbitrary reading of the referring-object, of which let v, be the true or most probable value, m, v, being thus the error of observation of the referring-object; then we ought to have the equations, m, -a, -o, m," - v, - A = of m,” - a, - B = o . . . . . The second and third arcs will give, m, -a, - of m,” — ar, – A = of m,” – w, - B = o . . . . . m, -a, - of m,” – a – A = o; m,” – w, - B = o . . . . . and so on. These equations would be identically true were the observations free from error. As it is, the left-hand members are the errors of observation, and therefore the sum of the squares of these quantities must be made a minimum in order to give the most probable values of A B C . . . . . and the arbitrary distances v, w, v, . . . . . of the initial point of the instrument from the referring-object in the different arcs. In order to make the result general, multiply these equations or errors by quantities wp, Vp? Vp'? . . Vp, Vp% w/p'? . . . . . each of these to be equal to unity when there is an observation, and to zero when the corresponding observation is wanting. Then the sum of the squares of the errors is, p, (m, - w,) + p.” (m,” – v. - A) + p.” (m,” – c. – B). 4. . . . . . + p., (m, - a,) + p.” (m.” - v. - A) + p.” (m,” – a – B) + . . . . . +p, (m, -a,) + p.” (m,” – r, - A) + p.” (m,” – a – B), 4. . . . . . &c. &c. &c. REDUCTION OF OBSERVATIONS. . 63 'Making the differential co-efficients of this quantity with respect to w, v, r, A B C . . . °Tual to zero, there result the equations, Pºm, +p!” m{0 +pº anº) + . . . = (p, +pſ) +pſ” + . . .)a, +p!” A+p!” B+p!” C + l p.m., +p,9m,G) +p,9m,'” -H . . . = (p, +p,” +p,” + tº ſº º ) a,-Hp,”A +p,9B +p,9C + . . p.m., +p,°m,0) +p,ºm,” -F . . . = ( p, + p," -H p,” + . . •) ar,4- p,” A+p,9B +p,9C + . . &c. &c. &c. (1) I tº º +p,0m,0) +p,”m, 24. • * = (p,0+p,” +p,” -H - .) A+p,"v, +p,"v, +pº, º *) + p,9m,'” +p,”m,” -H = ( p.9) -- p,” -- p,” + - •) B+ p.9%r, -- p,”v, +p," a',-- . . (£) O, m,G) +p,G)m,G) +p,9m,9) + ... • = (p,9-1-p,” +p,9) -- - - ) C +p,9a, +p,9a, +p,9a, + tº dº &c. &c. &c. The values of w, w, w, . . . being obtained from the equations (a), and thus eliminated rom (3), there results a final system of equations for obtaining A B C . . . º In these equations w, w, w, . . . differ from m, m, m, . . . by the errors of observation. Instead therefore of a, make w,-m, the unknown quantity, calling it still 4, which symbol *W represents the correction to the observation of the referring-object on the n" arc, and ** small quantity. Substitute in the above equations, and instead of m?-m, write m?, Which now does not mean the reading of the r" object on the q” arc, as recorded in the observation book, but that reading minus the reading of the referring-object on that arc. The cquations then become, p.9m,0) +p,9m,94. • * * = (p, +p,” +p,” + § . ſº ) (ºr +p,” A+p,” B+p,0) C + * * . • * (1) a) T. i ... ºr . . . =(pºp. Qº'Aº (2) Ps","4-pºm,94. . . . = (p, p,94–p,94. . . .) a, Ep,” A+p,” B+p,” C + . . . &c. &c. &c. (1) - i ) as I as º º +p,"m,"+p,9m,94. • * = (p,") +p,” +p,"+ tº º ) A+p,' 'w, 4-p,' 'a',4-p,”4,4 º l / t º +p,°m,” +p,”m,94. . . = (p,” 4-p,” 4-p,” + . .) B+p,°r, +p,"r,+p,”v,+ . . ) (3') p. 3 m,G) +p,9m,G) +p,9m,94. • * = (p,q) +p,” +p,” + tº ..) C+p,9a, +p,"r,+p,”v,4- gº tº &c. &c. &c. tº: *- ſº It is evident that when the number of observed points is very large it would be *Possible to solve these equations directly. This, however, is generally, indeed always, the case; and therefore recourse must be had to the method of successive approximation. Tirst, then assume w, a, a, . . . individually equal to zero, then the second set of Cquations will give, A’ = p.9m,0) + p,9m,” + p.9m,” + . . . T. p,” + p.” + p,” + . . " B' = p,0m,9) + p,ºm,” + p,9m,” -- . S. . . . (y) p,” + p,” + p,” + . . . ſ C = p,”m,” + p."m,” + p.”m,” + . . . —a sº. -- *-m- sº *-*-- *** * +º-ºººººººº lºs -- - p.9) + p,9) + p,9) + . . " - for the first approximate values of A B C . . . 64 & PRINCIPAL TRIANGULATION. Substitute these values in equation (&), and we get, = p.9) (m,0) tº º A’) + p.9) (m,” º B') + p.9) (m,G) tº-ºº: C’) + . . . " - 12, + p.” + p,” + p,” + . 2. F p,” (m,” i º A’) -- p,” (m,” * B') + p.9) (m,G) * C’) + . . . * {, , , (3) p, + p.” + p.” + p.” + . . . > = p,” (m,” i º A!) + p.9) (m,” tº º B') -- p.9) (m,9) ſº- C’) + . . . P3 + p." + p,” + p,” + . . . 471 43 * &c. &c. &c. These values substituted in equations (3') will give the next approximation to the values of A B C . . . , which are, A. - p,0 (m,” tº jº a',) + p,0) (m,0) º w,) + p,” (m,Q) tºº a,) +" tº ſº tº p,” + p,” + p.” + . . . -- B = P," (m.”-º) + p.” (m.”- “.) + p.” (m.”-ti) + . . . p,” + p,” + p,” + . . . } . . . () C º p.9) (m,G) — a',) + p.9) (m,G) tº-º- a,) -H p.9) (m,9) *=º w) + tº is ſº | p.9) + p,” + p,” + * ... º. - J &c. &c. &c. These values may be again substituted in equation (2'), and more correct values of ar, w, v, . . . . will be obtained. These last values of A B C . . . . have been used as the true or most probable bearings with reference to the referring-object. - Should the observation of this object bé deficient in the r" arc, then from equations (2) 771. F p,0) (m,0) — A) + p.9) (m,” º B) -- p.9) (m,G) — C) + . . . * p," -- p,” + p,” + tº ſº. - The practical working is as follows:—The means of the reading of the microscopes for each object are taken in the observation book, and to the reading of each object on any one arc a certain quantity is added, making the reading of the referring-object on that arc equal to a given quantity constant for the station. This constant reading of the referring- object is (for convenience) its calculated bearing from the south meridian line. These results are abstracted for each station in the following form, in which the reading of the referring-object is supposed deficient on the fifth arc:— 1st. Abstract of Angles observed at with tho Theodolite, commenced finished — . y Date | observer. . . R. O. A. IB. C. D. Iº. F. G. I 77? m," | m,” . . . . . . m.9 m.9 m.9) 2 771 m,G) ſº ſº m,G) m,Q) m,9 {º} - (1) ( 6 3 77; n, ºn, 2) m,G) & ſº º m, ) m,G) 77! (2) (3) 6 4. m,” m," mº) * * * m, ) mº) Means. 7?! 2n(1) m(2) m(3) m(4) m(s) m (6) m(7) | 5 it. iº ſº 1. { } i. m(3) * m(ſ) m(s) n(0) 7,07) REDUCTION OF OBSERVATIONS. To each r I is to be added, which eading in the fifth arc the quantity (7) 272%) tºº 77 (4) + m(s) tº-ºº: m(s) + mº ºl 77 (6) + ºn (7) — ?? ) . and the abstract will stand thus: i. m ) ºf Will then alter them to m,G) m," G. N b * F. º: R. O. A. B. C. D. E 6 (7 1. 77; 773 (1) 7)? (2) * m.9 m, ) ºl, |I X { } (5) ſº º * 2. 77? m,0) ſº * . m,G) m,0 7m, (6) (7) 77? 3 77. - m,” 'm.9) m.G) • * ºn, 'o 6 - ºr (2) 1 (3) m (4) m,” m, 4. 7?! º m, ni, 4. (6) m.(?) 5 m.G) n,G) n,(9 7t, I tº ſº º * I Means - 77, m(ſ) m(*) m(3) m(4) on(s) 272 The quantities a, ‘t’. * 471 - and similarly and the new from this last 4, 43. The following numerical example will suffice to illustrate the process:— º 3) thus:– . . are then calculated for each arc by equatiºn. º n,”) ) (2) (*) -- mºs) — m,(s) + m (9) — am,9 + m” – 7 *. # (ºn " — m,0) + me) – m, m I ing in the respective arcs, These quantities are applied to each reading in he means obtained modified readings abstracted again in the same form. The m abstract are taken as the final value of the bearings. *=– E. C. D. - O º b A. jº O as a 7 C as 2.71° 43 O º: and ºf . 9. 11° 7' 57° 34' 97° 54 22d 3 T-----|- .8 ... I C) OO 39.17 I 29.2 I 3: I4-o'7 47 4 #. ;: 2 Q - 2 I Ç * g º g s : ; II.86 tº * * 16.30 g 4. 29-2I 32°41 Io-71 ; I4. I7 ſº i. ; 29-2I º tº II-9 I * 18-59 4.I'O4. 29-2I tº * ** • 2. 39:46 Means 29-21 34-64 I2. I4. 47-40 I7-25 The errors of the arcs will then stand thus:– --msm-º: fººm- IB C D. D. Mean. R. O. A. tº . [. *==== - O - 2 +o.87 I • OO + I-40 + I-93 + O'44. # -: + O. 24. 2 i. I , 27 ſº tº º - O - O —o. 19 3 º tº: —o-28 ſº .nº O 4 —o. I9 4. • CO –2.23 - I-43 - I-35 - O 33 • —o-60 4. ..a - O - 2 **9° I. 11.35 | +3.9% ; • OO 23 . + I-34 || + I'5 • OO tº –mºmº 66 PRINCIPAL TRIANGULATION. The mean error for each arc being then applied, with contrary sign, the second abstract will stand thus:– * Number | R. O. A. B. C. D. E. of Arc. - 4° 21' 1 to 7' . 37° 34' 97°54' 220° 3' 2.71° 43' I 28.34 35. I7 I3-2O 46-97 18. I3 38-3o 2 28.97 35-67 I7.94 37.98 3 29:40 34°40 I2.05 39.61 4. 30-40 33.60 | II-90 47.24 17:49 5 29.81 I2.5I 48.90 I4.77 - 6 28-24 * ſº 17.62 4O'O? Means | 29:19 34-7I I2-42 47-70 17. I9 38-99. These last means are taken as the resulting bearings for the station. In this manner all the observations made with the two great instruments, and some with the 18-inch, have been reduced. All given in the abstracts in this volume have been thus calculated; the old as well as the new. It may perhaps be objected to this method, that it is not a sufficient approximation; but another approximation would have cost great time and labour, as, to be consistent, it must have been carried through the whole of the observations, and the advantage gained would, after all, be but small. The weights have been calculated from the final abstract, the differences of the indi- vidual readings from their means being considered the errors, in the usual formula, 20 = —*-2 * . 2 > (s”) When there are only two or three observations to a point, the weight thus obtained has not been generally used, as theoretically n is supposed large. In such cases the rule adopted by Captain Yolland was first to obtain the mean weight of a single observation at the station, and then to give to the mean of two observations twice this weight, and to the mean of three observations three times this weight. The mean weight of an observation is calculated thus: if n, w, n, w, . . . be the number of observations and weights corresponding to the different bearings, and w the mean weight of a single obser- vation at the station in question, then # *, + n, + n, + but if the weight that would thus be assigned to a bearing should exceed that due to it by the usual formula, then the latter was made use of, and not that resulting from the mean weight of an observation at the station, * * * = , . . . . . . . * * * * # * REDUCTION OF OBSERVATIONS, 67 The weights would have been materially increased in many instances by rejecting what Would appear bad observations; but the rule has been never to reject any, unless the observer has made a remark to the effect that it ought to be rejected. - (3.) The method of reduction of azimuthal observations is to take the last reading of Star before the reversal of the telescope at the elongation, and the first reading after it, and *ving corrected them for their respective level and collimation errors, to use their "*" as the final result for that star. If l be the recorded level error corresponding to £11). ºbservation as given in seconds, by the striding level, west readings being considered * (the scales are divided from the centre outwards) and east readings negative, then the Correction for level is, 2 being the zenith distance of the star, --! cot 2. If g be the error of collimation, as given by the referring object, then the correction for collimation is - - - the c cosec 2. In the case of the stars above named, it is sufficient to take the colatitude of the place of observation for the zenith distance; though indeed the latter has been generally *PProximately computed. m - If then, R. R. be the observed theodolite readings, l l the corresponding level errors, * the collimation er • - - ror, then the reduced readings are : -. R + l cot 2 + c cosec 2 ' + l’ cot 2 + c cosec 2 The °ollimation correction disappears in the result, but it is calculated in order to show º *nts of the individual results. The declinations of the stars are taken from the autical Almanac,” interpolating for quarter days. The small correction depending on the moon's longitude has not been regarded, as the observations have not sufficient precision to make it necessary. - Considering the great value of azimuthal determinations in deducing the final results geodetical operations, some experimental calculations were made by the method of least Squares for obtaining the most probable direction of the meridian as given by the collective observations of separate elongations. The method is as follows:—If a star be observed at * given time, a minutes, after or before an elongation, then its azimuth will differ from its *muth when at the elongation by the quantity - from 2 ** , sin 2 3 - # a si • In sº **cot I. (450 t) * sin I in a + } (900 t) * sin sin 2: o-, sin 26 . sin 2 ö - e. # a • OO ſº cot h #3 98.17 sing + - O 43 SIIl 2, ... seconds, where 3, 2, h, are the declination, zenith-distance, and hour-angle of the star. f he second term of this expression need not be used unless the star be 20 minutes or mº" * its elongation. + a. * w I 2 68 PRINCIPAL TRIANGULATION. Let &, 2, 2, . . . be the readings of the star at the times t, t, t,. . . . respectively; A, T, the azimuth and time corresponding to the greatest elongation, then for an eastern elongation these will be the equations: c., + p. (T – t ,)” – A = o c., + p. (T – t ,) * – A = o a , 4- p. (T – t ,) * – A = o a 4 p. (T-1)-4-o Where sin 2 3 p = • 98.17 : SIIl 2, the equations for a western elongation are formed by merely changing the sign of p. The left-hand members of these equations, being in general not equal to zero, are the errors of observation. We must therefore give T and A such values as will make the sum of the squares of these errors the least possible; that is, the quantity U=(2, 4 p. (T-t)*-4) + (*, + p. (T-t)’ –4) + tº q c (a + i. (T-t.)”-4) in which T and A are to be considered variables, must be a minimum. Making the differential co-efficients of U with respect to A and T separately equal to zero, there results, after a little reduction * (2 T4 tº) ([t']. -ſt.]’) = […]...-a, -t, -º ([t']. -[t-]’) 4 = 2n + P. (T. – 2 tº T' + [t'].) where [tº]" denotes the r" power of the mean of the quantities t, and [tº], denotes the mean of the r" powers of the quantities t. These equations furnish the most probable values of the greatest azimuth, or that at the elongation. In the case of a western elongation the sign of p. in these equations must be changed. In consequence, however, of the laborious nature of the calculation, and the often erroneous value of the time T resulting from the discordance frequently shown between the observations of the star in one position of the telescope previous to the instant of elongation and those taken in the reverse position after it, this method was not generally carried out. In those cases in which this calculation was made the result did not differ but by a very small fraction of a second from the result obtained in the usual manner. (4.) In some cases it has been necessary to combine the observations taken at different times and with different instruments at the same point. The following is the method of calculation:—Let & 3 Y " ' ', 2' 6' y' . . ., be the two sets of bearings, of points common to both sets of observations, w, w, w, . . . w, w, w, . . . the respective weights of their determinations; let q be a quantity to add to the second set of bearings, in order to refer REDUCTION OF OBSERVATIONS. 69 them to the same initial point of azimuth with the first observations, and let A B C be the most probable bearings to be determined from both sets of observations, then, by the theory of Probabilities, the quantity 20, (A – 2) * + 20, (B – 3) * + 20, (C — y) * + & C. C. + w,’ (A – c.' — ?) * + waſ (B – 3’ — ‘p) * + waſ (C – 7' – b)” + tº C º' *** made a minimum, A B C . . . . being considered independent variables. This will give the following equations:— (w, + w.") A = w; a + w,’ &' + w,’ & (w, + w.") B = w, 3 + w, 3' + waſ p Where (v. 4- v, + . . .) + = 0, (c. – 2') + v., (3 – 3') + . . . I - = – = — -- + w,' I I I I I v. Tw, " w” v. T v. (5.) It may be as well, in connexion with the subject of bearings, to explain the "ethod by which the position of a lost old station is calculated by means of the old bearings taken from it, and the new angles taken from a new station known to be very near the P*ition of the old station. ſº Let d, d, * . . . . bé the distances of the points common to the two sets of obser- *s, the nearer the better; o, o, ø, . . . . . their bearings, with the weights w, * * ' ' ' ' as given in the new observations; 2, 2, 2, . . . . . their bearings with the Weights w/ toº ”, “ . . . as given in the old observations: Ç Let w y be the co-ordinates of the old station, a being measured from the new point **irection of the line from which the bearings aſ are counted, and y perpendicular to it. let also 2 be a quantity to be applied to all the old bearings, in order to make them Sºmparable with the new bearings, 2 is then the angle between the directions of the line from which *: o, ø, are measured, and of the line from which 2, 3,' & ' ' ' ' ' are *ured: We then have the equations in th a sin c. – y cos 2, A = 0, -ī- 2 – 0. d, d, * * *2 = 9.995 °3 = 2, 4-2 — a d 3 3 3 * *nd so on. If both sets of observations were perfect, then these equations would be tº ion identically true, and any three would give the true values of w y and 2. But each . being affected by errors of observation, a y and z must be so determined {1S º à. * of the squares of the errors, each multiplied by the weight of its determin" 7o PRINCIPAL TRIANGULATION. minimum. Now the weight of each equation depends on the weights of the bearings from which it is derived; that is, the weight of the n" equation is— -- w, w,' 7), a --→ wn + 20, and thereföré the quantity - # * * ** Ç COS Cº., ' ' ... ' - -- U = v a. ** – y, * – 2 + ox, — or,' 2 sº I ò, 6, r sin & COS Cº. 2} - - a x- 2 COS 0. COS. O. 2. +v, (***-yº-z + 2, -a,) 3 3 ~5 -H tº º º º º tº º 'º º where 8, - d, sin I", must be a minimum with respect to the quantities a 3/ 2. If we write a, b, c, for the co-efficients of w and 3) and the quantity on-a, in the n” parenthesis, then the equations for determining the minimum are (v a”) a + (v a b) y – (va) * + (o (I. c)=o (v a b) a + (v bº) y – (v b) 2 + (v b c) = o (va) a + (v b) y – (v) 2 + (v c) = o where the brackets have the usual signification of summation; that is . (v a”) = v, a,” + v, a,” + v., a,”-- . . . . . (o a b) = v, a, b, + v, a, b, + v, a, b, + . . . - &c. &c. * * * These equations determine a y z and the respective probable errors. OBSERVATIONS, TERRESTRIAL AND ASTRONOMICAL, FOR THE PRINCIPAL TRLANGULATION, S E C T I O N IV. - THE first part of this section contains extracts from the reduced theodolite observations - of *strial objects. These extracts are confined chiefly, but not exclusively, to the principal points of the triangulation of Great Britain and Ireland. It has been. considered sufficient to give the ‘mean bearing” of each observed object, with the number of obser-. vations taken to it, their range, or the difference between the greatest and least observation, with the calculated weight of each mean bearing. The method of obtaining the mean bearings from the Observation Books is explained in the preceding section. The corrections to the observed bearings when the trigonometrical point is not the * observed, are obtained from the measured distance and bearing of that object from the “gonometrical point. There are, however, two exceptions, namely, in the corrections for reducing the bearings of the old stations at Delamere and Easington to the new stations; * corrections in these cases were obtained from the distances and bearings of the old *the new stations, as calculated from a comparison of the old and new observations at those points. In these cases the weight of the corrected bearing has been erroneously *med equal to the weight of the observed bearing, but the oversight is not of sufficient **itude to affect the positions of those stations. The bearings are referred to an approximate South Meridian Line. The second part contains the principal azimuthal observations in detail, and the results ºf those which are less important, together with their range and probable error. ***----...- *****... The third part contains the results of the observations made with Airy's and ** -*mith.Sectors for the latitudes of various points in the triangulation. 72 PRINCIPAL TRIANGULATION. EXTRACTS FROM THE GENERAL ABSTRACTS OF OBSERVATIONS. ACKLAMI WOLD. 18-in. Theodolite. IFrom 24th November 1841 to 26th March 1842. Observer: Corp. STEEL, R.S.M. No. IRecip. No. Recip. Objects. Dearings. of Range. ...of Objects. Bearings. of Range. of Obs. Weight Obs. Weight. O f/ f / O Af Aſ f Crowle • * * 3 13 o.81 || 3 | 5-27 | 3:30 Great Whernside • 99 17 24.43 5 £66 I.og Hemingbro' Spir 22 Io 9-72 6 12.72 5-26 IIambleton Down 127 47 57.76 || 5 || 3:45 o'73 Clifton Beacon • 23 41 28.67 || 2 | 1.16 o-33 Black Hambleton 133 24 33-60 | 6 || 9.82 2.84 Garforth Cliff 52 23 44.59 || 4 || 8-91 5-off. Botton Head I53 46 I5-82 5 |Io.20 4.99 York Minster 63 18 4.36 7 18.90 10.43 Saltergate Brow 191 26 2.87 8 16.82 6.63 Rumbles Moor 76 54 45-29 3 3:25 8 |29-85.31.57 4.84 wº Beacon 346 20 I-31 i ARBURY EIILL. 3-ft. Theodolite, D.O. From 20th January to 29th March 1843. Observer: Serg, DONELAN, R.S.M. > Amº, º ſº. * No. Recip. No. IRecip. Objects. Bearings. of | Range. of Objects. Bearings. of Range. of Obs. Weight. Obs. Weight. to * // Af O # // Af Epwell . . . . . . . 48 2 48.63 || 7 || 6.88 1.12 | Dumchurch Tower . 157 19 14.8o || 5 || 4 or o.89 l3roadway Tower' . . 62 41 46.15 5 5-38 | 1.47 | Bardon Hill . . . . I72 16 8.40 I5 5.5o o-25 Breedon Tower ' ' | 73 54 32.47 | 3 || i. 55 o.37 Referring-object. 185 7 13:94 |Ioz 7.39 o.o.3 Malvern, ' ' , , ' | So 37 49-72 || 8 || 6,81 o.94 | Naseby Čh. Tower 218 13 34-oo || 7 || 4.39 o.98 Lord Plymouth's Hanslope Ch. Spire 295 II. I.4.93 || 2 | I-46 2.13 Monument . . . Io? I6 40.87 o.78 o.o.7 | Dunstable . . . 31o 37 I5-24 Io 2.95 o.23 Bar Beacon . . . . 129 24 36:25 9.43 | 1.76| Wendover . . . . .329 55 17:18 || 6 || 3-84 o.53 Corley” ' ' ' ' | 138 I 19, 18 || 7 || 4.57 o.58|Brill . . . . . 347 28 19:38 || 6 || 3:36 o.º. § | A correction of + 3'39 to be applied to this bearing, to reduce it to the trigonometrical station. * A correction of + 9": 99 33 3y 33 OBSERVATIONS. 73 AXEDGE, 3-ft. Theodolite, R.S. From 21st April to 21st June 1842. Observer: Lieut. PIPON, R.E. FC Objects. tº No. IRecip. No. Recip. * Bearings. of Range. of Objects. Dearings. of | Range. of T--— Obs. Weight. Obs. Weight. t M f/ Ashfy tº Fº 39 Io 56-49 || 5 4%; o.86 || Ingleboro' º 16: I 5 53.81 5 5:30 I-56 9ng Mountain. 39 4%. 26.95 || 5 || 3:23 o.24 | Boulsworth . • 17o 5o 44, 13 || 4 || 4-69 I-87 *lowcopt . . 49 58 39:76 || 2 |9-78 |o. 15|Holme Moss . . . 187 (5 44.1% | 15 6.17 o-48 Yrn-y-Brain 53 33 35'93 || 1 |8-89 1-11 || Kinder Scout • 194 5o 53.66 || 18 9-54 o-68 howdon . iº 75 43 38. I4 || 8 || 2.78 o.19 || Lord's Seat . • 2 II 8 o' 19 I3 || 7-o/ o'54 Ioel Famman . 83 32 43'92 || 4 || 2:oo jo. 26 || Back Tor. • 218 38 2.57 | 12 5.82 o'45 iyington . 84 50 47.38 16 || 6-50 |o:56 | Heathersedge 243 34 45-64 || Io 3.52 |o-2 Whitão IHill. **9 47 4o.62 || 5 || 5.23 I. 16 || Lincoln Minster! 269 19 9.5I I | – || 6-o-; endle Hill . *56 33 21.96 | 16 |8.77 1.18 || Bardon Hill . • 323 32 35-24 || 7 || 3-27 | O'43 * 9-66 || 4 || 3-13 |o.97 ||Weaver Hill, New |346 A 3.08 || 13 ||3:07 | 1.f4 T-- ' A correction of ~ 2"'83 to be applied to this bearing, to reduce it to the station. BACONSTHORPE TOWER. 2-ft. Theodolite. T- Trom 5th August to 4th September 1843. Observer: Corp. BAY, R.S.M. Objects. * No. Itccip. No. Recip. Bearings. of IRange. of Objects. Bearings. of | Range. of T-– Obs, Weight. Obs. Weight. ſlingha -- am T. O / // Af waiti. §. 19 27 8.95 || 7 3.39 o-21 || Happisburgh Tower 28; 16 3%.71 8 || 3-19 o.26 ocking To. 59 15 42.85 | 9 || 4.61 o.42 | Norwich Spire . 34I 26 13.94 || 6 || 2:40 o'21 Rºo WQ1 . 92 4. I 53. I3 8 2. I3 o. I2 i l A cor { } Correction of + 2", 39 to be applied to this bearing, to reduce it to the observing station at Swaffham. IBALLYCREEN. 3-ft. Theodolite, B.O. ~ * **6th August to 24th September 1852. Observer: Corp. JENRINs, R.S.M. Objects. No. IRccip. No. Recip. Beari tº * ºſe, f T- earings. di. Range. wº Objects. Bearings. di. IRange will sº * e & 53 & f f/ Mount Leinst O / 3.31 32 #21 o. 18 ºrin M tº 2.95 * * Oe OUII]t LC111 St Cl’ 4O 3 I3' i. levo lºntain II 16 13.70 sº 3.4% .# ICnockanaffrin §o 6 6.84 18 5.9% o. 16 lackstairs *5 54 I2.95 || 23 5-20 |o.14 || Keeper . . . §2 28 31.74 || 36 5-88 §§ * 35 59 12-43 | 17 | 7.33 o-36 | Cullenagh . . 94 13 6.33 || 24 |4-14 lo'99 74 PRINCIPAL TRLANGULATION. BALLYCREEN–continued. No. IRecip. No. Recip. Objects. Bearings. of Range. of Objects. Dearings. of | Range. of Obs. Weight. - Obs. Weight. O / // Af O & ff f / i Cadeen ... Io.4 II 54.30 13 5.15 o.32 | Snowdon 262 53 I5. 19 12 || 4-27 o. 19 Lugnaquillia 129 28 14.83 15 3.97 o. II Collin . 27o 37 53-26 5o 5:57, o.o.5 Mullaghslaban . 172 33 42.02 18 7.49 o-28 || Bally mile 296 43 48.45 I9 || 4:25 o. I4 Rippure • 184 33 36.93 33 6.37 o'I5 |Precelly . . 3I4 20 29.8o Io 3.81 o-3o Douce . . . . . 199 42 45.03 ſ 21 4.5I o. 13 || Arklow Rock 318 42 35.26 34 || 7.69 o.12 Great Sugar Loaf . , 268 50 2.5% 22 5-or o. 13 | Tara . . . 337 35 41-81 74 6.81 o.o.3 Dunrain " . . . . . 227 14 29.96 25 4.9 I o' Io Croghan º 348 Io 53.70 28 5.85 o-I2 Carrickmarino 241 43 15:59 35 | 4:24 o'o6 * IBALNASIKERRISFI. º 3-ft. Theodolite, B.O. - From 1st to 9th October 1819. Observers: Major-Gen. Colby, Lt.-Col. Rope, and Capt. DAwson, R.E. No. Recip. - - No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. O A f/ A/ i O f f/ M/ Ben Vacher,' '..." | 51 43 4.52 | 5 || 7.70 || 3-62 |Scarabin . I97 8 Ig:5o || 3 || 5-63 |4. I5 Scournalapich, Oldi. 54 59 25.85 | 1 || – || 6-27 | Bin of Cullen 289 46 27.60 || 6 || 4.92 o. 75 Ben Wyvis . | 67 53 33-53 || 8 || 3.83 o.35 || ICnock 295 9 I4-o8 || 6 || 3:22 o.43 Airdross : • 76 57 I4. I4 || 6 || 3:03 o-45 || Findlay Seat 3II 31 36.93 || 6 || 3.77 o-62 Den Lundie . 138 21 20.88 || 6 || 3:02 o-36 | Corryhabbie . 326 38 29.86 || Io 5.53 o-59 Ben Horn I48 21 Io.58 || 3 | 1.14 o. 17 | Ben Macdui . 354 25 I4'45 || 5 || 7-49 || 2:70 1 A correction of + 16"" 53 to be applied to this bearing, to reduce it to the trigonometrical station. IBALSHIAM CEIUIRCH TOWER. * -*** * * * ~ * * * * * * * * * * * * * += n = < x - - 2-ft. Theodolite. - From 23rd May to 23rd June 1844. Observer: Corp. BAY, R.S.M. No. Recip. sº * No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. O A ſº f/ O * f f , ſº Tharfield . 62 7 52-oo 14 |4-49 o-28 || Peterboro’ Cathedral 142 22 4.79 || 2 | 1.71 o,73 | Royston . . . 67 48 37 or IQ |4-96 o°49 | Balsham . . . . . I5o 59 14.94 91 4.89 o.of Orwell ‘. . . 95 I3 2.95 || 8 || 3-69 o:37 | Ely Minster . 172 4ſ 47.36 14 || 4:30 o. 19 Keysoe Spire IoA 34 44-25 || 6 || 5-oš o.91 || Swaffham Spire' 2O3 39 57.66 || 8 || 4-74 o.43 Cambridge Observa- # Lawshall . º 264 49 IO-32 | Io 2.5o o. 11 tory Dome . 12o 45 58.95 II 5:44 o°36 || Thaxted Spire 355 22 26-44 || 9 |2-93 |o.28 : | A correction of + 2"'87 to be applied to this bearing, to reduce it to the trigonometrical station. OBSERVATIONS. 75 * * ** - ~ + . . * * * * . From Ioth to 27th Trom 24th to 26th BALTA. " " " ' ' ' 3-ft. B.o. and 7-in. Theodolites. August 1817. Observers: Major-Gen. Col.BY and Mr. GARDNER. February 1847. Observers: Privates JENRINs and CLARKE, R.S.M. l 2 * correction of Correction of From 6 Objects. . ** No. IRecip. No. Recip. Bearings. of IRange. of Objects. Bearings. . . of | Range. of T--— Obs. Weight. Obs. Weight. Fetlar O / / / A/ o / // . f/ Yell . . 19 15 31-65 | 9 || 6.65 jo.8o | Saxavord I6o 45 39-2I II] 4.87 o'5I Vallafield § * 23.70 | Io |4.94 o-31 || Nive Hill 181 20 56.07 || 35 86.66:15-12 *- 39 27°35 || 3 || 2 or o-45 Gerth of Scaw . I86 3o 49-64 || 35||113.8235-79. BANSTEAD. - 3-ft. Theodolite, B.o. -- - I- From 7th August to 11th October 1848. Observer: Serg. DoNELAN, R.S.M. Objects, tº No. Recip. No. * IRecip. Bearings, of Range. of Objects. Bearings. of | Range. of T--— tº Obs. Weight. Obs. Weight. Leith Hill *. -- o f f/ w - - elisk º: 35 4 30-43 I4 $64 o:36 || Wimbledon Spire . 18; 13 2.Éco II 624 O-47 ... Heath . . g 10t Berkhampstead . 187 II 22.78 || 3 | 1.16|o. I5 St. Anne's, Old . . . .% ºf 41 18 || 5 || 4:32 o-80 || Highgate Spire . I89 o 15.87 || 5 || 3:49 |o'59 | Ditto New . *** 38 20.73 || 9 || 4.70 |o.4o | Westminster Abbey | 196 24 57.78 || 32 6.64 o. I7 Windsor Castle St # *** 5; 29.49 || Io 3-55 o-27 | St. Paul's Cathedral 26o 14 8.63 | 9 || 6-or o'79 *mpton Church # **# 32 17:29 || 5 |5-21 1.29 || Chingford • 202 32 I6.59 || 18 || 7. Io o'42 King's Arbour ** 136 13 29-22 || 3 ||3-04 o.67 || St. George's Church - #amptoniº. If | 137 53 51-48 || 14 7. I7 || O-42 Tower, Ratcliffe . . 206 33 21.83 || 5 || 2.65 o°31 larrow Spire OllSe I39 Io 54'40 I3 || 5-2 I o-23 Epping • . . 208 23 34. I8 I2. 6.5o o:34 danger Éli Tower? 193 23 3.43 | 16 | 1.62 o:35 | Severndroog Tower 228 5i 8.69 || 13 || 8.87 I-o8 “*W*|165 38 53.3% is 3.73 ||3:3# T4 to 54 applied to this bearin Py 2. ‘92 Hºmº 39 33 IBARD ON HILL. 3-ft. Theodolite, B.O. 33 g will give the bearing of the present station on the Tower. -—“” 6th July to 29th December 1842. Observers: Lieuts, RoRINSoN and LUYKEN, R.E. Objects. B §ºw Tower . Malvern * * ord Ply ‘. . ymouth - Monument ll As * * T--— * A * Correction of - o" 28 to correction of + 8”. 81 33 25 32 Beari No. Recip. *: IR hºp. º ſº º €. earings. o: Range. win. Objects. Dearings. o: S. ang Weight. ... O W a f f O & // Aſ 34 45 34.83 || 5 || 2:05 o.26 Bar Beacon . 68 45 20.63 || 4 || 2.72 o°53 39 36 39.84 || 5 || 2.34 o.24 || Brown Clee . 73 28 56.64 || 1 || – || 2:57 46 o 58.31 || 4 || 3:35 o.74 || Longmount Pole 8o 21 56.54 || 2 | o'7I o'I2 Wrekin . . . . 87 2 6.67 4 o.74 o'o.3 51 26 20-57 || 2 |o.64 o. Io | Castle Ring, New 96 Io * 3 15|* be applied to this bearing, to reduce it to the trigonometrical station. IK 2 PRINCIPAL TRLANGULATION. IBARDON HILL–continued. No. Recip. # No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of Range. of Obs. Weight. Obs. Weight. Ashley Heath . . roš 5 33.85 3 #87 o-40 | Referring-object 213 47 1342 I47 602 loo, ..Mowcopt:... . . . . . 126 56 41.65 || 4 || 1.83 o-22 ||Lincoln Minster' 222 o 59:43 || 6 || 3:03 o'37 Weaver Hill, New 132 47 55.03 || 3 || 2:15 o.62 | Stathhearne . . 24I II 20.2O || 4 || I-73 o'2O Axedge • 144 2 31.59 || 3 || 4-02 || 2:18 || Buckminster Spire. 257 16 35-87 | 3 || 2.64 o.77 Back Tor. • | 161 54 48.02 || 2 | 2.74 I-87 Tilton . . . 283 52 49'o'7 Io 4.24 o'37 |Heathersedge . . 165 31 43.38 3 2.91 o.94 | Naseby Church Tr. . 327 24 16.62 II 4:25 o-i6 Sutton . . • 188 26 36.02 || 6 || 2.25 o.26 Arbury Hill . • 352 II 37.59 || 8 || 6-oo I'oo Holland Hill 20I 32 26-17 | 5 || 2.85 o.42 | Dunchurch Tower 356 58 37.34 || 2 || 2:09 || I'og 1 A correction of + 1"'86 to be applied to this bearing, to reduce it to the trigonometrical station. IBARROW HILL. 3-ft. Theodolite, B.o. IFrom 28th August to 26th September 1845. Observer: Serg. DoNELAN, R.S.M. º No. IRecip. No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. O A // W/ O & Aff # / Hensbarrow . . Ioz 37 50-o& 18 14.49 I.o.7 | Ryder's Hill . . . I55 44 51.53 20 4.91 o. 16 Maker . • Io9 44 32.42 || 6 || 4.35|o.75 Furland . . • 212 25 46.79 || 6 || 2.89 |o-39 Maker Tower • IIo 58 46.19 || 8 || 8.77|| 1.48 Pillesdon . • 223 9 27.32 18 || 6-3o o-33 IXit, Hill . • 127 25 36.60 || 3 | 1.59 o.3o Golden Cape • 227 I I I3-18 16 || 4.51 o.27 Kit Hill Tower. 127 28 40.02 || 8 |12.84|| 3:53 || Blackdown • 237 27 47.94 I2 6.61 o-56 Butterton, New I45 25 44.5o || 8 || 5.32 o.78 || Referring-object 352 32 29.98 || 9o II.53 o.o.5 BAURTREGAUM. 3-ft. Theodolite, B.o. From 29th July to 5th October 1831. Observer: Capt. PoETLOCK, R.E. ſº No. Recip. Objects. Bearings. * Range. Rºjº. Objects. Dearings. . Range. ºp Obs. Weight. Obs. Weight, O / / / Af O f f/ A/ Enocknagante ** 50 47 or || 5 || 5.69) 1.83 || Galtymore 26o 25 32 II | I | – || 9.1o Inocknadober 4+ 59 17. I4 || 9 || 3:41 o-25 | Taur . 265 35 25-62 25 || 7-ol 6.23 | Feaghmaan - 48 26 53.59 || 6 || 4.98 1.04 || Knockanaffrin . . . 265 42 45°95 || 5 || 3:56 o'76 Brandon 96 1833-84 Io 5.68|o.42 Knockmealdown 268 I3 45-65 || 1 || – || 9.io Bencorr ' ' ' ' | 180 59 22:56 3 4-69| 2.44 || Knocknaskagh 276 5 16:54 || 3 || 1:19. 6.15 Knockanore ' ' ' | 293 14 14-41 || 6 || 6.1o 1.42 Caherbarnagh 293 27 3.2% 6 || 3:39 o-33 Slievecallan . . . . 208 3 16.36 7 Io.58| 2.51 || Mangerton 317 56 43°39 22 9-44 o-A5 | Keeper . ' ' || 239 45 27.96 || 4 || 6.90|4.23 || Hungry Hill 357 27 47.76 | 12 || 6.33|o.48 Knockfeerina 246 27 32-46 || 6 || 3.68||0.53 sº OBSERVATIONS. 77 IBEACHY HEAD. I8-in. Theodolite. "rom 8th March to 16th May 1845. Observer: Corp. STEEL, R.S.M. *- Objects. wº No. Tecip. No. Recip. Dearings. &f | Range. ... of Objects. Bearings. of IRange. †: T--— Tº"--__ Obs. Weight. Obs. Weight. Dunnose * * 8 O / / / / O f f f Af Rooks' Hill 3 : 4°38||12 || 7-03 o.58 Brightling Observº 199 33 56.06 | 15 15.42 | 1.86 Ditchling . . 19348 42.47 | 1 - 23.68 ; IFrittenfield 218 3 32.58 17 | 13-06 | 1.48 Peith Hill Towa. :*:: *7 3.61 29 || 32.08 || 3:07 || Fairlight . 239 I3 45-86 28 II.3.I o'57 eferring-obi Wor 138 9 I5'89 20 | 14-45 I-o? | Dungeness Light- *ct 18544 (.84 Io.7 II. I6 o-I2 house 2.48 49 26.42 | 16 || Io-o2 I. I9 BEACON HILL. 3-ft. Theodolite, R.s. T- Trom 20th March to 17th August 1849. Observer: Serg. DoNELAN, R.S.M. Obi No. Recin, No. IRecip. jects, Bearings. . Range. º Objects. Bearings. . IRange. of T--— Obs. Weight. Obs. Weight. i Queen's Manor * O / // f/ * O / // f/ 'oringdon * 33 7.79 | 18 || 5 or o-25 ||Lansdown Obelisk 15: 12 49.34 || 8 || 9:05 | 1.68 Wyre Barrow *7 5 II:4I | 16 || 4.96 o.21 |Milk Hill. I57 20 8.40 26 6:59 o. 18 Sarum § 18 16.60 | 14 || 7.17 o.54 Teferring-object 212 52 57. I2 | 19 6.83 º: Sarum c. 3: 13:II 57 | 6.90 o-oš i Inkpen. • 223 36 47.94 || 25 5' 17 o' in. Cºns 3° 56-58 || 49 5.84 o.oã| Butser . . . 293 28 36.77 22 6-97 o'24 '9ur-mile Sto 5° 55 3:35 | 27 | 8.05 o-31 | Old Lodge • 316 17 13-40 || 31 || 7-40 || 0:25 endip . ne | 5° 39' 53:48 28 6.47 o.12 | Dunnose . . . . .329 26 22-62 ió | 6′oo .3% estbury. . 9% ºf 6-28 || 16 || 4.83 o. 18|Motteston . . . .346 12 53.15| Io | 6’18 o'5 Stoke Hill : *9 7'59 I6 4-10 o.19 || Dean Hill. • | 344 4 §: ; 4. ...; ſº ſº i. & I * tº 2 º * *— 34 45-09 || 46 || 6.74 o.o.9 || Thorney Down 354 57 54.85 9 BEACON HILL, TRESCOW. 18-in. Theodolite. *— From 25th July to 14th August 1850. Observer: Corp. WormERSPOON, R.S.M. | - ſº Objects. *: No. Recip. tº tº . Range Rºjº. T- Bearings. d; tº Range. w:ht. Objects. Bearings. di. ange. wit St. * , f A/ i. es Light- O / / / &/ Pertinny tº . 25i 4: 4. 57 20 6.66 o-27 arminnis . . . . * 17 56.64 || 14 9.86 | 1.00 ||St. Martin's Head 263 '8, 39.34 16 || 13:39 j; arn Galver . *4; 26 42.36 |25 | 9.97 o.51 | Telegraph Tower | 322 47 27.69 || 17 | 7-39 : I 246 9 3.39 24 12.49 o.52 | Peninnis Windmill 336 7 27.08 || 18 *43 PRINCIPAL TRLANGULATION. BELLEFIELD. 3-ft. Theodolite, B.o. Prom 2nd to 9th June 1807. Observer: Major-Gen. Col.BY, R.E. No. Rºjº. Object Rating. #|n, hºp º s r º - €CIS. à TIIlºs, €. O Objects. Bearings. di. IRange wint J g di. ng Weight. *º-- + i J # / tº º O Aſ f f & / | Delamere, Old 1 . 25 23 5% of 7 6.21 | 1.14|Rivington, 188 I Io.65 5 *:::: 7.30 Cyrn-y-Brain 48 42 2.93 || I — 15.99 || Knoll Hill 2I4 29 26.08 2 7.79 15-17 Heswell . . 86 27 35-79 4 | 4.81 | 1.66 Mowcopt . 317 4 38.60 || 4 | sº O'94 | Billinge • 152 I7 I3-65 6 6.85 | 1.79 1 A correction of – I" of to be applied to this bearing, to reduce it to the new station. IBEN CHIEILT. 3-ft. Theodolite, B.o. From 18th to 21st September 1819. Observers: Major-Gen. Colby, Lieut. Col. Rope, and Capt. DAWSON, R.E. º No. Recip. No. IRecip. Objects. IBearings. of | Range. of Objects. Dearings. of | Range. of Obs. - Weight, Obs. Weight. & O A // f f O & W/ f/ Scarabin . . 48 7 26-27 | 6 || 4:38 o.73 | South Ronaldshay | 206 5 33.83 || 6 || 9 oz 2.75 Ben Clibrig 8I 27 47.99 5 | 6′32 2-04 || Knock . . . . 336 12 57.95 || 9 || 7-04 || 1:43 Ben Hope . . 98 38 16:58 || 4 || 5.36 2.05 || Bin of Cullen 337 30 46.67 || 9 || 6.52 | 1.02 Ben Hutig • III 37 32.64 4. 4.48 2-03 Corryhabbie $ 354. I5 26-22 6 3'ſ o-48 Wart Hill Hoy . 181 58 23:46 | } 4’33 O-72 * | BEN CLEUGH. - 3-ft. Theodolite, R.S. - From 27th September to 13th November 1848. Observer: Corp. WINZER, R.S.M. No. 1 Recip. 1. - tº No. Recip. Objects. Dearings. of IRange. of Objects. Dearings. of Range. of Obs. Weight. - ..Obs. . . Weight. º O / / / & / º O / / / W/ Cairnsmuir on Craigowl . 228 49 38.69 || 19 7-O4 o.38 Deugh . I5 16 14.94 II | 8.49 | 1.02 | East Lomond 259 16 5:55 22 || 7.42 o.31 Merrick 2O 59 Io'o6 13 9-og o.69 || Largo Law 263 47 37.58 18 7.55 O-37 Corkmulaw 49 5 47. I3 21 5.33 o-3o | Sayrs Law 298 22 1.08 || 16 || 5.3% o.37 Bin of Campsie 5o 28 41.24 22 7.28 o.49 || Calton rº. Goat Fell . . 55 34 43.16|| 8 || 2.79 o.26|| tory Dome" 3O4 54 53. • 2 I O - RI Hill of Stake . 57 39 37.89 24 II. 13 o.41 || Arthur's Seat . 305 IO § % § .# | Ben Lomond º 90 54 22.98 48 I6. I6 o:36 Allarmoor. .. tº 3I.5 17 31.46 3o 7-35 o. 26 Ben Nevis 132 39 35-37 27 | 7:57 o-25 |Qarngthy Cairn 323 40 53.75 3o Io'27 of 57 Ben Lawers I45 I6 23-84 || 38 Io.4o o.26 | Dunrich . . 33I 36 3o-oo | Io 4.32 o-48 Ben Macdui . 183 31 26-17 | 26 6:55 o-22 || Hart Fell . . . 344 56 3.41 | 9 || 4-17 | o-34 | Glashmeal I97 4I 34.89 2I 7.32 o.32 Tinto . 354 I4 8.27 17 6.72 o.40 Mount Battock 216 Io 28-ol II || 7.84 o.78 4. - 1 A correction of + 9"'57 to be applied to this bearing, to reduce it to the trigonometrical station. - | - OBSERVATIONS. 79 IBEN CLIBRIG. I'r 3-ft. Theodolite, B.o. —tº" 5th August to 20th September 1839. Observers: Lieuts. Robinson, PIPON, and HAMLEY, R.E. * No. Recip, No. Recip. Objects. Bearings. . Range. º Objects. Bearings. . Range. º *=– -ms- Obs. Weight. Obs. Weight. IB Y----> O & Aſ A/ sº 1 9 II 42. I3 25 | 7. I9 o'4I | Dunnet Head . 23; f 33.23 6 464 O'95 torr ** 3 58.93|| 13 5:44 o.35|South Ronaldshay 233 55 25-86 || 4 | 1.80 o.22 Suilbheinn | 3: ... ; ; ; ;3|ºil . . . ; ; ; ; $9% ºf uinnam § 58 30-60 5 8.58 3-64 Scarabin i. 27I 36 34'34. 36 I4-78 o:5o Monach º 5. 4.75 33 Io:99 o-30 || Bin of Cullen 304 13 29.71 || 6 || 9.77| 4.92 £oinnebheinn 97 42 2I-30 | 16 || 14-23: 1-15 Findlay Seat . 316 3 30-17 | 3 || 4-05 | I '82 "ashven * | 125 42 7.95 || 5 || 5-60 1.56 | Duke of Suther- en. Ho e ' ' || 142 I 38-22 || 20 | Io-92 o'57 land's Monument 319 38 o'5o || 4 || Io.49 8.28 ºn #. I49 54 17.98 6 8.56 3-O2 Buck ſº ſº 32O 17 3.91 3 9.61 I2.7o Ritty Hill. 17o 25 45.44 |34 || I4-04 || o.56 || Ben Lundie ſº 321 33 2.76 28 || 14-25 | o'58 Wart Hill H ' ' || 2 I4. I4. 27.5o 3 7'4o 6.25 Corryhabbie {º 323 24 4I-65 9 3.85 o:36 °y 219 35 36.56 || 7 || 9.44 2.54|| Ben Macdui . 34o 49 4I-45 || 7 || II'oo 3:25 T- *— * A correction of + 38" 45 to be applied to this bearing, to reduce it to the new Station. " * *. BEN HEYNISH. • * - * , ºr 3-ft. Theodolite, B.o. *- From 2nd to 17th October 1822. Observers: Captains DAwson and WETCH, R.E. i. No. Recin. . No. Recin. objects. Bearings. ...? Range. º Objects. Bearings. º Range. † T-- Obs. Weight. Obs. Weight. Ben Ival O / / / f O & - f/ CI) i. | 43 53 6.84| 7 | #19 o's Ben More in Mull|27; 3 418 27 | 662 oºz torr . '. .. ist | 165 56 19.88 || 7 4.06 o.47 || Jura . . . . .316 46 38-20 | 17 | 5.75 || 0:14 en Nevis 200 42 52.45 I – 6.05 || Ben Tartevil . 339 38 i2.05 | 16 || 6-54 o°43 25r 1847.96 || 2 | o' g3 o.o. T--_ - REN HUTIG. * . . . - - -- 3-ft. Theodolite, B.o. *, - - From 11th July to 17th August 1838. Observers: Major-Gen. Col.Bx, Lieut.-Col. RoBE, and *-_ Lieut. Robinson, R.E. Objects. * No. | Recip. * No. Recip. — Bearings. d; º Range. wit Objects. Bearings. o: Range. will Ben Wvvi O / // º O / // f/ Ben #." 2 19 38.89 3 669 5.61 | Wart Hill Hoy . . 239 46 36.92 II | Io:25 | 1.3% £oinnebheinn 19 5o 9-65 || 7 || 6.84 | 1.38|South Ronaldshay 253 33 25.56 || 6 || 4.8% *::: "ashven 54 31 8-17 || 4 || 3:08 o.óo | Dunnet Head 238 18 17.93 12 | Io.78 I-4 noºghiubhais 33 + 49.54|| 6 || 2003 || 12.65 || Ben Cheilt 290 39 32.96 || 13 || 5:25 | ** |ºth Ronalisiºnal 3. 56 16:52 || 4 || 3-79 o-93 || Scarabin . . 363 56 51.08 || 4 || 4-od ; - Fitty Hill “ : 44 23.76 4 #. 51 | 1.28 || Ben Clibrig 356 go 33-48 || Io 8.77 7 | • 5C | . * . . tº tº *– 4 57.5 5 4I I-9 I | - * * * * + * ** tºº. *** - . *** r * s * :- *** * **, *... . s. ... ... s. * > *.*. * * * * * * 8o PRINCIPAL TRIANGULATION. From 12th October to 17th November 1850. Observer: Corp. JENKINS, R.S.M. PEN IAWERS. 3-ft. Theodolite, B.o. No. Tecip. No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of Range. of , | Obs. Weight. Obs. Weight. Merrick . . § 46 1.É67 I6 3.72 o'o6 Largo Law † 293 53 54:37 24. 4.90 o. 17 Hill of Stake . 22 56 28.65 23 6-88 o:28 | East Lomond 298 I3 I5-48 || 17 || 7-03 o-35 Goat Fell . . . . 3o 58 50.81 | 1.4 || 485 o'24 || West Lomond 299 55 24°57 I5 5-8o o-31 Ben Lomond . 32 59 47.29 |34 || 6′34 || 0:13 Sayrs Law 308 16 47.99 || 16 || 3.27 o. Io Jura . . . . . . . 37 31 39:38 22 5.97 o:26 || Allarmoor • 319 59 29.37 18 458 o. 14 Ben More in Mull 83 51 24, 12 22 6-97 o.20 | Carnethy Cairn 322 36 16-09 || 4 || 3:02 o'59 Ben Novis 12ó 39 3.03 || 42 6.20 o-o8 || Ben Cleugh . 324 54. 22.33 3I 5 oz o'o'7 Mamsuil 146 34 10-51 26 || 4-29 o. II | Hart Fell . 337 39 45-oš i I2 || 2:2O o-o8 Ben Amhlair . 153 34 Io:39 26 || 4:23 o. 12 Tinto . 341 39 15-31 || 6 || 3:94 o'55 Ben Macdui . 269 43 24.94 4o 6.93 o. Io | Bin of Campsie 355 5 56.71 31 22 || O ~ I I Glashmeal. 2.34 46 8.8o 41 || 7-19 o.o.9 || Corkmulaw 356 40 38.61 36 5:20 o.o.9 Craigowl . 269 16 o'29 || 35 | 6′37 o. II IBEN LOMOND. 3-ft. Theodolite, B.o. From Ioth to 19th August 1818. Observers: Major-Gen. Col.By and Mr. GARDNER. i. No. Recip. No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. O Af f/ O A # / Brown Carrick 3 18 52.81 | 3 #34 o:23 | East Lomond 265 37.4% II 5-66 o-64 Hill of Stake . . . I I I 47. Io I3 8.18 o.8o Ben Cleugh 27o II 16.06 26 6.8 4 o' 16 Goat Fell ' ' ' | 29 1841.69 || 4 || 5.83 || 2:37 || Calton Hill 285 34 57-62 || 4 || 3-74 I-46 Ben Tuirc 4o 29 20.66 || 6 7-40 || 2:43 Allarmoor . . 290 55 4.83 7 || 3.87 o'47 Inocklayd . 42 I9 7.32 || 3 | 1.46 o.27 | Bin of Campsie 302 22 59.85 3o 6.36 o. Io Jura . . . . . . 7o o 37.61 || 4 || 4.83 1.63 | Dunrich 306 36 53. II || 4 || 3-oo o'72 Ben More in Mull Io? 33 54.39 || 6 || 6-25 | 1.62 | Corkmulaw 306 4o 28, 15 9 || 7-33 I. I9 Creachbheinn . I35 37 2 I-o3 || 3 || 2.47 o.70 || Tinto . . . 3.17 16 3o. II | 5 || 2.53 o-28 Ben Novis . . I6 I 29 o'99 .5 I. I 9 || O'91 Hart I'ell . • 317 55 15:34 3 I-91 || O-4I Ben Amlilair . I88 24 21-86 || 4 || 5.90 2.85 | Cairnsmuir on Ben Lawers . 212 38 39.85 | 6 || 3:37 . o. 59 || Deugh . . 345 35 39.18 || 4 || 2:19 o'30 BEN LUNDIE. 3-ft. Theodolite, B.O. Trom 25th to 28th September 1819. Observers: Major-Gen. Colby and Capt. DAwson, R.E. TNo. IRecip. * * Objects, Bearings. . IRange. ºp Objects. Dearings. * Range. Rºjº. Obs. Weight. Obs. Weight. Airdross 37 22 43.71 II 544 o-33 || Bin of Cullen . 296 58' 28.48 6 $47 o-92 Ben Wyvis 42 35 o'42 || 7 || 4.81 o'92 || Knock . . • 309 22 47.68 || 6 || 6.97 2.27 Cairn Cruniach 57 I 21. Io || 7 || 7-93 I-66 || Balnaskerrish . . . .318 9 15.42 | Io 6.85 I.oo Cuinnag • II3 19 Io.83 || 3 || 5 II | 3.65 | Corryhabbie . 324 27 19:66 || 6 || 2.75 o.58 | Ben Clibrig . 141 51 38.94 || 8 || 8.37 | 1.34|Dornoch Spire |355 27 18:38 || 3 o.7% o.36 . .i -*: i OBSERVATIONS. 81 IBEN MACDUI. 3-ft. Theodolite, R.S. From 6th June to 16th August 1847. Observer: Corp. WINZER, R.S.M. º No. Recin. No. | Recip. Objects. Bearings. . Range. º Objects. earings. . Range. of Obs. Weight. Obs. Weight. #. $º º 3. 36 1%88 2O 3.55 o.23 || Ben Cheilt . 186 57 1499 I9 £60 O-2 I B Il †. e 3o Io 26.15 4I 7.23 o. 13 | Findlay Seat . 204 16 29.18 II | 6.40 o'72 CIl §ºir º 59 48 Io.o.2 2 5-48 o. 18 || Bin of Cullen 215 31 I-35 | 6 || I-69 o. I4 . evis . 7o o 26.92 39 7.66 o. 12 Corryhabbie 222 53 I2.34 2I | 6’47 o'27 amsuil * loš 29 3 I-40 | Io 4:49 o.29 | Buck . . . 239 47 27-61 I4 8-o& o°55 °ournalapich 1 I2 II 38. I2 35 .45 o. 15 | Dudwick . . 247 9 35.91 I4 5-68 o'24 i. Wyvis I4I 26 40-59 | 16 || 4-93 o-28 || Caerlock . . . . 277 29 6-28 || 14 | 6.98 o.43 ºn Qlibrig I6I 27 15.88 19 9-32 o-60 | Mount Battock . . 283 4 39.20 44 9.62 o. I6 i. Lundić I67 43 18:17 | 16 4.18 o. 19 || Glashmeal . 32O 5 23.60 23 4. IQ or II ºil. I74 32 I3-og | 4 || 3-68 o-93 iTargo Law 333 36 26.41 || 2 || 2.67 I-78 * . . . 183 2 15.99 || 19 3.17 o.11 Sayrs Law 335 15 29.91 | 15 6.8o o'57 BEN MORE, MULL. 3-ft. Theodolite, B.o. From 18th to 24th September 1822. Observers: Captains DAwson and VETCII, R.E. Obi No, Recip. No. Recip. bjects. Bearings. of | Range. of Objects. Dearings. of | Range. of Tº"-----— Obs. Weight. Obs. Weight. Af & Aſ §: T ... . 11° 16 37.80 6 49. o.88 || Ben Law.crs . 262 21 13:09 4 || 4-77 I'44 º #. º I9 Io I-72 | 15 6.76 o.37 || Ben Lomond . 286 24 57.96 1ó | 9.58 || 1:48 i. §. ~. 93 5o 28.62 15 6.34 o.61 Goat Fell . 329 42 28.99 || 3 | o'82 999 §. *ore, S. Uist 143 36 28.69 6 5.5; 1.5o Ben Tuire 343 31 40.47 || 7 || 3:44 9.4% Cr º ... ' ' | 175 II 39-22 || 3 | 1.39 o-22 || Carn na Leagh 353 8 21. 4 || 3.26 I-17 ºim 231 Io 45-55 || 4 || 2.76 o-60 Jura . . . .359 23 32.82 23 6.20 o'19 Il Nevis 235 5I 3-35 | 9 || 7-40 | I-36 *— BEN MORE, SOUTH UIST. 3-ft. Theodolite, B.o. *- From 5th June to 29th August 1851. Observer: Corp. JENKINS, R.S.M. º No. Recin. No. Recip. Objects. Bearings. . Range. . p Objects. Dearings. of Range. of * Obs. Weight. Obs. Weight. T--—— Cleish O / / / f / tº O / / / & f 8 r) Stor am . . 199 57 56-17 | 42 3.87 o.o.4 Creachblicinn 3oo 13 28.05 || 17 || 4'98 || 0:23 Sco . . . . 247 3 43.54 46 5-37 o.o.8 || Referring-object 305 4:I 44'45 || 34 5.8o o.or IV i. nalapich 263 5o 15.08 27 5.23 o. 12 | Ben More in Mull 319 22 13.89 29 6.31 o. 17 i. º 268 3 12.83 19 5-41 o-22 || Jura . . . . . 331 45 6.78 || 14 || 4 II .# Cn N ill. 287 I6 30.89 17 || 4-71 o.24 || Ben Heynish 345 37 43.61 45 || 6’4” * Nevis 289 I9 22:47 15 || 7-27 | o'52 L 82 PRINCIPAL TRLANGULATION. IBENCORR. 3-ft. Theodolite, B.o. I'rom 27th.J.uly to 31st August 1830. Observer: Capt. PortlocR, R.E. No. Recip. No. * . Recip. Objects. Bearings. .* Itange. of . , Objects. Bearings. . Range. ºp ſº - Obs. Weight. -- Obs. Weight. Hºum () 1° 1' 398 u 6 7.79 2-2I ºlogy 22° 9. 38.66 • 2. 444 4.92 §. º º 'º 12 35 49.98 || 5 J 7:44, 2.45|l\eeper . . 308 44 41-66 I3 8.92 o-84 ieve More . I62 39 3-o/ 8 4.22 o'50 Slievecarran º 31o 53 48. I3 29 8-12 o-39 The Reek. 197 7 35-60 || 5 || I-12 o.o.9 | Slievecallan . 334 36 o-28 || 18 8.77 o.68 Nephin . . 206 Io 36-40 | 15 | II'77 o'86 || Knockanore . . . .353 2 5 46.20 3 || 2:41 o-64 IBEN NEWIS. ºf - 3-ft. Theodolite, R.s. - From 1st August to 14th November 1846. Observer: Corp. WINZER, R.S.M. * No. | Recip. - - No. IRecip. Objects. Bearings, f tº ings. f tº jec s. ring o: S. Range. W.#ht. Objects. Bearings o: S. IRange W#ht. | O & M.W. Aff * * O / // # / †: re in M i 3. 16 to:63| 13 || 3.91 o.17 Scournalapich 176 57 15:22 50 | 6.94 o'Io | Cre j ull 3 i. £; 2: 9:47 o-30 || Ben Wyvis 194 26 41.61 42 7.96 || O. II : B *; j 2 46 13.65 | 18 8.93 o,42 |Corryhabbie 24o 9 I5-oo I4 7.87 o.46 - #. ey is: § 55 5-04 || 23 6.46 o.22 || Ben Macdui 248 53 44. Io 35 | Io-o5 | . o. 20 #. *...*. I 52 46-07 || 23 13.23 o.68|| Ben Amhlair . 266 29 31.38 || 19 || 3.83 o. I5 - #. #. • Uist III I4 50'35 | I3 9.14 o.90 || Ben Lawers . 299 59 3 I-59 || 38 Io-63 o°23 §. Ill II3 48 43-16 || 3 | 1.87 o.48 || Ben Cleugh 3II Ig 5-44 I6 || 7-40 || O'39 . R. i tº º I38 25 45-76 I4. 5.14 o.25 || Ben Lomond . 34I IO 43-o-; I9 || 7-55 o'49 | Tylam Sull - I72 3o Io-or || 8 || 2.94 o.19 - IBEN TARTE WIL. 3-ft. Theodolite, B.o. r From 17th July to 2nd August 1822. Observers: Captains WETCH and DAWSON, R.E. No. in. tº No. in. Objects. Bearings. . IRange. R p Objects. Bearings. . Range. hº p Obs. Weight. obs. Weight. Slieve Snaght 44" 3'5865 6 698 2.01 Jura 23. 1926.88 4O #90 o: 13 Ben Heynish : 169 2 5-73 || 9 || 3.92 o.29 |Qarn na Leagh ' || 317 20 48.58 16 || 8.27 o.54 Ben More in Mull 19848 39.51 14 || 7-39 o-80 |Qa or Cairnard 317 52 44-oo 25 | 6.72 o.25 Creachbheinn in - - |Trostan 343 17 28.44 || 5 || 5-31 | 1.59 Mull 205 37 37. Io | 4 || 4.67 | 1.48 || Knocklayd 348 53 59. I4 a 6.89 o-34 wº-mº- * : * * , wº- • * * . * > ***. º "-" - a-- * * -- rººt ºr *- : * ~ * * * **** * * f OBSERVATIONS. 83 A , * * IBEN WYWIS. 3-ft. Theodólité, B.o.” ". . . * * * if 3. * * •w, . ~ * *, .* * * * # From 8th to 12th September 1819. Observers: Major-Gen. Col.BY, Lt.-Col. Robe, and Capt. DAWSON, IR.E. ~. No. Tecip. * * ~ * ~ * No;-- - - - Recip. Objects. Bearings. of | Range. of Objects. Bearings. . of Range. of Obs. | Weight. obs. || 7 ||Weight. * Neyis 1: 4; 43.67| 4 || 3:69 597 |Balmaskerish 24; 14 24.99 || 3 | #99 || 4:03 sºil $ol. 1 36 24 44.61 I — 6.95 || Bin of Cullen 27,o 8 3.86 || 3 || 4.70 || 2:46 §.” #2 & #95 || 5 || 3:4: 93%|ººk. 274 49 51-43 || 3 || 2:5 I O'75 uubheinn I46 I 36.20 || 5 || 2.5o o-31 || IFindlay Seat . 277 25 48-39 || 2 | O.7o o. 12 unnºg. . . I55 Io 4.34 || 3 || 3:54 I-66 || Corryhabbie 293 36 I?-61 | 6 || 2.25 o. I9 Den Hutig • 182 16 15.23 || 2 || 3-79 || 3:59 || Ben Macdui ''. 32O 4o 42-90 || 7 || 3:53 O'47 Ben Clibrig ... • 189 3 7.63 || 8 || 7.83 | 1.08 || Ben, Amhlair . 355.5I I2°o4 || 5 | 9-89 || 4. Iş Scarabin i. 223 42 I7-47 2. I-73 o:74. * g * A correction of + 1'o"'54 to be applied to this bearing, to reduce it to the new station, BERKHAMPSTEAD. * 3-ft. Theodolite, B.o. * September 1823. Observers: Captains WETCH and DRUMMOND, R.E. ** * No. | Recip. i * - No. IRecip. Objects. Bearings. of Range. of Objects. Bearings. of Range. of *-m- - |Obs. - weight. r - - - - - - - - - - - obs, j- - - - -] Weight. Leith Hill Tower 1. 5 5 43.83 II 13.50 1.68 Chingford . wº 32; aſ 2329 2 I #40 o, IQ Dunstable * * II3 2 37.76 | 16 || 4.63 o. 16 || Wrotham Staff 329 39 56. II || 4 || 3-44 o'98 † Spire 235 28 I5-26 || 3 || 6.62 4.87 | Severndroog • 338 I4 49.47 || 5 || 6.49 || 2-or figh Beach . . 3: 26 53.02 || 13 6.03 o-51 || St. Paul’s “ . . . . . .356 3. I-60 5 || 7-31 || 3:02 IBER.Y.L. w + 3-ft. Theodolite, B.O. From 28th May to 3rd June 1868. Observer: Major-Gen. CoIBY, R.E. : Obi , | No. Recip. º *: Ran Rºjº. anri * ſº ges jects. IBearings. di. Range. W.3.ht. Objects. Bearings o: S. Weight, * - * O & . * * f/ Black Comb . . . 158 8 #39 6 1412 6.29 | Billinge wº 325 43. 23:44 3 4.61 || 3:02 lvington . . . .306 21 7.52 1 — 14-41 || Go Hill 344 6 52-63 || 4 || 4:51 || 3:10 IBESSY BELL. * 3-ft. Theodolite, B.O. *--— From 22nd May to 16th June 1827. Observer: Lieut. PopTLOCK, R.E. : * * No. Recip. iº * No. fy R;. ... -- objects. * || |hange |wi. Objects. Bearing" | |*|w. Cuileagh . 26 ſ 4. - a 6°41'45. 6 | 662 o.14 - 46 52°23 I7 | 20. I 2.60 | Sawel . 236 4I 41-39 || 3 "...a… l n. A Breesy. . . . . 66 35 § 9 : 3. Io | Slieve Gallion 232 31 8.5% | 8 || 4:39. ...; BărneşmoreConnell 97 8 25-36 i3 | 6.99 o.62 || Mullaghcarn . 275 46 37.74 6 571. 12. 3. Slieve Snaght ... 18; 53 43.39 18 10.36 o.57 | Slieve Donard 299 50 38.87 | * gº 5 L 2 84 PRINCIPAL TRIANGULATION. IBESSY BELL–continued. - No. Recip. No. Recip. Objects. ' Dearings. of | Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. O & W/ A/ O f f/ A/ Vicar's Carn . . . .309 27 46.18 8 || 10.99 || 2:96 || Shantavny . . 31547 48.43 21 9.33 o-38 Slieve Gullion . . 314 43 57.15 || 2 | 1.44 o'51 || Mullyash . . . . .326 5 19.84 || 6 || 11.66 3.88 Armagh Breagh 314 45 46.95 || 2 | o-82 o' 16 || Carnmore . . . 35o 18 8.95 || 17 || 4-o'7 o.21 wº- BILLINGE. 3-ft. Theodolite, B.o. From 15th to 21st June 1807. Observer: Major-Gen. Colby, R.E. No. Recip. i No. Recip. Objects. Bearings. of | Range. of Objects. Dearings. of | Range. of § Obs. Weight. Obs. Weight. O f f / W/ O Aſ f / £/ 3.24 I-29 || Go Hill . . . . I 15 57 33-48 || 13 || 7-7I o'79 6-62 5.04 || Rivington . . . 224 13 46.87 | 15 7.23 o'58 4,61 2.87 || Mowcopt . . . . .322 14 58.07 || 5 || 4-03 o-87 — 18.46 Bellefield . . . .332 Io 49-66 || 5 || 2:58 o°41 o:72 o. 13 || Delamere, Old" 356 16 8.02 . Io 9. 17 I-69 Cyrn-y-Brain 3o 29 57-39 Heswell Hill • 53 3 I5-27 Everton Tlagstaff 61 29 35.32 Snowdon . . . . 62 I4 3o.o.4 Great Ormes Head 76 4. I-90 i * A correction of +3".os to be applied to this bearing to reduce it to the new station. BIN OF CAMPSIE. 3-ft. Theodolite, B.O. From 2nd to 7th August 1818. Observers: Major-Gen. Col.BY and Mr. GARDNER. ſº No. Rcci 9. No. Recip. Objects. Bearings. of Range. of Objects. Dearings. of | Range. of Obs. Weight. Obs. Weight. *. o & J & A/ O / / / f/ Cairnsmuir on Ben Cleugh . . . 230 Io 35' 16 || I4 5'49 o°25 Teugh . . . . 3 Io 54-04 || 4 || 1.67 o.22 || Calton Hill 275 53 26. I4 || 4 || 3:15 o'79 | Brown Carrick . . 28 19 I7-89 || 3 || 3:55 | 1.43 || Allarmoor . . . 284 II 14:49 II 6-91 o.61 Corkmulaw Ç 33 28 3°41 4. o' 57 C - O2 Dunrich iſ: ſº º 309 I 7.87 4. 2.73 O-47 Hill of Stake . . . 62 15 44.35 | } 4.83 | 1.1o Hart Fell . . . 325 II 3-98 || 3 || 3:83 1.87 Ben Lomond ' ' | 122 47 53.47 3 3.og o-28 || Tinto . . . . 327 22 25'98 || 9 || 4.89 o.45 IBen Lawers tº tº I 75 9 48.33 | 7 4-95 o.82 IBIN OF CULLIEN. 3-ft. Theodolite, B.O. From 18th to 21st August, 1814. Observers: Major-Gen. Col.BY and Mr. GARDNER. - No. Recip. † No. Recip. Objects. Bearings. of | Range. of Objects. Dearings. of Range. of Obs. Weight. Obs. Weight. Buck . . . . § 1. 26.68 || 8 4:39 o.47 | Balnaskerrish . 11é 34 #23 £63 o:56 Findlay Seat 66 24 22. II 19 4.07 o. 13 || Ben Lundie • 117 58 6.23 2-off o. I2 Ben Wyvis . . . 91 34 39.35 | 7 | 1.91 o. 12 | Ben Cheilt 157 56 32-33 || 5 || 3:39 o.56 % OBSERVATIONS. 85 IBIN OF CULLEN–continued. tº * No. Recip. * No. Recip. Objects. Bearings. of Range. of Objects. Dearings. of Range. of Obs. Weight. Obs. Weight. Cowhythe . . . 266 56 58.76 6 5.oz I.og | Manor Lee . . 296 27 54.65 5 608 I-91 Mormonth . . 277 33 29.68 || 3 || 6.67 5-31 | Dudwick . . . . 297 12 19:38 || 4 || 5-oo 2-06 Alva . . . . 282 3 4-oS 3 5'44 3.31 IKnock . . . . 327 5 18.84 I2 8:45 I-o/ BLACK COMB. 2-ft. Theodolite. From 31st August to 29th October 1841. Observer: Lieut. DA CoSTA, R.E. No. IRecip. No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of IRange. of — Obs. - Weight. Obs, Weight. O / W.W * * f / O / / / ºf Snowdon . . . . 20 46 45.34 || 5 || 8.13 || 4.41 || Dent Hill . . . . 159 23 6.89 II | 14-48 || 2:66 South Berule . . . 82 42 23.61 | 16 || 6.76 6.83 || Criffel . . . . . 165 43 5-89 || 8 || 9.44 2.79 §nea. Fell . . . . 9o 56 40.86 || 9 || 8.75 | 1.94 | Sca Fell . . . . 199 3 18:04 Io 11.69 || 2:28 North Berule . . . 93 4 58.62 | 8 || 9.19 2.31 |Little Whernside 273 47 13:13 | 13 | 8.69 || 1:29 Chirnsmuir of Fleet I41 4 37-06 || 2 | 6.36 Io. II | Ingleboro’. . . . . 279 7 41.59 II | 12:41 || 3:05 Merrick . . . 143 38 36.78 || 1 — 22. Io Pendle Hill . . 302 17 49-oo | I — 22 IO Ben Cairn . . . 15. 3 28.87 || 5 || 8.46 || 3:33 | Whittle Hill . . 312 54 35-48 || 2 || 2.72 I-84 CairnsmuironDeugh 133 14 10-25 || 3 || 3.78 || 3-3 || Beryl . . . . .337 34 38.61 || 7 | 9.98 || 3:00 BLACKDOWN. 3-ft. Theodolite, B.O. From 3rd November 1848 to 6th March 1849. Observer: Serg. DONELAN, R.S.M. No. Recip. No. Recip. Objects. Bearings. of Range. of Objects. Dearings. of Range. of Obs. Weight. Obs, Weight. *=-— O J * f/ O & Z/ Af Barrow Hill . . 58 20 41.98 22 || 8.22 o.32 | Bull Barrow . . . 222 2 32.87 20 Io-99 || 0:55 Turland . . . 63 58 43.99 || 20 5-27 | o-17 | Horton's Gazebo 244 56 25-96 || 3 || 3-17 | 1:14 Ryder's Hill . . 78 34 21.30 || 8 || 6-73 | 1.24 Nodes Beacon' . . 271 24 28.53 13 || 2:55 o'07 Little Haldon . 79 30 37.05 || 12 3.25 o. 16 || Motteston . . . . 271 39 26.84 || 12 5-40 || 0:37 High Wilhays . 90 28 20.48 21 4.06 o.11 | Dunnose . . . . 274 2 20:86 25 || 5:41 || 0:13 Solden Cape . . . 161 51 5-47 || 5 || 3:43 | 1.31 |Coringdon . . . 278 47 35-84 || 3 || 4:03 || 0.3% impdon . . . 11o 9 28.12 Io 2.33 o.o.9 |Swyre Barrow 285 27 57.76 18 5-31 || 2:23 Pillesdon . . . . 123 45 6.19 II 4.96 o.44 | Referring-object 316 31 58.96 23; 6.8 I o-OI Mintern . . . 190 37 II.53 20 i 3.82 o.o.8 | Vern . . . . ; 329 28 39.19 18 * o-46 __e=" Tº"--__ – * A correction of — 27". 91 to be applied to this bearing, to reduco it to the trigonometrical station. - 86 PRINCIPAL TRIANGULATION. BLACK HAMBLETON. 3-ft. Theodolite, R.S. * - - Erom 4th October to 1st December 1851. Observer: Corp. GROSE, R.S.M. * No. - IRecip. : i. ºr - No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of Range. of Obs. Weight. Obs. Weight. am-- . . . . Great Whernside 71° 5 5 62o 22 6.84 o. 19 || Collier Law . I 38 o #4. 5 “2 o-48 Water Crag . Io.4 51 54-16 || 5 || 2: Io o.23 |Botton Head . 223 47 26.18 II 6.42 o.63 Cross Tell • II9 20 I2-98 12 6.95 o'60 Saltergate Brow. 264. 55 o.12 3 | "o:86 - d. Io BLACKHEDDON. 3-ft. Theodolite, R.S. I'rom 23rd January to 2nd March 1846. Observer: Corp. WINZER, R.S.M. No. Recip. No. IRecip. Objects Bearings, of | Range. of Objects. Bearings. of Range. of Obs. Weight. Obs. Weight. - | *f, º C f f / A/ O f & f f / Cheviot 37 32 Io.55 20 | 5-o& o. I2 || Lumsden . . 149 57 58-II | 19 || 5-oš o. 14 Dunrich 85 I 34.or || 5 || 2: 18 o.24 || Mordington I54 43 54-27 | 13 || 2: I9 o'o6 Sayrs Law 11648 33.68 23 5.16 o.14 - - IBLUE HILL. r 3-ft. Theodolite, B.O. From 13th to 21st July 1814. Observer: Mr. GARDNER. No. | Recip. No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of Range. of Obs. - |weight obs Weight. O f &/ Af > i * O & w/ Af Caerlock . º 6I 2 12-off I 5 6.53 o:31 Mormonth. tº I85 4o 7-44 3 || 2:94 I •o8 Mount Battock 66 49 27, 16 9 || 4.73 o.46 | Dudwick . . 188 13 33-18 II 8-02 . o. 92 i Buck º, ſº I 13 16 12.42 7 || 4-71 o.54|Little Stirling 204 57 13-84 || 4 || I-84 o-28 | | IBONIFACE DOWN. 18-in. Theodolite. 28th and 29th July 1846. Observer: Corp. STEEL, R.S.M. i. No. Recip. º No. Tecip. Objects. IBearings. of Range. of Objects. Dearings. of | Range. of Obs. Weight. Obs Weight. Littletown Down 2 § 53 51.8 5 8 18:10 9.81 | Shanklin Down • 162 53. I #31 4. 16.9 5 Io-48 Weck Down . 76 30 33-31 || 8 || 27.62 17.97 | Dunnose ...' ... 1834o 15:58 || 8 || 20.84 || 8.69 Wroxall Down 77 39 33%;| 6 || 3:68 || 3:33 |Boniface S. E. 324.45 A.H., | 8 | 1.3, 3.3% Nodes Beacon' Ioé 25 12-or | 8 || 16.90 7.24 - - 1 A correction of + 1' 21" 60 to be applied to this bearing, to reduce it to the trigonometrical station. ! OBSERVATIONS. 87 BONIFACE, S.E. 18-in. Theodolite. 3oth J uly 1846. Observer: Corp. STEEL, R.S.M. * No. Recip. No. Recip. Objects. Bearings. of l?ange. of Objects. Bearings. of | Range. of Obs. . Weight. Obs. Weight. Li l O Af A/ M/ O Af Af & A ittletown Down || 48 3, 47.08 | 6 || 12-o& 6-ol | Nodes Beacon! . . Ioff 39 15.47 || 6 || Io.87 4.24 Week Down . 79 44 53-64 || 6 || 3.82 o-66 | Boniface Down | 1.44 44 54.87 || 6 || 15-16 || II. I.4 Wroxall Down 96 # 3.4% | 6 || 23.84 32.31 High Port Cliff 329 37 51.08 || 6 || 12.78 9.82 1 A correction of + 1' 21"-20 to be added to this bearing, to reduce it to the trigonometrical station. BOSTON CHURCH TOWER. 18-in. Theodolite. From 16th July to 12th October 1842. Observer: Corp. STEEL, R.S.M. * T , , . . . . No. . . . . Itecip. * * * * - - No. Recip, Objects. Bearings. of Range. of Objects. Bearings, of Range. of * g. Obs. J. Weight. Obs. Weight. *=- - O / / / Af O / / / Easton Tower 4o 13 37.58 Io 2.83 2.21 | Swaffham Spire”. 307 iſ 15:02 - Buckminster . . . . 66 19 22-23 13 Io.56 3-04 || Lynn Tower”. . . .311 17 26.88 Lincoln Minster'. 129 58 21.81 || 2 | 12.64 || 3.95 || Walpole,St.Peter's 328 51 o'87 Docking Tower . . 286 54 o’97 || 7 | 12.26 6.1: 2.83 O-47 4-34 O-32 6.85 o-92 ; *m- A correction of + 9"07 to be applied to this bearing, to reduce it to the trigonometrical station. 2 A correction of — Io" 26 53 3y 33 3. A correction of + o''' 82 35 35 32 BOTTON HEAD. 3-ft. Theodolite, R.S. From 13th October to 27th November 1840. Observers: Lieuts. PIPON and CoILINSON, R.E. * * . - -- iſ . IBeari No. Recip. i. * No. T Rºjº. Objects. . . earings. . o: Range. Wi. Objects. Dearings. o: • ange. Weight. O / / / | # M C f f/ f f Black Hambleton 43 55 14-03 | 7 || 5.78 1.21 | Brandon Down 135 36 54.74 || 6 || 5.67 | 1.48 Great Whernside. 65 41 13° 17 6.44 o-36| Wordeslow . . . 156 9 2.57 || 4 || 6-79 || 399 Little Whernside 77 28 34. I3 | 2. 5'49 7:53 Easington' • 22 I 46 55-28 7 3. Io º: Water Crag . . . 93 20 35.67 | 6 || 6-64 1.36 | Saltergate Brow. 286 55 48.76 || 3 || 5:42 || 3:2 Qross Fell; . . . Iio 35 30-25 || 3 | o-93 ojo | Acklam Wold . 333 31 is 73 | f | – | *79 Collier Law . . . 125 33 41.52 | 7 || 5.3i o,73 || York Minster. . 359 A2 32.98 || 3 || 5:33 || 3:49 __--—-T * A correction of — 15" og to be applied to this bearing, to reduce it to the trigonometrical station. 88 PRINCIPAL TRIANGULATION. BRANDON. 12-in. Theodolite. From 3rd to 10th June 1840. Observer: Mr. FINAGHTY. º No. Recip. º * No. Recip. Objects, Bearings. of | Range. of Objects. Dearings. of | Range. of Obs. Weight. Obs. Weight. Loop Head Light- O f f f Z/ Baurtregaum . . . 27 § 58 422 | 6 || 1 589 8.46 : house . . . . 211 2 20.97 || 6 || 15:54 9-oo Knocknadober 348 34 48.24 || 5 || 14.64 13.66 IBRANDON. 2-ft. Theodolite. From 19th January to 12th March 1845. Observer: Corp. BAY, I.S.M. No. in * . in. * Objects. Bearings. . Tange. Hºp. Objects. Dearings. . Range. Rºp Ohs. Weight. Obs. Weight. O ſ ſº Af O A MA w/ Newmarket 36 24 43.79 || 8 || 5.79 o.53 | Swaffham Spire'. 189 49 30.92 || 9 || 5-63 o'52 Tharfield tº 46 18 8. I6 II 6.93 o.95 || Hingham Church Cambridge Qbic: Tower . . . . 231 40 54-48 || 9 || 12:33 || 3:45 yatoryIſeliostat §§ 29 29.8o II 7.97 o.81 | Bunwell Church Ely Minster '. 88 I6 26.66 I6 7' 54 o.66 Tower . • 254 25 23.66 8 7. I5 o-92 Peterborough Tr. Io.7 56 52.27 I * II.og South Lopham ſº 272 23 7-29 IO 8.26 I. I3 Iłeferring-object | 126 I5 30-04 || 62 6.99 o.16|| Lawshall Tower 345 5o 17:35 17 | 8-o/ o'45 A correction of + 1 1. '69 to be applied to this bearing, to reduce it to the trigonometrical station. * A correction of + 2 1"'92 33 33 55 BRANDON DOWN. 3-ft. Theodolite, It.S. Trom 6th September to 31st October 18 53. Observer: Corp. GROSE, R.S.M. º in. No. Recin. Objects. Bearings. . IRange. hºp Objects. IBearings. . Range. ºp Obs. Weight. Obs. Weight. - O * Af O / // Af Great Whernside | 17 3 3' 2#12 | 5 303 o,43 Durham Observa- Water Crag • 38 28 I-31 || 11 7.35 o.81 , tory Dome . 256 I 33°39 || 2 || 4.90 || 6-oo Collier Law . 95 27 35:45 Io 5.5 o.86 Easington ſº 29I 3 2:3 ; 992 o.21 Pontop Pike . I55 44 58.8o 12 6.45 o.55 | Burleigh Moor 296 Io 39.88 || 8 || 2.77 o. 18 Wordeslow 237 8 15.88 Io 6.54 o.91 ||Botton Head . 315 7 5 I-95 Io 4.5I o-44 | Durham Observa- Merrington Church 327 59 28-56 | 6 || 7.57 2.16 tory (Mark on) 256 o' 41-40 || 2 | I-94 o-94 Appleton Wiske 329 44 41.76 || 8 || 2.22 o. 16 Black Hambleton | 330 44 44-34 || 8 || 5.74 o.96 OBSERVATIONS. BRASS.A. 3-ft. Theodolite, B.o. From 25th to 29th August 1821. Observers: Major-Gen. Colby and Capts. VETCH and DRUMMOND, R.E. –-mº ~. No. Recip. No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of Ränge. of Obs. Weight. Obs. Weight. Tair Isle . 25 1. 1%23 II 7.99 I.oo Yell 186 32 1392 17 | 4%3 O - 22 Foula . . . 9I 35 47.38 I5 || 4-66 o-28 || Saxavord . I90 8 22-4I | 6 || 3:42 o-47 Ronas . 156 57 20:58 15 9:30 o.72 | Fetlar . 193 6 34'34 || 9 || 3:44 o'26 BRIMMOND. 3-ft. Theodolite, B.o. 17th June 1817. Observer: Mr. GARDNER. Obi i. No. - Recip. tº tº * . Rån Rºjº. jects. Bearings. o: * Range. W#ht. Objects. Bearings. o:S. ge. Weight. Mount Battock . 5* 4. 38.8; 7 566 o.81 || Over Hill . 220 3: 3 #83 9 | 4. I4 o°34 Buck . . . Ioff 34 44'57 || 8 || 6.92 | I-34 || Layton 226 4o 45-30 || 9 || II.24 || 2:15 Knock . I45 3 31.73 || 3 || 3-64 I-53 || Tarbathy • 246 34 24.71 Io 5.61 o'67 Mormonth 194 22 32.98 || 6 || 6.5o 1.77 | Blue Hill . • 322 I II-99 || 12 || 6:71 o°49 Dudwick . 2O2 49 27.81 || 5 || 5-60 I-66 BROADWAY TOWER. 3-ft. Theodolite B.o. From 3rd May to 9th June 1850. Observer: Corp. JENKINS, R.S.M. No. Recip. * * Range Rºjº. * ſº § º €, Objects. Bearings. o:* Range. W#ht. Objects. Bearings. o:S. ang Weight. O / / / w/ Q ºf f/ A/ : * * Cleeve . . 45 I5 43-29 27 | 7. I3 o. I6 | Bar Beacon . 175 13 2.31 26 || 8.69 o°28 May Hill . 7o 23 46.37 || 23 4.7i o.14 || Hampton Church 191 25 11.56 Io || 4-22 || o'82 Cradle . 85 18 34.88 31 5-15 o. II | Claverdon Tower 196 43 35.26 || 5 || 4.96 || I'o'; Breedon Tower - || Ioa. 17 54.89 I5 6. I4 o.35 | Corley . * 200 43 23.58 || 6 || 2:20 o: 18 Malvern . . . . Io. 45 52-28 || 51 | 6. I9 o.og | Bardon Hill . 204 20 53.08 || 23 || 4.83 o.o.8 Worcester Cathe- º Warwick Tower. 216 25 29-32 T4 || 7-36 o'56 dral Tower I24 54 20. I7 || 9 || 5.83 o.73 | Dunchurch Church - º: - * * Brown Clee . I34 13 57-60 | Io 9.2i | 1.49 Tower . . 226 51 51.93 || 3 || 7°og 5'59 | Walton Hill . . . 158 41 58. Io 20 9.67 o.29 || Arbury Hill . 242 12 45.70 | 20 || 6-76 ...; Lord Plymouth's Epwell . . . . . 257 18 2.74 47 || 7.46 o° Monument . 162 48 50-62 | 6 || 4-13 o.71 || Stow on the Wold 326 27 5.08 || 19 5.26 *:::: Oversley Lodge Tr. 174 24 31.91 || 5 || 8.57 3.29 | White Horse Hill 339 32 39.96 || 26 || 3:07 | * M Qo PRINCIPAL TRIANGULATION. BROWN CARRICK. 3-ft. Theodolite, B.o. From 16th to 25th September 1815. Observer: Mr. GARDNER, º No. Recip. tº Objects, Bearings. . Range. º Objects, Bearings. *: Range Rºjº. Obs. Weight. Obs, |weight. Saugh . . . . . 18 36 3. 5 W/ Hill O / / / &f - .59 15 || 6.54 o.46 || Hill of Stake I76 32 27.8 7| 21 || 5:43 o.24 #. • 19 21 32.12 14 || 5.73 o'39 || Ben Lomond; • 183 I4 53.98 2 || 2.61 | 1.of Carn iºni {º § 1 43.11 || 3 || 5.34 3.86 || Bin of Campsie 207 50 35'30 || 3 || 1:84 o.84 Čºf ll e. º I 33 23.61 I4. 4°50 O - 22 Tinto ‘. . . . . 252 21 38.64 8 5.72 o:58 ell . . . . 128 58 9.83 14 6.48 o.51 (Cairnsmuir on Deugh 297 47 14:14, 19 Io.83 o'74 IBROWN WILLY. 18-in. Theodolite. From 3rd October to 17th November 1849. Observer: Corp. WotRERSPoon, R.S.M. 4. i. No. Recip. No. Reci Objects. Bearings. of | Range. f † g p. Obs. ange W§ ght. Objects. Bearings. o: ſº Range. W#ht. E. ſº tº 19 4. 4% I4 I2 566 o:50 | Efford Beacon 186 57 13 co I4. 6:00 o°45 #. ' ' || 33 47 2.82 21 17.88 | 1.43 | Paracombe 218 26 22:56 || 3 || 2.99 || 1:25 i i. M. 44 41 17:48 || 9 || 6,66 | 1.19 || High Wilhays 255 39 12:20 | 18 || 12:57 | 1.51 * : , * 8 8 Ryder's Hill . . . 28o 18 1.94 | Io 17:32 || 4-21 St Americion 4ö 25 I ...; 8 15-31 || 5.05 || Kit Hill Tower 289 49 I-57 31 || 15.13 o.8o famimi # 2: 33.46 11 || 7-33 o.85 |Butterton : , ; , ; 291 14 18-34 || 6 || 8.61 3.20 Trevose Hai º § 44 ; 15 4.67 o.22 || Eddystone Light- § 3 ##| |&#| ||Lºi, |# #| ||}} {: { *: & sº •49 {l tº ſº 3.54 IQ - I {} I • Lundy I. Lightho.' I75 35 43-65 13 9.37 1.11 || 9-95 I3 9.83 O3 1 A correction of + 2' 17"'85 has to be applied to this bearing, to reduce it to the trigonometrical station. BUN WELL CHURCH TOWER. 2-ft. Theodolite. From Ioth October to 16th November 1844. Observer: Corp. BAY, B.S.M. * No. Her No r dº Objects. Bearings. f ſº tº • I. Recip. gs o: S. Range. Wà. Objects. IBearings. o:ſº Range. Wà. |Mickfield . . . . c. 48 46.61 | 1 || 3: IB o f f f w/ .49 o.29 | Baconsthorpe • 182 46 49.88 Io * * * iº 4O . 4; § I3 5.99 o-44 || Norwich Spire 216 41 i. I4. § ...; Swaffham Spire' . #: # §: : #. .#. #: ld 267 4: 14.61 || 7 || 2.17 o.14 Hingham Tower I34 32 42. 5-82 *f C 322 32 5'94 | 12 || 4.96 o.34 $º 32 42.5o Io || 3-62 o-26 1 A correction of + 17"'75 to be applied to this bearing, to reduce it to the trigonometrical station. OBSERVATIONS. 91 BURLEIGH MOOR. 3-ft. Theodolite, B.O. July 1806. Observer: Mr. Woolcot. g No. Recip. No. - IRecip. Objects. Bearings. of | Range. of Objects. Bearings. of IRange. of Obs. Weight. Obs. Weight. A/ ff O & Aſ O & A/ Wordeslow . . 14, 25 46.89 || 7 || 8.74 2.29 | Easington'. . . . 272 59 44.65 || 7 || 5:42 I-28 *The position of the present station at Easington is found, by comparison of the new and old observations at that point, to be 2'47 feet distant, and bearing 313°24' from the old station. A correction of — 7"'79 must therefore be applied to the reading of the old point to reduce it to the new. * IBURNSWARK, 2-ft. Theodolite. From 22nd March to 4th May 1847. Observer: Serg. BAY, R.S.M. - No. Recip. No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs, Weight. * O f f/ Z/ O / / / W Criffel . . . . . 52 39 13:18 13 | 6′o7 o.37 | Referring-object . . 204 52 13 oA 94 ". ... tº Cairnsmuiroffleet 79 22 51.73 || 4 || 3.75 | 1.io || Wisp . . . . . . 223 5 56.99 || 16 || 4-04 || 0:24 Merrick . . . . 94 II 32.41 22 || 4-75 o.12 || Cross Tell. . . . .316 21 13.36 | 16 || 4.98 o.16 QairnsmuironPeugh 167 7 39.42 21 || 3.93 o.1o | High Pike. . . . .341 54 38.36 || 4 || 3.92 | 1.38 Tinto . . . . . 156 26 38.55 | 13 2.19 o.o.5 | Sca Fell • 356 31 6.82 II I-68 o.o.4 Hart Fell . . . . 167 24 20.57 | 15 || 4-76 o.27 BUTSER HILL. 3-ft. Theodolite, B.O. From 1st December 1844 to 16th February 1845. Observer: Serg. DONELAN, R.S.M. f No. IRecip. No. Recip. Objects. JBearings. of Range. of Objects. Bearings. of IRange. of Obs. Weight. Obs. Weight. O Af f/ w/ Dunnose . . . . 21 8 51.87 22 6.27 o.23 Beacon Hill . . 11. 3. 33.78 Io 2.69 o'I6 Motteston : . . 4I 53 58.96 || 5 || 9:74 4.58|Inkpen ... . . . . 141 3 52.07 || 13 5. I2 o'32 Nodes Beacon' . . 49 2. I4-30 || 4 || 5-04 || 2:03 || Leith Hill Tower 242 24 51.06 | 12 6.33 o°58 Coringdon . . . . 61 53 4.85 13 5.39 o°52 | Crowborough . . . 263 22 26.84 || 12 || 4.93 o°25 Wingreen . . . . 91 2 16:56 18 || 7-08 o.23 | Ditchling. . . . 277 31 55.77 27 | 6.98 o'21 Dean Hill . . . . 97 20 58.48 || 5 || 4.22 o.88 || Rooks Hill . . 360 48 ſi.89 14 6.78 o'52 Referring-object Io& II I4.96 |136 tºº tº- | * * A correction of + 2.0"'43 to be applied to this bearing, to reduce it to the trigonometrical station. M 2 92 PRINCIPAL TRIANGULATION. From 21st to 3oth June 1832. CAEIERBARNAGH. 3-ft. Theodolite, B.O. Observer: Capt. PoETLock, R.E. No. Recip. * No. Recip. Objects. Bearings. of | Range. of Objects. Bearings, of | Range. of Obs. Weight. Obs. Weight. º O / / / - A/ O & My Af Slieve Buoymore. 3544 58.75 13 || 9:30 o'96 || Galtymore..... • 24o 59 39:77 || 3 || 6.20 || 4-78 Hungry Hill . . . . 48 5 44.97 II 9.89 | 1.37 || Mount Hillary, * | Mangerton, ' ' | 72 17 25-34 17 | 9. Io o'84 || North : • 249 6 49-40 || 31 || Io.37 o.28 Drung Hill 89 42 13-14 || 4 || 3:45 o.77 |ICnockmealdown 255 I7 9.97 I - || 7-95 Brandon . . . . . Io? 33 17.52 || 5 || 3.59 o.93 || Knocknaskagh 26o I7 34-31 || 9 || IO-42 I-86 Baurtregaum II3 57 51.04 || II | 8.11 o-'92 || Mushramore . . . 277 49 41.69 || 9 || 7-87 I-25 Crushylean 136 II 13.16|| 4 || 1.52 o.16 |Doolieve . 298 Io I5.88 || 5 || 8.13 || 3-64 Taur . . . . 188 5o 3.57 || 4 || 3:40 o.86 || Mullaghcorrin 299 49 57°55 I * 7.95 Knockfeerina • 206 59 16.52 || 4 || 1.29 o.15 Clara Mountain 322 o 42.97 || 3 | I-63 o-29 Keeper. . . 217 32 40.65 || 3 || 2.29 o-60 | Carrigfadda 352 31 6.81 | 12 II. 26 || I-2I CALTON HILL. - * 3-ft. Theodolite, B.O. - From 3rd May to 17th June 1816. Observers: Major-Gen. Col.BY and Mr. GARDNER. No. in. No. Recip. Objects. Bearings. . Range. Rºp Objects. Bearings. . Range. ºp Obs. Weight. Obs. Weight. ſº O f f/ # / O / / / # / Dunrich o 8 12-22 || 14 || 8.24 o.79 | East Lomond. I75 49 22:40 34 8:37 . o. 19 | Allarmoor . 22 35 49.8o 18 8.48 o.75 | Craigowl . . . . 188 55 34-23 || 8 || 4 of o-35 Corkmulaw 94 24 53-ol || 7 || 5.5o o.78 || Inchkeith Light- Bin of Campsie ' | 96 4o 40.93 || 13 || 4.62 o.22 house . . . 198 40 35.87 45 9.98 o.22 Ben Lomond . . . Iof 47 9.38 13 6.68 o.53 Largo Law • 207 I2 44-51 || 33 8.90 o-2I Ben Cleugh . 125 24 7-08 || 29 || 6-57 o-17 || Kellie Law 217 22 46.42 I4 Io-75 I. I 5 Ben Lawers . . . 136 2. 30.17 || 5 || 12.65 6.80 CARNETHY CAIRN. 3-ft. Theodolite, B.O. From 8th July to 24th August 1850. Observers: Serg. DONELAN and Corp. GROSE, R.S.M. - No. . Recip. º º NO. Recip. Objects. Bearings. of | Range. of Objects. Dearings. of IRange. of Obs. Weight. Obs. Weight. Hart Fell . . . º 31' 3:61 28 £5. o. 15|Bin of Campsie : 109 37'43.87 7 396 o°45 | Tinto • . • 41 18 46.49 31 || II.44 o-32 || Ben Lomond . II5 o 52.45 || 6 || 3.67 o.43 Middlefield . 62 18 39.73 || 6 || 6.91 I-82 | Ben Cleugh . I4I 5 32.65 I4 9.68 o:74 Hill of Stake 89 36 48.83 || 5 || 7-02 || 2:35 || Ben Lawers º I43 22 55-84 15 7.88 o,78 | Corkmulaw . . . Ioz I I2. I2 | 16 || 6.94 o'44 || Ben Macdui . 170 i 35-21 | 3 | 6.67 || 4.94 : | º OBSERVATIONS. 93 CARNETHY CAIRN-continued. g i. No. lèecip. No. Recip. Objects. IB tº * ings. i. f jects earings o: Range. W.#. i Objects. Bearings d; º Range Wint | Glashmeal. Ç 17; 5. 49.83 I I 7:32 o:56 || Arthur's Seat . 21; 54 $44 I6 891 I • O2 West Lomond 178 & 23.48 || 6 5-92 I-60 | Kellie Law 2I4 5 4o.37 20 | 5.78 o°29 East Lomond 184 8 28.61 1o 4.77 o.43 | North Berwick i $. * • I91 26 42.3.I II || 4-29 o.43 Law. . . . . 236 37 25.82 | 6 || 7.75 2-93 ount Battock 194 42 2.89 || 4 || 6.33 2.5% | Sayrs Law . . . 269 13 13.11 | 18 9.84 o-66 Largo Law • 206 20 55-41 I3 5-38 o-21 | Cheviot . . . . 299 2 I 36-12 23 Io.22 o'42 Allarmoor. . . . 207 32 35.34 || 5 || 6.98 o.99 | Dunrich . . . . .349 36 53.76 | 1.4 6.61 o-48 CARN CLONHUGH, 3-ft. Theodolite, B.o. From 12th to 19th November 1828. Observer: Lieut. Port LoCK, R.E. No. in. - No. IRecip. Objects. Bearings. . Range. Hºp Objects. Dearings. . Range. ºp Obs. Weight. Obs. Weight. Longford Spire : 33 17' #17 3 3.49 I-64 | Slieve na Callia . 279 4: 14.66 5 5 oz I • 22 Slieve Bawn South 67 II 51.23 || 9 || 4-29 o.49 || Ben of Fowre 292 20 I7. I2 || 5 || 4-o'7 || I.O.5 Cuilcagh . . . 171 54 3-oo | 6 || 4.89 o.88 Knockeyon . . 366 21 9-57 || 7 || 3.71 o.37 Carnmore . 209 I4. 4I-49 I 4.93| Croghan . • 330 22 8-oë | 3 || 5, 18 3-o/ Loughanleagh 257 48 24.99 || 2 | o'51 o-off Knockastia 352 Io 54.25 || 4 || 5:27 | 2:24 CARN NA. LEAGH. 3-ft. Theodolite, B.o. From 1st to 9th September 1818. Observers: Major-Gen. Col.BY and Mr. GARDNER. No. in. No. Recip. Objects. Bearings. . Range. Rºp Objects. Bearings. . Range. º p Obs. Weight. Obs, Weight. O f // */ O f // w/ Trostan . . . . 39 3 13.45|| 9 || 5-70 o.83 Ben Tuire 205 I9 o'3o II 9-35 I’33 Carnaleagh (Ire- Goat Fell . • 226 33 45-23 || 5 || I-65 o' 17 land) . . . 53 32 46.93 || 6 || 8.26 2.77 |Pladda Lighthouse 253 3 28-61 || 4 || 5.53 I-97 Knocklayd...', ' | 61 3 5-36 || 7 || 4:40 o.8o Brown Carrick 26o 40 38.75 | 5 || 2:32 o°24 Malin HeadLight- - Cairnsmuir on tº º house ... . . ." | 94 58 17.70 || 4 || 7-oo 3.18 Deugh . . . 272 57 53.02 || 4 || 6.29 2.8o InnistrahullLight- Ailsa Craig 278 42 32.93 || 6 || 5:71 I-20 house • 98 52 15:29 || 5 || 5-13 | 1.38 || Benereard. • 296 18 5-oz Io 4:19 o'35 Oa . . . . I37 44 13.35 | 4 || 6.82 || 3:03 || Corsill Lighthouse 31o 26 33-22 || 3 || I-II o'14 Ben Tartevil . 137 53 35'52 || 6 || 5.77 | 1.12 || Cairn Piot 316 39 50.83 || 7 || 5-27 | O'93 Jura . . . . . 167 55 24.8% | 4 || 7.70 || 4:42 | Copeland Light- : I, c. – ’ 61 Ben More in Mull 173 19 49.86 || 4 || 5-25 || 2.18 house . . . . .346 28 29.77 || 5 | sº O - 94. PRINCIPAL TRIANGULATION, CARRIGFAIDDA. 3-ft. Theodolite, B.o. IFrom 21st to 3oth July 1832. Observer: Capt. PopTLoCR, R.E. No. Recip. iº ſº No. - Recip. Objects. Bearings. of Range. ... of Objects, Bearings. of Range. of Obs. Weight. Obs. Weight. O f & f - f/ O £ £/ *g 7/ Cruckmaddee . . 72 52 41.06 || 5 || 4:34 I. I.4 Caherbarnagh I72 35 7'42 | 9 || 9.og | 1.25 Mount Gabriel 74 22 40-11 || 8 || 5.75 I'oZ || Mushramore . I90 45 26-31 || 4 | 1.58 o.16 Mount Ridd . . 81 54 23.13 || 6 || 4:51 o'78 || Corrin tº 232 27 13-99 || I5 7.52 o.76 Cruckrowra, . . . 9o 54 I-73 || 2 | I-52 o'57 || Mullaghcorrin 238 8 50.89 I tºº 6.99 | Hungry Hill . . . 97 I 53.41 Io 4.78 o.46 |Doolieve . . . . 248 26 54.97 Io 8.48 || 1.25 Mangerton | 1.44 20 53.95 || 2 | o-29 o.o.2 | Ballyroe . . . . 263 3 20:55 || 4 || 9:45 6.36 CASTLECOO. 18-in. Theodolite, From IIth to 23rd October 1826. Observer: Lieut. MURPHY, R.E. No. Recip. No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. i. O f f/ // " tº O & & f A/ Kippure ...: ' || 3 51 34.56 || 2 || 4-27 | 4.55 | Slieve Gullion 163 36 II.43 || 8 || 8.38 2.38 Garristown Wind- Carlingford 186 9 25, 18 I2 15-ol | 1.98 mill . . . . . . . I9 I6 II.47 || 3 || 9.85 | 11.17 | Slieve Tonard 206 53 8-17 | 5 || 13.05 8.79 Loughanleagh ' | IoS 3o 51.5o || 4 || 13.1% 12.25 | Lambay . 333 6 23:31 || 8 || 9.38 2.97 Mullyash . . I48 41 45-57 || 1: – 25.25 CHEVIOT. 2-ft. Theodolite. From 16th June to 13th September 1846. Observer: Serg, BAY, R.S.M. No. Recip. No. Recip. Objects. Bearings. of IRange. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. Q Af f/ Af O ſ J/ # £f Cross Fell . . . 14 18 57.45 18 4.11 o.19 | Blackheddon. 2.17 20 55'77 22 8.82 o.38 | Sca Fell . . . 31 21 4.26 12 4.10 o-16 || Referring-object 246 9 15-off 171 6:53 o.ör Wisp . . . . . . 67 49 9.oz | 16 || 4-28 o-25 || Alnwick 285 39 56:36 | 18 8.2% o.41 Iſart Fell . • | 84 53 4.68 21 8.02 o.33 Rufflaw, New 319 49 48-3o 18 3.71 o.68 Dunrich • 99 27 31.60 | 17 4:59 O' I5 Easington • • | 32O 6 40-56 I4 || 4 Io o, 17 Carnethy Cairn 12o 17 24.45 18 4.92 o. 12 || Wordeslow . . . 326 28 56.98 || 26 4.04 o.16 Allarmoor . . . . 123 4o 25.41 Io 2.93 o. 15|Botton Head . 339 5; 39.5% I5 || 3:47 o.og Sayrs Law • . I4I 22 39.87 I6 4.46 o:23 Pontop Pike . 34o I8 3I'55 I6 6. II o:23 Lumsden . . . . 175 26 34:37 . I2 6-ol o°58 Collier Law . 352 7 34.67 17 6.23 O'24. Mordington • 187 IA. I.4.90 20 7. II o'I9 *=-º- OBSERVATIONS. 95 * A correction of – 8"'o6 to be applied to this bearing, to reduce it to the trigonometrical station. CHINGFORD. 3-ft. Theodolite, B.o. and R.S. From 31st July to 28th August 1823. Observers: Capts, KATER and DRUMMOND. Prom 19th April to 29th May 1848. Observer: Serg, Don ELAN, R.S.M. º No. Recin. No. Recip. Objects. Bearings. . Range. º Objects. Bearings. . Range. º p Obs. Weight. Obs. Weight. Greenwich Obsery. o 5 £65 26 1663 o-22 || Hornsey Hill . . 48 53 28.65 26 6.57 o. 18 IHundred Acres . 21 43 17.66 I3 3.78 o. 15 Berkhampstead” 147 30 13.36 46 Io.28 o.12 Hanstead • , . . . . 22 42 7.12 I5 5.08 o.21 || Wrotham . . . 33o 38 38-42 52 8.18 o. 12 St.Paul §Sathedral 26 14 16.40 45 9:24 o. 12 | Severndroog • 347 13 40-48 |164 12-32 o.o.4 |Heith Hill (1822)"| 26 5ſ 17.78 i8 || 3:54 o.19 || Greenwich Óbser- WestminsterAbbéy 30 4 46.70 || 27 | 6′36 o.13 | vatory Transit. 359 59 53.97 | 11 5.09 o.26 * A correction of — 1' 19"'88 to be applied to this bearing, to reduce it to the trigonometrical station. * A correction of + o” 29 33 33 33 CLEISHAM. 3-ft. Theodolite, B.O. From 13th June to 27th August 1840. Observers: Lieuts. RoßINSON and HoRNBY, R.E. No. IRecip. No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of | Range. of Obs, Weight. Obs. Weight. º O f Af f/ * O # Af &/ Ben More, S. Uist 20 22 12-og | 7 || 6.82 | 1.32 || Fashven º 238 29 26.47 || 4 || I2.65 Io:31 North Rona . 2O3 49 54. I4 || 2 | o'67 o. II | Cuinnag • 254 Io 59.52 || 3 || 6′33 || 4.83 Monach • . . . 213 52 I-75 18 8.46 o.61 Ru Rea ... • 282 30 37-30 || 4 || I'o6 o'o6 Cape Wrath.Dight- Scournalapichl 3or 34 44-23 || 3 || 5-14 || 3:38 house . . . . . 234 30 21.85 || 2 | 1.53 o'59 || Mamsuil . . 306 I6 33-25 | I - I2 II Cnoc-ghiubhais 236 25 36.92 || 4 || 2.76 o.53 || Storr 323 19 56.97 | 12 || 4.90 o'47 1 A correction of + 33"-81 to be applied to this bearing to reduce it to the new station. CLIFTON BEACON. 3-ft. Theodolite, B.O. From Ioth to 23rd August 1801. Observer: Mr. WoOLCOT, From 26th April to 21st June 1842. Observer: Lieut. LUYKEN, R.E. Beari i. IRecip. Beari . T Rºjº. iects. earl InfºS. tº iects. Tings. allºC. i. Objects arings o:S. Itange W.3.ht. Objects Càrl di. § Weight. J O f W/ # / i. O f A/ A/ Referring-object 21 34 35.89 || 71 || 7.22 o.o.4 || Wilton Beacon 206 30 7.19 || 5 || 4:56 o,88 Lord's Seat 73 32 15.70 || 6 || 3.98 o.76 Nunburnholme 214 31 13-28 || 2 || 2:78 I-93 IBack Tor . 81 5o 59.99 || 6 || 5-53 | 1.03 || Hunsley 228 1 36.1o | 8 || 3.96 o°34 Holme Moss . IoI 5o 38. I5 || 6 || 11.76 4.77 | Crowle. . . . . . 236 47 8.69 || 6 || 3:39 o,6o Great Whernside 147 556.08 || 2 | 1.58 6.6% | North End Base . . 248 57 57.20 || 9 || 12.6% 2.89 Ledstone Beacon | 169 26 45-54 || 2 | 1.43 o. 51 | South End Base 269 45 20:49 6 || I5-48 || 7 º York Minster. 189 II 3-57 || 7 || 6, 15 | 1.31 || Gringley Beacon. 283 42 43-48 || 12 || 3:53 || 2. Acklam Wold 203 20 26-08 || 4 || 2.96 o.65 Lincoln Minster". 298 21 47-55 9 #36 o°52 96 PRINCIPAL TRLANGULATION. CNOC-GHIUBHAIs. - 3-ft. Theodolite, B.o. From 3rd to 18th September 1838. Observers: Licuts. Robinson and PIPON, R.E. Objects Bearings *: IR Rºº. Objects Dearings. *: Range. Rj. Jects. gS. o. |*|w.ht. Jects. Obs. Weight. m-- O f f/ &/ º O / // Z/ Cuinnag 5 23 12.52 II | 12 oz 1.62 | Ben Hutig 277 32 Io-og I4 5-53 o.26 Suilbheinn 9 46 36.02 || 8 || 8.47 | 1.28 || Fashven 297 18 35-49 II | 13.62 || 3-12 Monach . . 72 22 28.43 || 8 || 16.06 5-84 || Ben Hope: • 3IO 51 58.85 || 8 || 8.68 2. Io North Rona • 141 36 47-oi | 3 || 12.68 17.95 Foinnebheinn. 342 51 49 oz | 5 || 7-63 2.89. Dunnet Head. 263 34 II-66 2 o' 13 o.o.1 COLLIER LAW. 3-ft. Theodolite, R.S. From 22nd June to IIth August 1851. Observer: Corp. GROSE, R.S.M. bié Beari No. Recip. Beari *: R Rºjº. iects. º iects. º O àIlºe, Objects earings o: Range. Wi. Objects earings Obs. 8 Wit. O / / / &/ O / / / f/ Water Crag . I3 I2 44. Io | Io 8.21 o.86 | Durham Observa- Cross Fell. 77 I4 36.58|32 || 7.73 o.21 tory Dome . 27,o 33 42-27 | 9 || 5-84 I-II Cheviot • I72 I5 48.84 22 9.74 o.41 || Brandon 275 I2 46.83 || 9 || 8.68|| 1.44 Rathbury Crag • 187 44 42.56 4 || 3-19 o.91 | Easington : 286 56 II.og 22 || 4.5I o. II Rufflaw, Old . 195 I6 52-13 || 7 || 7-05 | 1.35 | Burleigh Moor 289 51 5-29 I4 || 7-oo o-39 Tufflaw, New I95 19 21'oz | 12 || 7.25 o.53 || MerringtonChurch 292 48 19. II || 4 || 5:55 2.58 Pontop Pike . 23o 26 I6.25 5 4.67 o'98 Botton Head 3O4 49 56.87 24 7-35 o°23 Wordeslow 256 o 29.8o 27 | 6.33 o.17 | Black Hambleton 317 24 16.61 || 6 || 6.35 | 1.69 CORINGDON. 3-ft Theodolite, B.O. From 22nd February to 14th March 1845. Observer: Serg. DONELAN, R.S.M. * No. Recip. º No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of Range. of Obs. Weight. Obs. Weight. # C f f/ Af º O / // &M Swyre Barrow 69 5o 19:45 14 555 o.39 || Dean Hill; 207 54 8-11 || 9 || 5:37 . o.6o Blackdown • 99 I3 32-31 || 9 || 6.55 o-66 Butser Hill 24, 5 44 oš 15 9.77 o.67 Pillesdon • Io8 33 23.60 | 16 || 6.65 o-31 || Nodes Beacon' 262 33 36.41 || 4 5-O2 2-ob Wingreen . 168 5 3.87 15 6.16 o.41 Motteston 264 56 II.06 || 3 | 1.87 o°43 Horton's Gazebo | 18.4 56 44.56 || 4 || 3:55 o-93 | Dunnose 27I 4 I6-31 | 16 || 5-oo o:31 Beacon Hill . 196 52 41-31 || 9 || 6-44 o.8o am – 1 A correction of –58"'76 to be applied to this bearing, to reduce it to the trigonometrical station. OBSERVATIONS. 97 CORRY HABBIE. 3-ft. Theodolite, B.O. From 6th September to 21st November 1850. Observer: Corp. JENKINs, R.S.M. * No. Recip. No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of Range. of Obs. Weight. Obs. Weight. Glashmeal tº 11" 17 3#68 22 6.33 o.26 Referring-object . 204 46 1896 31 8 of o. 21 Ben Macdui . 43 17 Io. Io 35 | 4.99 o.o.7 | Bin of Cullen 208 20 34.63 ||31 || 5.53 o. Io Ben Nevis 61 39 59. II 20 | 6.29 o.28 Cowhythe . . . . 220 II 24.43 42 8.40 o. Io Mamsuil 87 15 34.5I 27 7.96 o-24 Knock . . . . . 223 15 15-off 38 6.81 o.13 Scournalapich 92 II 19.91 31 6.82 o. 18 Alva . • 23o 24, 26.60 5 3.90 o.69 Ben Wyvis 114 46 22-oi 31 5.19 o.og | Manor Lee . . . 231 8 36.82 II 7.39 o.68 Ben Clibrig 144, 26 28.89 4o 5-oo o.o.8 || Mormonth . . . 247 8 17.88 47 6.25 o.o.9 Ben Tundie . 145 Io 30-27 | 20 5.98 o-28 || Dudwick . . . . 261 41 42.88 25 || 7.19 o.32 Balnaskerrish . . 147 9 35-52 23 4.15 o.o.9 | Buck 294 4I 33:81 59 5.23 o.o.5 Scarabin • 166 37 8.57 38 5.19 o.o.9 || Caerlock . . . . .313 35 1948 53 || 4.73 o.o.4 | Findlay Seat . I73 59 26.02 47 4.85 o'o6 || Mount Battock • 327 48 37. II 59 6.26 o.o.5 Ben Cheilt I74 22 46.32 || 34 5-oo o. I4 COWHYTHE. 3-ft. Theodolite, B.o. From 16th November 1846 to 8th February 1847. Observer: Serg. DoNELAN, R.S.M. No. Recip. No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of Range. of Obs. Weight. Obs. Weight. I Buck . . 23 6' #17 IO 8.76 I. 26 || Bin of Cullen 81° 7 43.42 18 3.87 O's II Enock Hill 31 57 I-24 41 9-og o-22 || Ben Lundie . 113 10 18-25 || 14 5-ox o'68 Corryhabbie . 40 38 28.86 22 8.09 o-36 Scarabin . 137 44 25-66 24 14:56 o°6o Referring-object | 66 27 31.99 |133 4.98 o.o.3 Ben Cheilt . I49 25 32-83 20 || 4-51 or 13 CRADLE, 3-ft. Theodolite, R.S. From 1st August to 3oth September 1843. Observers: Lieut. LUYREN, R.E., Corp. CoSGROVE, and l?riv. STEwART, R.S.M. No. Recip. No. Recip. Obj sets. Bearings. o: * Range. W.3.ht. Objects. Bearings. d;* Range. W#ht. Dunkerry . 20 19 $41 7 303 o. 12 | Cader Idris 147 31' I #31 7 £66 I-27 Paracombe 3o 57 14.8o | 8 || 2.95 o-31 || Snowdon . I52 51 22.89 I3 4'94 o'29 Llangeinor 42 5 53-oG | 6 || 2:41 o.24 || Llandinam 157 43 49-39 || 5 || 4-76 || 1:29 Precelly 90 19 41.91 || 9 || 3:37 . o.21 | Arrenig 158 42 28.89 || 3 || 4-64 2.99 New Inn . • 92 43 36.82 5 || 2:32 o.38 Radnor Forest 171 37 6.76 || 8 || 2:38 o' 16 Referring-object . 13o 56 37.98 |119 5.38 o-31 || Long Mountain | 181 44 18:51 || 5 || 6′33 | **ś Plynlimmon . . . 142 1 54.68 || 9 || 5.67 o.65 | Stow 190 o 66.69 || 7 | 5-63 || 1:04 PRINCIPAL TRLANGULATION. CRADLE–continued. No. Recip. r No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. O * f/ £/ ſº O Z Z/ f / Longmount Pole 194 54 16.52 || 7 || 3:II o°37 || May Hill . . . . 278 1838-14 || 4 || 0.8o o.o.4 Wrekin... . . . . 205 47 33-04 || 7 | 1.68 o'o6 |White Horse Hill|290 42 9.08 || Io 2.or o.o.7 Brown Clee . 2II 18 39-36 || 3 | 1.07 o°16 || Trellig . . . . 368 41 49-05 || 2 | 1.93 o-93 Malvern '... . . . 252 8 48.97 || 6 || 3:23 o°38||Dundry . . . 331 33 3-59 || 5 || 5-27 | 2.62 Broadway. Tower 264 17 55.98 || 4 || 1.37 o.12 || Mendip ... . . 333 38 o'61 || 4 || 1.81 o.22 Cleeve, Old . . . 272 13 26.80 || 6 || 2:37 . o.18 Staple Hill . . . .358 33 48.29 || 3 || 2:51 o.76 CRAIGOWL. 3-ft. Theodolite, B.o. * From 5th June to 4th July 1817. Observer: Mr. GARDNER. No. Recip. No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of Range. of Obs. Weight. Obs. Weight. Calton - § 3. 5%2| 6 || 3:1, o'Asſ Mount Battock ‘lace 22 3:39| 9 || 8:27 o'99 Allarmoor . Io 38 I3-88 || 5 || 6-42 I-85 Caerlock . . . . 212 52 4o'o6 || 6 || 4:74 o. 9o East Lomond • 20 37 o.o.3 25 || 7-2I o-27 | Broxy . . . . . . . 227 4 Io'96 || 4 || o-og o-oo Ben Cleugh . 49 27 15:14 || 7 || 2.98 o-22 || Red Head, Old 256 33 58.02 || 15 Io.94 o.81 Ben Lawers . . . 9o 15 46-09 || 4 || 3:33 o'81 Kellie Law • 336 25 9.77 I4 6.71 o°59 Glashmeal. 149 17 55-46 || 9 || 7-32 I'o6 || Largo Law • 351 o 23-14 21 7.92 o-38 CRIFFEL. 3-ft. Theodolite, B.o. From 23rd May to 8th June 1841. Observer: Lieut. HoRNBY, R.E. - r No. | Recip º No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. Q f // (ſ o / // A/ South Berule : 37 49 46.62 I – I3-II Dunrich. 2OI 41 I2.5o || 6 || 6.90 | 1.88 Glasserton - 65 18 19.66 || 3 || 5.61 3-53 Wisp Hill . 227 32 Io'97 || 6 || 9-os | 3:28 Ben Cairn. • 67 9 45-68 || 4 || 2:04 o.43 Burnswark • 232 22 17.8o 2 o°52 O'o6 Cairnsmuirof Fleet 95 9 29-16 || II | 8:40 o'81 || Cross Fell' ' ' || 289 21 43-38 || 7 | 12:38 5.59 Merrick . 112 43 29.77 | 12 6.24 o.41 || High Pike. . . 305 29 24.46 || 9 || 12.62 3.3% Goat Fell . 128 9 45-25 || 3 || 3-17 | 1.18 Helvellyn . . . 319 14 2-04 || 8 || 9-52 | 1.83 Cairnsmuir on .# $ga Fell ; ' ' | 333 25 22:23 || 9 || 6.35 o.92 Deugh . 133 30 o'32 || 8 || 4-72 9:55 |Black Comb 345 34 20.76 || 4 |1138||11.79 Hart Fell 195 28 13:51 || 7 || 3-91 || 3:56|Dent Hill . . . . .349 22 17-37 || 8 || 6.1o o.84 i OBSERVATIONS. 99 CROGHAN. 3-ft. Theodolite, B.O. From 3rd November 1828 to 13th January 1829. Observer: Lieut. PopTLoCK, R.E. * | – . * No. Recip. No. Recip. Objects. Bearings. of IRange. of Objects. Bearings, of Range. of Obs. Weight. Obs. weight Q & & f & f © f £f // Keeper. 45 16 30. Io || 6 || 12.96 || 5-26 Slieve Donard 223 25 7.76 I - I3'54 Knockastia II4 7 27.5o 24 II-75 o.77 | Lyons Hill . . . 276 51 29.20 II 7.07 o-81 Slieve Bawn, South 128 38 36.64 | 1 – I3-54 Kippure . . . 286 7 9.66 || 5 || 7-36 || 2:36 Qarn Clonhugh ' | 150 13 5-oğ | 5 || 2.47 || 3:33 || Hill of Allen . 295 2. 27.76 34 II-7I o°35 Cuileagh . • I59 56 18-91 || 3 || 9-05 || Io.56 || Church Mountain 3o4 49 32.95 || 3 || 9.88 || 12.96 Knockeyon I77 44 48-49 2I II.33 o.65 | Dunmurry • 305 21 47.83 22 Io. 9o o°59 Ben of Fowre 186 37 20-or | 8 || 8.87 I-42 Lugnaquillia • 307 26 58.39 || 6 || 4-48 || O'79 Slieve-na-Callia . 193 52 51.52 13 || 7.02 o'64 Cadeen. . . 313 3 15-93 || 5 || 4.88 I-33 Loughanleagh 201 32 28-89 || 5 || II.38 5-40 || Mount Leinster 337 21 56-46 || 2 || 2:59 I-67 Slieve Gullion 212 31 31.85 || 2 || 2.99 2.23 Cullenagh . . . 358 IG Io.67 Io 6:28 o'70 CROSS FELL. 3-ft. Theodolite, R.S. From 3rd October to 27th November 1841. Observer: Lieut. PIPON, R.E. tº No. Recip. No. Recip. i Objects. Bearings. of Range. of Objects. Bearings. of Range. of Obs. Weight. Obs. Weight. O / // & / C f f/ // -- Sca Fell i. 59 42 28. I4 I2 || 7.68 o.83 || Wisp . . . . . I54 46 49-oo || 5 || 5.5o I-69 Helvellyn ' ' ' | 6o 27 46-04 || 5 || 3.23 o-57 | Dunrich • I55 34 44-83 I — 8.52 High Pike. 90 38 39.84 || 3 | 1.85 o-42 | Cheviot . . 194 2. 34.32 || 6 || 8.92 || 2:51 Ben Cairn. . . . . . Io2 I 22-25 || 2 | 1.84 o.84| Collier Law. . . . 256 5o 16.58 || 3 || 3.79 I-90 Cairnsmuir of Fleet IoS 2 34.70 || 2 | o 27 o.of Botton Head . . . 289 27 25.84 || 9 || 9.72 I-69 Criffel * IIo I7 46.33 || 9 || 8.92 | 1.85 | Black Hambleton 298 20 2.13 || 4 || 9.8o 7:20 Merrick i. III 43 5o-93 || 4 || 6-80 || 3.05 || Water Crag • 320 28 22.19 || 4 || 2:53 || 0:44 Cairnsmuir on Great Whernside 332 5 31.69 || 9 || 8:41 I-71 Deugh . . II9 49 31-27 || 2 || 3.47 || 3-ol Little Whernside 354 4 8:57 || 4 || 7-02 || 3:47 Burnswark . I31 o I9'O3 I tºng 8.52 | Ingleboro’. . . . .354 26 22-of 4 || 4:32 I-31 Hart Fell . I43 42 25.97 5 || 6-89 2-oo CROWBOROUGH. 3-ft. Theodolite, R.S. * From 19th to 22nd September 1822. Observers: Major-Gen. Colby, Capt. KATER, and Mr. GARDNER. Obi * No. Recip. ſº * No. Rºjº. bjects. Dearings. o: * Range. W#ht. Objects. Bearings. o: i. Range. win t. Leith Hill of 1822|11o 17 1998 || 23 || 3:58 o'o6 |Tolsford 26. 59.3%;6|io || 4:37 o'4° Wrotham,. 197 22 34.93 || 23 3-27 o.o.5 Fairlight . . . . . . .301 4 59.55 I5 || 4-27 | **9 Stede Hill 239 20 55-76 I6 2.82 o.o.9 || Brightling Obser- " * Frant Church 239 33 36.94 22 3-67 o.o.5 vatory Dome . . .303 30 12.56 || 4 || 491 | ** * A correction of — 59" of to be applied to this bearing, to reduce it to the trigonometrical station. IN 2 IOO i PRINCIPAL TRLANGULATION. CROWLE. 18-in. Theodolite. From 9th April to 2nd July 1842. Observer: Corp. STEEL, R.S.M. #:º No. Recip. i. No. Recip. Objects. Bearings, of Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. | Gringley O Z // & / Hemingboro'spire 14939 1729, 7 | 828, 1.78 T111ſº º • IO O QC). OI •44 || 3°3O mingboro Spire * • 2. I-7 Čfifton Beacon . 57 6 #. % }; I-5 I Ackiam Wölä 183 Io Io:29 || 6 | 12.86 5.80 Back Tor....: ' | 69 54 15-30 | 1 – 11.23 || Wilton Beacon I85 31 9:35 | 3 || 5.5o 4.02 Garforth Cliff II 8 13 57.76 || 7 of I.33 Nunburnholme I95 I3 52'95 || 2 || 3:43 2.94 Ledstone Beacon | 119 26 7.63 | 1 — II.23 Hunsley • 218 5 45'99 || 5 || 7-63 2-4I Great Whernside 128 57 43.64 || 1 — II.23 Lincoln Minster". 335 9 31.57 || 4 || 3.82 I-14 1 A correction of — Io" 12 to be applied to this bearing, to reduce it to the trigonometrical station. CRUACH-NA-SLEAGH. 3-ft. Theodolite, B.O. * From 11th December 1847 to 17th January 1848. Observer: Serg. DoNELAN, R.S.M. * No. Recip. No. IRecip. Objects. Bearings. of Range. of Objects. Bearings. of Range. of Obs. Weight. Obs. Weight, O / / / £ f C & // Af ICnocklayd I7 24 40.56 I tº 2.52 || Ben Lomond 262 52 34.90 I tº ſº tº 2.52 Jura,. . . . . 35 43 9-69 || 3 || 415 | 1.93 || Ben Tuire 35o 37 41.46 || 2 | I-II o.30 Ben More in Mull 152 35 29.68 I º 2.52 CUILCAGH. 3-ft. Theodolite, B.O. From 17th June to 12th September 1828. Observer: Lieut. PortLock, R.E. No. Recip. * No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of Range, of Obs. Weight. Obs. Weight. - O / / / ... W/ tº O M. f.ſ. & f Keeper, . . . . Io 4o 26.23 || 5 || 2.5o o.44 || Slieve Gallion 228 37 19:oo Io, 5.88 o'42 Slieve Bawn South 17 35 59.45|| 13 9.46 | 1.31 | Shantavny 234 36 5-48 || 28 8.97 o-35 Mullaghanoe . 64 16 28.61 Io 6.20 o.74 || Carnmore . 257 35 33.56 || 38 || 12:33 o°36 The Reck ſº 68 43 5-24 || 7 || 4.5o o.65 | Vicar's Carn . 261 42 4I '93 Io 4.89 o'54 Nephin - 79 2. 26.60 13 6.45 o.68 || Slieve Donard 27o 18 14.77 I4 Io.27 o.82 ICnockalongy . 89 41 35.63 || 10 || 5.57 o-60 || Mullyash . 271 49 25-44 || 7 || 6-68 I •og Tawnaghmore 95 49 57.93 I – Io.85 | Slieve Gullion 275 I 35.5o I4, 7.24 o°55 Knocknarea 97 49 27.79 24 8.19 o.38 || Carlingford 278 50 I-34 I2 || 4:56 o°49 Slieve League 131 & 25-og 32 11.95 o.38 || Loughānleagh - || 298 i8 33:28 39 1933 o.84 Breesy . ... 157 48 9-92 || 31 || 7.98 o.32 | Slieve-na-Callia . 317 37 17:58 18 8.78 o.62 Barnesmore Connell||17o 22 28:50 || 4 || 2.75 o:55 || Kippure 318 45 13.93 || 2 | 8-73 19:05 Slieve Snaght 195 19 23.89 15 Io-oi | 1.32 | Croghan 339 30 33.70 || 6 || 8.98 || 2.68 Bessy Bell 2O6 26 33-oš 35 9:73 o.35 | Carn Clonhugh ' || 351 49 23.60 I3 8.1o o.79 Sawel . 215 39 52'24 32 13.98 o.49 |ICnockastia 351 57 33-04 || 3 || 3:39 I-56 Mullaghcarn . 216 18 24.75 27 | 16.60 o.33 OBSERVATIONS. IOI CUNDTHAM. 2-ft. Theodolite. July 8th and 9th 1829. Observers: Capt. DAwson and Lieut. MURPHY, R.E. * No. Recip. No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of Range. of Obs. Weight, Obs. Weight. ſº O f £/ Aff O & f/ # / - Slieve Snaght 95 58 46.73 II II.O2 | 1.71 | North End of Base 287 41 4-17 | 16 || 3-15 o.og Mount Sandy 271 3 29.92 | IG | 6-57 o.36|South End of Base 334 20 52.79 I6 6.23 o'29 Knocklayd . 272 9 28.4I | 3 || 3.90 I-69 || Sawel Mountain 352 II 23-23 || 4 || 4-4I I-70 CYRN-Y-BBAIN. 18-in. Theodolite. From 25th October 1852 to 24th January 1853. Observers: Serg. STEEL and Corp. WotRERSPOON, R.S.M. No. Recip. No. IRecip. Objects. Bearings. of | Range. of Objects. Dearings. of Range. of Obs. Weight. Obs, Weight. tº O & ff ſ'ſ O & Aſ Aſ Arrenig 7o 52 37.26 25 | 15.94 | 1.38 || Axedge 254 44 24:51 | 8 || II:32 || 3-89 Snowdon . . 93 32 7.78 17 25.20 3.90 || Mowcopt 262 4 49.5I I4 I2.98 || 2:05 Llanelian . 123 I3 54-09 || 17 22-25 || 3.82 || Longmount Pole | 339 o 47, 16 | 16 || 26.71 || 8-24 Delamere . . 237 49 28.74 20 29.61 5-86 DAN BURY SPIRE, 18-in. Theodolite. From 17th July to 15th September 1844. Observers: Corps. STEEL and BEATON, and Privates FRANCIS and WALLY, R.S.M. No. Recip. * No. Recip. Objects. Dearings. of Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. O f Af & f i O f Z/ # / Gad's Hill Obelisk' | 12 46 14, 15 || 2 | 1.30 o.42 Lawshall . 191 5o 44, 13 | 5 | 18-14 || 17-39 Wrotham . . . . . 24 24 27.90 Io 22.38 || 8.14 || Naughton . 211 3 22.62 | 5 || 6.88 2.64 Langdon Hill 3o 9 3.88 I4 17.41 2.61 | Stoke Tower . 2I 5 3.5 51-I 5 I9 || 30-90 4°13 Severndroog ~ 52 13 39-31 || Io 6.42 o'92 || Walton Tower 251 14 59.53 13 6.8o o'69 Epping Cupola 87 42 45-97 || 14 11.62 | 1.79 || St. Peter's Ch. Tr" | 303 22 17.85 13 || 23.57 | 6′49 Hatfield Broadoak II 8 19 30-56 || 4 || 2.53 o-45 | Norwood . . 331 45 61.21 | 19 || 13.42 I-64 Thaxted Spire I48 53 5.33 I9 9.53 o.78 Frittenfield 3.42 13 16.97 I2 8.94 o '95 . A correction of + 5'28"'57 to be applied to this bearing, to reduce it to the trigonometrical station. * A correction of + 2” 59 3y 33 22 IO2 PRINCIPAL TRLANGULATION. DEADMAN. 3-ft. Theodolite, B.O. * From 27th January to 5th March 1846. Observer: Serg, DoNELAN, R.S.M. º º No. Recip. * No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of Range. of Obs. Weight. Obs. Weight. Goonhilly Down • 54 18 1%, I8 #18 o:33|High Wilhays :: 227° 7 #79 25 £82 o. ICarnbonellis - 82 3 § 14 || 9-26 o'90 rº Hill Tower . : I7 32-14 || 8 3. 5o º: Karnbrea. Monu- Lansallos ... . . . 232 15 20.96 || Io 7.68 o.88 | ment. 90 5 I •og II | 3:17 o.18 Ryder's Hill . . 243 36 48.61 25 || 7-17 o-17 St. Agnes . . . Io? 54 51.68 14 8.88 I-97 Butterton . . . . . . 25I 28 13.69 || 6 || 3-94 o'55 Hensbarrow º 176 3 3.20 18 9-11 o.62 |Eddystone Light- Brown Willy . 198 55 44.82 | 15 6.66 o'3I house . . . . 276 3o 47-40 || 14 6.83 o.49 DEAN HILL. 3-ft. Theodolite, R.S. From 14th January to 17th March 1850. Observer: Serg. DoNELAN, R.S.M. in. No. in. Objects. Bearings. *: Range. hº p Objects. Bearings. . Range. Hºp tº Obs. Weight. Obs. Weight. & M. A M * # // J. J. Coringdon Hill . 28 1o 13.81 12 4.85 o-36 || Beacon E[ill . 164: 8 32.26 |32 || 5:29 o-og Swyre Barrow 33 31 58-37 9 5.og o-63 Old Lodge I8I 54 26.67 9 5.2 I O'45 Horton's Gazebo. 43 38 39.34 || 6 || 7-08 I '86 Inkpen 20o 5 37.03 21 | 6′48 o.19 Wingreen . • 81 12 15.66 15 5-98 o-48 IButser • 276 49 40.99 22 6.20 o.21 | Old Sarum Castle | 123 I 3 41.97 || 17 | 7.25 o-48 Ordnance Map | Four Mile Stone 124 39 30.90 I5 5.33 o°31 Office . . . 306 27 43.15 9 5.85 o'54 Westbury Down - | 126 52 I 8.39 23 6.5I O - 20 Dunnose - * | 324 54. 39.78 I9 IO-33 o:5 o Queen's Manor . I32 8 26.62 25 6.oz o'24. Motteston • . . 338 43 28-24 9 4'54 O'54 Stoke Hill 133 17 43.98 || 7 || 4.15 o'76 | Nodes beacon' 348 59 17.13 || 3 || 6.64 o.64 | Milk Hill . . . . I60 18 49.27 8 5'45 o-60 * A correction of – 23". 53 to be applied to this bearing, to reduce it to the trigonometrical station. DEERNESS. 3-ft. Theodolite, B.o. *. From 5th to 7th November 1821. Observers: Capts. WETCH and DRUMMOND, R.E. * No. Recip. No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of Range. of Obs. Weight. Obs. Weight. i O f & W Af O Af f/ * f South Ronaldshay 3o 34 I4’33 || 9 || 2.66 o. 11 || Fitty Hill. 158 59 5-67 5 2.53 o:34 Wart Hill Hoy 8o 46 20:56 || 9 || 4.5o o.37 | Stronsay . • 216 39 42-15 12 3.25 o.15 ; º * ‘OBSERVATIONS. Io3 DEL AMERE. 2-ft. Theodolite, B.o. From 24th April to 10th June 1842. Observer: Lieut. DA Costa, R.E. tº No. Recip. No. Recip. Objects. Bearings. of IRange. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. : º Ö f // &/ O & J f f f Long Mountain 23 1 51.44 || 1 || – || 6.78 || Lord's Seat 255 48 Io.5I | 5 || 2:16 o°27 Cyrn-y-Brain 58 I3 25.5I | 8 || 3:40 o.32 || Mowcopt . . 290 26 I2.34 || 7 || 9 of 2.23 | Garreg' . . IoI 20 56-27 || 4 || 4-62 I-73 || Mowcopt Tower 290 47 46.5o || 2 || 5-17 | 6.68 Heswell II.4. I3 40.96 || 8 || 8.77 | 1.75 | Nantwich Tower 327 I5 38-40 || 4 || 7-ol || 3:33 Billinge 176 17 23.65 || 6 || Io.53 || 3.71 | Ashley Heath 328 34 36.67 || 6 || 5.93 I.33 Rivington . 193 53 47-61 || 5 || 3:25 o-53 || Wrekin . . . . 351 36 I5'o6 || 6 || 2.66 o.25 Bellefield . . 205 19 16-17 | 5 || 4-18 o.88 Hawkestone Obe- Whittle . . 209 12 18-18 || 4 || o-97 o.o.7 || lisk • . . 354; 23 O-43 I – 6.78 Holme Moss . . . 236 13 26.23 || 3 || I-52 o-25 || Brown Clee . 355 58 39.69 || 2 | I-64 o'67 Kinder Scout . 25I 27 37.85 || 7 || 2-16 o-I2 s * The bearing of this point is inferred from the old observations at Delamere , and corrected for the difference of stations. See Description of Delamere. DOOLIEVE. 3-ft. Theodolite, B.o. From 31st May to 14th June 1832. Observer: Capt. PontLocR, R.E. No. Recip. No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of | Range. of Obs. . Weight. Obs. Weight. : O ſ f/ Af O # JA & f Ballyroe 31 I 7 19.93 || 7 || 6-45 I-32 || Rock Hill. I56 59 5.39 || 4 || I-76 o'27 Qarrigfadda 68 56 49-46 Io 3.43 o.19 || Knocknaskagh 182 45 25-82 I3 5.75 o'49 Corrin . • 74. I2 22-60 Io 5.42 o.67 Galtymore 196 31 16-22 || 4 || 4.5i | 1.56 Clara Mountain 98 9 20-14 | 11 6.02 o.56 || Knockmealdown 217 io 35.67 || 4 || I'92 || 0:27 Mangerton Ioſ I6 31.8o || 2 | o' 18 o.o.o Knockanaffrin 226 55 9.65 || 3 || 14-85 24:51 Mullaghcorrin III 31 26.20 | 8 || 3.59 o.27 | Bunnaloo. . 229 41 37.18 || 6 || 2:oo o'17 Caherbarnagh II8 44 15-15 || 6 || 8.76 2.72 | Slieve Grian . 24o 33 18:08 || 5 || 2:04 o'2I Mushramore . I25 4 4o'oz | 7 || 5.53 o.8o DITCHLING. 3-ft. Theodolite, B.o. From 16th October to 23rd November 1844. Observer: Serg. DoNELAN, R.S.M. No. Recip. No. Itecip. Objects. Bearings. of Range. of Objects. IBearings. of | Range. of Obs. Weight. Obs. Recip. D 68 o' 2306 6. 8 || Brightling Ob o f f* £f unnose. 9 23.90 I7 '35 | O-2 rightling Upser- Butser Hill • 98 I2 I 5.73 II | 6.20 o.43 vatory Dome . 258 42 6-og | 8 || 5-37 o.68 Leith Hill Tower 148 55 18.87 17 | 7.19 o.32 Fairlight . 272 44 54.21 17 || 7-13 9:47 Wrotham . . . . . 210 36 22.82 | 12 9.77 o.89 || Referring-object 274 23 17.16 96 || 5'55 º: Çrowbgrough. * 226 58 I7-92 9 8.39 I'34 Beachy IHead . 3C5 IO I9'43 II 3-56 o-3 Frant Ch. Tower 23o 19 50-67 || 4 || 3-62 I •o8 _mºnº- IO4. PRINCIPAL TRLANGULATION. DIVIS. 3-ft. Theodolite, B.O. From 24th July to 11th November 1825. Observers: Major-Gen. COLBY, Capt. ORD, and Lieuts. HENDERSON, Pontºock, DRUMMOND, and MURPIIY, R.E. º No. Recip. ſº º No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of Range. of Obs. Weight. Obs. Weight. §. g 11 36 4669 17 8:12 o. 53|Benereard . . . 233 5. 653 14 7:20 O'5I l §: ë. ion 26 go 41.0% 26 || 8.68 o.45|Merrick. . . . . 238 47 55.29 || 5 || 576 || 2:01 ś alºn v 47 21 16.71 14 || 4-7I o'27 Cairn Piot. • 245 23 I3-03 ; I2 I5'o3 2.43 R. . º 8o II 33.39 || 4 || 2.65 o'44 Cairnsmuir of Fleet 2.48 41 39-27 | 6 || 3-72 o-48 §. ..". 95 41 53°o? | 9 || 2:22 || O'I5 Mull of Galloway 267 28 50.03 I5 7.63 o'70 S . allion 16; 56 46.91 53 | 12.84 o-17 | Scrabo Hill • 279 57 o'35 | 13 II.58 I-52 §. ; , . . . Io9 5o 24-48 || 15 7.74 o'54 North Berule . . . 288 4 41.05 || 7 || 7.44 I-70 ieve Snaght. 128 I 45.91 18 6.85 o.24 Snea Fell 29O 20 52. I9 || 9 || Io-oo I-72 Benyevenagh , 134 30 7.62 || 5 || 6-27 | 1.99 || South Berule : 299 50 21.52 || 6 || 6-32 I-38 Inocklayd . . 166 24, 47.61 23 II.o.6 o'5o Calf of Man . . . .308 o 51.84 || 3 || 2:06 o-48 . • 169 44 31.59 || 6 || 4.8o o-'95 | Slieve Donard 352 27 5.77 24 I4.67 o'73 oat Fell . 2O4. 4I 46.7I I — 14.34 Slieve Croob 354 27 44.78 || 8 || I2.77 || 4-2I DOCKING CHURCH TOWER. 2-ft. Theodolite. From 31st May to 23rd July 1843. Observer: Corp. BAY, R.S.M. No. in. No. º Objects. Dearings. . Range. R p Objects. Bearings. . Range. Rºjº tº Obs. Weight. Obs. Weight. Referring-object . 46 4726. Io 35 ". – Boston Tower" roi" 2 5 2. 3.87 || 6 3.3% O-40 Lynn Old Tower; 42 14 21.87 || 7 || 2.95 o.22 | Baconsthorpe 272 16 3.47 || 6 || 4.1o o.65 Walpole St.Peter's 54 43 28.17 || 5 || 2.28 o.27 ' A correction of — 7"'86 to be applied to this bearing, to reduce it to the trigonometrical station. DRUNG POINT, 2-ft. Theodolite. IFrom 11th to 14th July 1829. Observers: Capt. DAWSON and Lieut. MURPHY, R.E. tº _ g No. Recip. No. Reci Objects. Bearings. f : Range. of jects. ings. P. * S earings o:S. ange Wint Objects Bearings o: Range. Wi.ht. O W f/ A/ C f J Mount Sandy. . . 256 53 42-oo 16 || 5-28 o-25 | South End of Base | 323 31 41. I º - North End of Base | 27O 39 53-II | 16 || 5 I 8 o'29 323 3 39 I5 5'oz o-31 t •.: º º OB SERVATIONS. 105 DUBLIN OBSERVATORY. 3-ft. Theodolite, B.o. June 1830. Observer: Lieut. PoſtTLOCK, R.E. From 9th February to 3oth 1.98 ~... • No. Recip. - No. Tecip. . Objects. Bearings. of Range. of Objects. Bearings. of Range. of s Obs. Weight. º Obs. Weight. 3 Fºr e O W & W. Af O / / / - */ Lyons' Hill, , , 50 39 55-52 II Io.42 I-25 | Dalkey Obelisk 3II 47 53.03 || 2 || 3-63 || 3:29 Maynooth Obelisk | 82 33 33.13 || 4 || 3:42 o.8ó | Brayhead Staff 323 43 41.66 || 5 || 3-17 | 1.23 Knockbrack . I94 25 16.54 || 5 || 5-63 I-83 || Fairy Hill. 339 I5 17:4I | 5 || 4-82 | 1.45 Howth . • 274 5I 53.68 I2 5-62 o.39 || Kippure 358 55 17:12 || 8 || 5-63 o'71 |Poolbeg Lightho. 29: 54 37.49 || 3 || 3:44 o.64 DUDWICK. 3-ft. Theodolite, B.o. From 10th to 12th June 1817. Observer: Mr. GARDNER. No. IRecip. * No. Recip. Objects. Bearings. of Range. } of Objects. Dearings. of Range. of Obs. Weight. - Obs. Weight. +. O £ Af f/ tº * O Af # / f/ Tarbathy . . . . . 4. 44 Io.26 || 7 || 4.89 o.86 || Corryhabbie . . . 82 40 Io. 12 || 4 || 3.81 | 1.42 Blue Hill . . . 8 18 9-13 I2 7.77 o'59 || ICnock . . . . . III 25 43.69 || 5 || 2:03 o-27 Qver Hill. I2 18 58.36 || 8 || 5.28 o.70 || Bin of Cullen II 7 54 31.29 || 5 || 5-90 I-47, Brimmond . . . 22 59 38.95 || 6 || 3.70 | o-45 || Manor Lee II.8 I4. I6-27 || 4 || 2:40 o°4I Caerlock . • 29 26 26.74 || 8 || 4-7I o.64 || Mormonth I8o 4I 45-33 || 7 || 4:37 . o.61 Mount Battock 38 47 11.36 || 4 4-31 | 1.47 Little Stirling 256 42 38.12 || 7 || 3.8o o°41 Buck tº º is 74 4o I-24 || 9 || Io-38 I-89 || Layton 357 52 36.86 | 8 || 5.87 I-97 | DUNIKERY. 3-ft. Theodolite, Rs. From IIth October to 4th December 1844. Observer: Corp. STEwART, R.S.M. No. Recip. - No. Recip. Objects, Bearings. of | Range. of Objects. Bearings. of Range. of Obs. Weight. Obs. Weight. º ſº g O / // Af O / / / * * A/ High Wilhays 29 29 12-14 Io 6.66 o.76 || Ogmoor 177 57 o'96 || 12 6.14 o°49 Kit Hill . . . 35 5 2.52 || 3 | I-40 || O-28 || Llangeinor 18i 3 25.39 || 9 || 7-3o o'81 Brown Willy 48 43 I 8.23 || 7 || 4-23 o.62 | Cradle . 199 57 12-28 || 13 8.53 o'72 Gadon Barrow 54 34 50.26 || 4 || 3-ol o'73 | Dundry . 247 58 II.47 || 5 || 3.92 o'73 |Referring-object. § { 9.98 || 78 5.78 o.o.4 || Mendip i. 264. 43 37.42 I2 4.49 o°29 £ºbe • 94 23 24-27 II | 8.06 o.77 | Staple Hill . 3o4 16 18.87 || 6 || 5.51 I-3. §. I37 4 47.oo || 4 || 2.58 o.5o Pillesdon . 306. 31 49.1o 18 7.82 o'47 i. ryn 14o 31 7.90 || 8 || 6.97 | 1.34 | Dumpdon . . . . .321 37 50-84 || 7 || 6-67 || || 3. M º I49 I4 IO-2O I Hº ; 6.32 |Little Haldon 356 31 37.90 || 3 | 1.56 || 0:49 argam I7o 4. o:35 3 o°45 $ O 106 PRINCIPAL TRIANGULATION, DUNMURRY. 3-ft. Theodolite, B.o. From 4th to 6th October 1846. Observer: Capt. PontLoCK, R.E. No. Irecip. No. Becip. Objects. Bearings, of | Range. of Objects. Bearings. of | Range. of + - Obs. Weight. Obs. Weight. Cullenagh . . 39 I' 48.78 2. 303 2.29 |Maynooth Obelisk 232°24' 693 I " | 5-OI Cushina • . . 88 19 52.22 || 3 || 1:56 o°27 | Hill of Allen ' ' || 232 59 54.91 || 4 || 3:57 || 0.80 Ballyduff. • • ‘Ioš 47 14.60 I 5.of Lyons' Hill ' ' | 2.48 42 7.53 || 4 || 5-06 | 1.71 ſº ICnockastia . . . 123 I7 39-40 || 1 tºº 5-OI | Kippure 272 57 26-2I | . I * - 5-OI Crºghan . . . . 125 38 36.96 | 5 || 3:31 9:49 | Slieveroe... ' ' |277 33 23.54|| 4 || 2:46 o'51 E[ill of Carbury . 171 55 36.56 || 3 || 6.94 || 6-08 || Lugnaquillia • 309 ió 59.41 || 1 || – 5-OI DUNNET HEAD. 3-ft. Theodolite, B.O. From 5th to 18th November 1838. Observers: Lieut.-Col. Robe and Lieuts. Robinson and " *** * * * * g w: -- PIPON, R.E. No. Recip. w No. IRecip. Objects. Bearings. of | Range. of Objects. Bearings. of | Range. of * - 5 Obs, |Weight. Obs. Weight. | - O / fM ; Aſ f O / // f / Ben Cheilt . . . o. 37 52-94 | 8 || 2:41 o.11 ||Fashven. ... ' ' | 83 o 19-40 || 2 | 2.77 | 1.91 Scarabin . . 14 29 35.8o || 3 || 3-16 | 1.38 || Wart Hill Hoy 184 o 6.45 || 5 || 3-64 o.63 Ben Clibrig . 51 54 43.99 || 6 || 2.80 o.37 || Deerness . . . . . . 228 29 3-oi | 1 * † = 3-2I Ben Hutig . . 79 ió 48-32 || 5 || 2.91 o.39| South Ronaldshay 242 55 15-92 || 5 || 3-67 || 6-64 DUNNOSE. 3-ft., R.S., and 18-in. Theodolites. t From 6th to 23rd July 1844. Observers: Corps. STEWART and CQSGROVE, R.S.M.; - 4th and 5th August 1846. Observer: Corp. STEEL, R.S.M. º No. in. No. Recin. Objects. . Dearings. of | Range Rºp • Objects. Dearings. . Range. º * * * * * * ... • Obs. Weight. 5. Obs. Weight. - iº - o 1 1/ Af o / // Z/ ' IBoniface Down • 3 40 12-69 || 9 || 12.60 3.38 Dean Hill... . . . [45 I5 29:58 || 17 4.89 o.15 | Wroxall Down 29 31 49'19 || 9 || 20:34 || 7-11 || Beacon Hill . . . . I49 5o 52-II | 6 || 4-26 1.17 Week Down • 48 5o 33-30 || 2 | oºgol 6.02 || Ordnance Map Swyre Barrow 89 5 44.64 || 9 || 7-88 o.98 Office • I56 21 32-09 || 20 6.55 | O-3 I Shanklin Down 9o II 43°37 || 9 || I5-52 6.11 Inkpen . . . . I67 I2 27.96 || 19 5.56 o.26 Coringdon 91 4 3.5% | 12 | 6’47 o.49 | Butser Hill . . . 200 58 27.85| 26 || 6.68 o.30 IBlackdown 95 5 6.88 II 4.61 o:33 || Rooks' Eſill 225 42 56-53 || 6 || 3-67 o.48 Nodes Beacon' . . Ioz 38 58.26 || 3 || 2:16 | 1.jó | Ditchling . . 247 IS 44 oz | 13 || 6-14 o-39 Motteston - Ioč 24 44'53 || 6 || 5.27 o.85 Beachy Head 261 55 24-63 | 19 || 7-91 o.53 Horton's Gazebo | II6 57 5:54 || 3 || 2:04 1.04 || Referring-object . 339 12 1999 |Iof 7.62 o.o.3 Wingreen . I22 50 5-64 I3 5:37 . o. 37 1 A correction of + 1' 22"'57 to be applied to this bearing, to reduce it to the trigonometricăl station. --º % *.*-.* - *- - :* tr* .-º- i} º OBSERVATIONS. Io? From 7th September to 3rd November 1850. Observer: Serg. DoNELAN, R.S.M. DUNIRICH. 3-ft. Theodolite, R.S. No. IRecip. No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of | Range. ...of - - Obs. - Weight. Obs. Weight. º O £ A/ f/ O & A/ Z/ - Criffel . . 22 2s 43-28 || 20 7.87 o-40 | East Lomond 178 I6 58-45 26 8.4I o-34 | Hart Fell . 36 53 25-12 12 || Io.42 I-20 | Calton Hill" . 18o 8 13.41 || 3 || 2.67 o.87 Tinto . . . 94 36 55-61 | 11 5.79 o.54|| Arthurs Seat . . . 182 o 55.67 || 5 || 8.68|| 4.52 Hill of Stake . IoG 47 32-53 || 4 || I-82 o-27 | Sayrs Law 226 23 12-69 24 || 13.54 o'56 Dungoyne I26 22 53 or | 3 || I-85 o.42 | Referring-object 242 28 42.12 || 45 || – I-64 Ben Lomond . . . 127 48 46.8o 17 | 5-15 o.19 || Mordington 249 o 32.5o | . I — 8.19 Bin of Campsie ' | 129 48 7.44 .7 6.21 | 1.15|Blackheddon . 264 8 52.39 |.I.5 5.29 o-22 Ben Cleugh . . . 152 5 27:Io 34 IQ. Io o-27 | Cheviot ... . . . . 278 36 II.46 || 13 || 11.38 || 1.45 Carnethy Cairn 169 4: 15.19 | 16 || 6-57 o.37 || Cross Fell . . . .335 o 4.58| 26 || 5.21 o.16 Allarmoor . . . . I 74 36 53.36 19 || 3.69 o'Io Wisp . . . . 336 38 43-84 || 9 || 5.02 o'57 1 A correction of — 4"-64 to be applied to this bearing, to reduce it to the trigonometrical station. IDUNSTABLE, + - 3-ft. Theodolite, B.o. - From 15th April to 29th June 1843. Observer: Serg. DoNELAN, R.S.M. - No. Recip. - No. IRecip. Objects. Bearings. . of | Range. of Objects. Dearings. of | Range. of - Obs. Weight. º Obs. Weight. O / ſſ a O f f/ Z/ *…, §ºtchamfly ... 59 14 IQ'o6 || 8 || 4.06 o°41 || Keysoe Spire • 189 44 Io.41 || 9 || 4-60 o'50 W hite Horse Hil 66 7 52. I2 Io 3-64 O. I 5 Royston • • 239 26 9.78 7 4°og o:63 Brill . . . . . . . . 84 46 8.25 5 | 6.98 || 2.33 | Tharfield . . . . 243 29 49.83 || 9 || 5.33 o'68 Epwell, Qld . Io9 54 3.20 | 8 || 3.25 o.24 Epping Cupola • 291 4 35-15 4 2-oğ o°35 . Arbury Hill ..' ..., |131 - 9 52:31 || 8 || 5.56 o.82 | Berkhampstead 292 43 21:72 || 8 || 8:45 I-35 Hanslope Church r - | | | | | | | | | Wrotham. . . . . .316 37 14.86 || 7 || 5.91 || 6.9% | \, Spire . . . . . I44 1443’59; 5 5.47 | 1.71 | Leith Hill Tower |351 35 21.66 II | 6’īo o°55 Naseby Church Tr. 133 33 59.36 7 6:34 o'96 |Leith Hill (1822)|351 25 56.30 to 5-60 o'53 EASINGTON. 2-ft. Theodolite. º * From 25th February to 12th April 1846. Observer: Serg. BAY, R.S.M. *— - - No. Recip. - No. Recip. Objects. Bearings. of | Range. of Objects. * Bearings.” of | Range. of. - Obs. Weight. º Obs. Weight. T--— O -- ſº Z/ jº s I5 45'1347 7 #62. I. I5 || Pontop Pike . . . 120° o' 23.67 | 6 || 2.63 o°31 §. Head . 4I 58 40-39 12 || 5.5o o-30 | Referring-object 128 38 55.03 || 75 4'92 || 9.9% jº . 8o 4o 59-20 || 2 || 2.72 | 1.84 || Wordeslow 130 16 57.13 | 18 I-30 || 9.9% ë.ºr 93 9 30.36 | 16 || 5.57 o.37 || Cheviot | 1.41. Io 55.97 II || 2:3 .# aw . roy 52 2.37 || 6 | 1.70 || 0.14 | Saltergate Brow. || 338 32 51.35| 3 sº 1.7 O 2 Io8 PRINCIPAL TRLANGULATION, ISAST LOMOND. 3-ft. Theodoſite, no. From 31st May to 14th June 1818. Observers: Major-Gen. Col.BY and Mr. GARDNER. ! No. Recip. No. Recip. Objects. Bearings. of | Range. ... of . . . Objects, Dearings. of | Range. of Obs. Weight. Obs. Weight. - O * £f Af O Af */ f/ * Allarmoor . . . 1 2 5 43.16|| 12 5-27 | o'29 |Caerlock . . . . . 207 58 I5'47 I * 8.04. Tinto . . . . . . 21 A. 16.75 Io 5.83 o.71 | Red Head, Old . 226 58 I5-57 || 3 || 2.62 o.86 Ben Cleugh . 79 43 I 7:45 I6 7. I5 o.53 Kellic Law . . . 268 26 28.86 || 7 || 5.71 | 1.44 Ben Lomond . 86 48 9-32 || 5 || 3:9.I o.94 || Largo Law . . . 272 48. I-55 13 Io-97 || I-28 Ben Lawers • II9 2 37.87 6 9. I3 3:25 Lumsden • 3oo 6 32-98 4. 5-O2 I-90 Glashmeal. . . 173 43 33.66 || 9 || 6.95 o.87 | Sayrs Law . . 321 48 56.96 || Io || 7-28 o.74 Mount Battock . . 26o 18 26-17 || 4 || 4.89 | 1.52 | Calton . . . . . .355 47 29. Io 13 3.89 o-21 Craigowl . . 200 26 40.18 I7 | 8.48 o.55 | Dunrich . . 358 I5 II.87 | 5 || 4:36 | 1.31 IEASTON CHURCH TOWER. 18-in. Theodolite. From 12th July to 22nd August 1843. Observer: Corp. STEEL, R.S.M. - & No. Recip No. Recip. Objects. IBearings. of | Range. of Objects. Bearings. of | Range, of Obs. Weight. Obs. Weight. O Aſ A/ £f O f # / * & W Naseby Tower 51 38 26-33 || 8 || 12-o; 3.84 St.Peter's Church, - # Tilton . . . . 93 56 59.86 || 8 || 8.49 | 1.5i Walpole . 257 I6 40.54|| 6 || 9.09 3-oo BuckminsterSpire | 1.45 28 58.47 | II | 9.99 || 2.37 | Ely Minster . 295 58 I2.89 || 4 || 5-48 || 2-off IBoston Tower" 219 5o 24-05 || Io 9-03 | 1.60 Keysoe Spire . 352 42 52°o2 || 9 || 4:59 O-7I Q 1 A correction of + 5°31 to be applied to this bearing, to reduce it to the trigonometrical station. BLMS HILL 3-ft. Theodolite, R.S. Prom 18th March to Ist May 1848. Observers: Corp. WINZER and Private BATE, R.S.M. f - - No. Recip. rt No. IRecip Object Bearings. of Tange. º º ry g Jects. Carl I.] c. *gº wit Objects. Dearings. ...] Range. wit m"- º t O J. A/ Af O & W/ # / | Ben More in Mull o 54 Io-27 | 27 | Io.47 o:30 || Ben Ival, North * Ben More, South + - Uist. . . . 128 Io 54.89 2. 3. I2 || 2:43 Uist - • | IoS 2I 55-30 || 28 || 6-30 | o-21 || Ben Nevis. . 292 58 35-7I 31 II.57 | o-37 i * | OBSERVATIONS. Io9 IELY MINSTER, º 2-ft. Theodolite. From 23rd July to 29th August 1845. Observer: Corp. BAY, R.S.M. - No. . Tecip. No. Recip. Objects. Bearings. of | Range. of Objects. Dearings. of | Range. of Obs. Weight. Obs. Weight. Tharfield . . . . 2 544 £iol 15 | 6’44 o:32 Walpole,St.Peter's 17 5. 48 #86 11 3.86 o:36 Cambridge Obser- º - Grey Friars' Tr., vatory Dome 29 II 5.49 || 7 || 3.43 o-31 || Lynn 193 I2 15:24 II | 4.99 o'34 Keysoe Spire . . 76 55 58.69 | 15 || 3:66 o.17 | Swaffham Spire". 236 5 (7.33 |12 || 3.48 o.o.7 Easton Tower II6 35 30-13 || 25 | 5.02 . o. 12 | Brandon . . . . 267 59 24-18 21 6.73 o°18 Peterboro’ Cathe- . . " | Newmarket . . . . .325 I 8-10 || 7 || 6-89 I-72 dral . . . II9 45 33-18 || 6 || 3:52 o'51 || Balsham Tower - || 352 39 30.66 I6 || 8-37 o'42 1 A correction of — 1"'53 to be applied to this bearing, to reduce it to the trigonometrical station. LPPING POOREIOUSE CUPOLA. 2-ft. Theodolite. From 15th July to 18th August 1844. Observer: Corp. BAY, R.S.M. No. IRecip. No. Recip. Objects. Dearings. of | Range. of Objects. Bearings, of | Range. of Obs. Weight. Obs. Weight. I . -T O Af # / Z/ O Af Af f/ | Severndroog Castle 9 22 54.73 || 8 || 6.16 o'92 | Dunstable . . . . III 35 39.86 12 2.27 o.og | Greenwich Obser- Tharfield . I62 43 6o-I4 || 15 5-8o o°39 vatory Transit 18 55 43.20 || 7 || 2.70 | o-22 || Thaxted Spire . . 208 25 13.79 | 19 11.31 o'85 Leith Hill Tower 30 30 33.72 | 13 || 4:34 o-31 || Danbury Spire 267 22 I-54. I4 12-og I’og St. Paul's, London 35 55 6-22 || 7 || 6.91 | 1.38 Hollingbourne 32I 55 58.07 || 9 || 3:49 || O'20 WestminsterAbbey 37 37 26-30 | 1 ſº 7.16 || Gads Hill Obelisk*| 323 41 36.34 || 2 | 6.79 II-52 Highgate Spire 51 33 38-i I | 8 || 3.75 | 6.39|Referring-object . 34, 30 4.97 |Ioo || – - Harrow Spire. . . 65 43 io.32 Io 6.36 o.55 Wrotham . 345 ig 56.54 15 7:35 | 0:46 Berkhampstead' IoS 47 45.54|| 8 || 7.02 | 1.f4 -- I 1 A correction of — "'88 to be applied to this bearing, to reduce it to the trigonometrical station. * A correction of — 2' 35" 55 33 33 33 FAIR ISLE. 3-ft. Theodolite, B.O. f r Observers: Major-Gen. Col.By and Capts. WETCH and DRUMMOND, R.D. i From 17th May to 3rd July 1821. No. Recip. . IR Rj. º º º ings. C. 0 Objects, * Bearings. o: º IRange. W#ht. Objects. Dearings o: S. ang Weight. O / / / † Af O / // A/ r) - Stronsay º • 46 ‘I6 36-41 || 7 || 2.22 o. I2 || Foula . . . . . 158 46 53-90 I3 I2:55 | ***3| Štart Lighthouse. 55 3 23.42 | 13 || 4.64 o-28 || Ronas . . . . 185 19 43-66 || 4 || 2:10 || 9°9 Nº. Ronaldshay Brassa . . . 204 33 28.32 13 || 7-22 || 2:49 Fi ºte: 67 & 55.78 || 9 || 7.89 | 1.06 || Noss 20% ºf 50.54|| 16 || 3-86 || 0:44 rty run. 7o I2 21.71 || 9 || 5.79 o.86 | IIo PRINCIPAL TRIANGULATION. FAIRLIGHT. 3-ft. Theodolite, B.o. From 5th September to 6th October 1844, and from 23rd to 29th August 1822. Observers. “Serg. -- - DONELAN and Priv. WALLE, R.S.M. Capt. KATER and Mr. GARDNER. No. Recip. f * 3: No. 1 . . Irecip. Objects. Bearings. o: IRange. Wi. Objects. Dearings. o: { } - hange wi. - o Z // • f : O / / / w/ Beachy Head . . 59 30 38.86 || 14 5-16 o-27 | Frittenfield 2O2 26 8.98 || 20 6.53 o.30 Ditchling . . . 33 18 32.69 | 16 |Ioo.88 o'82 || Tolsford • 23I 57 5-49 || 49 || 6.88 o.o.8 Brightling Obser- * | Paddlesworth . . . 234 o 14.67 | 16 || 4-60 . o. 23 vatory Dome . 119 5 43' 13 19 || 6-67 o-25 || Folkstone . 238 47 20.84 53 8.27 o. II Crowborough . . . 121 26 34°51 36 8.15 o. 18 Lydd Church. 247 38 28-55 | 6 || 4-40 || 0.73 Frant Church. 135 Io 5:47 19 776 o-45 | Blancnez , . . . . . 265 36 39.21 | 8 || 6.51 o.85 Wrotham . . . . . 15432 66°38 || 4o 5-o-; o.66|Referring-object 276 5 8.93||105 || – * Goudhurst Church 157 13 62.20 | 12 II-62 2.51 Napoleon's Monu- - Hollingbourne 184 6 13.85 13 || 3:46 o.33 ment. 281 45 15.87 || 7 || 5-96 o.95 Stede Hill. 186 29 1279 || 38 Io.21 o.29 || Montlambert . . . 283 ió 4.38 || 6 5. Io O'91 Tenterden Church 192 37 18:29 || 7 || 5.5o o.77 1 General Roy's station of 1787 bears 308° 4' o", and is distant 87° 73 feet from this station. From 25th September to 19th October 1839. Observers: Lieut.-Col. RoDE and Lieuts. Robinson and PIPON, R.E. FASHVEN. . 3-ft. Theodolite, B.O. Deari . IR Recip. Ob !. Beari . R Hºp. * nºs, O all ge. iectS. Carl IngS. Il QC. O Objects. earing Obs. ge will Jec º o, “ e Weight, o / // Af * O M / / "f f Cuinnag 12 48 33-30 || 14 5-15 o-31 || Wart Hill Hoy 246 4o 30.42 || 7 || 12.78 || 4-23 Suilbheinn . 15 38 33-34 || 6 || 7-03 || 2:39| Dunnet Head 26I 42 I-64 || 3 || 8.58 || 9-29. Cleisham . 6o 6 53-40 || 2 | I'oz o.26 || Ben Hutig 272 54 56.79 || 13 | 8.98 o.69 Monach 75 2 8-95 4 6.45 3'34. Ben-Hope - ſº 3I4. 1 23:19 || 7 || 5:32 o-92 Cnocghiubhais 117 22 59.36 || 5 || 12-83 || 16.36 || Ben Clibrig . 321 36 49:47 | 16 9.83 | 1.13 North Rona . 14o 6 24-27 | | | – || 21:36 | Foinnebheinn . 356 25 56-31 5 8-31 || 3.87 FEAGHMAAN. f 13-in. Theodoſite. * From 18th to 21st August 1832. Observer: Capt. PontLOCK, R.E. No. Recip. º No. Recip. oject. Dearings. di. Range. win. Objects. . . Bearings. o: IRange. w#ht. o / / / fº. tº * ºmº-º-º-º-ºmmº- sº r ... O W Af - - - Bray Head Watch . . . ; ; Brandon . . . 192 1449.67 3, 5 g 4.67 | Tower - • 52 47 6-23 4, #. 62.12 | Baurtregaum . 228 2 I4.02 || 2% ## | 73:16 Bray Head 35 33 48.73 || 4 || ##| || 8.94 |Knocknadober 236 16 53:63 || 3 || # 243.50 Mount Eagle . 16% ºf 34.26 || 3 | * 22:49 |ISnocknagante . 276 21 26-22 || 4 || Fº 2.05 OBSERVATIONS. III. From 20th to 22nd August 1821. Observers: Major-Gen. Colby and Capts. VETCH and DRUMMOND, R.E. FETLAR. 3 ft. Theodolite, B.O. i. No. IRecip. No. Recip objects. Bearings. of | Range. of Objects. Dearings. of | Range. of . Obs. Weight. Obs. Weight. : - O f : §: Head § 17 3927 6 388 o:57 || Wallafield . . I66 9. 43.84 I ". 3-O4 * • e º I3 18:41.21 I4 5.93 o.39 || Saxavord . . I83 7. 30.85 Io 3.47 o-3o j • * * * 56 18 50.78 21 || 3.46 o.o.8 || Balta . . . 196 II 26-oo | Io || 4:33 o-27 OIlāS • , , 73 25 42.34 I3 3.72 o. I6 FINDLAY SEAT. 3-ft. Theodolite, B.o. - Prom 24th to 27th August 1814. Observers: Major-Gen. Col.BY and Mr. GARDNER. tº No. tr k. Recip. No. 1. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of Range. of § i. - Obs. . . . . . Weight. - Obs. Weight - * * O Z // . Z/ o f ºf f/ Ben Macdui 24 38 3-54 || 3 | o'37 o.o.1 || Ben Chielt . I74. 27 40. I5 || 5 || 2: I5 | O'24 Ben Wyvis . . 98 33 33-31 || 4 || 5-46 2.21 | Bin of Cullen . . . 246 5 34.14 | 18 5:43 or 17 Balnaskerrish . I32 o 19-08 || 9 || 9-27 | 1.34 || Knock . . . 268 25 52.94 | I 7 || 5'57 o°35 Ben Lundie ' ' | #34. Io 42.64 || 9 || 4.7% o.53 FITTY HILL. 3-ft. Theodolite, B.o. bservers: Major-Gen. Col.BY and Capts. WETCHandl) RUMMOND,T.E. From 31st August to 21st September 1821. O 3-ft. Theodolite, R.S. * * > No. Recip. No. Recip. Objects. Bearings. of | Range. of Objects, Bearings. of | Range. of Obs. | Weight. Obs. Weight. .. O & Af * Fº f f/ &# Wart Hill Hoy 24 24 6-46 15 || 4.32 o.20 | North Ronaldshay O * * - Ben Hutig 47 22 36-28 || 5 || 0.81 o.o.5 Lighthouse 252 51 35.60 || 7 || 7-09 || I-73 Foula. ---. 207 49 40'42 12 5-28 o.33 || Start Lighthouse 271 17 27-27 || 7 || 5 13 o'79 Fäir Isle ºf 249 I 34-28 || 14 || 4,60 o.28 || Stronsay . 309 9 19.18 37 6-o-; o-oš Deerness . . 338 46 8.75 I3 || 4:56 o'30 IFOLESTONE.1 From 31st August to 27th October 1822. Observers: Major-Gen. Colby, Capt. KATER. Mr. GARDNER, and *=– Mons. ARAGO. º - No. IRecip. No. Recip. Objects. Dearings. of | Range. of Objects. Dearings. of | Range. of Obs. g Weight. J g Obs. Weight. Dungeness Light- O / / / # / South Foreland o ' " // 8 i 1OllSe tº º * - • ?? - .8 ſº + tº 37 59 31.30 II 6-28 o'55 | Lighthouse - 248 I 6.29 || 3 || 5-89 || 4:3 ; º * | 59 I4 I7-42 I7 || 4-75 o.22 NotreDame, Calai 288 4 42.67 || 4 || 3:37 o.8o Lydd 95 32 13.8o 21 || 4:49 o.11 || Blanchez . . . . 297 26 4'59 || 24 6.35 º: 5. Castl 337 45 23-of 3 || 5-37 || 3-32 || Montlambert • 33% 27 50.98 || 24 || 5:53 | *3 -Lover Uastle . 246 48 I3-93 I4 5°23 O-29 * 1 General Roy's station of 1795 is distant 3 feet from Captain Rater's of 1822, and bears from it 43° 55' south-west. 112 PRINCIPAL TRIANGULATION. IFORTH. 3-ft. Theodolite, wo. From 16th October to 2nd November 1829. Observer: Lieut. PontLock, R.E. 3-ft. Theodolite, B.O. No. Recip. No. Recip. Objects. Bearings. of l{ange. of Objects. Bearings. of Range. . of Obs. Weight. Obs. i. Weight. Q f Af £/ O & f/ Z/ Slieve Grian . 69 22 53-o? | 3 | I’or o. II | Winegar Hill . 181 40 26-47 | 6 6.42 I-45 Knockanaffrin 87 55 7.13 || 9 || 8.19 I-37 Lugnaquillia . 185 IO 57:2O || 3 || 2.53 o-71 Slievecoiltia 95 56 53.83 I4 Io. Io o-93 | Slieve Buy 187 26 13-24 || 17 5.2 o:32 Slicvenaman . 166 43 49.88 || 7 || 4-78 o.81 || Ballycreen. 191 7 5.46 || 5 || 14:24 Io-o/ Carrickbyrne º II 2 I 5 I-77. I9 7-22 O-47 Croghan & tº ſº 196 45.39°44 7 4.82 o,77 Brandon 127 43 41-22 || 2 | o-84 o. 17 | Carrickrew 20I 1646.76 I2 6.74 o-47 Blackstairs 147 32 57.9% 12 || 6-12 o.55 | Tara . . 208 38 21.85 20 7.32 o-3o Mount Leinster . 156 i8 9:36 13 || 3-99 o.17 | Procelly 287 52 45°o5 || 4 || 3:07 o-83 Bree Hill . . 162 34 48.35 | 8 || 5-69 o.74 JFOUL.A. From 10th to 3oth July 1821. Observers: Major-Gen. Col.By and Capts. VETCII and DRUMMOND, R.E. tº ; R Recip. IBeari . T Hºp. tº - ingS. O * 4. * işearl InſtS, º Objects. IBearin Obs. ange wº Objects ung ot. ange wit. + - O / // f / O / / / & f Start Lighthouse. 9 27 53°31 || 1 || – 4.72 || Yell. . . . . 23o 25 II.38 || 6 || 2.94 o-31 North Ronaldshay Noss Head 269 33 49-44 || 8 || 14-71 || 4:45 Lighthouse. Io 31 54-75 10 8.93| 1.41 || Brassa • • 27o 43 44-62 | 18 || 4-24 o'I2 | Pitty Hill. 28 36 39.4. 7 || 4:36 o.73 || Fair Isle . . 338 22 52.82 20 | 8.53 o'42 Ronas . . . . 219 I 41.38||12 || 7.75 o.º.) º FOUR-MILE STONE. 3-ft. Theodolite, B.O. From 27th November 1849 to 6th J anuary 1850. Observer: Serg. ToSELAN, R.S.M. . R Irecip. IBeari . R Rºjº. # * ~ * inſis. () Range. ſº à TIIlºs, gº Objects. IBearing Obs. will Objects. caring 0. ange wint o / // Af § O / // # / Wingreen . . . . 4959 50.78 I5 8.03 o'59 Thorney Down . 276 36 9-94 21 |º o:63 | Westbury Down. 138 12 43-21 | 16 || 6-03 ; o;8 || Queen's Manor . 296 3 21-18 30 6.70 | o-24 Stoke Hill. • I39 49 2-o& 17 19:21 o'81 |Old Sarum Gun . 3oz 26 40.85 27 | 6,66 o.18 Milk Hill . 186 46 9:28 Io 6-77 o'65 |Dean Hill . . . . .304 29 45-94 36 r 8.66 o.20 Beacon Hill . 232 24 45-97 24 Io'55 O'34 Qld Sarum Castle 308 28 58-60 || 48 H. 8-79 o. 15 Old Lodge 263 - 8 33.75 I3 7-08 o.62 | Salisbury Spire 325 19 51.8o | 9 || 8.53 | 1.27 OBSERVATIONS. II3 FRITTENFIELD. 3-ft. Theodolite, B.o. - From 17th June to 21st July 1844. Observer: Serg, DoNELAN, R.S.M. * No. Itecip. No. Recip. Objects, Bearings. of IRange. of Objects. Bearings. of | Range. of Obs. Weight. Obs. |weight #.º.; 2235's '56|| 1 || 3:37 .39||Wigham, . . tº 4:3; 15 gº 2:7; enterden Church Stede Hill . . II6 46 22.86 || 4 || 6.5o 2.92 Tower . . . . 34 15 10-37 Io 9.62 1.74 || Danbury Spire • | 162 25 27.96 || 9 || 7.81 I-o8 Beachy. Head 38 30 13.78 I2 9-27 | o-88 || Norwood . . . 179 46 36.71 || 7 || 4.94 o-84 |Brightling Obser- Walton Tower 203 2 35-14 | Io 3.72 o°26 Vatory Dome . . 49 55 50.43 13 4.31 o-40 || Referring-object . . 231 8 Io. II |IoS 3.71 o'oz | Goudhurst Ch. Tr. 68 45 26.86 || 1 || 5.94 o.68||St. Peter's Tower 246 11 41-31 || 1 || 7.58 o.89 Srowborough . . 7o 56 27.95 || 11 || 5.24 o.32 | Paddlesworth . 295 34 is 78 15 7.49 o'66 Frºnt Church Tr. 73 23 29.99 || 13 | 6.43 o.37 || Tolsford . . . . 363 45 51.94 || 7 || 5.52 o'95 | Leith Hill Tower 88 15 13.73 || 13 6.8% o.27 | Lydd Church Tr. 349 51 32-33 || 9 || 7-06 | I'5o GAD'S HILL. 2-ft. Theodolite. From 11th September to 25th October 1845. Observer: Corp. BAY, R.S.M. Objects Beari . Recip. Obi Beari No. R Rºº. CIS, ſº º *- J earings. C. S. Itange. wit ject3. earings di.º ange W* O f W/ &/ O Af £/ £/ Šºvºndroog ' ' | IoI 5o 59-3o 19 2.19 o.o.3 || Danbury Spire • | 192 46 53.69 || 14 || 3.87 o°19 St. Paul's . . Iod I 5-63 || 2 | 1.39 o.42 | Norwood . . . . . 269 54 51.79 19 || 2:49 o'04 Epping Cupola 143 54 53.6% 16 3.69 || o. 17 | Referring-object 307 II 50-o/ | 71 sº tº . Langdon . . I69 21 38-34 || 8 || 6.0% o.78 || Stroud Hill. . . . .31% 59 56.63 || 5 || 5-66 I-65 GARFORTH CLIFF, 3-ft. Theodolite, B.o. From 26th December 1841 to 12th April 1842. Observers: Lieut. HoRNBY, R.E., and Serg. DoNELAN, R.S.M. No. IRecip. No. Recip. Objects. Bearings. of IRange. of Objects. Dearings. of Range. of Obs. Weight. Obs. Weight. O Af Af ſ/ O & Af &/ Woburnstand Mo- Acklam Wold 231 54 50.20 | 15 Io.32 I'o6 nument . • I 56 23.12 || 8 || 11.21 4.68 Wilton Beacon 238 48 8.or 2 o-oo o°oo Stain Cross 23 45 54. Io II | 11.25 I-71 || Nunburnholme • 25I 30 o'92 || 5 | I-65 o°14' #. Moss . 5i 35 8.07 || 5 || 2.88 o.38 || Hunsley Beacon 267 38 58.19 || 5 || 6-7 || 3-18 #.º. - 94 5o 20.54|| 4 || 9-37 6.43 | Ledstone Beacon | 284 34 38.60 18 9.88 995 É. A. | 3: 34.5%| 7 | 16%| 4:4|grºws |297 36 5393 || 5 || 5**|, ... *Hambleton | 18; 3; 33.8%| 3 || 3:33 1.29| Gringley Beacon. 334 39 j.64 - I4'09 York Minster 223 I8 35-78 22 II.68 o:79 P l I4. PRINCIPAL TRIANGULATION. 1805. Observer: Major-Gen. Colby, R.E. GARREG. 3-ft. Theodolite, B.o Object I} *: IR - Rºy. Beari - . IR IRecip. º tº ange, O wº ſº º i. Jects earings. 6. § Weight. Objects earings d. S. ange wit • O f // fº o , a £f Arrenig . . . 35 33 31.5o | 7 || 5’25 o'91 |Gwaunysgaer II6 2 46.61 I5 3.28 o.12 Snowdon tº 0 º 64. 27 35-39 6 7-47 I-89 Billinge tº $ & 238 22, 36.66 4. 2°44. o,61 Llanelian . tº I 44 5.83 I4 7'12 o-68 Delamere' . . 28o 51 23'44 || 4 || 4-79 I-90 Orme's Head . . . 96 56 29.26 || 8 || 8.82 I-75 Cyrn-y-Brain 343 20 34.91 12 || 7.77|| 0.92 1 A correction of + 5"'46 to be applied to this bearing, to reduce it to the new trigonometrical station. GERTH OF SCA.W. - 7-in. Theodolite. From 30th January to 2nd February, and on 19th April, 1847. Observers: Corp. STEEL and Private JENRINs, R.S.M. No. IRecip. No. Recip. Objects. Dearings. of Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. O / / / f/ O / / / f/ Balta • . 186 29 8:34 3o 7ooo 20.59 || Saxavord . . 288 7 393 || 29 |IIo-oo. 39.98 Nive Hill . I95 9 12-51 3I 93-34 30.82 - GLASHMEAL. 3-ft. Theodolite, B.o. From 17th June to 2nd July 1818. Observers: Major-Gen. Col.BY and Mr. GARDNER. * No. Recip, No. Recip. Objects. Dearings. of Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. Ben Cleugh . 18 1. 3348 7 5'86 1.25 || Mount Battock 2 57 12" 37.68 I4. 773 o:56 Bin of Campsie . . 26 45 28:or || 4 || 4-11 | 1.13 | Red Head, Old 297 46 35-20 || 4 || 3:36 o.94 Ben Lawers . . 55 22 18.84 || 6 || 3-84 o.56 | Craigowl • 329 o Io:37 . I4 6.66 o.38 Ben Amhlair . . . 84 49 45-20 | 6 || 3:41 o.55 Kellie Law 332 I? 59.88 2 o. 13 o.o.o Ben Macdui . I40 20 35-39 || 3 || 3-12 | 1.31 || Largo Law • 338 53 28.67 Io 5.37 o.63 Corryhabbie . . . 191 8 49.89 9 || 16.42 | 1.70 | East Lomond |352 36 3.15 15 13.64 o.77 GLASSERTON. - 3-ft. Theodolite, B.O. 5th and 6th August 1815. Observer: Mr. GARDNER. No. § No. * - Objects. Dearings. of | Range. Rºjº. : Objects. IBearings. . Range. Rºp. Obs. Weight. Obs. Weight. O Aſ f f - Af O & Af / -ºrms=g: South Berule II 6 56-53 2  o:7o | Cairnsmuirof Fleet 196 45 IG. I.4 || 8 3.89 o:36 Mull of Galloway 7I 4 47.96 || 8 || 3:21 o.32 Bencairn . 243 40 32-31 || 9 || 5-og o.65 Cairn Piot ... • | II5 I4 I2.32 || 4 || 7.56 || 4 or | Criffel . 244 35 58.33 || 4 || 6.95 o.oë Benereard . . . 144 39 33.77|| 6 || 5:43 I-97 ||North Berule . . 353 3 19:39 || 4 || 6.16 2.97 TMerrick . 18o 59 59-80 || 4 || 5-o.4 || 2:08 || Snea Fell . 358 3o 23-64 || 4 || 2:35 o:58 5.-*. - t: OBSERVATIONS. II5 GOAT FELL. 3-ft. Theodolite, R.S. From 12th August to 2nd November 1852. Observers: Colour-Serg. Don ELAN and Corp. GROSE, R.S.M. * Objects. Bearings. *: Range. Rºjº. Objects. Bearings. - . Range. Rºº. - - Obs. Weight. I Obs. Weight. º O Z/ Z/ O & Aff lº &ſ Slieve Donard . 16 30'3661 6 | 1.62 o.o.9 || Ben Cleugh . 234 24 Io-or | 18 4:53 o'I5 Divis . . . . 25 22 29-25 | 18 6.51 o-22 | Bin of Campsie 236 20 13.92 || 14 || 6-46 o'42 | Trostan . . . 43 5o 16.81 | 12 2.95 o. 17 | West Lomond 238 59 45-49 || 8 || 5.5o o'66 Qarnºna-Leagh . . 4; 2 59.84 || 15 10.8%| 1.17 | Carnethy Cairn |237 49 A-81 | 12 || 3:35 o-16 Knocklayd • 52 52 33.93 || I2 5-o/ o.5o | Tinto Cairn, New 271 37 38.56 I6 4.5o o'I7 Slieve Snaght | 71 28 55.91 || 8 || 4:31 o.39 || Hart Fell . • 281 21 39.62 20 | 8.26 o'37 Ben Tuirc". • 74 39 36.69 | 15 || 6-32 o-37 || Cairnsmuir on º Oa . • 9o 58 35-og I9 || 6.96 o°43 Deugh . • 303 I2 22:15 16 || 7-69 o°34 Jura . . . . . . . 121 28 IA-23 19 7.5o o.33 | Criffel . . . . . . .306 52 36-27 | 16 || 3.89 o-IS |Ben More in Mull 15o 23 32.91 19 || 4:33 o. 15|Brown Carrick |308 34 40.87 || 14 6.38 || o'53 Qreachbheinn . . 171 24 38.29 18 3.48 o.o.) | Merrick . . . 319 27 16.93 16 || 6-04 o°25 Ben Lomond . . . 268 51 9-33 ||31 || 5-43 o. II | Benereard . . 344 3o I2:43 I3 4. I5 o°23 Ben Lawers . 2Io Io 9:45 24 || 8.05 o.29 | South Berule • 348 15 25-73 II || 3:65 o'22 Hill of Stake . . . . 230 5 32.75 | 15 || 4.3% o.16|| Cairn Piot . . . .333 49 4.75 15 6:17 o:29 Referring-object . 233 3 2.31 47 º *- GOONHILLY. 3-ft. Theodolite, B.o. From 5th December 1845 to 17th January 1846. Observer: Serg. DoNELAN, R.S.M. ſº No. Recip. No. IRecip. Objects. Bearings. of | Range. of Objects. Dearings. of | Range. of Obs. Weight. Obs. Weight. t O / // f/ O f f/ (ſ/ Grade Church Tr. 8 38 3I-II I4. 5-36 o°32' Tregonning tº I22 5I 34-24 20 5-58 o°23 LizardLighthouse, ICarnbonellis . . . IG6 35 I4-75 I4 || 4'57 o°21 East * . Io I 57-o/ | Io 5.68 o.46 | Hensbarrow . . . 214 I4 51.86 || 14 | 6’40 o°52 LizardLighthouse, St. Just, Windmill 218 55 55.95 || 6 || 3.95 o'69 West . . . Io 24 I5.68 9 7.98 o.86 l Deadman . . 234. I 27-22 || 13 5-62 o:73 The Wolf Rock • 76 17 4.58 9 2.38 o. I4 St. Kevern's Spire 265 55 22:77 I8 6. I5 O 2C) Srtinney . . . . IoI 3o 59.84 22 || 4-21 o.16 || Referring-object . 342 58 II.99 || 77 ---> tºº Rarn Galver . II3 Io 27°42 || 5 || 2.91 o-44. + GORLESTON CHURCH TOWER. 18-in. Theodolite. From 22nd December 1843 to 3rd February 1844. Observers: Corp. STEEL and Private MºMALLY, R.S.M. ſº No. Recip. No. Recip. I Objects, Bearings. of | Range. of Objects. Bearings. of | Range. of Obs. - Weight. Obs. | Weight. - O f W/ Aff - O f f/ w Aff - jº. * 9 6 24 13.15 || 2 | 6.98 || 12.18 || Norwich Spire • IoI 49 Io-48 || 9 || 8.19 • I.8o oft's Tower . 49 58 29.60 | Io | I4.5o 154 33 14.66 | 16 | 12.61 || 1:21 4.02 || Happisburgh . P 2 II6 PRINCIPAL TRLANGULATION. From 7th to 14th November 1850. GREAT STIRLING, 7-in. Theodolite. Observer: Serg, STEEL, R.S.M. No. Recip. No. IRecip. Objects. Bearings. of Range. of Objects. Bearings. of | Range. of Obs, Weight. Obs. Weight. Af O & aſſ f/ Little Stirling . 68 45 of 14 | 6′36||36.8: "...m.9" Windmill . I77 5 4I-90 I2 6o.78 |34.94 Mormonth . . . 136 46 14.82 || 6 || 28.61 39-or Reform Monument 169 56 21.60 13 45-oA 42.95 GREAT WHERNSIDE. 3-ft. Theodolite, R.S. From 5th to 20th September 1840. Observer: Lieut. PIPON, R.E. No. Recip. No. Recip. Objects. Bearings. of | Range. of Objects, Bearings. of Range. of Obs. Weight. Obs. Weight. : O W & M &A O Af f/ &/ Boulsworth . . . Io 41 56-66 Io 6.65 o.56 || Cross Fell I52 29 I-83 || 4 || 3:53 o-85 Whittle Hill . 17 51 18-30 || 6 || 3:36 o.45|Water Crag . 166 38 6.29 || 9 || 3-13 o.26 Pendle Hill 31 IG 42-51 || 4 || 3:09 o.68|Botton Head . . . 244 56 47.85 || 7 || 5.28 o-66 | Ingleboro' . . 9I 29 49.88 || 5 || 3.71 o.70 || Black Hambleton 251 18 31-61 || 4 || 3: Io I.O.4 Little Whernside IOS 54 53. I4. 2. o: I.2 o-oo Wilton Beacon . . 282 II 33.60 2. I-47 O-54 Sca Fell . . . II2 57 Io-45 || 5 || 4-off o.88 || York Minster 289 51 55.72 || 3 || 5-31 || 3:46 Helvellyn . I2I 59 38.12 || 3 || 3.67 1.64 Holme Moss 353 43 22:54 || 3 | 1.49 o'30 GRINGLEY. 12-in. and 3-ft. Theodolites, B.O. From 21st July to 26th September 1843. Observer: Mr. CAMPBELL. 18or. Observer: Mr. WOOLCOTT. No. Recip. No. Recip Objects. Bearings. of Range. of Objects. Bearings. of IRange. of Obs. | Weight. Obs. Weight. Q f Aſ f f/ O W &/ &A Sutton . . . . 34 28 6.68 || 3 || 4:34 2.38 | North End of Base 174 26 57.33 || 5 || II.44 || 6-13 Laughton Spire • | 84 22 43.81 || 4 || 9.94 | 6.72 Axholme Church 195 Io 16-40 || 4 || 9-oo 6.24 Clifton. • rog 58 34-28 || 9 || 4:36 o.38 Crowle . . . . . . I'89 57 I4.69 17 | II-66 o.84 South End of Base 155 9 46.68 || 6 || 14.97 7.83 || Lincoln Minster' 309 37 48.29 64 24.89 o.77 * A correction of - 14"-21 to be applied to this bearing, to reduce it to the trigonometrical station. GWAUNYSGAER. 3-ft. Theodolite, B.O. Ist October 1805. Observer: Mr. Woolcott. Objects Bearings . R hºp. Beari *: R Recip. CCIS. * allºC. i. * O º J Obs. 8 wint Objects. carings Obs. ange win. O f # / & O f f/ fy East End of Base 52 I4 31.79 || 6 || II.5I 4:20 | West End of Base 76 28 29-29 || 6 7.09 1.68 Moelfre Issa • 54 48 4'23 || 7 || 5.24 o.90 | Orme's Head . 92 30 39'52 || 3 || 3-24 1.16 OBSERVATIONS. 117 HAMPTON POORHOUSE. 3-ft. Theodolite, B.O. 1792. Observer: Gen. MUDGE. Objects Beari No. Tecip. Obi tº. *: R Rº {} earings. di. gº Range. w:ht, I jects. Bearings. dº. ange, Weight. 3. O / 44 aſſ * O / // Z/ St. Anne's * 73 51 37.07 || 8 || 4.57 o'52 Hanger Hill! • aog 54 38.87 || 7 || 4.56 o'69 King's Arbour . I35 18 II.63 || 2 | o-87 o.18 * A correction of — 4o' 55".71 to be applied to this bearing, to reduce it to the Tower on Hanger Hill. HANGER, HILL TOWER. 3-ft. Theodolite, B.o. From 15th February to 7th April 1848. Observer: Serg. DoNELAN, R.S.M. * No. Recip. No. Recip. Objects, Bearings. of | Range. of Objects. Bearings. of Range. of Obs. Weight. Obs. Weight. Leith Hill Tower 7 26 59.75 26 3.25 o.11 | St.Paul's Cathedral 27. I 5 33.12 I3 5:38 o,28 Hampton Ch. Tr. 19 30 36.76 || 5 || 7.83 2.54|WestminsterAbbey. 282 29 33.79 23 5.96 o.21 Hampton Poorho. 23 16 46.19 || 9 || 4.88 o.46 | Severndroog . . . 284 4 13.13 | 13 | 6.5o o'52 St. Anne's 48 20 42.95 | 12 || 3:06 o.15 || Forest Hill . . . 297 9 52.51 | 17 | Io.15 o'46 King's Arbour 65 19 25-17 || 2 || 4.5o 5-off Wrotham • 299 I5 20. Io I2 3.60 o' I5 Windsor Castle Banstead ' ' ' | 345 34 44.15 Io 3.64 o°29 Flag-staff . 78 27 48.70 || 6 || 3-o8 o.33 || Kew Pagoda • |357 4I 32-65 | 6 || 4.65 o-61 HAPPISBURGH CHURCH TOWER. 3-ft. Theodolite, B.o. From 8th to 3oth September 1843. Observer: Serg. DoNELAN, R.S.M. No. Recip. No. IRecip. Objects. Dearings.” of | Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. iſ . * O Af A/ AM * * O & Af &/ Worwich Spire. | 35 51 46.73 || 9 || 7.52 | 1.09|Referring-object . 145 28 59.61 34 7.62 o.16 Baconsthorpe Ch. Gorleston Tower | 334 24 44-62 || 4 || 3:48 o'93 Tower . ro5 34 39-45 || 4 || 2:52 o'5o | Tofts Tower 355 25 38.61 | 3 || 5.97 420 HART FELL. 2-ft. Theodolite. *=– From 30th September 1846 to 4th March 1847. Observer: Serg. BAY, IR.S.M. -* No. Recip. No. Recip. Objects. Bearings. of IRange. of Objects. Bearings. of IRange. of Obs. - Weight. Obs. Weight. | Criſfel . º I § Af º &/ tº * , O f */ Z/ tº 39 2 I-ol | I7 9.52 o°53 || Cairnsmuir on |º Cairn . . 2; "6 49.92 | 16 || 3.63 | 1.3%| Dough . . 72 8 50.71 || 4 || 8-10 || 4.3% Cºuis of Gºtº... : ; ; #7: ; *9°| #. $100t, s , - i. tº- tº . * : * * 5I 37 52-4 2.87 o. Hill of Stake . II9 I9 4-25 || I ry Merrick . . . 36 38 .# .# § ...; Ben Lomond . 138 56 34.96 || 13 6.62 o.62 II.8 PRINCIPAL TRLANGULATION. HART FELL–continued. # No. Recip. No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of IRange. of Obs. Weight. Obs. Weight. ; : O f ſ/ f/ - * O f &/ &A . Tinto , , " : " | I4I 9 23.99 20 8.77 o.38 || Cheviot . . . . 263 51 24.56 24 9-II o°59 Bin of Campsie 145 47 36.68 || 8 || 5.68 o.61 || Wisp . . . . . . 296 23 49-33 21 7.8o o.33 Ben Lºwers ' ' | 158 20 12-23 15 9.85 o.65 | Cross Fell . . . .322 57 24-32 24 9.90 o.38 Ben Cleugh . . . 165 I4 30.78 || 13 7.17 o.74 || High Pike . . .344 i3 3ool | 5 || 3:24 oºg Carnethy Cairn 189 24 58.51 | 15 6.66 o.38|Burnswark . . . 347 18 27.56 11 || 3:53 o.33 Allarmoor. ' ' | 191 o 50.92 || 9 || 8.55 | 1.07 || Referring-object 35o 20 29.89 |16I 8.57 o.o.4 Dunrich • • |216 43 o-16 || 24 7.46 o-40 | Sca Fell . . . . . .353 23 I7-of 24 12-3o o°49 Sayrs Law • 222 59 54.81 13 6.99 o'37 HENSBARROW. 3-ft Theodolite, R.S. From 18th April to 4th June 1845. Observer: Corp. STEwART, R.S.M. tº No. Recip. No. Recip. Objects. Bearings. of | Range. of Objects. IBearings. of | Range. Of - Obs. Weight. Obs. Weight. & O / / / f/ O f f/ d Af - Goonhilly. ' ' || 34 30 53.52 II 3.93 o.28 Brown Willy. 213 37 I5'93 Io I3-2O || 2:29 ICarnbonellis . 52 42 I3-22 || Io 5.27 o.46 | High Wilhays 239 19 58-22 | 18 5.72 o. 18 Carnbrea. Monu- IGit Hill . . . . 247 5o 56-34 || 7 || 5-7I I-36 ment 59 36 I2-2I | 3 || 3.87 | 1.90 | Butterton . . . . . 266 51 24.70 I5 5-35 o'24 Pertinney.' 62 43 56.99 || Io 4.27 o.35 Maker Church ICarnminnis . . 67 52 6-og I5 4:36 O • 2 O Tower - • 274 52 44.68 4. 5-49 || 2:OO St. Agnes 73 22 46. Io | Io 3.81 o.21 Maker __. . . . 275 38 6.8o || 6 || 7-90 2.67 Referring-object 78 25 55-or 119 5.93 o.o.2 | Barrow Hill . . . 281 45 46.62 | Io 2.27 o.16 Trevose Head : I4o 28 53-94 || 8 || 6.56 | 1.02 || Lansallos . . . . . . . . 284 48 40. Io | 6 || 4.97 I of Lundy Island Eddystone Light- Lighthouse' ' | 186 40 24, II || 2 || 6-09 || 9-27 | house . . . . 299 32 15-24 || 7 || 6′oz o'91 Cadon Barrow 195 22 26.65 || 7 || 3.19 6.38 || Deadman . . 356 2 14-28 || 6 || 2 18 o.18 * A correction of + 1' 38". 57 to be applied to this bearing, to reduce it to the trigonometrical station. HIGEI PORT CLIFE. 18-in. Theodolitc. From 20th to 22nd July 1846. Observer: Corp. STEEL, R.S.M. Dearings *: IR hºp. . R Recip. iects. €ºlrlººs. O all ſe, O * sº ings. † Objects g C. “* |wºn. Objects. IBearings c. *ge wint sm-- O M M ſ &M ſº o f W/ a Littletown Down | 123 2 6:33 II | 18-99 || 4-75 | Boniface, S.E. 149 37 54.63 II | 12:20 | 1.87 T- OBSERVATIONS. II9 IHIGH WILHAYS. 3-ft. Theodolite, B.O. From 9th June to 20th July 1845. Observer: Serg, DoNELAN, R.S.M. º No. IRecip. No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of | Range. of Obs, Weight. Obs. Weight. Eddystone Light- O / / / A/ O f f/ £f house ' ' ' | 17 59 8.89 || 5 || 7:10 || 3:51 | Precelly . . . . 159 31, 15.74 14 | 6′22 o.32 Hºnsallos . . . 45 13 42.33 || 3 || 4.33 3.jo |Paracombe . . 196 33 16.75 13 | 6.78 o.61 Kit Hill . . . . 47 go 32.68 || 3 || 8.13 || 3:37 | Dunkery . . . . 269 3 24.23 Io 6.89 o.64 Deadman . . . . 47 43 44.26 || 4 || 2:22 || 3:42 || Mendip . . . . . 239 29 58.61 | 12 5-97 o-39 Hensbarrow . . 59 57 17.73 || 13 | 8.31 o-97 || Staple Hill . . . 243 56 43.55 | 6 || 3:31 o.19 Brown Willy . . 76 6 47.23 II | 7-12 o-65 | Dumpdon . . . . 254 31 56.91 || 4 || 3:33 | 1.16 Cadon Barrow 86 3 48.54|| 7 || 3:42 o'53 |Pillesdon . . . . . 266 17 49.55 || 17 | 4:37 . o.15 Bradbury Castle. | 122 23 38-45 || 4 || 1.88 o-22 | Black Down . . . 269 26 26.66 || 6 || 2.46 o.36 Lundy Island Swyre Barrow 272 59 12. I9 || 8 || 5'99 o-95 Lighthouse. I39 17 21.39 || 5 || 12.76 6.67 | Vern . . . 276 16 51.17 | 8 || 4-28 o-46 Lundy Island Sta- Little Haldon. 290 56 24.94 || 8 || 4-17 | o'52 tion . . . . . Igg 18 57-28 || 15 4.19 o.13 | Ryder's Hill . 336 54 3I-64 I5 6:34 o°39 HILL OF STAIKE, 3-ft. Theodolite, B.O. Erom IIth to 18th October 1816. Observers: Major-Gen. Colby and Mr. GARDNER, No. Recip. No. Recip. Objects. Bearings. of Range. of Objects. Dearings. of | Range. of Obs. Weight. Obs. Weight. O Af & f f/ C) J f/ Z/ Benereard . . 7 o 49. II | 2 | o'57 o.o.8 || Glasgow Observy. 262 I 3-49 || 7, 6.12 I-ol Goat Fell . . 5o 26 5I-47 || 3 | 1.55 o. 26 | Dunrich • 285 29 40.86 || I — 6.18 Jura . . . . . .96 28 22.61 | 1 º 6. I8 || Tinto . . • 290 33 59-69 || 4 || 5'97 || 3:16 Ben Lomond . 190 55 39-29 || 12 8.48 || 1.18 || Cairnsmuir on Bin of Campsie 241 44 41.58| 21 4.52 o.13 Deugh . . 331 27 28. I4 || 5 || 2:33 o'47 Corkmulaw . . . 243 33 58-59 || 8 || 7-12 | 1.18|Brown Carrick |356 30 17-30 || 8 || 5.71 o'74 HINGHAM CHURCH ToweR. 18-in. Theodolite. From 17th May to 3rd July 1843. Observer: Corp. STEEL, R.S.M. No. Recip. i No. Recip. Objects." Bearings. of Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. | Weight. O f A/ º A/ O Af &/ &/ - Brandon . . . . 51 59 7.87 || 5 || 8.87 3-40 || Norwich Spire 25445 1.5I II Io.58 I-90 Swaffham Spire. III 16 5-52 Io 20-13 5.04 || Bunwell Tower 314 24 6-53 || 8 || 13:38 4.8o Baconsthorpe . . 199 I9 53. Io | 9 || 7-83 I-63 || South Lopham Tr. 357 19 2 I-58 || ||7 º 2-94 * A correction of + 27"'64 to be applied to this bearing, to reduce it to tho trigonometrical station. | I2O PRINCIPAL TRIANGULATION. HOLME MOSS. 18-in. Theodolite. From 24th August to IIth November 1841. Observer: Corp. STEEL, R.S.M. biccts Bearin * Recip. b Beari * |r Rºjº. iccts. º iects. C º €, O Objec gS o:8. Range. Wà. Objects arings o, ang Weight | O & Aſ f/ ſº C & Z/ Af | Kinder Scout . . . o 1 53.60 Io 13.64 2.62 Little Whernside. I56 I3 I5'79 || 3 || 4.49 || 2:45 |Axedge, . . . 7 1851-72 || 5 || 13.98 || 7.26|Great Whernside. 173 45 13.25 | 8 || 6.33 o.86 Cyrn-y-Brain Tr.l 57 37 52-53 2. I-92 o:92 Garforth Cliff. • 231 Io 47°oo 2. 2-32 I'34. Whittle Hill ' ' | 119 29 7.56 || 8 8.72 | 1.57 |Staincross . . . . 256 25 28:78 || 3 || 4:54 || 2:29 Pendle Hill 143 *; 17:21 || 7 || Io.23 3.23 | Clifton . . • 281 I.8 34-65 | 3 || 2.33 o.72 Boulsworth . . . 154 28 14:44 1% 19:53 || 4.43 || Back Tor . . . . .318 59 43-84 || 5 || 13:49 8-65 * A correction of — 49".75 to be applied to this bearing, to reduce it to the trigonometrical station. HOWTH. 3-ft. Theodolite, B.o., and 7-in. Theodolite. From 29th November to 19th December 1829. Observer: Lieut. PoETLoCK, R.E. From 28th August to Ioth September 1844. Observer: Mr. GoRDON. No. i No. Recip. Objects. , Bearings. . IRange. Rºjº. Objects. Bearings. . Range. ºp Obs. Weight. Obs. Weight. O * & W f/ - O Af &/ f/ Bray Head * 22 22:24 20 5.14 o.19 || Garristown Wind- Great Sugar Loaf | 12 33 4.8% I7 || 6-57 o-25 | mill . . . . . I34 39 59:21 I2 | Io'57 | I-62 | Douce Mountain Loughanleagh 137 33 32. II | 6 || 8.58 2.73 or Joice's Hill 22 57 3.07 9 || 8.20 | 1.13 Knockbrack . I5o 24, 37. I3 || 5 || 5-O4 I.I.9 Ringstown Obser- Slieve Gullion • I64 3 5I-83 2. 2. I8 I. I8 vatory,' ' ' | 24 56 1996 || 15 Ioo.89 |279.88 Carlingford ' ' || 172 39 28-30 || 5 || o'96 o.o.4 Fairy Hill. 38 Io 38:44 18 || 6.9% 6.42 | Slieve Donard I86 9 16.29 || 4 || 4.33 I-62 Kippure... , , 39 ° 43'25 |32 || 8.66 oºs | Lambay Island . 1943; 27.94 || 48 || 3.3% o.o.8 Poolbeglighthouse 57 34 6:57 | Io 5.82 o-63 | Holy Head . . . 273 33 3-24 || 7 || 7-75 2-12 Lyons Hill . . , 73 38 46.5o | I5 4.90 o-25 || The Rivel . . . . 291 26 27.92 || 3 || I-94 o-45 Maynooth Obelisk 89 25 59.58 7 2'54 o-24 Collin . . . . 359 34 Ig'55 || 7 || 7. II I-18 Dome of Dublin s -- - * Observatory 95 4 50:46 || 8 || 3.73 o. 45 HUNGRY HILL. 3-ft. Theodolite, B.o. From 11th to 16th July 1832. Observer: Capt. PortLocR, R.E. e No. Recip. No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. Tº ºmº- O Af & / &/ & 4'ſ -ms Mizen Hill º 2 7 40-28 || 5 || 4-25 | o'77 | Baurtregaum . 177 25 3# I4 || 6 & I-61 | Bolus Mountain . . Io9 29 33.63 || 7 || 2.98 o-27 | Carn Thuil 185 36 29-oš 5 || 3-94 o,76 Rnocknaskerita • II9 4o 3'43 || 5 || I-64 o. II | Mangerton. 213 59 28-36 || 6 || 3.73 O'52 Knocknadober 142 23 56.96 || 4 || 2.97 o'55|Caherbarnagh 227 3647. II | Io 6.40 o.37 Brandon . . . . . 152 49 53:60 || 2 || 3:32 2.75|Slieve Buoymore. 24; 47 12.34 12 | 1.69 o-oš Knocknagante | 15647 46.92 || 5 || 2:31 o'26|Carrigfadda . 276 29 2:19 II 4.46 O-32 Colly Mountain 159 2 13-74 || 5 || 3.97 o.85 || Mount Gabriel 309 44 6.62 | 9 || $.99 || 0.34 OBSERVATIONS. I2 I INEOPEN. 3-ft. Theodolite, R.S. From 2nd May to 24th June 1844. Observers: Corps. STEwART and Cosgrove, I.S.M. º No. Recip. No. Recip. Objects. Bearings. . Range. ºp Objects. Dearings. . Range. . p Obs. Weight. Obs. Weight. i. Beacon! tº 4. 3. 23.88 2 #so o:56 || Brill . . . . . 206 55 58.75 II 11.82 I'54 #. Hill; • 20 13 57.92 || 4 || Io.86 7.73 Nettlebed . . . . 232 32 33.81 || 6 || 13.og | 6’44 ºacon Hill . . . 43 48 44.83 || 8 || 6.51 || 6-97 || Windsor Castle i ingreen . . . . 48 o I-60 19 | 12.59 o-87 || IFlagstaff - . 255 56 o'oo 5 7.64 2.86 Westbury tº 78 I 32-35 | 8 || 4:55 o°5o | Leith Hill Tower 283 58 7.57 14 || 4.47 o.24 Mendip . . . 79 13 $5.85 | 6 || i.26 o.o.7 | Referring-object . 315 g 39.94 |12ó | 8.7% o.o.4 Upcot. . . . . . . 126 43 44.37 | 1 – II.68 Butser Hill . . . .320 4o 46-o5 || 13 5.8o o.42 Whitehorse Hill | 164 3 57.29 15 9:50 o.77 | Dunnose . . . .346 59 50-48 || 13 | 16.48 o.89 Scutchamfly 199 57 35-74 || 4 || 3.8o 2.17 | Motteston , , 357 58 35.85 Io 8. I9 o-97 * A correction of – 6' 13 to be applied to this bearing, to reduce it to the trigonometrical station. JURA. 3-ft. Theodolite, B.O. Trom 30th July to 12th November 1847. Observer: Serg. DONELAN, R.S.M. No. Itecip. No. Recip. Objects. Bearings, of | Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. O Af Af */ O f f/ w/ Trostan • 5 47 24. II | 15 5.77 o.34 || Ben Nevis. 2II 26 I-32 31 6.19 o'I5 IGnocklayd | Io 48 52-09 || 10 5.53 o.54|| Cruach-na-Sleagh 215 29 41-27 | 17 | 8.87 || 9'57 Qa . . . . . \| 31 Io 27.44 12 6.78 o.45|Ben Lawers . 236 22 15.88 21 8:36 o:36 Mount Sandy. 36 32 47.43 II | 8.25 o.76 || Ben Lomond . . . 248 52 28.43 | 12 || 6-06 || 9'51 Slieve Snaght. 47 26 18:39 19 3.69 o.13 | Hill of Stake . . . 275 26 26.70 || 5 || 4.97 || 1:13 Ben Tartevil . 54 41 18.95 | 12 6.67 o-48 || Goat Fell . . . . .306 47 51.72 | 13 5:35 o'36 Ben Heynish . . . 137 32 32.73 28 8.07 o. ig | Merrick . . . 31o 34 52.92 14 || 3-94 or II Ben More, S.Uist 152 49 42-66 || 9 || 4.01 o-31 || Ben Tuire. . . .323 28 53:55 14 9-6; I-12 Ben More in Mull 179 24 7.32 21 9.65 o.36|Carn-na-Leagh - |347 44, 21.69 || 5 | 1.36 o' To Creachbheinn . 2Oo 55 II-74 || 6 || I-61 o. Io IXARNIBONELLIS, 3-ft. Theodolite, B.o. 1796. Observer: Gen. MUDGE. i. ſº No. Recip. º § º R Rºjº. Objects. Bearings. o: tº Range. W#ht. Objects. Bearings. o:S. ange. Weight. O / / / Z/ O f MA £f .87 |Buryan . 67 20 29.93 || 5 | o.88 o.o.3 | Hensbarrow 232 23 16.62 | I | - #: Karnminnis 93 43 28.3% | 7 || 7.64 | 1.45|Deadman . . . . 261 43 41'4" | 3 | *79 St. Agnes : I83 26 59.87 || 8 || 2.86 o.23 -- Q "I22 PRINCIPAL TRIANGULATION. IKARN GALVER, 18-in. Theodolite. Trom 24th August to 12th October 18 50. Observer: Corp. WotRERspoon, R.S.M. * > No. Recip. tº No. IRecip. Objects. Bearings. of | Range. }_of Objects. Bearings. of | Range, of Obs, Weight. Obs. Weight. tº O / // &/ O / // A/ | Pertinny • . . . . 19 29 14.99 22 || 14.56 I.oé | Trevose Head 223 52 6.61 | 15 13.57 | 1.37 | St. Agnes Light- - Brown Willy. 236 I5 34.86 || 3 || 6.36 4:49 house º • 6o I5 3.65 I2 II-37 2-16 || Karnminnis 239 51 33'54 25 | I4-55 I. I.4. Peninnis Windmill 6o 16 58.20 I2 9-09 | 1.62 | Hensbarrow . . . 246 28 33.39 16 || 19.96 || 2.76 Telegraph, Tower 62 16 2.95 | 12 8.34 | 1.11 || Carnbrea Monu- St. Martin's Head 64 57 37.51 | 12 | 12.36 | 1.68 ment . 256 26 24.81 37 I5-86 o.61 Beacon Hill, Tres- Karnbonellis . . . 265 52 9:59 || 2 I | 7:55 o°31 cow, Watchhouse' 66 41 47.82 II | 15.36 3.46 | Goonhilly . . 292 5o I. Io I7 | Io-28 o-75 1 A correction of + 1' 3" 15 to be applied to this bearing, to reduce it to the trigonometrical station. IKARNMINNIS. 3 ft. Theodolite, B.O. From 7th to 27th October 1845. Observer: Serg. DONELAN, R.S.M. * No. Recip. i. No. Recip. Objects. Bearings. of IRange. of Objects. Bearings. of IRange. Of Obs. Weight. Obs. Weight. * , O W f/ Z/ O f & / Z/ Pertinney. 39 Io 57.56 13 5.20 o.27 | Carnbrea Monum" | 261 42 51.32 || 7 || 4-28 o-48 Karn, Galver . 59 55 4.87 || 7 || 5.86 o-93 || Karnbonellis : 273 29 24.8o 13 || 8.76 o.79 St. Martin's Day- St. Keverne Spire | 296 27 9.87 || 6 || 2:55 o.21 mark' . . . . . 64 26 7.15 || 6 6.32 | 1.37 | Tregonning . . . . . .303 5. 26.60 I4 5-52 o.38 Trevose Head 221 58 46.52 | Io 5.98 o.66|Grade Church Tr. 313 36 20-33 17 | 8.95 o.48 Cadon Barrow 228 53 39-16 || 2 | 5-22 || 6.81 || LizardLighthouse, Brown Willy . 236 I I2'o6 || 2 || 0.8o o. 16 || East . . . . . . . . .317 33 37.24 || 7 || 4.77 o.82 St. Agnes Beacon 24o 59 26.70 | Io 3.83 o-25 || LizardLighthouse, Hensbarrow . . . 247 19 I-71 | 1.4 8.66 o.70 | West . . 317 39 17-48 || 8 || 2:24 o.16 1 A correction of + 39”. 58 to be applied to this bearing, to reduce it to the trigonometrical station. ICEEPER. 3-ft. Theodolite, B.O. From 16th September to 29th December 1830, and from * May to Ioth July 1831. Observer: Capt. Port LoCK, R.E. No. IRecin. tº sº Objects. Bearings. . Itange. ºp Objects. Dearings. . Range. Rºjº. Obs. | Weight. Obs. Weight. *smº--ºn- O Af # / f/ | O ſ & / A/ ICnocknaskagh 9 39 44.75 || 9 || 5’74 o.83 || Bencorr . . . . 129 58 Io.94 || 3 || 2.82 o.88 Caherbarnagh 38 16 20-51 || 3 || 5-64 || 4-17 | Nephin | 153 45 54-75 || 6 || 4.95 | 1.17 Taur ſº 46 8 20.94 || 2 || 2:21 I-22 || Slieve Bawn, S. 18643 ig.14 || 1 || || IO-24 Baurtregaum ' ' | 61 o 2'o.4 || 6 || Io.91 4.69 | Cuilcagh 192 1842-o4 || 3 || 2:32 o.61 ICnockanore 74 59 26.98 || 4 || 4.57 I-69 || Knockastia 208 35 12:30 || 6 || 5.81 | 1.29 Meelick 83 39 17.13 | 15 9-69 o.72 Croghan • 224 29 2I-65 | 9 || 6.60 o.76 Slievecallan 98 42 7.94 | 13 | 6.29 o-46 Arderin 23I 32 30.78 || 24 | 18.86 o.92 Gortourka . . . Io9 19 3-96 || 8 || 4.5o o.54|Kippure . . . 249 6 44.84 || 3 || 8.33 8.78 Slievecarran 127 36 19:24 25 9.57 o-28 | Cullenagh . 25I 4 23:56 18 9.93 o'57 OBSERVATIONS. I23 IXEEPER—continued. -- No. Recip, No. Recip. Objects. Bearings. . Range. º Objects. Bearings. . Tange. of Obs. - Weight. Obs. weight *19. To = O / / / f/ O / / / f/ Devil's Bit. . . 251 27 52.19 | 89 8.61 o-off Slievenaman . . . .306 56 58.70 || 21 13.43 o'71 Lugnaquillia º 258 4 I-37 || 3 || 5-43 3.87 || Knockanaffrin 317 52 7-12 28 II-84 o°45 Mount Leinster . 277 5o 2.59 || 9 || 6.97 | 1.1o Knockmealdown 337 54 57.82 21 Io-o2 o'56 Blackstairs 282 17 45-29 || 2 | I-II o-30 || Galtymore • 352 33 o'52 || 3I | Io.33 o°31 IKELLIE LAW. 3-ft. Theodolite, R.S. Trom 15th December 1846 to 6th March 1847. Observer: Corp. WINZER, R.S.M. i. No. Recip, No. Recip. Objects. Bearings. of IRange. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. º O W Af f/ O f Aff W/ Cºmethy Cairn 34 30 5.44 11 6.80 o.68|Mount Battock | 181 42 45.29 22 || 5:64 o.22 Allarmºor º 35 8 20-27 || 7 || 4.86 o. 71 || Caerlock . . . . . 191 45 36.06 || 7 || 8.18 I-72 Arthur's Seat 35 II 52.83 || 14 || 7.73 o.67 || Red Head . . 203 21 47. II. I5 8.94 o'6o Calton Hill! . 37 42 43.20 || 6 || 6-34 I-38 || Isle of May Light- º Largo Law 8o 3 7.79 17 | 8.36 o'54 |_ house . . . . 296 38 22.40 I4 7:45 o'54 East Lomond. 88 48 23.45|| 25 | 12.74 I-35 | Lumsden . . . 316 27 40-61 || 31 8.37 o. 18 Glashmeal. I52 47 14:05 || 17 | 7.91 o.67 | Sayrs Law 35I I4. 7. I2 3o I3'o6 o°43 Craigowl . I56 36 47.70 | 19 || 6-39 o-27 i * A correction of — 1"'81 to be applied to this bearing, to reduce it to the trigonometrical station. ICEYSOE CHURCH SPIRE, 18-in. Theodolite. From 9th March to 8th May 1843. Observers: Corp. STEEL and Private M*NALLY, R.S.M. tº • No. Recip. * No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of | Range. of *mºm-a-—- Obs. Weight. Obs. Weight. O & Z/ Aſ : O f A / ſ/ Dunstable . * 9 49 19.77 || 7 || 4:08 o.55 | Easton Tower 17247 II-20 || 5 || 4.66 I'oS Hanslope Spire 66 57 14.97 || 8 || 14-49 6.84|Ely Minster . . 250 22 54.76 || 1 || 14-37 || 2:64 NasebyChurch Tr. 113 22 i.45 || 6 || 4-48 || 0.96 || Royston . . . 3.12 1737.54|| 6 || 13.59 || 6-16 Tilton . . • I46 2 I 9-og I3 4.43 o.21 || Tharfield • • 313 41 2.06 || 6 || I'oz o' 17 IKING'S ARBOUR, 3-ft. Theodolite, B.o. May 1792. Observer: Gen. MUDGE. Obie "No. R hºp. Objects IBeari . Itange Rºjº. ects. IBearings. f tS. rinſ&S, O ſº o J earings oil. ange. wint Jects earing Obs. Weight. 2 O f M Af O / W/ A/ s º St. Anne's 'S 29 28 4394 5 || 2 oo o.21 || Banstead, Old' 317 42 22.70 || 3 || 997 | * IO : Hampton Poor-ho. 3I5 I4. I2-off 5 2.5o o:35 | * A correction of + Io” oA to be applied to this bearing to reduce it to Banstead, News Q 2 I24. PRINCIPAL TRIANGULATION. ICINGSTOWN OBSERVATORY. 7-in. Theodolite. Ist and 2nd October 1844. Observer: Mr. H. GoRDON. wº No. Recip. ſº No. Recip, Objects. Bearings. of | Range. of Objects, Bearings. of | Range. of Obs. Weight. Obs. Weight. ſº O / / / &/ O / / / f/ Poolbeg Light- Howth . . . . 204 53 37'52 I2 37.19 14.83 house . • I66 48 II.58 I2 117.13|I59.56 ICIPPURE. 3-ft. Theodolite, B.O. From Ioth June to 16th July 1829. Observer: Lieut. Portlock, R.E. No. Recip. -- No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. | Ballycreen. . . 4. 3 5 2íos IO 6:1 3 o.54 | Slieve Gullion . 176 23 26 '53 2. 646 Io.43 Lugnaquillia . . . 20 46 22-26 30 7.84 o.19 | Dublin Observº 178 55 36.47 | 13 || 4.41 o-36 ICnockanaffrin! 4O 58 38-24 8 7.08 O-97 Castlecoo - - - 183 48 19:58 4. 3-64 O'94 | Galtymore • 54 47 43.41 || 4 || 5.47 2.37 | Slieve Donard I93 31 23.96 I2 8.31 o.87 Cullenagh , 68 33 57'24. 4. 5-87 2.28 Howth . & Cº. 218 48 5-63 34 Io-o3 O - 2 O ICeeper . . . 7o 39 14.or || 7 || 7-off I-48 || South Berule 224 48 35-40 || 2 | o-33 o.o.2 Slieveroe . • 86 39 39-oo | 3 || 7.67 6.85 Moel Rhydladd 258 4o 49-72 || 4 || 3:21 | 1.06 Dunmurry 93 26 26.96 || 8 || 6.45 | 1.13 || Holy Head • 26I 35 1992 || 4 || 5-21 | 1.79 Croghan 166 52 36.51 | 18 12.75 | 1.04 || Snowdon 273 43 II.82 || 4 || 2.61 o.49 | ICnockastia Io9 7 17.74 || 2 || 3.62 || 3-27 | Rhiw 287 55 59.56 || 1 || – || 8.4o Lyons Hill ' ' | 132 39 15.38 22 || 14.66 i.oo | Precelly . . . . .321 46 7-25 || 7 || 5.47 o-90 Cuilcagh . • 139 56 47.42 || 3 || 2.89 2.53 Collin . . . . 328 13 17.36 || 3 || 1:23 o.18 Loughanleagh I55 16 50.91 || 9 || II.06 2-13 || Tara . . . . 351 45 12.93 || 7 || 5 of o-6o * A correction of — 6' 25 to be applied to this bearing, to reduce it to the trigonometrical station. IXNOCIK. 3-ft. Theodolite, B.O. From 4th to 14th August 1814. Observers: Major-Gen. Colby and Mr. GARDNER. + No. Recip. No. Recip. Objects. Bearings. of | Range. of Objects. IBearings. of | Range. of Obs. Weight. Obs. Weight. O f & Aff O & f/ - £/ Buck . . . . . . I9 43 3592 16 || 7-off o.47 || Cowhythe • 21 I 51 9-52 I2 | 3.75 o.2 Findlay Seat ' ' | 88 49 34.18 12 || 3.98 || 0:49 || Manor Lee . . . 262 30 22.43 || 8 : § Balnaskerish • II6 I 4I-72 I tº 8.72 Mormonth º 267 2 Io:33 || 13 7.36 o-84 Ben Lundie 121 27 18.73 || 2 | o.84 o.17 | Dudwick : 290 48 21.93 13 4-60 o-35 Ein of Cullen 147 Io I5'39 II 5.51 o-56 Caerlock . . . 346 o 56.59 || 9 || Ii.62 2°45 Ben Cheilt I56 43 39.68 || 5 || 4:34 o.87 |Mount Battock 358 20 12.72 || 5 || 11.61 5.93 OBSERVATIONS. I25 ICNOCIXALONGY. I8-in. Theodolite. From 8th to 15th September 1828. Observer: Lieut. MURPHY, R.E. * No. IRecip. No. Recip. I Objects. Bearings... of | Range. of Objects. Bearings, of Range. of . Obs. Weight. Obs. Weight. I O Z */ Aſ/ O Aſ ſ/ Z/ Knockma . . 9 36 I7-20 || 2 | I4. I3 || 49.91 | Truskmore . . . 231 28 35.17 | 8 || 9.91 || 3:24 The Reek . 5I 3 30-33 || 7 || 20-62 | Io.77 Cuilcagh - • 268 55 22.98 || 6 || 14-off 7-48 Nephin . 63 23 43.33 || Io 20-16 || 5.87 | Slievel»awn, South 319 7 24.77 | 1 - 33.90 Tawnaghmore IoI 53 I2-6o 4 || Io.52 || 7-22 || Mullaghanoe . 355 22 45.87 || 3 || 5-72 4.46 Slieve League 183 5I 57.16 II | II-48 || 3-04 RNOOKANAFFRIN. 3-ft. Theodolite, B.o. From 3rd August to 4th October 1829. Observer: Lieut. PortlocR, R.E. Ob | I} *|n Rºjº. Ob B *|R Rºjº. jects. ings. f º iects. arings. O 31I] gºe, O Jects earings ði, ange wint Jects carings Obs. g Weight. º † O / // // O / / / &/ Slieve Grian . 2I 5o 30.97 | I3 5.64 o.32 | Cullenagh , , I96 19 53.37 || 19 || 8.30 o°39 Doolieve 47 36 42.49 || 6 || 2:24 o.20 || Kippure 219 58 51.93 || 9 || I2.26 || 2:32 Knockmealdown | 73 3o 34.99 |34 || 11.41 o.23 |Lugnaquillia . 224 38 7.2I Io 5-25 || O'44 Baurtregaum . 87 29 20-21 || 3 || 3-28 || 1.26 || Ballycreen . . . 229 8 15:52 || 4 || 5-49 || 2:40 Taur . . . 87 32 38-oo || 4 || 4-06 | 1.14 || Mount Leinster . 235 46 55-53 || 23 || 7.87 o'39 Galtymore Io2 7 I4, 18 21 7.25 o.29 || Mount Brandon 239 3 33.91 || 2 || 2:or I-91 Keeper. I38 24 26-57 35 | 8.58 o.19 |..Blackstairs 24o 58 44.64 || 19 || 6-oo o'24 Devilsbit . I59 15 20:14 || 17 | 9:57 o.62 | Carrickbyrne . . . 26o 16 50 or Io 5-18 o.43 | Arderin I76 41 7-04 || 9 || 16.63 | 1.82 | Slievecoiltia . 262 33 20-40 || I4 || 6′39 o'32 Slievenaman . . I85 7 44.74 || 36 7.77 o.20 | Forth Hill . 267 6 37-33 8 || 3.92 o-39 ICNOCIKASTIA. 3-ft. Theodolite, B.o. From 21st to 24th September 1836. Observer: Capt. PoETLocR, R.E. No. Recip. No. Rºº. Objects. Bearings. 3. Range. wi,ht. Objects. Bearings. di. IRange. wint - Corr Hill . ° 35' 38.8 ry £68 • II i Enock ° 10' 3. 7 2 1.81 o.81 4O '85 || 2 || O o. II | Isnockeyon 227 19 8.5 * A , º, . . . . ºf Monksland 84 ; ; 3 || 4.84 2.60 | Croghan 293 5o 26.08 || 5 || 9-03 #, Sievºwn,South I37 5 23.95 I tºmºs 3.82 Ballyduff * 335 4 I 59°34 3 4-47 Carn Clonhugh . I72 I4 56.67 || 2 | 2-22 | 1.23 126 PRINCIPAL TRLANGULATION. KNOCKLAYD. 3-ft. Theodolite, B.O. From 8th July to 17th August 1827. Observer: Lieut. PortLock, R.E. No. Tecip. * Objects. Bearings. º Itange. ºp Objects. Dearings. * IRange Hºp* Obs. Weight. Obs. Weight. tº tº O 4. & f */ O f # / A/ Slieve Gallion 34 31. 21.18 17 9.21 o.8o Jura . . . . . . I90 36 34.79 22 || 8.57 o.34 Carntogher • 47 53 Io-36 | II | 7.52 I-19 || Ben Lomond . 22O 58 54'41 || 6 || 5.83 | 1.41 Sawel . 53 15 36.63 || 31 || 13-oo o.46 || Ben Tuire 223 38 7.85 34 II.46 o.32 | Benyevenagh . 83 3 35.29 61 9-32 o. 12 || Goat Fell . 232 o 6.81 || 4 || I.5o o.15 Scalp 84 o 33-oo 15 8.37 o.81 | Carn-na-leagh 24o 39 52.96 || 42 I5-46 o°46 Eskaheen . . 84 50 25.17 | Io 6.70 o-63 | Cairnsmuir on Mount Sandy 93 11 12-og 17 | 5.27 o' 17 Deugh ' ' ' | 264 33 30-14 || 2 || 3:05 || 2:32 Slieve Snaght 93 36 47.49 || 31 7.86 o-21 ||Merrick • 270 33 19.86 I –" | 12:45 Magilligan Tower 94 33 1.52 23 13:18 || 1:24 Benereard • 276 38 33-29 | 12 I4.43 2.15 Ben Tarteyil . 169 3 29.57 ||31 | 16.12 o-39 Cairn Piot • 292 52 32-93 || 9 || 8.33 I-23 | Mull of Kinoe 173 46 28.91 || 7 || 14-24 || 5-36||Nachore • 312 I 43°37 || 5 || 6-3o I-94 Qa . . . . . . 177 3 53.87 41 || 13.92 o-39|Trostan : • 334 43 48.97 45 16.65 o.34 Scarib • * 184 13 45.61 13 6.68 o.44 | Divis . . • 346 I3 22-81 31 || 13.67 o-48 RNOCKNADO.B.E.R. 12-in. Theodolite. From 21st to 31st July 1840. Observer: Corp. DONELAN, R.S.M. ſº No. Recip. º No. Recip. Objects, IBearings. f | Range. f Objects. ings. |- ºsmº- Je earings dº. ange W: ght- Jects Bearings 6. Range. W3.ht. Feaghmaan . . 56°24' 57.72 7 Icog 3.76 |ICnocknagante . 303 48' 2470 7 26'82 I3'92. ! Brandon • | 168 38 13.26 || 5 || 6.44 2.54|| Hungry Hill . . . .322 5 59.12 || 2 | 2.97 || 3:30 Baurtregaum ... • 2.24 43 o.66 || 6 I2.97 || 6-49 ENOCKNAGANTE, I2-in. Theodolite. From 5th to 13th May 1840. Observer: Mr. BEALE. ſº * No. IRecin. g tº Objects. Bearings. . Itange. ºp Objects. Dearings. ; Range. Hºp * Obs. Weight. Obs, Weight. Feaghmaan 96. 4; 4$16 5 *6 Baurt O 6' A/ */ gnma; tº º 2I-09 || 29-37 aurtregaum IQI 40 25. I3 o. 28 i. Enocknadober 124 o 2I-73 || 6 || 13.72 6.69 fºungry Hill º 336 41 35-61 % ; ; OBSERVATIONS. '127 ICNOCIKNASKAG.H. 3-ft. Theodolite, B.O. From 21st to 30th October 1831. Observer: Capt. PontLoCK, R.E. Objects B No. Recip. IB * | R Fºr i ſº carings. f | Range. f Objects. ings. €. arings dº. ange W.§ ght. jects earings ði, ang Weight. ſº O f Z/ W/ O f // A/ Doolieve © a s 2 46' 33-79 || 6 || 7.70 || 2-ol Taur . . . . . . Io? 23 42.51 || 8 || Io:59 2.63 Carrigfadda : ' || 41 13 12-39 || 5 || 9-04 || 3.77| Slievecallan . . . I45 27 44.52 | 1 || – || 13.87| Qara Mountain 47 5, 52.35 | | | 6.98 || 16.51 | Knockfeerina . | 1.48 7 17:38 || 5 || 8.66 | 1.45 Slieve Buoymore | 64 32 38.79 || 4 || 3:47 2.52 | Keeper . . . 189 I2 33.46 | Io 8.58 I-84 Mushramore . . 74 41 58.36 || 6 || 5-31 | 1.54|| Galtymore . . . 211 1 4.96 || 8 || 13.26 || 4-co Mangerton . . . 78 39 32.87 || 2 | 1.19 o.35 | Slievenaman . . . 238 43 26.65 || 3 | 1.85 | 6:40 Caherbarnagh 8o 52 49-09 || 7 || 8.54|| 2:32 || Knockmealdown. 249 i 37.95 || 7 || 6.16 | 1.04 Mount Hillary, S. 89 II 23.51 | 11 6.73 o.8o | Slieve Grian . . . 279 21 42-05 || 9 || 16.35 || 4-23 Mount Hillary, N. 96 51 37-00 | 12 5.75 o.46 || Bunnaloo . . . . 288 II 27.47 || 7 || 5-I4 o.82 Baurtregaum . . . 97 II 18.52 || 4 || 11.33 8.16 LAWSHALL CHURCH TOWER. 3-ft. Theodolite, B.o. From 27th November 1843 to 28th January 1844. Observer: Serg. DoNELAN, R.S.M. –mºmº tº No. Recip. No. Recip. Objects. Bearings. of IRange. of Objects. Dearings. of IRange. of *— Obs. Weight. Obs. weight. * O / // f/ O f f/ £/ Thaxted Spire . 49 41 51.60 | 3 || 5-63 3.84 || Hingham . . . 200 21 19-80 || Io 4.31 o'52 Balsham Church South Lopham • 214. 4I 21.26 || 8 || 4 oz o°37 Toyer . . . . 85 8 58.81 || 5 | 1.32 o.o.7 || Mickfield”. . . . 256 43 50.82 || 2 | i-44 o'51 Drandon . i. I65 55 22:95 12 5.75 o.50 | Naughton . . . . 290 47 5.94 | 12 | 12:39 || 194 Swaffham Spire'. 177 36 32.% 4 2.43 o.41 || Stoke Tower . . 328 3 57.76 | 12 I3-oS | 1.5° { 1 A correction of + 7". 73 to be applied to this bearing, to reduce it to the trigonometrical station. * A correction of + o' 35 33 33 $3 LAXFIELD CHURCH TOWER. 2-ft. Theodolite. From Ioth May to 3oth June 1845. Observer: Corp. BAY, R.S.M. Obi IB * R Recip. O . R Rºjº. tS. ings. * f iccts. ings. alſº Jects earings ði. ange w; ght. bjects Dearings dº. 5 Weight. Otl O / / / &/ ſº º O / / / “28 .46 lº |ja 32 35 22:53 | 12 4.67 || 2:37 ||Norwich Spire 173 to 33:92] : 6-28 || 9.4 sº ‘. . . 59 4 35-11 | 12 8.16 o.73 || Tofts Tower . . . 213 21 ió.79 16 || 2:32 || 297 i. Popham 113 38 17.73 || 11 || 5.59 o.54|Southwold Tower | 262 4 15-86 19 || 5'92 || 2:Z| . ... . . . . 142 4o 19.9 | 19 | }.}}| 0.33|Örford Castle | 333 58 56.37 15 5-69 | *35 Referring-object . 1.5 # 33.33| 3 | ". ſº | * A correction of + on '41 to be applied to this bearing, to reduce it to the tri gonometrical station. 128 PRINCIPAL TRLANGULATION. LAYTON. 3-ft. Theodolite, B.o. From 7th to 9th June 1817. Observer: Mr. GARDNER, tº No. Recip. * No. ..Recip. Objects. Bearings, of | Range. of Objects. Bearings. of Range. }__of Obs. Weight. Obs. Weight. Z { IBlue Hill . . 16 23 &ool 6 27, o:36 Over Hill . 60° 16'46.18 || 6 5.31 | 1.58 i Tarbathy * I9 3 41.39 || 6 || 7.68 I-72 Dudwick . I77 53 9. I4 || 6 || 4.56 o-90 Brimmond . . . 46 5i 26.3% 5 2.18 o-25 LEITH HILL TOWER. 3-ft. Theodolite, B.O. and R.S. I'rom 3rd to 5th June 1792. From Ioth to 17th October 1822. From 13th February to 29th April 1844. Observer: Serg. DONELAN, R.S.M. Observer: Gen. MUDGE. Observers: Major-Gen. Col.BY, Capt. ICATER, and Mr. GARDNE R. * No. Recip. No. Recip. Objects. Bearings. of | Range. of Objects. Dearings. of Range. of Obs. Weight. I Obs. Weight. O Af f/ Af f &/ Chanctonbury Ring I 27 II or Io 5 or o.46 St.Paul's Cathedral 206'45 28:16, 18 6.81 o.42 |Rook's Hill 40 26 39'51 || 9 || 3:47 o.63 | Epping Cupola 2Io 7 I2-94 | Io 3.75 o. 19 | Butser Hill 62 52 47-27 | Io 6.18 o.9% | Banstead, Öld' 2I4 52 35.85 || 3 || 2:59 o'79 Inkpen . . ..., 194 49 16.76 13 || 5:45 o.57 | Referring-object 22I 32 45°o5|179 tºº * Whitehorse Hill I18 31 54.72 II 5.26 o:36 || Severndroog • 222 46 41-24 45 5'98 o'o6 Bagshot . . . 13+ 3 34°51 || 2 || 4:34 || 4-71 Wrotham . . . 25o 54 I5'IQ 4o 4, 16 o.o.5 Windsor Castle + Wrotham, Old 251 48 50'24 || 5 || 2:54 o'26 Plagstaff I54 42 18-98 || 2 || 1:25 o.39|Hallingbourn. 261 23 18:18 II | 6-or o'54 St. Anne's . . . . 156 34 49-69 I tºº. 1.96 || Frittenfield 267 19 12.35 | 8 || 6.49 o.84 Wendover . . 156 42 II.O.4 || 6 || 3.71 o.55 | Frant Church 28o 43 30.98 Io 3. I4 o°49 | Dunstable . . . . 171 32 56-47 | 9 || 4:57 o°36|Crowboro' . . . . . 289 51 45.8o 31 6.61 o.o.9 | Hanger Hill Tower 187 23 42.91 || 31 6.73 o-13 |BlackheathWindm. 295 5o 5.37 || 1 tºmº I-96 Berkhampstead 194 44 fo.or II | 6-04 || o'44|Beachy Head ' ' || 317 4o 1.56 || 8 || 4:45 o.51 WestminsterAbbey 205 6 29.1o 26 || 9.47 o-30 | Ditchling . . 328 42 47.76 || 9 || 8.99 || 1.46 * A correction of + 12”.47 to be applied to this bearing, to reduce it to Banstead, New. LINCOLN MINSTER. 2-ft. Theodolite. From 29th June to 24th September 1842. Observer: Lieut. DA CoSTA, R.E. - No. _ _ º No. in. Objects. Dearings. . Range. Rºjº. : Objects, Bearings. .# Range. Fº Obs. Weight. Obs, Wei ght. : º * O f f & f O / / / // Buckminster Spire | 12 38 7.20 || 4 || 1:30 o.15 | Sutton Hill . 73 55 38.32 || 5 || 6-40 | 1.88 | Stathern ... ' 26 4; 39°35 | 4 || 3-80 | 1.58|| Axedge g 90 26 29.90 || 4 || 2.60 o'55 Bardon Hill, 42 38 8-84 || 8 || 9:49 2.72 | Back Tor . Io.ſ. 58 54-40 | I - || II • OO | Holland Hill 59 54 16.35 | 4 || 4:39 | 1.36 | Referring-object . . Io9 23 54.8o IIo | 19.1o o.12 OBSERVATIONS. I29 LINCOLN MINSTER—continued. tº Deari - No. Recip. º tº No. Range. Rºjº. Objects. arings. o:º Range. W#ht. Objects. Bearings. 6. ang Weight. º O Af Af Z/ O & £/ Af Clifton Beacon 118 53 55.72 | 6 6.95 | 1.78 | Flint Hill . . . . 262. 2 27.90%| 6 || 4-oo o'5t Crowle'. ' ' ' | I55 22 27.67 || 6 || 5.39 1.60 || Greetham . . . . 273 7 11-04 || 4 || 9:35 | 5:49 Normanby, ' ' || 2: 20 55-65 || 4 || 4.39 | 1.42 | Boston Tower 309 34 o'52 | 8 || 15:14 || 4.89 Maidenwell 259 o 21.62 || 7 || 6-34 | 1.30 | Wellingore Spire | 359 3649-25 || 5 || 4 oz o-82 * A correction of +5"'54 to be applied to this bearing, to reduce it to the trigonometrical station. LITTLE STIRLING. 3-ft. B.o., and 7-in. Theodolites. From 5th to 7th July 1814. Observer: Mr. GARDNER. From 7th to 23rd November 1850. Observer: Corp. STEEL, R.S.M. Objects. Beari No. IRecip. Beari . R Rºjº. º * º º €. O jec * |&|*|wº. Objects. * || |*|wº. Blue Hill . . . . 2 § I 3. ifor 3 £oy 1.91 |Peterhead, Old O / ſſ £f Caerlock . . . 38 18 17.65 || 3 || 3.82 | 1.93|_ Windmill . 190 13 32.49 || 2 | 17.75 78-76 Pudwick. . . . 76 53 62.07 || 6 || 3.8o o-48 || Reform Monument | 192 3 36.72 21 | 62.13 || 30-59 Mormonth . . 14o 28 Io.89 || 6 || 5.72 | 1.5o || Great Stirling 248 44, 27.81 || 23 ||37.54 || 7-14 LITTLETOWN DOWN. 18-in. Theodolite. From 31st July to 1st August 1846. Observer: Corp. STEEL, R.S.M. * No. Recip. No. IRecip. b Q ings. º * ge. of Objects Bearings o:º Range. W3.ht. Objects. Dearings. o:& Range Weight. sº o / // f/ O f f/ Af Ventnor Ch. Spire | 26 4o 49.89 13 | "- – | Boniface Down . . 205 5242-56 || 9 || 12.98 || 3:37 Week Down . 84 31 36.46 || 9 || 7.83 o.99 || Boniface, S.E. 228 2 4°o8 || 9 || 13:55 3.87 |Wroxall Down | 123 59 19.39 || 3 |49.8% 129-30 | High Port Cliff 302 59 44, 16 || 9 || 20:07 || Io-71 LLANELIAN. 3-ft. Theodolite, B.o. *—- 1805. Observer: Major-Gen. Col.BY. Objectse - º No. IRecip. º º Nº. R Rºjº. *— jectse Bearings. d;º Range. W.#ht. Objects, Bearings. o:S. ange. Weight. Arenig © f f/ A/ 68 G 6 O / 8.81 4. 4:30 I-4. I - ~2 , " " | I 3o 32-25 || 4 || 7'oz 3. arreg . . . 20I 22 48. - • 5C 1" Qrme's Head . . I36 3o 39.84 16 II-28 o.69 || Moelfre Issa • 275 16 27.19 || 4 || 9'99 º: Billinge . . . 247 4 30-33 || 4 || 8.90 5-43 Cyrn-y-Brain. 302 47 3-2 I | 7 6.o8 || I-3 Gwaunysgaer 251 38 33-34 || 1 tº-º - | - | R I3o PRINCIPAL TRIANGULATION. LONGMOUNT POLE, 3-ft. Theodolite, R.S. From 10th October to 9th November 1843. Observers: Lieut. LUYKEN, R.E., and Priv. STEwART, R.S.M. . . iº No. IRecip. tº No. * Recip. Objects. Bearings. of | Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. O ſ Z/ A/ O & f/ Wº Cradle . . . . . I5 6 20-66 20 8.32 o-31 | Ashley . . 217 56 31.33 || 7 || 3:11 o.42 Stow . . . . 25 25 I7.65 7 3.72 | O'5I Axedge tº º 218 26 52'o6 6 2.5o o°28 Radnor . . . 36 39 16.65 || 5 || 4.41 I.i.5 | Bardon . . . . . 259 8 5'90 || 4 || 1:54 o.15 Llandinam 7o 4o 26.64 | 16 || 7.66 o.65 || Lord Plymouth's Plynlimmon | 82 28 39.68 14 || 7.32 o.40 || Monument. 287 46 20.5o I - 5.61 Cader Idris . . . IoA. 6 29.26 12 || 3.64 o.19 | Brown Clee . 292 59 37-40 || 4 || 6.90 || 3:56 Snowdon . . . . I25 57 62.92 || 5 || 5-69 | 1.67 | Cleeve • 319 31 18-79 || 8 || 9.21 | 1.41 Cyrn-y-Brain I59 I5 37.13 || 7 || 3.79 o°41 || Malvern • 323 36 6o.20 | 9 || 2.93 o. 17 Mowcopt . . . 2I4 23 42.65 I tº 5.61 |May Hill . • 338 19 39.7I | 3 || 3-79 I-86 LOUGHANILEAG.H. 12-in. Theodolite. * * From 19th September to 17th October 1828. Observer: Lieut. HENDERSON, R.E. No. of No. Recip. tº No. of No. IRecip. Objects. Dearings. Repe-Jof Simple of Objects. Bearings. Repe-of Simple of |titions. Arcs. | Weight. I titions. Arcs. | Weight. O & Af O & & W. | Croghan . . . 2I 5o 40°23 57 o-og |Mullyash . . . . 207 Io 56.46 15 O'4I. Inockastia • 43 3 24-80 | 19 o: 14|Slieve Gullion 232 5 59.42 39 3.36 Slievel}awn South 75 6 48.17 | 12 o:60 | Slieve Donard 244 23 35.62 | 15 3°4I Carn Clonhugh ' || 78 27 51 or 30 o'o6 |Castlecoo . . . . 287 59 56.76 || 45 O OI |Cuilcagh . . . II9 2 4I. I2 98 o-o8 || Hill of Howth 316 53 11-62 | 12 o-o:3 | Carnmore . . I48 58 I9'23 || 51 o:75 | Rippure . . . 334 49 16.84 || 61 O-I4. From 23rd November 1827 to 25th January 1828. Observers: Lieuts. HENDERSON, MURPHY, and MoULD, R.E. LOUGH FOYLE BASE, NORTH END. 2-ft. Theodolite. t Objects, Bearings. *: IRange. R; p. Objects, Bearings. . §º. Rº: P. Obs. Weight. Obs. Weight. sm-- O / Z/ &A O f ſ/ */ Sawel . . . . 8 55 54.08 || 2 | 2.99 || 2:24 | Cundtham . . 197 49 47-66 II || 9 og | 1.02 South End of Base | 17 12 28-36 || 6 || 5.68|| 1:21 |Magilligan Tower | 168 43 44.59 || 4 || 6.7% o.o.4 Drung Point . . . 9o 49 46.56 Io 452 o°39|Mount Sandy 197 12 24.41 26 || 4.46 o.14 Slieve Snaght • IoI 37 42.67 || 9 || 6’23 o'89 : OBSERVATIONS. From 8th November 1828 to 14th January 1829. Observers: Capt. PRINGLE and Lieuts. MURPHY, LOUGH FöYLE BASE, SouTH END. 2-ft. Theodolite. HENDERSON, and MoULD, R.E. ~ * No. of No. Recip. No. of No. Iłecip. Objects. Bearings. Repe-of Simple of Objects. Dearings. Repe-of Simple of |titions. Arcs. Weight. titions. Arcs. Weight. | ſº O / ſ/ - O / // Slieve Snaght . 129 31, 56.89 27 25 o.o8 | Cundtham . . I54 26 43.58 || 17 | 18 o. 16 Ballykelly Church | Mount Sandy I97 9 34:20 II 4 || O'34 Tower . . . 14o 4 59.08 || – 2. – | North End of Base 197 9 35.12 || 5 || 17 o:23 Drung Point . I43 38 42-61 20 25 O - 2 I - - LUMISDEN. 3-ft. Theodolite, R.S. From 20th April to 17th May 1846. Observer: Corp. WINZER, R.S.M. No. Recip. No. Irecip. Objects. Dearings. of | Range. of Objects. Dearings. of IRange. of Obs. Weight. Obs. - Weight. O & Z/ &/ O f f / £f Sayrs Law . . 77 8' 24 oz | 13 5.69 o.38 || Craigowl . I45 I2 I5. I4 || 4 || 2:04. O-3 I East Lomond . . . 120 57 6.35 | 4 || 3:15 o.68 Glashmeal. I46 45 28:95 || 6 || 48o o.84 Largo Law . . . 129 26 20-27 || 7 || 2:06 o.13 || Mount Battock 164 19 13-28 || 6 || 3.72 o-33 Kellie Law . . . . 136 56 20-64 13 || 3.5o o.14|Caerlock . . . I7I 29 4'50 I – 2.88 | Isle of May Light- Blackheddon . 329 43 41 o'7 || 9 || 3.87 o°29 house - • I44 53 47.86 7 º - || Cheviot 355 23 36.69 26 || 5'92 || o' 17 LUNDY ISLAND. 3-ft. Theodolite, R.S. From 17th February to 9th April 1845. Observer: Corp. STEwART, R.S.M. No. IRecip. No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of Range. of Obs. Weight. I Obs. Weight. O / / / WM º * O f f f Z/ Cadon Barrow 2 6 49.87 || 4 || 3:43 o.78 || Referring-object 194 25 50.99 || 77 4.25 o.or Hensbarrow * 6 48 31.46 II | 1.87 o.o.5 | Llannon 208 54 o-84 Io 6.52 o'73 || Trévose Head 20 31 44.54|| 11 || 6-of o.53 |Cefn Bryn 218 42 21-27 | 6 || I-95 o'I3 St. Ann's . . . I49 42 30.58|| 8 || 2:49 o. 15|Margam Down 234 55 24-22 || 9 || 7-14 || O'91 Highgate . I61 26 20-25 || 5 || I-97 o.23 || Llangeinor 235 o 26-oz || 4 || 3: Io o:64 Newton Down I65 I 46.99 || 4 || 1.5o o. 16 || Paracombe 268 43 51.51 II || 482 o:36 Précelly I75 22 41.09 21 5.31 o-17 | High Wilhays 318 47 54.93| 19 || 5-63 o?” Marros Beacon 184 17 42.47 || 6 || 6.74 | 1.63 Brown Willy . 355 34 34.88 II : 3.22 o-20 R 2 I32 PRINCIPAL TRIANGULATION. LYNN TOWER. 2-ft. Theodolite. From 12th March to 14th May 1843. Observer: Corp. BAY, R.S.M. tº No. Itecip. No. Iłecip. Objects. Bearings. of | Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. * f/ O & ſº Ely Minster . . . I 3° 18' I £66 II 4:42 o:30 || Great Massingham Af Walpole:St.Peter's 78 4 53.21 || 5 || 4-75 | 1.3o | Church . • 261 51 31.67 || 2 | o'73 o.13 Boston Tower' . 131 37 33.21 || 8 || 4.85 o.36|Swaffham Spire”. 3oo io 57.5o || 7 || 4-25 | o'73 Docking Church Tower . . . . 222 3 31-04 || 9 || 491 o.43 * A correction o f — 26".95 33 33 33 ! A correction of + 6”.42 has been applied to the observed bearing, to reduce it to the trigonometrical station. LYON'S HILL. 3-ft. Theodolite, B.o. From 18th to 23rd January 1829. Observer : Lieut. Pontlock, R.E. No. Recip. * No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. O f // Af & A O f // &/ Cadeen ... . . . . 441 48.89 || 5 || 3.94 || 0.78|Dublin Obser- Church Mountain 7 17 9.5o || 3 || 2.70 | 1.oo |_vatory • 23o 39 27.65 || 9 || 7.77|| 1:19 Cullenagh . . 52 38 42-48 || 1 - || 6.47 |Howth . . . . . . . 253 16 17.71 || 9 || 6-77 o'77 Dunmurry • 69 I 16-14 || 11 5.95 o.32 || Poolbeg Light- Hill of Allen . . . 72 54 2.15 || 14 || 3:19 o.13 house . . . . 257 II II-09 || 2 | of 86 o.18 Croghan ..... ." | 97 27 11:52 || 4 || 1.96 o.24|Rippure ... • 312 29 27.32 | I3 I2. II | I-98 GarristownWind- | Lugnaquillia • |352 26 29.94 || 5 || 3:34 o-05 mill . . . . . I97 I3 33. I9 || 6 || 4.69 o'99 MAIKER, CHURCH TOWER. 3-ft. Theodolite, B.O. From 8th May to 5th June 1846. Observer: Serg, Don ELAN, R.S.M. No. in. tº * Objects. Bearings. . Itange. Hºp : Objects. Bearings. *: Itange. Rºjº. - Obs. Weight. Obs. Weight. Eddystone Light- " ' " " | | Kit Hill Tower 158 4' aſ 63| 8 | #52 | 1.39 house . . . . I7 I9 o'85 | 8 || 5-46 o.87 | Black Down • 189 21 41.09 || 6 || 5-30 | 1.34 Maker . • 64 45 31.87 |Io2 5-52 o.o.2 | High Wilhays 198 7 4-33 II || 3.78 o.22 Deadman . . . . 72 34 40.5o 21 || 9.34 o°52 | Butterton, New 25o 37 o-91 || 7 5. I9 || I'o6 Lansallos • 88 23 12-80 || 7 || 7.52 | 1.56 || Butterton, Old 25o 4o 33.42 2 5.34 || 7"I2 Hensbarrow 95 22 o'47 || 32 || 6.92 o.16 || Barrow Hill . 290 36 I-87 || 25 | 7.77|| 3:38 i OBSERVATIONS. 133. MALVERN. 3-ft. Theodolite, R.S. From 28th November 1843 to 27th January 1844. Observers: Corp. Cosgrove and Private STEwART, R.S.M. tº No. Recip. No. Recip. Objects. Dearings. of | Range. of Objects. Dearings. of | Range. of Obs. Weight. Obs. Weight. * : O & A/ Af O & & f ff Mendip, 8 18 15-31 || 2 || 3:37 2.83 || Lord Plymouth's May. Hill . I6 37 20.5I | 9 || 3:52 o.32 || Monument . 216 26 32.22 || 1 - || 2:35 Trellig . . . . 32 31 32.67 || 6 || 3.81 o.30 |Bardon . . . . . 225 12 34-95 || 2 | o-48 | c.66 Cradle . . . . . 72 45 56.74 || 7 || 3-94 o.5o |Arbury . . 259 45 8-ol || 8 || 2.79 o'I9 | Radnor . . Io'7 23 40-59 I – 2.35 | Broadway Tower 284 22 17.73 || 8 || 1.8o o.o.7 Stow . . . . . . . 122 44 35.65 || 4 || I-66 oºzo Breedon Tower . . 284 45 37-31 || 1 - 2.35 Longmount Pole | 1.44 2 9-46 || 9 || 5-I4 o'54 || Cleeve'. . . . . . .311 51 16-28 || 8 || 2.48 o.25 | Brown Clee . 156 47 59-22 || 9 || 3:36 o-22 | Whitehorse Hill |317 37 6.20 || 7 || 4-76 o-58 ' A correction of -1" o4 to be applied to this bearing, to reduce it to the trigonometrical station. MAMSUIL. 3-ft. Theodolite, R.S. From 29th July to 31st August 1848. Observer: Corp. WINZER, R.S.M. No. IRecip. No. IRecip. Objects. Bearings. of Range. of Objects. Dearings. of Range of Obs. Weight. Obs. Weight. Creachbheinn 1; 34 57.66 17 9.79 o-66 || Ben Wyvis 2. I § 57.43%; 34. 8.52 O-25 Ben More in Mull 30 9 24-09 || 9 || 4.76 o-50 |Corryhabbie . 265 38 38.35 | 29 || 6-83 o-21 | Ben More, South Ben Macdui . 284 I6 43-37 19 II.64 o'58 Uist . . . 89 52 66.71 21 | Io. 15 o-38| Glashmeal . . . . 292 21 18.68|| 4 || 4.97 || 2:07 Storr . . II2 3 36-22 || 32 6.45 o-17 | Ben Amhlair . . . .322 14 8.46 21 || 7-11 || o'26 Cleisham : I27 42 37'92 || 14 6.44 o.37 || Ben Lawers . 325 48 38-og 24 9°37 o°37 Scournalapich 2Oo I5 29-23 44 || 8.38 o-17 | Ben Nevis . 352 24 15-99 || 27 | Io-28 || O-46 MENDIP. 3-ft. Theodolite, R.S. From 6th September to 6th October 1844. Observer: Corp. STEwART, R.S.M. No. Recip. No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. | tº O / / / Aſ O / / / f/ Pillesdon . . 23 59 8.40 | 1.4 5.74 o-31 | Symonds Hall 198 IA. 24.33 || 6 || 8-79 2:21 Staple Hill . 5i 14 48.51 || 5 || 6.13 | 1.60 | Whitehorse Hill 239 20 40-27 || 7 || 4-06 || o'42 High Wilhays 6o 38 4-12 || 6 || 6.15 1.5o |Inkpen • 258 23 8.23 Io 5-70 o-62 Dunkery tº • 85 32 6.21 | 12 || 4.19 o.24 || Westbury 26o 26 28.88 II || 4:19 o°21 Referring-object 114 34 10-06 || 95 tº-º: — Beacon Hill . . . 273 32 18:81 | 12 8.51 || O'7% Cradle . . . . . I54 4 52.05 II | 7. Io o-66 || Wingreen . • 316 9 18.32 15 5-67 o°39 Dundry 161 & 42.69 || 7 || 4.76 o.65 | Bull Barrow . . . .338 38 39.61 || 8 || 4 oz || 2:39 Malvern 188 8 Io.86 14 | Io.78 o.99 || Mintern . . . 355 46 46-64 || '5 3.9% o'74 I 34 PRINCIPAL TRIANGULATION. MERRICK. 3-ft. Theodolite, B.o. From 25th May to 2nd August 1852. Observer: Corp. J.ENKINS, R.S.M. No. Recip. No. Recip. Objects. Dearings. of Range. of Objects. Bearings, of | Range of - Obs. Weight. nº Obs. Weight. Glasserton 1° o 47.50 I6 5.37 o.21 || Corkmulaw † 191° 18' 2.É. 5 5 3's 5 I-37 South Berule 6 47 45.72 35 | 6.24 o. II | Bin of Campsie ' | 191 53 31-22 || 5 || 5.83 | 1.97 Mull of Galloway | 24 8 34.59 ió | 6.88 o.35 | Ben Cleugh 2Oo 24, 27. Io Io 5-46 o.52 Slieve Donard 41 52 49 o8 24 6.23 o.19 || Tinto 225 2 52'22 22 8.02 o.38 Cairn Piot . 5o 4o 46-oo 21 || 7-04 || 0.36 | Cairnsmuir on Divis . . . . . . . 6o 3 52.46 11 9.83 | 1.06 || Deugh . . . . 231 I5 32-31 || 37 || 6-03 o. II Referring-object | 71 27 o'36 24 tºº. – l Pſart Fell . 245 45 7.87 | 28 || 5 II o. 14 Benereard 74 26 21.96 28 7.8o o.19 Wisp . . . . 259 47 3.98 || 15 || 3:34 o-o? Trostan . . 85 Io 12.67 32 5.20 o.o.6 || Burnswark 273 I2 28-29 || 2 || 6.49 IO-53 Knocklayd 92 o 50-72 26 5.56 o. 15 | Cross Fell • 290 6 Io. II | Io 5.29 o'55 Carn-na-leagh Iog 32 48.27 | II 9.44 1-05 || Criffel . . . . . 292 I 53.45 20 || 4-72 o.23 Saugh- . 116 15 51.02 || 39 6.65 o'Io || Ben Cairn 31o 7 15:36 | 19 || 7-95 o'38 Ben Tuirc 124 47 55.94 || 14 || 6-oi o-36 | Sea Fell . . . . .312 48 54.59 |32 || 6-3o o-I3 Jura . . . I31 50 45.62 | 18 7.41 o-31 || Black Comb 322 42 25-75 || 36|| 6-52 o'I2 Goat Tell . . . . 14o 2 48.31 | 12 4.51 o.26 || Cairnsmuir of Ben More in Mull 146 31 5-II | 13 5.33 o.35 | Fleet . . . 336 8 51.54| 24 || 4-74 o. II Hill of Stake . I66 43 6.57 20 | 7.51 o.40 | North Berule. 357 3 53.75 || 5 || 3.73 o-83 Ben Lomond . I75 o 4o-oo 29 5.59 o.o.8 || Snea Fell . 359 44 2 I-66 || 5 || 4:54 I-35 Ben Lawers . I85 33 23.73 || 19 || 4.94 o. 18 MERRINGTON CHURCH TOWER. 12-in. Theodolite. Prom 19th June to 15th July 1854. Observer: Mr. CAHILL. No. Recip. No. ! IRecip. Objects. Dearings. of | Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. - Weight. Water Crag . 50 59 2. 398 4. 1.1%77 | 11.69 | Durham Observa- O / / / * * A/ Collier Law . I 12 38 40-42 19 17.09 || 2:04 || tory . . . . . I 82 43 5-I4 || 2 | 8-79 | 19.31 Brandon Down I.47 35 7.62 25 25-49 2.94 || Wordeslow 209 II 47. Io I5 I6. II | 2-97 | MICICIFIELD CHURCH TOWIER. 18-in. Theodolite. From 3oth January to 25th February 1845. Observer: Corp. STEEL, R.S.M. +º. No. || in. { } º Objects, Dearings. . , Itange. Rºp Objects. Bearings, . Range Hºp. obs. # Weight. Obs. Weight. * = - O / / / - Aſ O / / / #/ Naughton . . . . 43 45 I4-22 || 2 I 22.29 2.34 Bunwell . . . 180 45 20.14 28 8.77 o-44 Lawshall • 77 2 6-28 || 21 15.38 | 1.65 | Laxfield 238 53 3:53 20 8.13 o.44 South Lopham 157 3 39:76 12 || 7-38 o-84 || Otley Tower . . . .316 54 32.70 || 27 | 17.13 o.33 OBSERVATIONS. 135 MILK HILL, 3-ft. Theodolite, R.S. From 27th March to 13th May 1850. Observer: Serg. DoNELAN, R.S.M. ... & No. Tecip. No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of | Range. of . . . Obs. Weight. Obs. Weight. Four-mile stone & 46 698 3O 995 o. 17 | Inkpen . . . . 27 # 28' 53:21 I4. 6% O-47 | Wingreen. . . 22 33 36.80 || 33 II.36 o.47 | Old Lodge . . § 6 #. 22. § o:39 Šºkº Hill, 51 33 38.32 17 | 735 oší |Beacon fill . . .337 13 60.15 40 7.4% of 8 Westbury Down 37 33 10.58|| 36 Io-og o-37 || Dean Hill . . . 34o 8 59.05 21 5.89 o.22 Mendip ...: ' ' || 70 20 3-65 22 || 6.95 o-23 || Thorney Down 341 53 54.93 28 16.87 o.60 Cleeve Hill . . 17o o 32.47 II 4.3% o:39 || Queen's Manor 347 45 43.15 27 | 8.44 o.23 Upcot Down . . 194 49 34.51 23 5-17 | o 18 |Old Sarum Castle 354 I2 7:45 20 ! 3.42 o-oS Whitehorse Hill. 221 32 44-62 || 3 || 5.86 3.84 * I “ . MISTERTON CARR BASE, NORTH END. 3-ft. Theodolite, B.o. I8or. Observer: Mr. WoOLCOTT. º No. Tecip. No. Recip. Objects. Dearings, of | Range. of Objects. Dearings. of | Range. of Obs. Weight. Obs. Weight. O f f/ A/ i. O / / / Z/ South End of Base | 8 56 43-oo || 5 || 2.68 o.32 || Gringley . . . . .354. 27 o'Io || 5 || 415 || I-off Clifton Beacon 69 14 o'76 || 4 || 4:42 I-64 MISTERTON CARR BASE, SOUTH END. 3-ft. Theodolite, B.o. 18OI. Observer: Mr. Woolcott. º No. IRecip. º No. Recip. Objects. Bearings, of | Range. of Objects. Dearings. of Range. of Obs. Weight. Obs. Weight. O & f/ &/ O Clifton Beacon 99 I. I.4-21 || 6 || 5.5o | 1.49 || Gringley . . . . .335 9 North End of Base | 188 56 39-04 || 8 || 8.88 || 2:04 Af &A Z/ . 40-46 | 9 || 9.84 || 2:15 MOELFRE ISS.A. 3-ft. Theodolite, B.o. 1806. Observers: Gen. Col.By and Mr. WoOLCOTT. No. Tecip. No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of | Range. ...of Obs. Weight. Obs. Weight. - tº f Af &/ Planelian & Q & 95 24. 3.23 4. 394 2.66 |Gwaunysgaer 23: 39 39-69 || 5 || 3:49 ...; Orme's Head . . II 7 13 28.34 || 5 || 6.29 2.06 | East End of Base 236 41 33'59 5 6.96 || 2: West End of Base | 17%. 3, 20.36|| 7 || 5.56 || 0.75 Cyrn-y-Brain. . 3io 51 stay 4. 4-3 tº & Af 136 PRINCIPAL TRIANGULATION. MONACH. 3-ft. Theodolite, B.o. From 23rd October to 6th September 1839. Observers: Lieuts. Robinson and HoRNBY, R.E. * N Recip. D. i. Objects. Bearings. . Range. º p Objects. Bearings. jº IRange. Rºjº. ºmº- Obs. Weight. Obs. Weight. º O Af z, £ *- Af gº tº º 34 17'34.22 28 16:23 oš5 Ben Clibrig . . 276 5.2%g | 11 1987. 443 ë. W. *Li 198 23 18.91 || 6 || 7-16 || 2:28 Suilbheinn. • 290 44 45°41 I3 o'59 5'99 º: rath Light- Scournalapich' 325 25 55-65 || 6 || 9-51 || 3.5o cºi iii. 248 I 17.64 || 8 || 8.36 2.28 || Ru Rea '. • 33o 49 47-2I | 7 || 9'o.2 2:32: fashvi: iubhais . 251 14 38.60 | 1 - 2I-44 || Storr . . • 355 23 32.70 || 20 6'93 o'32 àSily CIl e • 253 5o 2.38 || 13 || 7-22 || o'86 - 1 A correction of + 38". 61 to be applied to this bearing, to reduce it to the new station. MORDINGTON. 3-ft. Theodolite, R.S. From 6th March to 15th April 1846. Observer: Corp. WINZER, R.S.M. i. No. Recip. tº 1 * sº Objects. Bearings. . IRange. ºp Objects. Bearings. * Range. Rºp. Obs. Weight. Obs. Weight. tº O & W/ */ f & § ' ' ' || 7 18 1494 41 || 6-11 o'o6 |Sayrs Law, . 96. 52' 1937 I6 6:15 o:38 Wisp Hill . . . . 44 31 36.96 || 13 4.43 o-28 |Referring-object 148 27 44.92 | 89 ºm iº Dunrich . . . 69 55 53.87 24 7.56 o.20 |Blackheddon 334 3631-82 II || 5-06 || O.43 MORMONTH. 3-ft. Theodolite, B.O. From 22nd February to 22nd April 1847. Observer: Serg. DONELAN, R.S.M. • . . & No. IRecip. No Reci Objects. Bearings. of | R * f iects, * lº ecip. Obs. ange wä ght. Objects Bearings. ði. Range. wi,ht. Qudwick, . . . o 41'5473 23 935 o-39 || Manor Lee 88” 56 8:24 7 3:46 o:35 #. . 13 44- 3. : 3:62 o'86 |Scarabin. I27 19 52.89 20 4.53 o.13 . 4 32 48.95 I 6.95 o-60 || Ben Cheilt . . 135 4I 6-ol I9 || 4-43 o. 18 Caer . º k 22 24 37.36 29 | 668 o.15|Peterhead, Old - Mount Battock • 3. 44. . 28 6.82 o-22 |, Windmill . . . 305 I 22.02 || 5 || 2.56 o.40 Buck bbi º 3. 3. 58-99 || To 453 9:35 Teform Monu- Corryha si. 4. 8 52-11 || 37 | 6′35 o'Io , ment.Peterhead | 311 11 51.15 11 6.56 o°73 Referring-object . 4. 55 I7°o2 |I5o tºº – Little Stirling 320 I6 52-92 22 9:07 o-35 Knock • • | 87 39 35.32 I3 || 4.92 o°3o 3 OBSERVATſūNs. 137 MOUNT BATTOCK. 3-ft. Theodolite, B.O. From Ioth March to 3rd July 1847. Observer: Serg. DoNELAN, R.S.M. No. Recip. -> No. Recip. Objects. Bearings. of IRange. of Objects. Dearings. . of Range. of Obs. Weight. Obs. Weight. tº O f M/ f/ O Af & f f IXellie Law . I 44, 36.83 || 8 || 2.87 o-21 || Mormonth 2 Io 8 * 17 | 505 oz3 Largo, . . . . . 8 8 44.90 || 2 | 1.26 o-39 Dudwick . . . . . 218 II 31.52 9 2.73 o.18 Carnethy Cairn 15 8 24.21 Io 4 or o.29 | Brimmond 23o 39 I2-oo 18 5.29 o-3o Craigowl . 20 36 1.99 || 16 || 7:46 o.35 | Referring-object 238 28 21.5o II *E*E. * East Lomond. 20 42 15.68 || 13 || 4-29 o-27 | Blue Hill . 246 18 30.84 18 6.19 o-25 Ben Cleugh 37 I 4o-95 | 16 || 6′49 o°41 || Caerlock 256 17 57-64 I7 4.90 o. 26 Glashmeal. . . 77 43 54.99 || 28 5:53 o’lo || Broxy * 278 I5 57.36 I2 5.20 o. 26 Ben Macdui . 103 51 13.60 33 || 6-06 || o-II | Red Head . 337 33 33-o5 14 || 5-65 o'56 Corryhabbie . 148 II 18.5I 25 || 4.97 o. I6 | Lumsden • 343 52 19:28 20 || 3-74 o' I2 Buck º 159 53 9-51 24 6-62 o-21 | Sayrs Law 357 54. 26.38 I4 2.66 o. II ICnock . . . 178 21 48-49 I4 || 3:16 o.13 -- MOUNT SANDY. 2-ft. Theodolite. - From 24th June to 6th July 1829. Observers: Capt. DAWSON and Lieuts. HENDERSON and MURPHY, R.E. - No. : No. IRecip. No. of No. IRecip. Objects. Dearings. Repe-lof Simple of Objects. Dearings. Repe-|of Simple of titions, Arcs. | Weight. titions. Arcs. | Weight. Q ſ f/ O & &/ Sawel . . . . . . 9 39 17-31 || – | 16 o-64 | Slieve Snaght 93 46 32.44 | – || 17 o'38 North End of Base | 17 13 II-94 | 12 22 o'o6 Magilligan Tower | 121 4 13.12 || – I - I South End of Base | 17 13 15-38 || – | 15 o.21 || Ben Tartevil . 206 51 3-oo - || II 2.25 Drung Point . 77 4. 22. I3 | – || 17 o-22 || Jura . . . 215 46 5o:53 - I jºr Cundtham • 9I 13 I-16 || 5 || 17 o. 19 || Knocklayd 272 37 4o. 18 || – | 16 o'37 MOWCOPT. 3-ft. Theodolite, B.o. From IIth March to 18th May 1851. Observer: Corp. JENKINs, R.S.M. . No. Recip. No. IRecip. Objects. Dearings. of | Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. *=-—— O / // f/ * O / f f Af Referring-object . 28o 37 6.87 27 | 6-07 | – || Cyrn-y-Brain 82 51 5-27 | 12 8.35 o°75 Brown Clee . 20 17 50-68 || 12 4.72 o.33 Snowdon . 88 22 37.53 || 4 || 2.83 o-66 Black Bank 24 6 54.56 29 6-96 o. 17 | Delamere . IIo 48 33.86 20 || 7-14 o'21 Ashley Heath 27, 14 25-41 28 7.81 o.20 | Bellefield : I37 22 24-55 I4 || 7-79 o'54 Longmount Pole 34 54 58.85 27 7.22 o. 24. Whittle Hill . 176 42 54.73 26 || 5' 14 o' 12 Hºme Obc- Holme Moss . 204 49 21.81 | 18 § o-o'7 1SR • * ~ * 26 24, sº | Io 6.16 o-66 | Axedge . . 233 19 29.94 | 40 || 8-40 || 0:47 Nantwich Church 44 4°55 - #. Hill . ; % . 36 || 8:38 o-28 Tower Vane 75 38 1-62 | 15 6.89 o-57 Bardon Hill . . . .306 13 50-oš | 16 | 4.67 o'20 s 138 PRINCIPAL*TRLANGULATION. NASEBY CHURCH TOWER. 18-in. Theodolite. From 24th October 1842 to 3rd March 1843. Observers: Corp. STEEL and Priv. M*NALLY, R.S.M. *. † No. Recip. No. heir Objects. Dearings. of Range. of Objects, Bearings. of Range. of obs. Weight. Obs. Weight. tº O / / / * f/ • , a | , |Arbury Hill 38 24 50.73 II || 1771 3.64 | Easton Tower 231 IG 3 or .6 . I5-84 Io-oš Bardon Hill . . . I.47 39 59:43 || 5 | 16. 6-48 || Keysoe Spire . . . 292 55 18-90 || 4 || 9:78. 7. rºw is 75 4. y p i. 9:7 49 Tilton . . 19636 28.05 || Io II.96 | 1.96 || Hanslope Ch. Spire 34o 42 o'84 || 6 || 8.51 || 3-og NAUGHTON CHURCEI TOWER. º 18-in. Theodolite. . . . From 9th November 1844 to Ioth January 1845. Observer: Corp. STEEL, R.S.M. No. IRecip. No. ' ' ' | Recip. Objects, Dearings. of Range. of Objects. Bearings. of . Tange. of Obs. Weight. Obs. Weight. O f Af Z/ O f Af Af Stoke Tower 18 22 2.83 || 15 7.85 o.62 | South, Lopham 185 20 15.8o I - II-45 Uanbury Spire 31 21 38.20 || 3 || 5-69 3-69 Mickfield" , , 223 37 I8-oz I7 I5'43 I-73 Thaxted Spire • | 68 49 53.38 || II 6.55 o°45 Otley Tower . 254 I 5'98 7 7. I4 I. I 5 Lawshall Tower IIo 57 22.84 19 6.24 o'36 Walton Tower . 318 39. I. I? | 18 7.20 o-39 NEPHIN. 3-ft. Theodolite, B.o. 1 A correction of — 1". 31 to be applied to this bearing, to reduce it to the trigonometrical station. From 25th September to 2nd November 1828, Observer: Lieut. PontLock, R.E. - ſº & No. * Recip. º No. IRecip. Objects. Dearings. of | Range. of Objects. Bearings, of | Range. of Obs. “ Weight. Obs. " | Weight. I * * * * * O & M ſ a ! ~ . * * " & " " / //" " // | " * * * Dencorr 26, 31 13:51 || 6 || Io.90 || 3-94 Cuilcagh . 257 46 5I-47 II | II-95 || 2:25 The Reek , 34 go 55-15 17 | 5.90 o-27 || Mullaghanoe . 28I o 52.90 || 4 || 3: II o.7o Slieve More . . . 89 46 54-48 || 12 | 16.60 | 2.89 |Slieve Bawn,South 290 28 o' I? | 2 || 3-2I 2.57 Tawnaghmore | 154 28 24.12 || 6 || 3-65 o.70 || Keeper 33I. 52 45.74 | | 2 | O'9I o°2O Slieve League 21o 56 29.82 II | 14-7I | 3:49 |ISnockma . • 335 28 50-67 || 7 || 2:54 o. I? ICnockalongy • 242 54. 14.74 18 9:29 o'83 | Slieve Carran - 346 43 19.93 || 2 | 1.31 o.43 NIVE HILL, i 7-in. Theodolite. ** * * * From 27th February to 6th March 1847. Observer: Priv. JENKINS, R.S.M. º No. " ' Recip. º * No. | | Recip. Objects. IBearings. 6. Tange. wi,ht. Objects. Bearings. ði. Range. wi.ht. | O f WW - ., ſº o 1 // Wy Balta {} I 20 56.07 18 95°oº 21-27 | Gorth of Scaw 195 Io 43.57 19 | 68.67 32.88. Saxavord . . . .41 43 Io. I5 I9 69.08 31-22 || sº * * * * * * **, *.*.*... sº ++...ºf r * * **, * * * º: , , ºf # *****r.º. tº Jº k +* * * * * * **, ºr OBSERVATIONS. I39 - sº 2.52 -NODES BEACON. 18-in. Theodolite. From 17th May to 23rd June 1845. Observers: Corps. WINZER and STEEL, R.S.M. No. Tecip. No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of | Range. of obs. weight. Qbs. Weight. O f Aſ/ Z/ O & A/ &/ sº Swyre Barrow 8o 22 42-4I 12 Io.33 I-73 || Sussex Lodge 2Io 47 5.77 | 7 || Io. 23 3-2I Coringdon . . 82 53 22-23 I5 7-og o.52 | Butser . 228 36 6.16 || 2 I I4.31 o. 9o Black Down • 92 Io 44.82 || 6 || 7-47 I-83 || Rooks Hill 245 25 I6-40 | I4 9-22 o.62 | Wingreen . 131 48 4.83 13 Io-oo o-'98 || Motteston 274 41 Io.72 II 9-25 | I-68 Dean Hill . 169 3 35.12 8 6:30 o'92 | Dunnose • 282 24 15-43 18 I5-97 | 1.84 Inkpen . . 183 59 53-04 || 8 || 8-62 I-75 Week Down . . . 289 21 38.81 || 4 || 9-og 5.28 Southampton . 199 29 5.59 Io 6. I9 o'92 º F * NORWICH CATHEDRAL SPIRE. 18-in. Theodolite. From 9th November to 8th December 1843. Observers: Corp. STEEL and Priv. M*NALLY, R.S.M. * - *-- No. Recip. . | No, Tecip. Objects. Dearings. of Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. * * * → ** === += < * * * * * * ** ... O . ./ -/ſ--- - &A ! O - f & M. - Z/ - Bunwell Tower 36 49 o'53 || 7 || 8.80 2.42 | Gorleston Tower 28I 31 22.57 || 5 || 17-38 I3:25 Hingham Tower 75 o 56.67 || 7 || 7-28 || 1.87 || Tofts Tower . 308 II 26.39 || 2 || 4-29 || 4-60 Baconsthorpe º I6I 34 58.78 4. 3.24. O'92 Laxfield Tower . 353 9 38-24 I ſºm, I8-ol Happisburgh . 215 42 35-41 || 2 || 3.68 3.38 NORWOOD, I8-in. Theodolite. From 30th April to 31st May 1844. Observer: Corp. STEEL, R.S.M. No. t Resin. No. Recip. Objects. Bearings. of IRange. of Objects. Bearings. of | Range. of -- Obs. Weight. Oos. Weight. Stede Hill. 29 36 394 1 | ". . . 3.32 Gads Hill Obelisk' 89. 58 56.27 2. #33 O'44 Hollingbourne 36 28 8.56 | 16 12.70 | 1.29 || Langdon Hill. I 18 34 15-96 II | Io:94 I:51 Deptling . • 53 II 3-79 I5 16:31 2.09 || Danbury Spire 151 58 21.96 || I4 Io-25 | I 12 Wrotham . . . 74. 23 7.5o 4 o.66 i o.o.2 | Walton Tower 211 57 41-c8 I4 9:72 || 1:34 Chatham Observa- St. Peter's Ch. , 277 22 43.36 I2 Io:72 I:41 tory . 84 45 32.67 4 Frittenfield . 359 46 51-42 | 13 9.87 || 1:14 I ſº . -> * • 4. **rection of + 13' 8".og to be applied to this bearing, to reduce it to the trigonometrical station. **-* * * * * ~ *- : *- :-...-a, - ... x* * * : I4O PRINCIPAL TRLANGULATION. OA or CAIRNARD. 3-ft. Theodolite. From 25th June to 14th July 1822. Observers: Major-Gen. Col.BY, Capts. VETCII and DAwson, R.E. * } No. Recip. tº No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. Benyevenagh º 34°46'5"o, 5 2.87 o:5o Goat Fell . . 270° 3 66.58 3 #72 O'34. Slieve Snaght 54 7 27.34 3 || 2:05 o'55 || Ben Tuire 278 36 36-31 || 9 || 6.51 o.73 Innistrahul Light- Carn-na-Leagh ' || 317 18 52-03 || 13 || 5.79 o.44 house 69 47 6o-oo 4 || 3:07 o-66 | Cantyre Light- - * Ben Tartevil . I38 o 9-29 19 || 7.or o.29 house • 318 5o 57-58 || 2 | o-66 o. 11 Ben More in Mull 191 2 46.82 || 2 || 3:50 3.06 || Trostan • 352 I7 3.95 || 3 || I-63 o-34 Jura . . . . 2io 56 3.97 12 8.20 o.67 || Knocklayd 357 I 49.61 .7 | 6.5o I. 18 Ben Warn . 221 38 sº 25 6.81 o-21 OLD LODGE BEACON. 3-ft. Theodolite, B.o. . . • From 26th October to 6th December 1849. Observer: Corp. JENKINS, R.S.M. º * No. Rccip. º No. - Recip. Objects. Dearings. of IRange. of Objects. Dearings. of | Range. of Obs. Weight. Obs. Weight. Dean Hill. { } I” 54 23:83 I8 3.38 o.13 || Four-mile Stone . 83 18'ſ 392 II 8.5 5 I-Oo Salisbury Spire 53 38 34.38 39 8.48 o.13 | Westbury. Down 112 Io 56.81 23 5.45 o.19 Thorney Down 56 59 59.75 48 || 6-73 o.1% | Stoke Hill II.7. 57 34:29 42 5-65 o.o.9 Wingreen . . . . . . 62 57 58.43 || 17 4.74 o.18 || Beacon Hill I36 20 45-o.4 47 5.78 o-off Old Sarum Castle 67 30 27.76 27 | 5.82 o.19 |Milk Hill . I52 IG II-39 42 || 7-41 o. 16 Old Sarum Gun 67 45 53.27 28 3.81 o.o.9 |Inkpen . . . 2O7 39 39-95 27 | 8:08 o-29 OLD SARUM CASTLE. - 3-ft. Theodolite, B.o. From 19th July to 27th August 1849, Observer: Serg. DoNELAN, R.S.M. Objects. * Bearings. . IRange. Rºjº. Objects. Dearings. §§* IRange. Rºjº. Obs. Weight. Obs. Weight. Four-mile Stone . 128° 36'44'12 I 'o6 o:57 | Thorney Down 255'4' 451 I8 7. O - Stoke Hill I37 55 26.77 : #: o.23 Queen's Manor 281 21 23.26 23 % : Milk Hill. I74 13 50.91 || 3 | 1.02 . o. 12 || Dean Hill. tº 5 33.97 || 13 || 6-44 o.59 | IBeacon Hill . 209 57 27.71 22 || 4:35 o.17 | Salisbury, Cathe- Old Sarum Gun • 242 3 55.68 I6 I5-65 I-62 dral Spire º 349 51 48.43 IO 4-61 O'5I Old Lodge 247 22 24-2O I5 4:59 o. 28 -: OBSERVATIONS. I4I OLD SARUM GTJN. 3-ft. Theodolite, B.O. and R.S. From 18th June to 8th July 1849. Observer: Serg. DONELAN, R.S.M. No. IRecip. I No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. O & f / r & M O f & f £/ Qld Sarum Castle 62 4 59.82 19 || 4:06 o.11 |Old Lodge 247 38 51.96 22 || 4.97 o. 18 Four-mile Stone 122 29 26.42 49 8.71 o.o.9 || Thorney Down 256 54 2.47 || 44 7.35 o'o.9 Beacon Hill . 208 27 46.74 5o 6.29 o.o.4 Queen's Manor 287 Io 59.48 52 || 7-09 || o'o6 ORFORD CASTLE. 3-ft. Theodolite, B.o. From 14th October to 14th November 1843. Observer: Serg. DoNELAN, R.S.M. No. IRecip. No. IRecip. Objects. Bearings. of IRange. of Objects. Bearings. of Range. of Obs. Weight. º Obs. Weight. : O f f/ £f O f Af */ Walton Tower 33 I4. 27. II | II 7.42 o.69 || Laxfield I54 8 48.25 I2 || 3.78 o-20 Referring-object | 68 51 29.77 27 * = . – l Southwold . 2OI 9 38-31 || 8 || 7-oo o-91 Otley IoG 4 4.5o | Io 4.5o o'42 OTLEY CHURCH TOWER. - - 18-in. Theodolite. From 30th September to 31st October 1844. Observers: Corps. STEEL and BEATON, R.S.M. No. Recip. No. Recip, Objects. Dearings. of | Range. of Objects. Dearings. of | Range. of Obs. Weight. Obs, Weight. O / / / ſ/ * * O / fM o Stoke Tower . 5I 57 31:35 I4 || 7-37 o-67 Referring-object 207 24 Io-oo 57 tº º Naughton . 74 13 32.86 || 14 7.56 o.73 |Orford Castle . . . 285 47 7.61 23 13-16 o'71 Mickfield' . I36 59 14. II | 13 || 14-25 | 2.56 Walton Tower . 351 33 20.8o 22 9.91 o°46 Laxfield 2Io 18 24-off I6 II-95 | 1.33 - 1 A correction of — 5" 46 to be applied to this bearing, to reduce it to the trigonometrical station. OWER HILL. 3 ft. Theodolite, B.O. 15th June 1817. Observer: Mr. GARDNER. No. Recip. No. Recip. Objects. Bearings. of | Range. of Objects. Bearings. of | Range. of --- Obs. Weight. Obs. Weight. | ºr O £ f/ f/ tº O A Af A/ Blue Hill . 3 46 37.68 || 5 || 3:38 o-60 | Dudwick : I92 I5 24-oz || 5 || 7-35 | 2:22 Gaerlock 38 6 51-49 || 4 || 2.94 o-60 | Little Stirling 217 58 54-48 || 3 || 2.60 o'77 I3rimmond • 4o 38 13.93 || 5 || 7-28 2.42 | Layton 24o I2 44-04 || 6 || 3: I5 o°33 || Mount Battock . 48 42 Io-40 || 5 || 5.53 I-79 || Tarbathy • 335 9 4.8o 6 5-40 || 1:19 Mormonth. I86 34 I.54 || 4 || 3-oo o'58 - * - 5 I42 PRINCIPAL TRIANGULATION, * PADDLESWORTH, 3-ft. Theodolite, B.o. From Ioth May to 9th June 1844. Observer: Serg, DoNELAN, R.S.M. º * No. Recip. º in. Objects. Dearings. . Range. º Objects. Bearings. . Range. Fºr - *** - Obs. | Weight || Obs. Weight. | *. O f - . - - - - - Fº Tr. 42" 8'24.13 I4 769 o-75 Gº Church , a " . . . . all I’ll ſtill, | - *. º * 54 24 O-36 I 4-7I o'24. ower . . . . 9o I4, 34-84. 12 •48 o. ºº: . 13 6 Fº • * | I s 5 48 *::: 8 º: .# { C - 72 43 24°3 4. I • 7 O - 20 alton l'OWer I 7 2. 5. 5 IO 3.8 O-2 ... : : 3 #2;4|| 6 || 4:3; sº sº.” 3 | ... o. 27 F §. P º 0. 85 o 24.73 I2 7'45 o:58 Tower . 2I4 5o 43.8o I 2 9.76 O'95 rant Church Tr. 88 41 47.2% | 5 || 3.75 o.75 Folkstone 296 43 o'o.5 I4 || 4-63 o-27 - PARACOMBE 3-ft. Theodolite, R. S. From 8th December 1844 to 8th February 1845. Observer: Corp. STEwART, R.S.M. No. Recip. * Objects. Tearings. º ... Range. º Objects. Bearings. * Range. Hºp. # Obs. Weight. Obs. . . . . Weight. , / a & High Wilhays II o' I ſº I 11 & o:79 Prºcely 143 53 29.43 Io 3.48 o.68 IGit Hill . . . . . 22 48 39:72 2 o'95 9:23 Cefn Bryn I56 44 24.93 || 4 || 2.94 o.69 Bradbury Castle. 22 58 Io-97 || 4 || 1:13 o.o.8 || Llannon . . . 102 33 54.99 || 7 || 5.39 o.84 | Brown Willy . . 39 o 59.94 12-06 | 1.76 ||New Inn 16443. I6-77 || 3 || 2.74 | 1.of Cadon Barrow 45 49 45-36 || 6 391 oš1 |Margam Down 193 I5 2.75 || 7 || 4-06 || o'4o Referring-object . 87 45 7.06 19 6.95 – Llangeinor 2OI 4 4.29 Io 8.30 o.88 Lundy Island * --- Ogmoor Down 208 49 51.90 | 9 || 6.35 o.91 Lighthouse 89 21 53.42 | Io 12:32 2.37 || Cradle 2Io 22 18-29 12 4:45 o-3o Highgate . . . . 126 9 38.73 || 2 || 3-64 3-31 | Dunkery : 274. Io 27.46 16 || Io.98 o.91 Marros Beacon 14o 59 8-31 | .5 6:32 | 1.96 1 A correction of + o''' 62 to be applied to this bearing, to reduce it to the trigonometrical station. PENDLE HILL. 2-ft. Theodolite. From 28th October 1841 to 7th January 1842. Observer: Lieut. DA CosTA, R.E. * ſº | No. in. -- - tº Objects. Bearings. of Range, Hºp Objects. Rearings. *: Range. R; P. sm-m------ Obs. Weight. Obs. | Weight. Rivington • 28°26'23.54 6 || || | ºr s Wy tº °22'48. , f/ | Go Hill 8 6 - 7:53 2.01 || Little Whernside 17o 22 40.38 Io 8-22 || 9.98 §. d i. 5o I '49 || 3 || 5.95 || 4:35|Water Crag . . . 189 34 22.95 || || — 16:63 º #n § 4. 41'55 || 4 || 9.83 6.6% Great Whernside 21.1 2 24.71 || 8 || 8:45 2.54 ; tº, I2 3o *:::: 4 3-69 1.17 | Boulsworth 294 34 o'o.5 | 9 || I3-76 || 4-75 S *: " * 23 7 : 9 II: 17 2.63 | Holme Moss 323 5 I5-6o 7 | Io-95 || 3-76 i. Il e # 55 jº: 8 || 6.76 | 1.47 || Kinder Scout . 333 3 4.52 || 6 || 5:42 | I-35 #. § 3 ; ; , i. 3 #|{\º 34I 44 I.9-30 || 4 || 6. I6 2.87 ngleboro I08 50 41.8o | 9 || 9-og 1.82 | Whittje 334 35 IQ-80 || 8 || Io.96 || 2.92 | º ſ - OBSERVATIONS. f43 PENINNIS WINDMILL, 18-in. Theodolite. From 29th April to 21st May 1850. Observer: Corp. Wotherspoon, R.S.M. , “...: * * * No. * : IRecip. ; ... * * No. . . . . . . Tecip. | Objects. Bearings. of Range. of Objects. Bearings. of | Range. ...of. Obs. Weight. Obs. Weight. St.-Agnes' Light- | o , a . . . . . . . . St. Martin's Day- o / 41 || || ". . . . . . house ... ... " | 59 Io 45.95 62 | 17.37 o-36 markl • 203 I7 45-4T | I:2 . I9'59 5°24 Beacon Hill, Tres- | > || Rarn Galver . 239 44 56.14 | 18 . I6-o8 I-51 | Cow . . . . . . 156 9 12.81 12 || 28.76 9.21 | Pertinny .. 244 42 I5'92 || I? | 16. I5 2. Io Telegraph Tower 182 37 * II | 24-36 || Io.29 || Wolf Rock 263 9 32.8o || 5 | Io'57 5-96 1 A correction of — 7' 28” 99 to be applied to this bearing, to reduce it to the trigonometrical station. - -ī-, * * * * * * * : * ~ * * PERTINNY. 3-ft. Theodolite, B.o. From 31st October to 30th November 1845. Observer: Serg. DoNELAN, R.S.M. º No. . . . . Tecip. No. IRecip. Objects. . . . . . Bearings. of . Range. of | . . . Objects. Bearings....... . . of | Range. of r Obs. Weight. Obs. Weight. +x O f f/ &/ * O M & ſ , . . Af Wolf TRock 33 I5 3.73 || 8 || 9:30 || 2:33|Hensbarrow . . . 242 5 44.94 21 || 3:28 o-o? Lighthouse, Scilly --- | | | | TKarnbrea. Monu- o - * * * * Island . . . . 64 52 26-off 9 4.97 o.52 ment . . 245 4o 41.60 | 8 : 8, 12. I.18 Peninnis Windmill 65 12 32.99 || 8 || 4.64 o.55 || Rarnbonellis . . . 254 2 57.34 Io 7.46 o'79 Telegraph Tower 67 29 40.74 || 8 || 4.81 o.79 Tregonning . 265 12 34.54 || 9 || Io-63 I-72 -St. Martin's Day- - * || St. Keverne Spire | 278 38 46.86 || 8 || 4.86 o-66 mark..... ... • 7o 54 37.63 Io 5.19 o'53 || Goonhilly . . . . . 281 8 53.93 29 || 7-27 | o'22 Beacon Hill, Tres- § Grade Church Tr. 292 31 24.68 Io 7.53 o'83 çow Watch-house" 72 12 43.32 || 3 || 5.62 || 4-2.5|LizardLighthouse, Centre of Tor, on | Last . . . . . 296 59 47.32 || 7 || 4-8o o'75 Western Scilly 73 55 52.8o Io || 4.68 o.38|LizardLighthouse, Karn Galver . I99 27 37.85 || 7 | 2.99 o.33 || West . . . 297 3 51.07 || Io 6:23 o'71 ICarnminnis 219 5 50.74 18 6.86 o.33 || Referring-object . 31 21 40:02 || 51 5:19 - ------ A correction of + , 43"-28 to be applied to this bearing to reduce it to the trigonometrical station. * A correction of + 1' 4" oz 33 33 33 . PETERHEAD OLD WINDMILL. 7-in. Theodolite. 12th December 1850. Observer: Serg. STEEL, R.S.M. * . IR Recip. . Rai Rºjº. iects. Bearings. 2. f Objects. IBearings. alſ, ſº, O Objects earings o: s. I ange Wint jects earings o: S. g Weight. O / / / - Aſ - o f f/ &/ Reform Monument 7 II 41.29 || 9 |46.22 || 41.8o || Great Stirling * tº -: Little Stirling Io I3 45.73 9 37.8o 26.98 Sector Station . 357 5 23.5 I Q . 36.61 35.95 I44 PRINCIPAL TRIANGULATION. PILLESDON. 3-ft. Theodolite, B.o. From 12th April to 1st June 1845. Observer: Serg. DoNELAN, R.S.M. *w- No. IRecip. * No. Recip. Objects, Bearings. of | Range. of Objects. Dearings. of | Range. of Obs Weight. Obs. Weight. O & Golden Cape • 4. 24 23:16 9 3:42 O-23 Staple Hill I31 17 joz 8 911 1.88 Parrow Hill . 43 49 37-80 || 6 || 1.99 o.15 || Mendip 203 46 21-98 || 15 8.37 o.65 I'urland . . 46 37 6.67 15 5.85 o.29 || Wingreen 248 29 4-97 | 19 || 6,66 o.26 Little Haldon 6I 48 16.19 16 || 6.78 o.74 || Coringdon . 287 54 35-33 18 9.8o o.59 High Wilhays 81 13 I-25 | 13 | 6.95 o.61 Swyre Barrow 292 54 23.77 I4 3.5o o. 17 Dumpdon . . . 96 I4 36.17 || 2 | o'16 o.o.o | Black Down • 303 32 I.3. I2 || 23 I6.63 | 1.51 Dunkery • I27 7. 23.57 I9 7. I5 o'39 POOLBEG LIGHTHOUSE. 7-in. Theodolite. 11th September 1844. Observer: Mr. H. GoRDON. No. Recip. No. IRecip. | Objects. Bearings. of | Range. of Objects. Dearings. of Range. of & . Obs. Weight. Obs. Weight. O / / / &/ O / / / &/ Howth . . . . . 237 30 9-ol | 6 || 33-40 || 35-42 || Kingstown Obser- - - vatory • • 346 46 46-48 || 6 || 28.33 28.85 Pl{ECELLY. 3-ft. Theodolite, R.S. From 12th April to 19th July 1843. Observer: Lieut. LUYREN, R.E. No. Recip. No. Recip. Objects. Bearings. of | Range. of Objects. Bearings, of -| Range. of Obs. Weight. Obs. Weight. ſº * O A Af ºf f O f Af w/ Highgate ' ' ' | 19 46 15-25 || 5 || 6-04 | 1.64 || Trigarron . . . . 242 57 9. I5 || 8 || 6.75 I. Io St. Ann's • ‘ 44 9 II-62 || 2 | o-og o.o.o | New Inn . 264 20 15.82 || 7 | 8.79 2. I3 Forth . . . . . Io9 I7 7.20 || 4 | 1.94 o.35 | Cradle : 269 I 18.oo || 6 || 2:52 o-25 Mount Leinster II9 2 5 49. Io | 1 — 5-52 | Llangcinor 29I 46 37.13 || 7 || 6-67 | 1.23 Tara ' ' ' ' | I3o 58 32.43 || 7 || 3:41 o.37 || Lannon 296 36 17-48 || 4 || 6-8o 3.49 Croghan I32 27 I-81 || 4 || 3.89 | 1.05 || Margam 298 4 22.48 || 6 || 9-61 2.70 Kippure • I43 o 5.47 || 2 | o-54 o.o.7 Cefn Bryn 312 49 32.60 || 6 || 6-30 | 1.47 Rhiw . . . . . 185 35 16-oo || 8 || 7-33 | 1.41 Dunkery . 316 8 41-59 || 7 || 2.68 o-36 Snowdon . . . . 200 3o 37.13 | 12 || 4.54 o.26 Paracombe 323 Io 24-48 || 5 || 2:23 o.24 Pengarn . 211 33 49-64 || 9 || 7-62 | 1.03 |Marros, Beacon 333 27 6:43 || 3 || 1:72 o.36 IReferring-object 2 II 58 3o-o!) 127 sº – IIigh Wilhays 338 55 14.87 | 6 || 2.73 o.41 Cader Idris : 214 48 14:20 | 1.4 5:45 o.29 |Lundy Island 355 17 53.94 || 6 || 5-36 | 1.65 Aberystwith . . . 221 29 36.29 || 5 || 1:16 o'99 || Lundy Lighthouse 355 19 36.21 5 || 3.39 I-37 Plynlimmon . . . . 229 4 38.06 || 13 8.46 o.67 Cadon Barrow 357 58 1973 || 6 || 3.2% o.18 | OBSERVATIONS. I45 QUEEN'S MANOR. 3-ft. Theodolite, R.S. From 9th September to 2nd October 1849. Observer: Colour-Serg, DonELAN, R.S.M. No. IRecip. No. Recip. Objects. Bearings, of | Range. of Objects. Bearings of Range, of Obs. Weight. * Obs. Weight. -- © f f/ J/ * * , O & W/ & f Wingreen . . . . . 65 54 34.44 Io 4.94 o.53 Milk Hill . . I67 48 29-79 I - || 4-72 | Old Sarum Castle | Ior 22 39.74 4o 8.28 o.15 Beacon Hill . I99 29 44.66 43 6.73 o. Io Qld Sarum Gun Io? II 3-62 51 9-67 o.14| Thorney Down 228 31 29.56 || 43 || 13.69 o.19 Four-mile Stone 116 6 4.60 2 6.28 o-17 | Butser Hill . . . 282 15 13.92 | 15 2.87 o.o.8 Westbury Down 125 18 13.53 || 4 || 3:01 o.64 Dean Hill . . . 312 i 23-27 | 1.4 5.95 o.42 Stoke Hill . I33 32 4, 13 || 14 || 7-65 o°43 IRED HEAD.1 3-ft. Theodolite, R.S. From 22nd March to 29th April 1847. Observer: Corp. WINZER, R.S.M. * i. No. s Recip. No. Recip. Objects. Bearings, of Range. of Objects. Bearings. of Range. of Obs. - Weight. º Obs. Weight. Sayrs Law 7° 2. 5. 4:42 I5 83 5 o.76 Glashmeal . 118 36 14.67 I5 I foi o,89 ICellie Law 23 35 59:24 20 5-39 o°35 | Mount Battock ' | 157 45 55.95 || 3o 7.07 o.20 Largo Law 32 22 5-03 || I4 5-or o-23 | Caerlock . . I79 I5 59.54|| 28 9.82 o.26 East Lomond 47 33 34.46 I3 || 4:30 o-25 || Broxy. . . . . . 200 4 21 of 19 6.34 o.26 Craigowl . 76 58 48-56 || 23 || 6-70 o.24 Lumsden • 347 I2 37.14 | II | 3:41 O'24 | * This point is not identical with that observed in the old observations: the old station is calculated from these obser- vations, and those taken at the old station in 1814 to have been 48' 57 ft. distant from the new, with the bearing 293°11'. I&HUDDLAN BASE, EAST END. 3-ft. Theodolite, B.o. 1806. Observer: Mr. WoOLCOTT. No. Recip. No. Recip. Objects. Bearings. of | Range. of Objects. Dearings. of | Range. of S Obs. Weight. Obs. Weight. O A // &/ O & iſ f &A | Moelfre Issa 56 46 27.47 || 5 || 5-58 | 1.37 |Orme's Head . . . IoI 37 20.84 2 o.o.3 o-oo West End of Base 96 58 59.85 | 9 || 3.91 o.26 Gwaunysgaer 232 iſ o.86 || 8 || Io.94 || 2:4o IEHUDDLAN BASE, WEST END. 3-ft. Theodolite, B.o. I806. Observer: Mr. WOOLCOTT. No. IRecip. No. Recip. Objects. Dearings. of | Range. of Objects. Dearings. of Range. of Obs. Weight. Obs. Weight. 3. O & º & f fº O f A/ £2 Orme's Hoad . Iog 24. 47.23 || 5 || 6-88 1.99 | East End of Base 276 54 3.23 5 6.87 .# Gwaunysgaer 256 20 I-63 || 5 || 5-15 | 1.27 | Moelfre Issa • 352 39 23.95 || 6 8.28 2-6 I T I46 _PRINCIPAL TRLANGULATION. RONAS. 3-ft. Theodolite, B.o. * *. From 4th to Ioth August 1821. Observers: Maj.-Gen. Col.BY, and Capts. VETCH and DRUMMOND, R.E. • * * . …-- tº - No. 1. :* Recip. . No. - -- -Recip. Objects. Bearings.- of | Range. of Objects. Bearings. . of | Range. of - Obs. Weight. -- Obs. weight. – O & f/ * f/ o z, ſz * &/ Foula • 39 35 37-90 || 9 || 6.71 o.80 ||Yell . . . . 265 14 21:12 || 31 7.30 o-31 Saxavord . 224 59 32-31 || 13 || 7.65 o.69 | Noss Head 3& C 47 9:38 4 — * - Wallafield . 229 2I 48. I5 I “– – l Brassa • . 336 39 5-90 || 9 || 3.81 o.24 | Fetlar . 252 55 19.67 IO 6'54 o:70 RU R.E.A. 3-ft. Theodolite, R.S. n From 22nd May to 26th June 1 848. Observer: Corp. WINZER, R.S.M. - No. in. * N tº º IRecip. Objects. Bearings. . Range. ºf Objects. Bearings. .# * Range. ºp Obs. . Weight. Obs. Weight. – - o, w † 7, o 1 Z/ . * y/ Storr • | 34 2 I 52.82 || 31 6.64 o. 16 || Monach ; : 15, 1746. Io 16 7.23 o.5o Cleisham . . . . .] Io3.24.I:39].22 || 4-79 ..o.21 | Cnoc-ghiubhais | 208 33 9-90 || 7 || 4:54 o.75. T}ārvās . . . . . I37 I5 53°37 || 3 || I-93 o.47 | - RYDER's HILL. 3-ft. Theodolite, B.O. From 26th July to 22nd August 1845. Observer: Serg. DONELAN, R.S.M. + tº - No. Hºl Recip. >. No. |. IRecip. Objects. Bearings. of | Range. of Objects. Bearings. . of | Range. of Obs. |Weight. - Obs. Weight. -, * * * - *r . in ºr -. § o “*y Z/ " ' • * * * - // - - * * * * * * * # = // - - &A * .# Eddystone Light- - Pillesdon . . . 245 25 16.65 | 15 5'49 o°33 house 36 33 46'55 | 8 || 5.79 o-84 Golden Cape . 25I 2.2 5-27 | 9 || 6-89 o.82 Goonhilly Down 61 23 I-16 || 20 5.65 o-22 |Little Haldon . 255 2 16:56 11 || 7.46 o.66 Deadman , 94.19.483.]. 7.1.2.17... o. 14|Black Down . . ; 257 32 16:59 || 12 || 3:32 o. 14 Lansallos 69 4 4.1 og 7' 4.53 o.57 | Swyre Barrow . . 264 19 37.28 || 9 || 3.69 o:29 Honsbarrow - 78 41 28.21 | 15 8.19 o-44 Vern . 265 51.24-26 || 14 || 5-15 o.23 Rit Hill Tower | 93 6 59' 16 || 5 || 4:58 I-49 Furland . . . . 302 35 46.65 || 5 || 6-35 I'99 Brown Willy . . . . ... ; ; I2 || 6.82 + -o-57. Referring-object “| 31 or o 44-97 138 6.16 o.or. Cadon Barrow 106 II 43.81 I5 7 or o'42 Barrow Hill . 335 35 49.97 II || 4.68 o.41 High Wilhays 157 o 20:43, 14 | 6-4I O-49 - , * ; . OBSERVATIONS. . . I47 ST. AGNES’ BEACON. 3-ft. Theodoſite, D.O. From 20th to 23rd May 1797. Observer: Gen. MUDGE. º No. ci p. * No. Recip. ... Objects. Bearings. ... . . of | Range. of. Objects. Bearings. of | Range. ...of: Obs. Weight. Obs. weight *...* º * - & - £f Karnbonellis tº º 3. 27' 26:26 I ". 7.79 | Hensbarrow 253 4 18.68 7 11 3 o-o3 IXarnminnis 61 I4 4.20 || 7 || 4-70 o-5o Deadman . . . . 287 35 38-79 || 3 || 6.63 5.25 | Trevose Head 205 54 16.89 || | 6 || 7-40 | 1.94 - - ST. ANNE'S. 3-ft. Theodolite, B.O. April 1792. Observer: Gen. MUDGE. º No. Recip. No. | Recip. Objects, Dearings. of Range. of Objects. Bearings. of | Range. of Obs. . . Weight. - - Obs, Weight. ~. o / 7/ Af - - º ºf ” “ o "7" // Af - - - King's Arbour 209 8 55.69 I – o.68 Shooter's Hill 258 38 25.oo 2 o-oo o-oo Hanger Hill' - || 228 Io 7.99 II 3.92 o.18 || Banstead (Old)' . . 292 6 54.18 || 7 || 2:54 o-25 Hampton Poor- - # Leith Hill (1792)*| 336 9 56.72 2 i.18 o-35 house 253 27 47.75 | 5 || 3:21 o-25 - 4 & g . A correction of - 16' 20" 56 to be applied to this bearing, to reduce it to the station on the Tower. * A correction of + I4"'97 33 33 Banstead, Now. • * * A correction of + 1' 18"–38 33 33 the station on the Tower. ST, MARTIN’S HEAD. 18-in. Theodolite. From 29th June to 13th July 1850. Observer: Corp. Worſterspoon, R.S.M. º No. Recip. - No. | Recip. Objects. Bearings. of IRange. of Objects. Bearings. of | Range. of - Obs, Weight. 4.- : * Obs. || - | weight. tº º e - e. O / / / f/ * - O f f/ - Zº Peninnis Windmill 23 II 57.05 | 19 || 8.69 o.53 Karnminnis . 243 53 I-85 I3 || 4:51 o'31 Telegraph. Tower 32 33 34°75 I7 6.17 o:51 IKarn Galver . 244 27 23-25 || 25 | I2.5I ſ o.66 | Beacon Hill Tres- 4. - Pertinny . 25o 26 49.18 19 6.29 || O'43 cow, Watchhouse" | 83 3 29.78 | 8 || Io. 57 2.48 || Wolf Rock 273 55 34'Io .7 | 7.12 I-37 * A correction of + 8, 32”. 97 to be applied to this bearing, to reduce it to the trigonometrical Station.’ T 2 * PRINCIPAL TRLANGULATION. ST. BETER'S CHURCH TOWER. 18-in. Theodolite. From 14th February to 15th April 1844. Observer: Corp. STEEL, R.S.M. No. IRecip. tº Objects. Bearings. . Itange. ºp Objects. Bearings. § i. Itange. Rºº. Obs. Weight. Obs. Weight. *- © ºf f/ f / : tº O / / / &/ Folkstone . . . . . . 27 35 32-17 || 5 || 6.79 || 2:43 Deptling ' ' ' | 83 o 23.37 21 II.38 o.96 Paddlesworth 35 4 14-13 | 16 || 4.84 o-38 | Norwood . • 97 50 Io.63 I - 9-33 Frittenfield 66 39 16.78 || 5 || 4.66 || 1:13 || Danbury Spire' ' | 124 2 9-17 || 5 || 4:39 || 6.98 Hollingbourne 78 54 46.17 | 16 5.36 o.57 | Walton Tower I7o 48 35-69 24 9.34 o.5o 1 A correction of + 9". 93 to be applied to this bearing, to reduce it to the trigonometrical station. SAWEL. 3-ft. Theodolite, B.o. From 24th August to 20th September 1827. Observer: Lieut. PontLocR, R.E. * No. Recip. No. Recip. Objects. Bearings." of IRange. of Objects. Dearings. of Range. of Obs. Weight. Obs. Weight. Shantavny • 4. 43' 58.36 8 450 o-48 || Benyevenagh 193 28 38.66 3I 648 o: IS Carnmore . . . . I3 58 38-27 | 6 || 6, 18 I-44 || ICnocklayd • 232 36 55-I4 || 14 7.46 o.63 Cuilcagh . . . 36 I7 4o.47 || 8 || II-45 4. I9 || Trostan • • 245 42 3-63 || 9 || 3.92 o.39 Bessy Bell . . 56 59 9:35 || 23 || 7-31 || o-31 | Divis . . . . . . 289 o 24.91 II 6.12 o.57 Barnesmore Con- Slieve Gallion 298 32 21.29 12 6.26 o.61 nell . . . 8o 22 38.67 || 2 | 12.89 |41.54|Slieve Donard 314 2 12-06 || 3 || 2.21 o.69 Lskaheen . I51 49 37-31 || I5 5.95 o°33 | Slieve Gullion 332 55 40.85 | 1 || – • 22 Slieve Snaght 155 54. 24.72 II | 5-21 o-39 || Vicar's Carn | 333 33 36.69 || 2 || 4.47 4.99 North End of Base | 188 51 27.97 || 26 8.07 o.19 |Armagh Breagh . 337 8 22.70 || 1 tºmº 7.22 Mount Sandy 189 34 6-97 || Io || 3:39 o' 19 || Loughanleagh ' |354 55 29.64 || 6 || 2:05 o.16 SAXAWORD. 3-ft. B.o. and 7-in. Theodolites. 28th August 1817. Observer: Mr. GARDNER. From 28th January to 23rd Rebruary 1847. Observers: Corp. STEEL and Priv. TURNER, R.S.M. • No. Tecip. No. Recip. Objects. Dearings. of | Range. of Objects. Dearings. of | Range. of Obs. Weight. - Obs. Weight. s=--- O / / / Z/ : • - o f Z/ Af Fetlar . . . . 3 8 42.54|| Io 5-61 o°45|Gerth of Scaw 288 5 32.77| 27 102.85 48.96 Brassa • . . . Io 21 43-ol || 5 || 3-14 o'59 || Nive Hill . 321 4o 27-16 || 28 99.63 26.75 Yoll 23 27 52-27 | 12 | 6.93| o-66 | Balta . . 340 42 47'94 || 9 || 3.90 o-35 | Ronas . . . 45 31 7, 16 || 8 || 6-39 || I'oo sº OBSERVATIONS. 149 SAYRS LAW. 3-ft. Theodolite, R.S. From 27th May to 5th July 1846. Observer: Corp. WINZER, R.S.M. † No. IRecip. No. Recip. Objects. Bearings, of Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. º O & ff &/ O & ſº */ Wisp . . . . . IG 47 9.91 || 6 || 5.77 I-20 | Largo Law • 159 49 32.06 || 8 || 3.79 o'4o Hart Fell . . . . 43 35 51.65 || 3 | 1.40 o-22 || Craigowl • 164 48 50.73 || 6 || 3:59 o°43 Dunrich . . . . 46 48 48.76 || 6 || 3.97 o°49 |ICellie Law 17I 19 46.26 || 7 || 3:35 o°23 l Allarmoor . . 96 35 7.71 II | 3-74 o°22 Mount Battock • 177 58 14-17 | 3 || 3:02 | 1.13 Corkmulaw 1oo 31 37.88 I - || 4.89 || Caerlock . . . 184 4o 24-48 || 8 || 3:39 o-3o Bin of Campsie Io2 3 8-o& I — 4.89 || Isle of May Light- r Ben Lomond • Io8 9 I7-31 || 3 || 5-26 || 3-13 | house . . . . I90 32 II-94 5 ſº Hºmº Arthur's Seat Io9 34 6.66 || 5 || 2.58 o.26 Lumsden . . . . 256 45 27-61 I4 6.63 o-3o Referring-object II3 50 20-oo 85 8.67 – | Mordington . . . 276 22 26. Io Io 5.59 o'4o Ben Cleugh II9 I6 40.33 || 8 || 4 oz o.35 | Blackheddon . 296 II 22.70 || 9 || 9:74 I-5o Ben Lawers . . . . 129 33 34-Io | 9 || 6.59 o.96 || Alnwick . . 399 42 II-58 I — 4.89 Last Lomond 142 16 32.82 || 8 || 4.33 || 9.38 || Cheviot 320 56 49-39 I4 || 7-66 I-23 Glashmeal. • I59 36 2I-83 || 9 || 4 of o°33 SCA FELL. 3-ft. Theodolite, R.S. From 8th July to 20th September 1841. Observers: Lieuts. PIPON and CRAIGIE, R.E. tº No. Recip. No. IRecip. Objects. Dearings. of | Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. O f // . £7 O Af Af | Blackcomb I9 I4 52.8o Io 3.og o.23 || Criffel . • I53 45 43°29 II 9°53 I-37 Snowdon . . 2O 38 31.85 || 3 || 4.83 2.93 || Hart Fell . . . . I73 32 25.97 || 5 || 6-7I 2.48 Llanelian . . 3I 45 38.86 || 4 || 14-91 | 16.11 || Wisp . . . . . 189 31 25.96 || 6 || 7.68 2.59 Holyhead . . 37 45 50.86 || 2 || 4:32 || 4.66 || High Pike . I99 23 59:43 || 7 || 3:58 o'38 South Berule. 7o 55 36.88 || 6 || 5.14 o.97 || Cheviot • - || 2 Io 28 54.36 I ſº 9'54 Snea Fell . . 75 51 IG-39 || - 7 5-76 o.90 | Helvellyn . . . . 237 7 18:55 || 7 || 4:36 o-64 North Berule . . 77 7 o'84 || 8 || 3-16 o-36|Cross Fell . . . . 239 6 52.22 || 11 7.06 o.63 Mull of Galloway Ior 23 34.47 | 3 || 4:30 2.20 || Water Crag . . . 271 6 11-28 || 5 || 7.96 3-25 || Dent Hill. Io? II 2.27 | 5 || 3.81 o.71 || Calf . . . . . . 281 41 13.39 || 6 || 9-30 || 3:56 Glasserton - . Io9 41 21.28 || 4 || 4-22 || I-18 Great Whernside 291 58 11.83 || Io 6.13 o-61 Benereard • | 122 26 36-47 || 3 || 3-06 | 1.05 |Little Whernside. 295 ió 15.73 || Io | Io.73 || 2:56 Cairnsmuir of Fleet 128 59 39.77 || 6 7.61 2.5o | Ingleboro’. . . 3oo 5o 23.35 | 7 || 13.54 6.36 | Merrick • 133 50 41.88 || 7 || 8.52 | 1.88 || Boulsworth . 314 4 59.36 || 2 | 1.02 o°26. Ben Cairn. I35 45 48.06 || 2 | 1.12 o-31 || Pendle . . . . . .317 Io 43.86 || 5 || 4-52 O'91 Cairnsmuir on - + Whittle Hill . . .324 23 43.98 || 6 || 4-75 o'89 Deugh, tº º I44 37 56.91 4 5-67 2.03 IBeryl º, º ſº tº 35o 43 43. I2 5 3-62 o'73 I5o PRINCIPAL TRIANGULATION. Trom 11th June to 23rd July 1839. Observers: Lieuts. HoRNBY, Robinson and Pipos, R.E. SCARABIN. 3-ft. Theodolite, B.o. From 25th October to 3rd November 1822. Qbservers: Major-Gen. Col.BY, Capt. KATER, and Mr. GARDNER. r Trom 20th January to 29th March 1848. Observer: Serg. DoNELAN, R.S.M. . 3-ft. Theodolite, B.o. and its. † No. IRecip. g No. Recip. Objects. Dearings. of | Range. of Objects. Bearings. of | Range. of * Obs. Weight. - . . Obs Weight. Ben Macdui : 2” 6'1565 2. sº 7.07 || South Ronaldshay aro 50'5; o; 17 12 or o-98 Duke of Suther- - Ben Cheilt 22756 36-28 || 41 14.22 o.57 land's Monument 42 47 51.61 | 3 || 4:36 || 2: I I Mormonth . . . . . . .306 o' 53:52 || 7 . 4.93 o'86 IBen Wyvis 44 32 34.66 18 Io.84 o.97 Cowhythe . 316 57 3.70 || 6 6.3% | 1.19 Ben Clibrig 92 18 27.60 34 i 14:25 o.56 Manor Lee 319 46.57-2I 4 ° 2'54 o.59 JFoinnebheinn 106 18 46.26 4 4.02 | 1.41 Bin of Cullen 325 Io 23:42 7 ° 9-90 3.35 Ben Hope . 11o 15 1.08 || 6 || 6-31 | 1.45 ICnock . . . . 325 19 56.99 || Io 13-of 2.38 Ben Hutig . . . 124 43 58.81 33 Io.22 o.25 l'indlay Seat 343 24 9. 16 | I - || 14-15 Wart Hill Hoy 190 48 26.60 | 16 || 6.93 o.49 Corryhabbie . 346 17 4-05 || Io 8.69 I-37 Dunnet Head 194 18 25-oo 28 II.25 o-48 r: - l SCOURNALAPICH. - 3-ft. Theodolite, B.o. - - * From 15th July to 25th October 1846. Observer: Serg. DoNELAN, R.S.M. No. Recip. º º No. Recip. Objects. IBearings. of Tange. of Objects. . Bearings. of | Range. of * * Obs. Weight. Obs. Weight. o , a i &/ 7 . . . .” O M M f & Af Mamsuil . 20 18 32.79 / 12 || 4-13 o-30 || Ben Wyvis 2 IQ 4o 27°55 2 6.84 o-3o Ben More, South * Balnaskerrish 233 56 37.36 22 || 6-47 o.27 |Uist . 85 43 13.33 20 || 3:38 o' 19 | Balrinnis, ; ' ' | 267 I5 13-ol II 7-2 o:90 Cleisham • 123 4. 25.94 | 18 º: o, 28 Corryhabbie º 27o 37 21:55 32 6.75 o.15 Monach • | 1.46 30 20.95 II || 4-7O o°34 Ben Macdui. 29I I 46.95 31 9'93; O'24. Glashmeal, Ross 166 51 I5-51 || 9 || 5-65 o'52 Referring-object 35I 58 39.99 |240 dºmº imº Ben Clibrig 201 31 57.87 II 8.97 o'86 Ben Nevis 356 54 21:54 34 | 7.91 O-23 SEVERNDROOG. - No. IRccip, … . . . . Objects. Dearings. of | Range. ; Objects. w Bearings. ** Range. Rºjº. Obs. Weight. Obs. Weight. O W M / *A O Aſ f f . &/ Leith Hill Tower 43 7 6. I6 8o | 12, Io o.o.8 || Greenwich Obser- * Banstead, New 49 4 5.68 || 4 || 3-86 1.02 | vatory Dome . . Io9 21 22.94 | 11 5.40 o.46 Hundred Acres 5o 48 36.69 || 4 || 4.44 1.53 St.Paul'sCathedral 115 33.25.63 33 6.18 o. is St. Anne's, Old 79 3I 51.5o 9 6.60 o.89 || Berkhampstead | 158 23 44-85 22 5.59 o-24 Windsor Castle 4 * Chingford . I67 I6 45-76 94 | Io-49 o.o.6 Towcr . . . . 92 39 20-67 .4 º 3.66 Epping Poor-house ! . . . . Hanger HillTower to: 19 21-66 39 7.85 3.1o Cupola. 189 20 1.08 19 | 5.83 o-31 Westminster Ab- Gad's Hill 28I 32 I4-53 14 6:59 O'44. bey Pole Ioff 42 Io-og 2I 6 cal o.33 || Wrotham . . . 316 42 58-45 II2 Io.86 o-off 1 A correction of – 7' 48"'57 to be applied to this bearing, to reduce it to the transit. | OBSERVATIONS: , I5 I SHANKLIN DOWN. 18-in. Theodolite. 8th August 1846. Observer: Corp. STEEL, R.S.M. -*-* . . - No. Iłecip. - No. - Recip. Objects. learings, of | Range. of Objects, Dearings. of | Range. of * sº . . . Obi. . . . . Weight. - tº Obs. Weight. O / / / f/ * 4 o / // &/ Week Down | 40° 58' 55.14 | 8 || 8:84 1.87 | Boniface Down 342 53 16.23 || 8 || 6.74 I-II Dunnose • 270 * 3498 .8 || 3:30 | o:31 * - SHANTAVNY. 3-ft. Theodolite, B.o. From 4th to 15th May 1827. Observer: Lieut. PontLock, R.E. No. i IRecip. - No. Recip. Objects. Bearings. of Range. | of Objects. ‘Dearings. of IRange. of Obs. º Weight. dis. Weight. ſº O f & W | #/ t O W Af l W/ Cuilcagh . 55 II 31'47 || 3 || 8.59 9:59 | Slieve Donard 294 39 36.88 || 3 || 0-68 o.o.5 Bessy Bell I36 2 58-73 15 25-45 || 4-30 || Vicar's Carn . . . .305 o 52.84 || 7 || 8.78 || 2:15 Mullaghcarn . I57 35 25-17 | 13 11.82 2.1o | Carlingford . . . .311 27 50-62 2 || I-78 o'79 Sawel . . . . 184 40 46:12 |.. y | 9-57 | 1.53 |Armagh Breagh ' |314 19.16-10 || 3 || 6-84 6-89 Slieve Gallion 218 47 46.75 15 8.22 o.6o Slieve Gullion 314 28 17.96 || 3 || 3-12 | I oë Divis 259 19 20.79 || 2 | o'79 o. I5 || Mullyash . . . . .323 4. 49-15 || 5 || 13:41 || 7-31 * SLIEVECALLAN. - .g. 3-ft. Theodolite, B.o. - - From 22d September to 2nd October 1837. Observer: Capt. Pontlock, R.E. Objects r . - No. IRecip. |- No. Rºjº. YCCUS, * - - - - tº i. iects... ... . . . . . . º -. - , , Range. - Of . J * * * * *- * -- º-range -- wº. . . . . ... Objects. -- Bang- 6: IRange Weight. Baurtregaum . . 28 29.3%iz 1 || “.. 8.26 || Meclick . . . . . 289° ro' 3.75 I 1 – 8.26 Slievecarran ſº 2II 42 58-75. I '- . . . . 8.26 Newtown, Lime- Gortourka 245 38.56-57 || 6 || 7-09 || 1.80 | rick . . . . . 299 43, 3.46 I 8.26 Mooghane * 283 3o 5o.58 I — 8.26 Clonoula . g 338 3 3I.63 T * = 8.26 * war * * * * **** ========l– SLIEVECARRAN. 3-ft. Theodolite, B.o. From 9th to 18th August 1837. Observer: Capt. Portlock, R.E. *r - - * ... * ~ * - . . . No. 1 . . - |..Iłecip. . . . . . . . . . . * * * * * * * * No. Recip. Objects. Dearings. ! of | Range. of Objects. Dearings. of IRange. of * Obs. ... Weight. I Obs. | Weight. Gortourka. - . . . . +2° +++3.62. 9 | -5:30 F-1:77. Newtown, Galway r;3°31′-fºod. "4 T 3.34. o:39 §ºlº 31, 55.30-19 || 5 || 2:79 o.46 || Gorathorna • 297 36 28.97 || 3 || 2:7 I O'95 É.iend ' ' ' | Io9, 58 43-15 || 5 || 3:55 o'58 Keeper . . . . . .307 o 29.56 || 3 || 3:79 || 19° * ' ' ' | 131 31 33-17 || 1 | - || 5.65 | - |.… I I52 PRINCIPAL TRLANGULATION. SLIEVE DONARD, 3-ft. Theodolite, Rs. From 19th August to 18th December 1845. Observers: Corps. FoESYTH and WINZER, and Priv. STEwART, R.S.M. º No. Recip. ſº No. Recip. Objects. Bearings. of Range. of Objects. Dearings. of | Range. of Obs. Weight. Obs. Weight. *- O / // &/ O / / / # / Howth . . . 6 I6 22:49 | 12 || 7.33 o.57 | Trostan . . . 171 9 49.62 24 | 6.92 o.21 Rippure ...: ... 13 51 12-oo 26 11.33 o.51 | Divis © I72 3I 46 oz 4o 15.02 . o. 28 GarristownWalmill 24 32 45°41 || 5 || 5.34 | 1.71 || Benercard . . . . 21248 32.88 II | 6′oo o.53 Castlecoo . . 27 9 44.81 || 5 || 14.73 || 13.15 | Cairn Piot . . . 216 14 o'42 I4 || 7-II o-48 Croghan • 44, 30 43-65 Io 4.6% 3.39 || Merrick . . . . . . 220 41 42.5o | 8 || I-96 o-o; | Loughanleagh ' || 65 II 21-20 || 2 || 5.37 7.31 || Mull of Galloway 233 18 29.34 || 4 || 3:25 o'78 Slicve Gullion 79 13 27-26 || 9 || Io.52 2-48 || Criffel . . . . . 239 20 50-og | 12 || 4-73 o'36 Mullyash . • | 89 31 13.86 || 5 || 13.42 7.95 || Sca Fell . . . . . 259 5 Io-o2 I3 || 6-84 o°46 Cuilcagh . . 91 50 Io-oš | 7 || 2.52 o.24 | North Berule . . . 262 22 21 or || 2 | I-o? o.28 Vicar's Carn . IoG 53 2-45 II II.3o 2.69 Snea. Tell . . . . . 263 51 34.86 || 2 | I-97 o-97 Referring Object | 130 5 13.06 |16.1 *- — | South Berule . . . 271 53 16.88 19 7.75 o-37 Sawel . . . . . I34 56 41.86 |34 || 6.55 o.18 || Snowdon . . . 314 38 39.43 21 || 6-40 o-22 (SLIEVE LEAGUE. - 3-ft. Theodolite, B.O. From 14th November 1827 to 5th January 1828. Observer: Lieut. Portlock, R.E. * in. No. Recip. Objects. Dearings. ; | Ran ge. R; p Objects. Bearings. of Range. ºp Obs. Weight. Obs. Weight. O Aſ Z/ &/ • O w A/ A/ - ICnockalongy 3 54 32.99 || 13 22:30 4.18 | Slieve Snaght ..] 234 51 13.82 || 2 || 3.75 || 3:51 |Nephin tº 31 28 44-93 || 7 || 6.35 | i.41 |BarnesmoreConnell 259 55 18:33 || 8 || 16.74 2.68 The Reck . 32 28 15-92 || 3 || II.26 17.85 | Breesy . . . . . 288 5 53.78 || 4 || 8.51 5.73 Slieve More . 51 28 45.90 || 2 || 4-40 || 4.84 | Cuileagh ' ' ' || 31o 24, 46.20 || 5 || 5-oA | I-57 Tawnaghmore 55 51 17.92 || 6 || 16.87 | 8.7i |ICnocknarca • 348 49 38-45 || 14 | 8.38 || 1:13 SLIEVE MORE. I2-in. Theodolite. - * From 17th to 19th August 1831. Observer: Serg. Doull, R.S.M. - tº No. - IRecip. No. IRecip. Objects. Dearings. of | Range. of Objects, Dearings. of Range. of Obs. Weight. Obs. Weight. - O & Af - O J A / Tawnaghmore 223 20 56.16 Io |Repeated o'oZ The Reek . . . 316 29 54.14 || 27 Repeated O'27 Nephin ſº tº 269 I3 Io-97 Io Angles. o.o.7 Bencorr • 342 25 55-61 7 | Angles. 4.84 : r -r .* ! i OBSERVATIONS. I53 SLIEVE SNAGHT. 3-ft. Theodolite, B.O. From 29th September to 2 5th October 1827. Observer: Lieut. PortLock, R.E. - No. Recip. No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of IRange. of - Obs. Weight. Obs. . Weight. O * # / Af * - O Af A/ -- &/ Bessy Bell . 3 56 43.66 || 8 || 5.72 o.83 || Mount Sandy. 273 26 45.74 || 14 | 5.05 o-28 Cuileagh . . I5 42 47.17 | 6 || 9:59 2.90 | Cundtham . . . . . 275 48 30.68|| 15 6.65 o°41 | Barnesmore Connell . . 37 52 38-29 || 4 || 6. I4 2.59 || North End of Base | 281 1843-61 | 13 5.81 o-36 Slieve League 55 58 38.5o || 4 || 4-77 I-53 | Trostan . . . . 282 5 30-75 || 6 || 7-25 | 1.82 Ben Tartevil 223 20 I.33 || 3 || 2.92 I of Divis . . . . . . . . .307 7 15.09 || 3 || 6.99 || 5.48 Jura . . . . . 226 20 30-56 I – 7.18 | South End of Base 309 15 51.55 || 8 || 8.18 | 1.70 Carn-na-leagh. 261 55 29.69 || 2 | 1.54 o'59 | Slieve Gallion 324, 24. I7-73 || 5 || 3:55 o-60 |Knocklayd . . . 272 43 29.64 || 5 || 451 | 1.08 || Sawel . . . . .335 39 50.08 21 | 8.51 o-31 SNOWDON. º 3-ft. Theodolite, R.S. * * From 16th July to 21st November 1842. Observers: Lieuts. PIPON and STANLEY, R.E. No. Tecip. No. IRecip. Objects. Bearings. of IRange. of Objects. Bearings, of IRange. of Obs. Weight. Obs. Weight. - O Af £/ Af O Af f/ W/ Precelly . . . 21 4 12.58 || 6 || 2.47 o.24 || Beryl . . . . . . 218 16 40-48 || 2 | 1.79 o.8o Rhiw . . . . . , 55 6 6.42 || 5 || 7-04 || 2:05 || Ingleboro' ' ' ' | 221 35 53-74 || 4 || 4-26 I. I.4 Tara . . . . 74 56 27-38 || 3 | 1.82 o.37 || Moelfre Issa . . . 239 15 23-27 || 7 || 8.88 2.18 Kippure • 95 31 34°54 || 2 | 1.54|| o'59 |Whittle • 24o 2I Io. I7 || 5 || 4:39 I.O.I Howth . • Io5 5 44.54 || 2 | o'54 o-o? | Billinge . . . . 241 8 48.83 || 7 || 5.5o o-69 Holyhead . I24 28 IS-91 || 6 || 5.06 o.91 | Heswell . . . . 245 1829-91 || 3 || 4-21 || 2:47 ‘l Slieve Donard I36 7 51.72 || 4 || 4.91 2-17 | Axedge . . . . 261 5o 24.62 || 3 || 6-56 || 4-79 Moel Rhydladd - || 137 43 39.85 || 4 || 4.96 I-70 Cyrn-y-Brain . . . . 272 49 o'91 || 8 || 5.88 o-64 Llanelian . • I58 II 20.74 || 7 || 8.92 2.14 || Longmount Pole 305 o 16:42 || 4 || 7-03 || 3:14 South Berule . . . I62 Io 9. I3 4 IO-92 Io. Io Plymlimmon º 343 25 I:29 || 4 3.48 o:79 Snea Fell . . . . . 169 1844-44 || 3 || 3.24 | 1.17 | Cader Idris . . . .344 34 56-30 | 16 8-91 o-66 North Berule . . 171 20 59.85 || 2 || 6.20 9.61 | Tregarron . . . 35o 24 40.73 || 2 | o'59 o-o8 Sca Fell . . . 199 56 40-20 | 3 || 3:47 I-35 | Pengarn . . . 356 8 19:58 || 5 || 4-73 I'or Black Comb . . . 200 Io 26-25 | 1 || || – 7. II | Aberystwith . 359 44 47-72 || 3 || O'53 o'O3 SOUTHAMPTON, Io-in, Theodolite, - From 16th to 24th May 1845. Observer: Priv. Scott, R.S.M. w- B *|R * Ob IB *| n Rºjº. iects. ings. \. ſº iects. ings, C. O Objects earings ði, ange W§ ght. jects earings ð. ang Weight. Motteston º Q 3. 19 37.77 IO 27.65 I4-28 Dean Hill . . . 126 38 £75 IO 45.84 40.66 Nodes Beacon! . I9 34 36-61 8 31.4I 37.83 Dunnose . . . 336 II 3-28 || 17 || 44-77 12-oo * A correction of + 2"-85 to be applied to this observation, to reduce it to the trigonometrical station. U I54 PRINCIPAL TRIANGULATION. From 20th June to 6th August 1845. Observers: Corps. STEEL and Forsyth, and Priv. MoUNTAYNE, R.S.M. SOUTH BERULE, 3-ft. Theodolite, R.S. |- ; . i No. Recip. - No. Recip. Objects. Dearings. of Range. of . Objects. Dearings. of | Range of Obs. | | Weight. i Obs. Weight. ſº - O f # / Af O. f J/ * f/ IGippure • 46, 9 I7-55 I6 5-58 o.27 Glasserton • 190 58 I5-o9 | 15 || 7 O3 O'43 Howth : 47 28 38. II || 8 || 6-62 I-oo | Cairnsmuirof Fleet 19248 41-09 || 3 || 4-28 || 2:35 Slicye Donard 92 54 35.32 24 IO-23 o-60 | Criffel . . 216 58 59-61 | 18 5-63 o.21 Divis 12o 56 26.59 || 9 || 5-63 o-60 Snea Fell . 226 5I 29.99 || 18 || II. I2 o.86 Trostan 136 41 52'20 | 17 | 14-85 | 1.25 | North Berule 228 48 Ig-og | II | II-25 | 2-oo Carn-na-leagh 151 32 26-80 || 4 || 3:34 o.79 || Dent . 242 22 49.92 I3 7.02 || O.67 Cairn Piot 162 58 20.61 || 17 | 12.43 | 1.02 || Sca Fell 249 44 48.27 | 17 | 6.92 o.49 Referring-object | 167 21 27.42 | 20 | . — | – || Black Comb . . . 261 37 15.82 || 24 | 12.02 o.47 Mull of Galloway | 167 21 38.5o I5 6.38 o-40 || Ingleboro’. 268 21 27. I3 | Io I3-oo 3.76 Benereard . . . 171 2 8.05 || 6 || Io. 18 || 3:52 | Snowdon . • | 34I 4I 50-13 20 | II.O4 || O-6 I Merrick . . 186 38 21.37 20 | II-99 o-8I SOUTH LOPHAM CHURCH TOWER. - ---, * * * * 2-ft. Theodolite. -- Prom 26th November 1844 to Ioth January 1845. Observer: Corp. BAY, R.S.M. | No. § IRecip. i. * No. º: Recip. Objects. Bearings. of IRange. of Objects. Bearings. of | Range. of Obs. Wei ght. * Obs. º: Wei ght. * O W A/ f/ O / f/ f/ tº Lawshall Tower. 34 5347.71 II | 5:58 o.39|Bunwell Tower 220 18 32.90 | 13 741 o.61 Brandon . 93 40 41-48 || Io 7.56 | 1.15 Laxfield 292 20 51-65 || 9 || 6.70 || o-73 Swaffham Spire' - || 143 35 8-97 || 4 || 2.5o o.52 Stradbrook Tower 294 24 53:65 | Io || 4-76 o-35 Hingham Tower. 177 18 42.69 || 6 || 2.18 o.17 Mickfield*. . . 336 57 51.06 Io 3-74 o'36 | Referring-object . 190 II 6.82 55 * -º Hºmº 1 A correction of + 17"'41 to be applied to this bearing, to reduce it to the trigonometrical station. * A correction of + 2"'54 33 33 º 3} x ºf SOUTH RONALDSHAY. - 3-ft. Theodolite, B.O. From 19th to 26th October 1821. Observers: Capts. VETCH and DRUMMOND, R.E. i. .. * * * No. | Tecip. No. Recip. "Objects. Bearings. of | Range. of Objects. . Dearings. of Range. of - | Obs. | Weight. f - Obs. Weight assm- i. ſº O / / / . . f* - O / / / w f/ Ben Cheilt . 26 27 48:42 i3 || 5:55 o.58 || Ben Hutig . . 74 53 54.61 | 1 - || 4-27 Scarabin . 31 24 6-43 || 6 || 3:50 o.54|| Wart Hill Hoy | 120 8 45.22 i7 || 6-07 || -6.36 Ben Clibrig 55 Io 38-2I | 3 || 3-70 I-53 || Deerness . • 2Io 24, 19-25 | 20 || 4-42 o. I2 Dunnet Head 63 I7 I2.86 || 3 || 2:8o | 1.65 - .l .-- OBSERVATIONS. I55 SOUTHWOLD CHURCH TOWER, 2-ft. Theodolite. From 7th to 30th September 1844. Observer: Corp. BAY, R.S.M. Recip. No. Recip. No. Objects. Bearings. of | Range. of Objects. Bearings. of | Range of Obs. Weight. Obs. weight O & w/ ſ/ O f Af £/ Orford Castle 2I 14 33-59 || 9 || 4.82 o-45 || Toft's Tower . . . I59 38 41.4I | Io 4.89 o.43 Laxfield Tower 82 19 13.84 || 11 || 7.61 o.99 || Gorleston Tower | 186 22 18-04 || 10 | 1.28 o.o.3 STORE CHURCH TOWER. * 2-ft. Theodolite. From 19th January to 2nd May 1844. Observer: Corp. BAY, R.S.M. No. IRecip. -- No. 1 Iłecip. Objects. Dearings. of | Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. º O / / / * f/ O / / / : f/ Danbury Spire 35 5I 33.69 || I3 5.85 o.39 || Otley . 231 42. 24.60 | Io I-oo o.o.2 Lawshall Tower . I48 II 4I'39 I3 6. Io O'45 Referring-object • 272 34° 49'95 89 iº wº Naughton Tower | 198 19 25.77 Io 5.02 o.41 || Walton Tower 296.49 49.72 I4 || 3:32 o'I2 STOKE HILL. 3-ft. Theodolite, B.O. From 17th December 1849 to 4th February 1850. Observer: Corp. JENKINS, R.S.M. # No. Recip. *. No. IRecip. Objects. Dearings. of | Range. of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. tº o ſ A/ // O Af */ Af * Wingreen . 5 4I 47.79 24 8.33 o.35 | Thorney Down 306 26 46-13 || 6 || 5-34 o-84 Westbury . 76 57 42'o6 || 48 || Io.32 o.14 || Dean Hill. 312 58 2.92 22 || 6-37 o-2I Milk Hill . 23.I 45 36-38 24. 6.51 o. 28 Queen's Manor . 3I3 I9 26.04 T I 4:36 o:28 Inkpen . . . . 257 38 22-93 26 || 4.49 o.II | Old Sarum Castle 317 43 52.81 | I3 || 4.94 o'32 Beacon Hill . 292 1842-30 || 25 | 8.35 o.21 | Four-mile Stone 319 39 8.95 || 27 | 9.95 o°33 Old Lodge ' ' | 297 37 58-45 | I2 5-54 o.49 STORR. sº 3-ft. Theodolite, R.S. From 26th September 1847 to 26th February 1848. Observer: Corp. WINZER, R.S.M. s No. Recip. º - No. - IRecip. Objects. Bearings. of Range. of Objects. Bearings. of | Range. of -* Obs. Weight. - Obs. Weight. iº O M // * f/ * tº ; : O / / / & A/ Ben Heynish . 21 20 18.84 || 6 || 3.85 o.71 Cnoc-ghiubhais . 21o 2 36.12 | 19 I4'32 || O'9% Ben More, South * * Ru Rea. . . . . 214 o 45.81 | 19 || 4-8o o.16 Uist. ' ' | 68 o 2.91 24 9.70 || 0.37 || Ben Clibrig 23; 37 12.21 || 17 | 8.95 || o.8o Cleisham . 143 52 7.42 33 7.23 o-24 || Mamsuil 291 9 52.14 || 22 || 7-87 o:36 Monach • I75 3o 21.81 25 8.88 o:23. Ben Nevis tº ſº 317 26 I7-O3 || 41 II.33 ...; Ru Stoir . . . . 269 24 37.72 | 13 5.65 o-40 || Ben More in Mull 355 3 25-22 || 17 8.83 o' |U 2. I56 PRINCIPAL TRIANGULATION. STRONSAY. 3-ft. Theodolite, B.o. From 28th October to 1st November 1821. Observers: Captains WETCH and DRUMMOND, R.E. Wingreen . . . 178 41 I8-76 I3 5.33 o:42 | Dunnose . . . . . 268 24 o'I5 | I5 Io.4I No. IRecip. * No. Recip. Objects. # Bearings. of IRange. of Objects. Bearings. of Itange. of ; Obs. Weight. Obs. Weight. sm----ºn- o f Af &/ - O iſ f/ x &M Decrness • • 36 50 18.97 23 5-66 o.18 || North Ronaldshay Wart Hill Hoy . 65 8 16.5o | I2 8.5I o'77 Lighthouse . 196 57 18:31 || 5 | 1.88 o.19 Fitty Hill . . . I29 32 53.86 || 17 | 6:55 ošo | Start Lighthouse 205 3 47.23 || 8 || 6.71 | 1.18 -- IFair Isle . . . . 225 29 33°49 || 9 || 2.93 o-2I SWAFFHAM CHURCH SPIRE. 18-in. Theodolite. Erom 7th September to 30th October 1843. Observer: Corp. STEEL, R.S.M. # No. Recip. * * Mo. IRecip. Objects. - Dearings. of | Range. of Objects. Dearings. of IRange. of f Obs. Weight. Obs. Weight. C & ff *. f/ | dº O * f f f/ Brandon . . . 9 53 5.37 || 8 || Io-64.] 3.21 || Boston Tower. 127 36 2.48 || 5 || 1998 || 6-24 Cheveley Tower. 17 53 49.20 || 6 || 8.80 3.73 || Baconsthorpe Tr. 229 53 32.38 || 4 || 8.31 5-69 Newmarket . . . . 21 35 31.94 || 8 || 12-17 | 3:08 || Hingham Tower 291 I 41.58 22 | 18.61 | 1.44 Ely Minster . . . 46 25 29.88 || 13 Io.49 | 1.19 S. Lopham Tower | 323 2I I2. II | 5 || Io-17 | 5-or St.Peter's, Walpole 166 1 49.75 | 12 || 13.86 || 3:38|Lawshall Tower 357 34 51.63 || 8 || II.5o 2.82 Lynn, Old Towerl|| 120 25 26.42 | 15 12.04 || 1.88 1 A correction of – 3"o7 to be applied to this bearing, to reduce it to the trigonometrical station. 2 A correction of – 4".35 3? 33 J3 SWYRE IBARROW. - 3-ft. Theodolite, B.O. From 18th March to 8th April 1845. Observer: Serg, DoneLAN, R.S.M. * * ſº No. IRecip. - No. Recip. Objects. Dearings. 9f | Range. of Objects. Bearings. of | Range. of n Obs. Weight. Obs. Weight. o / // Aſ O / / / &As Vern . . . . 79 16 13:05 | 12 || 4.64 o.26 || Horton's Gazebo | 198 43 48.36 || 4 || 7.81 || 4.89 Little Haldon 88 7 13:50 || 7 || 3:15 o:32 | Beacon Hill . . . 202 o 54-31 || Io 7.32 o.8o High Wilhays 94 28 Io-93 Io 8.57 1.36 |Dean Hill . . . . 213 Io 55-52 | 12 3.79 o.20 Black Down . . . IoS 43 57-51 | 13 9:76 o.83 || Coringdon . . . 249 45 25-96 || 12 | 6.86 o.68 Pillesdon . . . II3 28 I5'oï Io 6.88 o.88 || Nodes Beacon! . . 259 57 50-or || 2 || 5-28 || 6.97 o.65 1 A correction of — 46":30 to be applied to this bearing, to reduce it to the trigonometrical station. ; : : **i.- OBSERVATIONS. 157 From 8th to 20th November 1829. Observer: Lieut. PoſtTLOCK, R.E. TARA. 3-ft. Theodolite, B.o. * No. IRecin. No. Recip. Objects. Bearings. . Itange. ºp Objects. Bearings. º | Range. * Obs. Weight. Obs. Weight. Forth . . . . 28 54 46% 5 || 17 8.98 o.85 Ballycreen º I 57 43. 46.84 || Io 594 o.6§ Vinegar Hill. 46 II 1438 Io 4.73 o'57 |Kippure,' ' ' || 171 50 34.71 Io || 3:42 o'28 |Slievecoiltia . 5o 45 20:52 || 4 || 2:34 o-35 | Collin Hill . . . 203 I3 23-67 Io 5-od o-45 Blackstairs 67 29 12-94 || 7 || 5.81 I-o8|Snowdon . . . . . 253 13 56.80 || 3 || 2.64 |. o.85 Mount Leinster 76 55 9-48 || 8 || 8.87 | . I-37 |The Rivel . . . 254 56 19:09 | 4 || 7-91 || 4:20 Croghan * I46 I4. I4°54 Io 4-65 o' 5I Precelly • • 309 5o I3-36 6 6.61 I-51 TARBATEI.Y. 3-ft. Theodolite, B.O. From 7th to 30th May 1817. Observer: Mr. GARDNER." - No. Recip. | No. Recip." Objects. Bearings. º Range. ºp Objects. Bearings. º Itange. º Obs. Weight. Obs. Weight. º O f #3 J/ º O / Aff J/ - IBlue EHill . . I4 44, 38.95 || 7 | 1.18 o.46 |Over Hill . . . . I55 Io 57.80 || 6 || 3.18 o.62 Caerlock . . . . 45 37 o.62 || 5 || 3-66 o-64 | Dudwick • • 184 42 29-38 || 4 || 2.97 o.61 Mount Battock 54 36 7.91 || 3 || 3.95 || 2:18|Layton. . . | 199 I 31.92 || 6 || 3:34 o'34 Primmond 66 42 54.85 || 8 || 2.76 o.16|Little Stirling 209 21 52.14 || 4 || 18.26 27.57 TAUR. - 3-ft. Theodolite, B.o. From 5th to 13th August 1832. Observer: Capt. PortLock, R.E. Obi * * No. . . Recip. º º so . Recip. jects. Bearings. of IRange. of Objects. Dearings. of | Range. of Obs. Weight. Obs. Weight. o , a Z/ - O / W/ - f/ Calherbarnagh ' || 8 52 32-4I 22 6.55 o-22 || Galtymore . . . . 257 12 58.92 || 6 || 4.46 o'99 | Mangerton . . . 39 37 21-31 || 8 || 5.91 | 1.02 |ICnockanaffrin 266 19 27.99 || 3 || 5:32 3.82 Colly Mountain 62 I5 21:04 || 4 || 4-25 | 1.40 || Knockmealdown 270 I9 21:55 || 3 || O'63 o.o.5 Baurtregaum . 86 8 43-94 || 7 || 2:35 o-17 || Knocknaskagh 286 5o 54-31 || 22 || 5.51 o.18 Brandon 90 II 7.77|| 1 - || 3:99 |Rock Hill; . . . .303 18 35-46 || 2 || 1:72 o'73 IXnockanore . 134 2I 36-Io | 7 | Io.8o 2.58|Mount Hillary • 305 54 29.88 29 5.68 o.o.9 Mcclick 207 45 o'75 || 2 | I-43 o'51 || Musheramore 337 54 45-92 || 4 || I.33 o. I5 | Recper . 225 27 Io'44 || 7 || 7. II | I-53 TAWNAGHMORE. I2-in. Theodolite. From Ioth to 13th September 1829. Serg. Doull, R.S.M. No. of No. of | Recip. - No. of No. of | Recip. Objects. Bearings. Repe- simple | of , Objects. Bearings. Repe-I simple | of . , titions. Arcs. | Weight. titions Arcs. |Weight| Slieve More . 43' 43 31.68 º I4. 2-oč Knockalongy º 28° 12 3306 2O — o°3I Slieve League 235 7 43.90 28 I o.68||Nephin . . . 334 17 16:39 52 || 3 || 934 WI58 PRINCIPAL TRIANGULATION. TELEGRAPH ToweR. 18-in. Theodolite. From 28th May to 19th June 1850. Observer: Corp. WothERspoon, R.S.M. º # No. Recip. No. IRecip. Objects. Bearings. of Range. of Objects. Dearings. of | Range. of Obs. Weight. Obs. m Weight. mm -— tº & e sº O / W/ f/ O / // Z/ Peninnis Windmill 2 37 47.78 I7 | I2-69 | 1.52 | St. Martin's Head 212 31 55-52 22 | 12.60 o.88 St. Agnes' Light- * ' Rarn Galver . 24I 44 7.18 26 || 11.87 o.68 house 36 4o 30.90 24 I7-23 I-43 | Pertinny . 246 59 25-oS I4 5-16 || o.34 Referring-object | 4o 30 20.03 || 79 i-mºn — Wolf Rock 266 49 56.5o | I5 II-90 I-54 | Beacon Hill Tres- r cow Watchhousel | 1.42 54 24-28 || 12 || 14-21 || 3:20 1 A correction of — 5' 11".84 to be applied to this bearing, to reduce it to the trigonometrical station. f THARFIELD. • 3-ft. Theodolite, B.o. From 15th July to 23rd August 1843. Observer: Serg. DonELAN, R.S.M. No. Recip. * No. IRecip. Objects. IBearings. of | Range. of Objects. Dearings. of | Range. of Obs. Weight. Obs. Weight. O A // A/ * O & W/ f/ Berkhampstead . 12, 8 12.89 || 9 || 5.95 o.62 | Ely Minster . 205 29 37.98 || 13 || 8.18 o.76 Dunstable • 63 53 20:36 | 19 || 6.76 o.25 | Brandon 225 46 36-62 || 6 || 4:03 o'67 | Hanslope Ch.Spire | roi 2.1 54-48 || 4 || 5-40 || 2:04||Newmarket 23o 57 31-17 | I2 5:17 o'5o Referring-object . III 38 29.96 |II2 7.29 | – || Balsham . . 236 35 II-89 || 9 || 3:59 || O-27 Reysoe Spire • 133 59 28'92 || 13 || 7.67 o.88 || Balsham Tower . . 241 51 5-61 | 8 || 9:57 2.87 Royston . . . . 152 2 25.46 || 5 || 5-40 || 1.57 | Thaxted Spire 285 3 32-32 6 || 4.5o o'76 | Orwell. 184 6 I5'29 || 3 || I-36 o.21 | Epping Cupola • 342 36 18-64 || 5 || I-52 o'Io ..THAXTED CHURCH SPIRE. I8-in. Theodolite. From 8th June to 11th July 1844. Observer: Corp. STEEL, R.S.M. º * * No. Recip. No. IRecip. Objects. Bearings. of IRange. of Objects. Dearings. of | Range. of Obs. Weight. Obs. Weight. mºm- O / // f/ .* A * Z/ Epping Cupola 28 35 24.75 | Io | 6′59 | 1.03 || Lawshall Tower'. 225 23 I4.25 I8 23.81 3-II Berkhampstead 55 50 18:47 22 20-22 | 1.85 | Stoke Tower 263 52 I4’33 || 8 || 9-oo 2-off Tharfield...: ' ' | 105 21 26.3% II 14.96 || 4-16 |Danbury Spire . 328 42 30.38||18 || 17.95 || 2.8% Balsham Tower 175 23 35-86 19 18.82 | 1.91 • 1. # * .- | OB SERVATIONS. 59 TEIORNEY DOWN. 3-ft. Theodolite, B.O. From 12th September to 15th October 1849. Observer: Serg. DoNELAN, R.S.M. –wºmmº No. Recip. IBcari * Ra Rºº. iects. ings. - º iects. º Ilſº C. O Objects - Bearings - - 6. IRange wi,ht. Objects carings Öº. 9 weight O f // w/ O Z // || Wº Coringdon 20 18 20.92 | Io 3.82 o.23 || Four-mile Stone 9642 49.94 | 16 || Io:38 o-62 Horton's Gazebo. 32 II 1.93 || 8 || 7-38 1-o& | Westbury Down 119 26 8.41 || 6 || 4-76 o'79 Queen's Manor - || 48 35 27:29 29 8-oz o°2I Stoke Hill I26 43 22.92 24 || 6-12 o'I9 Salisbury Spire . 51 15 II.47 19 9:24 o'45 Milk Hill. 162 o 36.02 || 3 || 8-28 || 7-8o Wingreen Beacon | 63 56 42.59 || 7 || 2.94 of42 || Beacon Hill 174 58 29-71 33 Io.28 o-21 Old Sarum Castle || 7; 46 1.86 18 || 5-8o o-20 Inkpen. . . . . . 212 17 23.71 || 3 || 1:28 o' 19 Old Sarum Gun . 76 58 2-12 19 || 4.87 o.19 |Old Lodge . . . 236 56 57.85 I5 8.64 o-'79 TILTON. * 3-ft. Theodolite, R.S. From 29th January to 23rd March 1843. Observer : Corp. MULLIGAN, R.S.M. No. Recip. -- No. Irecip. Objects. Bearings. of Range. of Objects. Bearings. of Range. of Obs. Weight. - - Obs. Weight. w C / / / &/ - o / // - w/ Naseby Tower 1642 I-o? | Io | 738 o.82 | Sutton . . . . . . 155 29, 25.69 || 6 || 2:12 o'15. Bardon Hill. . . . IoA 14 9-40 || 5 || 6-25 | 1.67 || Holland Hill . . . 159 o 48.14 || 4 || 1.61 o'17 Breedon Hill Tr. . ] II6 36 46.59 7 4-68 O'5I Stathern . . . I84. 46 17.67 7 4.98 o,7o Weaver Hill . I2I 56 6.52 I – . 6.04 || BuckminsterSpire | 213 56 20-90 || 8 || 3.88 9:33 Loughborough Tr. I22 21 5°94 7 | I2-90 || 4-2I Laston Tower 273 4o 5-2O I º 6-O4. Elvaston Tower . 127 48 II - 22 I * = 6.04. Reysoe Spire . • 325 41 II:43 8 4’33 O'45 TOFTS CHURCH TOWER. 2-ſt. Theodolite. From 29th March to 26th April 1845. Observer: Corp. BAY, R.S.M. No. Recip. No. "| Recip. - Objects. Bearings. of | Range. of Objects. Bearings. of | Range. [...of . . . - f Obs. . . . . Weight. Obs. Weight. * O W A/ º 4. C A A/ . &W - Paxfield Ch; Tr. 32 30 49.78 II 14:21 2.34 || Happisburgh . . 175 26' 58.64 || 9 || 5.93| 2:55 Stradbººk Tower 45 13 $4.27 || 7 || 4.19 o.é; Gorleston Tower. 22; 31 go.o.3 it Io-og | 1.4°]. Bunwell Tower . 88 5 9:24 ió | 11.73 || 0.78 || Referring-object . 273 34 59.98 || 36|| . . . . os + Norwich Spire • | 128 22 3:55 i2 || 3-94 o.26 | Southwold Tower | 339 33 26-oz | 15 II.62 I'o **, I6o PRINCIPAL TRIANGULATION. TOLSFORD. 3-ft. Theodolite, R.S. From 6th to 8th September 1822. Observers: Major-Gen. Colny, Capt. ICATER, and Mr. GARDNER. º No. IRecip. N . Obj ects, Bearings. of Ran * } f tº Beari O. Recip. Obs. ge wilt. Objects. earings. . či. Range. wi.ht. Fairlight tº ſº º 52. 18 29'86 I9 5 oz O's I { } O f f/ Aſ | | º sº i. -17 | NotreDame,Calais 286 Io 59. Io 2.8 • 26 Tenterden . . . . 82 16 40.8o 3 3.18 I. I.4. Blancnez . 2 4. 40.8o 7 I • 4. º Crowborougl 8 26 *. 93 43 4. 49 || O' I4. Stede ###". • 85 42 37.26 || 7 || 6′37 | 1.26 Fienne . . 299 o I2.64 || 5 || I. 19 o'o6 Folkest lli • 121 26 28.5I I6 3.38 o. 12 || Montlambert . . 316 3o 28.18 || 3 || O.79 o.o.7 | Rolkestone . . . 275 26 43:23| 18 || 415 || oog | TREWOSE HEAD. 3-ft. Theodolite, B.o. From 12th March to 25th April 1846. Observer: Serg, DoNELAN, R.S.M. No. in. * Objects. Bearings. 9f | Range. Hºp Objects. Bearings. . Range. Rºº. : Obs, Weight. Obs. Weight. O & W/ * : - Carnbrea. Monum' 22 57 I3'Io 7 5.78 o:87 || Lundy Island . 200 5 1986 Z/ * (i. 33 8.2 o, I8 ; Agnes. • 26 3 ...; I2 6-57 o.68 || Cadon Barrow • 243 27 30-31 || I3 ; §: ..". • * , 42 º 3.16|| 23 5.89 o.20 || Brown Willy . . . 261 5 57.71 22 9.46 o.44 Rarn Galver . . . 44 18 55-31 || 8 || 3.73 o.49 | Hensbarrow 320 19 6.73 || 13 | 8.78 o.83 TROSTAN. 3-ft. Theodolite, B.O. Trom 23rd June to 5th July 1827. Observer: Lieut. PoſtLock, R.E. tº - . No. Reci . N º Objects. Bearings. of Range. p ſº Objects. * 0. Recip. Obs. ge w;ght. jects Bearings, ði. * wi,ht. Slieve Gullion • 10 : 5:09 2 3.13 1.13 || Jura . . . . 185 39 45.95 6 6'14 I.66 sº ####| || #| #|É..., |####| ||'; ...; Sawel “. 66 68 8-99 || 1.38 Carn-na-leagh , 218 44 45-90 19 8.5i o-48 i. º tº ſº .# 24'9 9 || 13:52 2.60 |Goat Fell . . 223 2 3o. II | 3 || 2:51 o'73 #.g. : ; ; #| || || |*...". ." |ass i +. ; tº º 2. ‘55 o.68|| Deugh . . . . 258 29 58.85 | 3 || 5-22 || 3:25 iºns ºd i I 7 º: º: 33 I4. *::::: 1.78 |Bencreard. . . 267 51 16. Io | 8 || 4:38 o.64 |...}...m. |# . ; ; ; ;|...”. . . ; ; ; ; ;|..}}}|... CIl 3, ...: #|*:::: .39||... ..., |3: 3% 3 || || 3: Oa - - - - - || I72 23 54'32 I 7:55 o°53 | Slieve Donard • 35o 58 27-08 || Io II-80 || 2.21 '. # . i f s % * §i4 ºt OBSERVATIONS. - 161 UPCOT DOWN. 3-ft. Theodolite, B.O. From 24th March to 23rd April 1850. Observer: Corp. JENRINs, R.S.M. . No. Tecip. t # | No. Recip. Objects. Bearings. of Range. of Objects. Bearings. of | Range. of Obs. . Weight. Obs. Weight. Milk Hill . . . 14 5: 54:34 2. I 453 o: 3 || Cleeve . . {º 164° 27' 21:49 23 403 Os IO Stoke Hill . . . 37 46 43-97 || 13 || 4-76 o-28 |Whitehorse Hill . . 237 8 50.65 29 5.77 o. 12 Westbury Down 44 o 21.71 || 14 || 6-07 o-37 || Inkpen • 3oo 27 54-62 I2 || 7-36 f o-78 Mendip . . . 6o 51 44.82 | 17 2.43 o'o6 WICAR'S CARN. 3-ft. Theodolite, B.o. From 17th to 22nd April 1827. Observer: Lieut. Portlock, R.E. No. *. Recip. -- No. IRecip. Objects. Dearings. of Range. of Objects. Bearings. of | Range. of * Obs. - Weight. Obs. Weight. Armagh Breagh . 9. 144.68 8 8 or I-41 || Armagh Transit • I so 222 #65 2 608 9:24 Mullyash . 18 56 33-12 || Io 7-49 || I-46 || Sawel . i. I53 55 II-64 || 2 || 4:38 || 4-79 Cuileagh . 82 4I 54:37 . I — 15.51 | Slieve Gallion I67 37 31. I4 || 6 || 6.65 I-73 | Carnmore • 86 2. 26.99 || 6 || 7-66 2.59 || Divis . . . . . . 226 52 58.79 || 7 || 4:34 o.41 Shantavny 125 24 38.89 || 8 || 8.94 2.49 || Slieve Croob . 263 I2 56.18 5' 19-17 | 15.89. Bessy Bell I3o 6 42-I2 I – 15.51 Slieve Donard 286 20 Io. 15 || 7 || 8.47 2-13 Armagh Observa- Carlingford 318 3o 47.53 || 4 || 6-56 || 3:59 tory Dome . 150 25 I-67 || 9 || 12.60 || 2:41 |Slieve Gullion : 331 26 35-10 || 6 || 8.19 || 2:39 WALPOLE ST, PETER'S CHURCH TOWER. 2-ft. Theodolite. § From 23rd September to 20th October 1843. Observer: Corp. BAY, R.S.M. Beari . Ra Tecip. . Ra Rºº. i. s O * * . tº in or * Objects. earings Obs. nge W.*ht. Objects Bearings. 6. nge W: ght. O f f/ f/ ; : O f A/ Af Peterboro’ Cathe- Docking Tower 234 24 16.49 12 II-98 I-45 dral . • 61 6 48-27 | 5 || 3:55 o'99 || Lynn Old Tower” 257 56 36-49 || 15 9.95 o'75 Easton Tower - 77 51 50.32 | 8 || 2.67 o-I5 | Swaffham Spire” . . 285 39 25-45 Io 4.55 o-26 Boston Tower" I49 3 14-03 || 9 || 6′31 o.88 Ely Minster . . 355 45 47.77|| 9 || 6-47 o'81 Referring-object - | 19447 29.96 5o. – tºº * & tº * A correction of — 4”-66 to be applied to this bearing, to reduce it to the trigonometrical station. i * A correction of + 4”-78 *. º - 39 33 * A correction of — 1;":35 33 33 X --w. - -i:--. i I62 PRINCIPAL TRLANGULATION. WALTON CHURCH ToweR. 2-ft. Theodolite. "From 4th November 1843 to 9th January 1844. Observer: Corp. BAY, R.S.M. º No. Recip. \ No. | Recip. Objects. Bearings. of | Range. of . Objects. Bearings. of | Range. of - - - - . . . . . . . . Obs. | . Weight. * +* * ... . - . . . . . . . .Obs. | . . . Weight. s º ºr " O / / / f/ O f f/ // Stede Hill 3I 4I 5o’95 I tºº 6.03 || Otley Church Tr. I7I 36 43-14 || 6 || 3.8o o.41 Danbury Spire 71 49 1.23 || 8 || 6.61 o.8ó|Orford Castle ... 213, o 56.8i || 7 || 3:14 o.65 Stoke Church Tr. 117 8 14.77 || 9 || 5.83 o.63 |St. Peter's Church'ſ 356 42 37.60 || 3 || 7-05 || 60.6 Naughton Ch. Tr. 138 54 50-od | 7 || 2.57 o.21 * 1 A correction of + 2"40 to be applied to this bearing, to reduce it to the trigonometrical station. WART HILL HOY. 3-ft. Theodolite, B.o. * From 25th September to 16th October 1821. Observers: Capts. VETCH and DRUMMOND, R.E. º No. IRecip. * . . . No. Recip. Objects, Bearings. of Range. of Objects. IBearings. of | Range. of Obs. Weight. Obs. weight. * O / W/ > * f/ O & f/ º A/ Ben Cheilt . . . 2 o 18.57 || 7 || 4.26 o.65 | North Ronaldshay * - - Dunnet Head. • 4 I 38.43 || 4 || 6.99 || 3:32 || Lighthouse 225 25 25-74 || 2 | o' 16 o.oo Scarabin . . . . II I I3-03 || 2 | 1.31 || 0.36|Start Lighthouse 232 20 24.74 || 3 | 6.85 5.27 Ben Clibrig . . . 49 3o 26-48 || 12 6.57 o.81 | Stronsay . . . . 244 27 18:54 || 8 || 5-86 || 0.84 Fashven . . . . 68 o 28-54 I - 5.77 | Deerness . . . . 26o 16 2.78 || 12 5-84 o'47 Fitty Hill. . . . . 204 6 42.60 || 9 || 3:21 o-17 | Copinshay . . . . . . 270 20 Io.io || 5 || 4-07 | o.77 South Ronaldshay | 299 48 21.29 || 23 6, 13 o.16 WATER CRAG, 3-ft. Theodolite, R.S. Trom 17th April to 5th June 1852. Observer: Corp. GRose, R.S.M. - • No. * s * No. IRecip. Objects. IBearings. . Tange. Hºp Objects. Bearings. . Itange. º º Obs. Weight. Obs. Weight. O W & Aſ ºff O / / / a Little Whernside 39 I8 26-48 7. 8-13 I-85 MerringtonChurch 231 2. 55.87 3 3.8o I-85 Sca Fell . . . . . 91 59 43.45|| 13 6.6% o:52 | Easington ... . . . 259 38 56.97 I3 4:20 o.16 Cross Fell . . . I4o 46 26-40 | 18 6.95 o-34 Appleton Wiske . . 267 40 28.97 II 4.81 o.28 Mickle Eell 148 Io 28-13 9 3.86 o.37 | Botton Head . . . 272 30 37.13 | II | 6.04 o.8o Collier Law • 193 6.23.85 | 8 || 4.46 o:59 | Black Hambleton 284 9 48-26 13 | 12.63 | 1.52 Brandon Down 218 6 57.29 II | 6.41 o-48 KirklingtonChurch 3ol. 5 48.44 I5 || 3:43 o-I6 Wordeslow 223 41 28.60 | 8 || 5:84 o';o Great Whernside |346 32 39-53, 9 || 6.16|| o-88 : OBSERVATIONS. 163 WEEK DOWN. 18-in. Theodolite. From IIth to 14th August 1846. Observer; Corp. STEEL, R.S.M. iº No. Iłecip. No. Recip. Objects, Bearings. of | Range. of Objects. Bearings. of Range. of Obs Weight. Obs. Weight. Nodes Beacon! 105 36 3.08 . 6. %22 2.8o | Boniface Down • 256 36 23.57 9. 1:34 2-93 Motteston, • 117 25 28.78 || 7 || 9.93 || 3.70 || Boniface, S.E. 259 44 6.83 || 9 || 9-31 || I-70 Shanklin Down 226 58 59-31 || 9 || 17.3% | 3:37 |Littletown Down 264 33 33.5% | 9 || 16.45 5.72 Dunnose . . . . 228 5o 28.76 |. 9. I2.44 || 3-62 * - ". 1 A correction of + 1' 29". 30 to be applied to this bearing, to reduce it to the trigonometrical station. WESTBURY DOWN. 3-ft. Theodolite, B.O. From 8th February to 17th March 1850. Observer: Corp. JENRINs, R.S.M. ſº - No. Recip. º No. . . Recip. Objects. Bearings. of Range, of Objects. Bearings. of | Range. of Obs. Weight. Obs. Weight. tº O & ff • Z/ - : º i. O / / / f/ Mendip . . . . . . 8o 45 7.31 || 35 | 7.94 o. 15|Milk Hill. . . . . 237 32 12.76 | 20 || 4:03 o'12 Dundry ChurchTr. 114 20 39.41 | 12 6.64 o.68|Stoke Hill . 256 53 37-2I 32 4:74 o'I2 Lansdown Monu- Inkpen . . . . 257 29 26, 19 22 5.95 o°2O ment . . . . 136 45 23.61 | Io || 4:34 o.34 || Beacon Hill 285 59 o'42 || 14 || 4-85 o°29 |Farley Down Mo- * Old Lodge 291 47 15-98 || 13 || 4:15 o°26 nument . . . . . 144 17 36.85 | 13 5.81 o-43 || Thorney Down 299 5 29-05 || 3 || 5-40 || 3:24 Marshfield Churcl * * || Queen's Manor 305 I 3o.56 I5 5-43 o°27 Tower . . . . 151 58 1974 || 8 || 6′37 o-99 |Dean Hill 306 28 34.73 19 3.87 o'14 Lord Somerset's * Four-mile Stone . 307 58 42.72 || 7 || 5-II o'8o 1V10nument . 16o 25 57.51 | 8 || 6-09 || o.91 || Salisbury Spire 3ri 45 34.76 | 13 || 5'34 o°31 Hansdown Obelisk 218 5 33-35 || 23 5.94 o.23 || Wingreen . . . 355 22 15-76 16 || II:44 o'93 Upcot Down . 223 44 ° 2'22 33 5.5I o'o6 - From 1st March to 27th April 1844. Observers: Corp. Cosgrove and Priv. STEwART, R.S.M. WELITEHORSE HILL. 3-ft. Theodolite, R.S. Object No. Recip. | jº. R Hºp. S. - tº i. C. * = - J * ...] harge will Objects. Bearings. Č. *|w.ht. §: Down s 57 19 37.83 I ". 5'43 Wytham * 216 12 4.#43 6 423 Os 83 S ºndip, g 6o 6 36.08 3 3-og I •o8 Brill 229 58 4O'44 8 4."O3 O'35 㺠Hall IOI 2 37. II 3 4-97 2.75 Shotover 233 I3 34.81 7 3. I4. o:35 Mº * * III 55 5-33 Io 4°29 || O'34 Dunstable - 245 I9 2.79 I3 4°59 o. 18 Cleeve . I38 Ig II-85 || 7 || Io.27 2.47 || Wendover- . 25o 3 34-49 Io 19:23 :35 IBroadway To..., | # 59 46.75 | 12 || 4:5; o.29 |Leith Hill Tower 297 3; 43.79 || 4 6.89 o'52. .# * | *śg 45 9.4%| 11 $38|| 0.91 |Inkpen . . . .343 38 37.42 | 15 5.5% | *3" y i. I98 35 49.68 9 4." IO o:39 º X 2 -- 164 PRINCIPAL TRLANGULATION. From 14th May to 23rd June 1841. Observers: Lieuts. PIPON and CRAIGIE, R.E. WHITTLE. 3-ft. Theodolite, R.S. Object IB No. Hºp * : Objects T} ... • *tº Fº i. €CŞ. ings. iſ º earings. i. J earings či. IRange wit. gs Ös. Range wint O f W/ &/ 3) O / / / Af | | Delamere . . . 29 32 I.3°49 I lºmº 3. Io Ingleboro. • I71 I3 39.18 || 4 | 5.09 || I-66 Cyrn-y-Brain . . .41 12 30.og | I I | 3. Io | Pendle Hill . I74 33 40.88 || 4 || 5.33 2.27 Billinge . . . 59 26 52-31 || 3 || 3-10 || 1:12 || Great Whernside 197 38 22-25 || 7 || 3.35 o.76 Snowdon . . . . 61 48 I5.06 I * -º 3. Io | Boulsworth . . . 211 53 50-66 || 2 | 2.26 1.27 Rivington . . . 76 8 33.76 || 6 || 2.85 o-30 || Holme Moss . . . 299 Io 3o:23 || 7 || 3:53 o.34 Beryl Hill ' ' | Iio 54 54,72 || 5 || 3-12 o.53 || Kinder Scout . . . .321 21 3.08 || 5 || 415 | 1.66 Black Comb 133 45 53.87 || 3 | 1.85 o.39 || Axedge . . . 336 17 54.36 || 4 || 3:08 o.6o Sca Fell . . . 145 g 32.5o || 4 || 1:19 orio || Mowcopt . . . 356 4o 16.87 I * = 3. Io Hamilton Hill 162 37 31.98 2 o.22 o.ol - WINGREEN. ſ 3-ft. Theodolite, R.S. --- From 29th July to Ist September 1844. Observers: Corps. STEWART and Cosgrove, R.S.M. sº No., IRecip. * No. Recip. Objects. Bearings, of Range. of Objects. Bearings. of | Range. of 'Obs. Weight. Obs. Weight. O / W/ ſº £f - : O / // ºff Worn , , , 26 22 37'oo | II 9-og | 1.04 || Dean Hill . . 26o 5o 25-63 || 8 || 4.62 o. 5o Mintern • 61 II 50-51 | Io 5.85 o.46 || Butser Hill 27o 9 8.74 15 8.65 o.66 Pillesdon . . 69 2 19:39 || 8 || 2.91 o.17 | Dunnose ' ' ' || 302 7 29.47 I3 || 6.38 o.34 Referring-object 85 58 34.88 9o tºº - || Motteston 306 39 34:37 . I* | 7.94 o.64 Staple Hill . . . 86 36 16:57 Io 7.87 | 1.02 |Nodes Beacon' ' | 311 22 8.77 || 7 || 5.35 | 1.72 Mendip . . . . I3o 29 49-49 I4 || 7.73 o.59 Horton's Gazebo |322 44 54.77 | Io 5.35 o.48 Westbury . . 175 24 9:52 | 8 || 2.87 o.20 | Coringdon . . . 347 59 24.08 21 5-13. o.15 Inkpen . . . . . 227 29 52.86 20 9.82 o. 59 Swyre Barrow 358 4o 33°o2 20 | 5.65 o-19 Beacon Hill . 23o 36 54. I5 || 5 || 3-66 o.83 * A correction of — 35"'o6 to be applied to this bearing, to reduce it to the trigonometrical station. WISP. 3-ft. Theodolite, B.o. From 5th to 8th August 1809. Observer: Mr. GARDNER. y * No. in. Objects. Bearings. § Range. Rºjº. Objects. Bearings. of . Range. Rºp Obs, Weight. Obs. Weight. O Af Af WW © W/ &/ Criffel . . . . . . 48 4 22°o 5 II II. I5 1.96 Dunrich . . I56 49 3o. I? 23 6-II o.20 Cairnsmuiroffleet 69 Io 14-oo || 5 || 6.7% 2-38 || Sayrs Law 196 32 24-off || 4 || 8.01 || 6.8o Cairnsmuir on Cheviot . 247 8 41.44 Io 7.04 o.98 Deugh . 88 13 34°55 || 7 || 7.54|| 1.52 | Cross Fell. 334 22 50°93 || 2 | 9-13 | 20.83 Hart Fell i. II6 44 57.78 IO 4-98 o:57 -- + OBSERVATIONS. 165 WORDESLOW. 2-ft. Theodolite. From 18th April to 28th May 1846. Observe r: Serg. BAY, R.S.M. 3.27 | * * * No. | Recip. - No. Recip. Objects. Dearings. of Range. of Objects. Dearings. of | Range. of , . . Obs. Weight. Obs. Weight. Great Whernside 26 5' 1798 I5 4:11 o.18 || Pontop . . . 96 12' é94 9 6.63 o.83 Merrington Church 29 48 38.67 || 3 || 3-25 | 1.23 | Cheviot . . . . 147 4 28.49 22 4.75 o.12 Water Crag . 44. I4 57.45 || 4 || 4:49 I-73 || Rufflaw New I52 35 57.90 I4 || 4-79 O'25 Brandon . . . . . 57.20 42.80 || 6 || 3.8o o'46 | Easington . . 309 48 I5. I7 I6 || 4:39 o' 19 Referring-object . 57 51 498 |Io4 tºmº — Burleigh Moor 32I 7 I-67 || 8 || 4-oo o'34 Collier Law . . 76 27 41.24] Io 2.78. o, 18 | Botton Head • 335 52 26,81 | 13 5-54 o'38 "WROTEIAM 3-ft. Theodolite, B.o. and R.S. - r From Ioth to 17th October 1822. Observers: Capt. ICATER and Mr. GARDNER. From 28th July to 30th August 1844. Observer: Serg. DoNELAN, R.S.M. No. IRecip. No. Recip. Objects. Bearings. of IRange. of Objects. Bearings. of | Range. of Obs, Weight. Obs. Weight. O / // % & W * O f f f s f/ Frant Church 2 29 54-40 | 16 || 8.33 o'71 || Chingford . . . . I5o 52 13.87 18 3.36 o.o.9 Crowborough ' ' | 17 28 51.14 5o 6.8o orio || Epping Cupola • 165 27 25.06 | 12 || 4-65 o.23 Ditchling 3o 54 42.18 I9 || 7-13 o'38 |Danbury Spire . . . 204 II 22-14 || 14 || 4 oz o'I9 Leith Hill Tower 71 25 8.83 || 41 || 6.42 o.11 || Gad's Hill Obelisk* 229 12 11.12 || 6 || 5.04 o.91 Stede Hill. . IoA. I2 I-93 ||38|| 6.93 o. II | Norwood . . . . . 253 57 42.19 II | 8.16 o-69 Hanger Hill . II9 43 o'46 || II | 2.53 o'Io | Referring-object 274 56 45-II (144 * ~. Tº | Wendover . . . . . I23 52 20-o/ | 9 || 3.06 o. 16 || Deptling . . . . . 275 25 46.86 || 7 || 4.70 o-67 Westminster Abbey, Hollingbourne 286 59 8.09 || 10 || 5.64 o'56 left Tower . I25 23 35'90 || 4 || 6.72 3.22 || Frittenfield . . . 287 39 45.5o 17 || 7-43 o°33 WestminsterAbbey, Tenterden Church - * right Tower" | | I25 25 14-07 || 4 || 6-28 || 2.54|| Tower . . . . .314 19 37.34 || 11 || 7-3o o-69 St. Paul's . . I29 34. I4.5I | 12 6.16 o.58 Goudhurst Church Severndroog • 136 53 29-64 || 65|| 7.44 o.o. Tower . . . 331 19 38.70 || 8 || 2:49 o'I6 Dunstable . . 137 I5 56-29 || 8 || 4.83 o-60 | Fairlight . . . 334 17 42.21 38 4.73 o'o6 Berkhampstead 149 59 23.59 II | 7.76 | 1.20 |Brightling Obsery |350 37 34.47 13 6.13 o'50 ==m--am– 1 A correction of + 2"'62 to be applied to this bearing, to reduce it to the trigonometrical station. * A correction of —20' 5"'54 53 35 3? WROXALL. 18-in. Theodolite. 29th July 1846. Observer: Corp. STEEL, R.S.M. Objects Deari § R IRecip. No. IR Rºjº. CCtS, tº ſº tº tº * 4. O J earings dº. ange wi.ht. Objects Dearings. 3. ange Weight Shanklin Down . 181 32 3#33 2 3.05 I'o6 Doniface S.E. º 270 52' 1367 2. %28 I3-24 ... #. D 3oo 31 52'oo || 2 | 2.28 1.29 Littletown Down 3o4 o 51.5o 2 3.62 Boniface OWI) • 257 59 20:33 2. 4-o5 4. Io ió6 PRINCIPAL TRLANGULATION. YELL. * 3-ft. Theodolite, B.o. From 12th to 15th August 1821. Observers: Major-Gen. Col.BY, Capts. WETCH and DRUMMOND, R.E. - . No. Recip. - No. | Recip. Objects. Bearings. of | Range. of Objects. Bearings. of | Range of Obs. : Weight. Obs. Weight. *m-w- O / / / | w/ O / / / (ſ/ Brassa • ' ' ' | o 32 36-94 | 1.4 8.1o o.67 || Saxavord . . 203 I4 49'53 II | 7.47 o.79 Foula . . . . 5, 17 43.32 Io 5.67 o.44 || Balta . . . . . 215 46 33.68 Io 6.61 o.6% Ronas . . . 86 3 I'oz 16 5.25 o.24 Fetlar . . . . . 236 7 6.20 15 8.37 o.5i Wallafield , , 200 59 28.18 2 gº * YORK MINSTER. 2-ft. Theodolite. Trom 7th November 1845 to 14th February 1846. Observer: Serg. BAY, R.S.M. - No. Tecip. - No. Recip, Objects. Bearings, of | Range. of Objects. Bearings. of Range. of Obs. Weight. Obs. Weight. O f f ºf Aff O W f/ f/ Clifton . . . 9 17 37.29 14 || 3:69 o'14 Acklam Wold 243 3 28.71 I3 9:47 I. I2 Garforth Cliff 43 32 51.27 20 5-84 o.27 | Calais Beacon 258 42 41.79 || 3 || 4:36 || 2:33 Great Whernside IIo 36 32.14 | 12 || 6.84 o-39 Referring-object 26o 26 25.03 150 tºº tº- Botton Head . 179 42 48.99 || 14 9.33 o-64 || Hunsley . . 298 29 12-62 iſ 4.39 o.32 | AZIMUTHAL OBSERVATIONS. - *** BALSEIAM. Name and Computed Corrected - Computed ſº “Date. Elongation of * # g * * Resulting * gº ºsº |…]º reºsºno º Aºto. 1844; O / ºf 66 O J ºf O ş ºf C , f ºf June tº a 23o 48 52°40 |+13'82 ‘22 I99 I9 25'40 i. - * 9 |Polaris E. 81 “40 – 6' 21 75' 19 28-40 | * 28 57 24 I5o 59 13'43 J 202 22 28' 8o |+ 6'85 35' 65 17o 52 59' oo || * s sº , 3. IO 3? 33 60°oo l— o' 84 59' 16 2 ” OO 57'25 Io 34 18o o 16°oo |+ 3 + 37 19° 37 || 148 30 27°8o † - * * * * * 14 | 1. • 35 ... [t 3.3% '33. *::::: 57'71 I 3 '92 - I78 32 20°oo |-|- I 24 || 2 I 24 I47 2 35 °40 ; : * * 33 I5 33 33 17'oo -H o' 69 gº 8 36: oo 57 71. I 3 94 º 173 28 7-80 – 1 - 37 | 6’ 43 I4 I 58 18' oo º • * * * » 16 , 33 I '8o |— or 56 I 24 16' 20 57'71 Io' 97 124 I 52 '80 – 2 '99 || 49'81 92 31 67-40 * * 3) 22 3) 33 #. + 4° 28 53-88 #: 58 2O I2 oš ſº r I97 24 b8"bo + 2*79 71 - 39 17o 52 66 bo ſº * . , 11 Polaris W. 52'60 – 2 25 5o 35 71.60 57° 43 * Io'80 3, 22 I41 4o 12' 60 — o' 25 | 12:35 | 115 8 29°40 58' 20 16.72 33 33 Io' oo |+ 4* 2 I I4° 21 27' oo Mean of Eastern Elongations 150° 59' 12" 44 General Mean 150° 59' 12" 77 3 Western 33 ,, , 13"'76 IProbable Error + o”. 48 |BARROW HILL. Name and Computed Corrected Computed Resulti Date, Elongation of | Reading of Star. || Lºei liteading Reading of R.o. Azimuth of Starl A..."...#, a - §."Il O eading of Star aſºn. .# eading O ..". Azimuth of R.O. 1845: o 1 a 8 O 6. C F ºf o * , , Aug. i. * | IoS 33 53°33 – 18° 58 34°75 95 43 64’33 --- --- g 3 I Polaris E. 22 * OO +13'66 35' 66 39' 67 2 22 IO 6o 352 32 27 39 Sept. 2 3. 62 22 57°oo |–27: 52 29°48 52 32 68' oo 9.66 27.28. 3. 35 I24 5 I 3.3% #: #3; 31 '67 i J 6 ‘b7 |+|14-71 23° 38 II5 I 29' oo - . tº 3. m 25 * 39°oo |–21 63 || 17° 37 8 3.3% 7'47 27:42 iſ . » 7 y 91 20 35' oo |+ Io: o3 || 45' 08 || 81 30 57' 67 * OO 22 - 85 | " 3. 33 1. 57'33 – 8°78 || 48° 55' 69-67 7 3' 85 | " 9 , , 58 43 58.33 + 7:22 || 65.5; 48 54 2.23 5°90 28° 35' 3. 75°oo — 19: I2 55'88 27° 33 Aug. 28 |Polaris W. 177 37 89'67 – 12'34 77° 33 172 32 67° 33 Il '77 20 o4" 56°oo |+29°38 85' 38 39°oo - 3) 29 33 163 33 24'67 —II '78 12 '89 158 27 63.67 - II 3o 31 I9 sº 33 ić. + 2'46 18- 13 3.3% - 3. O I5I 29 46' 67 – 26' 40 20-27 || 146 23 84' 67 *. S º º " "| 3. ii.; #.; 51-67 Io '83 28' 52 | ept. 20 7 & ‘oo |+ Io'82 18' 82 II5 I 51 ‘oo ºn ſº * - 33 33 * - - 39 33 — 12 63 26'70 62-67 7' 23 26 84 3y 7 23 86 36 34’33 – 8 96 || 25' 37 81 31 5°oo 6-73 26.70 33 36: oo – 2 '88 || 33-12 6 §§ -* ... 8 ' ', 7I 24 45°oo |+ Io' 35 | 55' 35 | 66 19 28°67 * tº **~~~|~º....----...-- .22 ----------77:67 — 16 off ## is 4 I ‘oo || - 6 14 r - 30-21 * 9 || 2, 53 59 44’33 – 2 '97 || 41 ° 36 || 48 54 I4’33 e. • o? * * 3 ". 42' 67 |- 4-66 38 or I2 ° 33 5-67 27-9 Mean of Eastern Elongations 352° 32' 26".86 3 * Western 33 35 ,, 28' 57 General Mean 352° 32'27 Probable Error l * . - * º sº º A considerable discrepancy in the readings of the microscopes: rejected in the mean. + o "'79 ": 36 IPRINCIPAL TRLANGULATION. -- . .i.- I68 BEACON HILL. I)ate. Fºr Reading of Star. cº º Iteading of R.O. A.; se Resulting Star. and Col”. of Star. ...] Azimuth of to tº “” - Ö // // Aft”, 8 Urs. Min. E. Io? & ;I º ; is: a; ::::: s: º * ſ 㺠Jy ,, . Polaris 39 IO4. 57 º-º: #3; 135 27 ; : 2 23 iros 69's 3, 20 y? , 150 55 ...; :# I 24 §§ 2 23 18: II 67'95" , 26 || Urs Min. , | * * ::::::::::::::: * *:::: ; 26 is 6. 56' 50 , , , , , | * * *:::::::##|##| **::::: 49 sº 56' 38 , is | | | | * * ::::::::::::::: * *::::: ; 26 lºgy | 84% , so |, , , |* * * ::::::: |##| * : ; ; ; 26 14:35 6o'oz is , , |* * :::::::#|##| “... : : * * 59-23 , , , , , ; ; ; ; ; ; ;|##| **::::: 49 sys, 48-6s , Io | Polaris 33 2. 2 I #. £º § 32 51 :... 2 23 27' 23 57.68 April 5 | Polaris W. * * ::::I.3.3 ::::: I 35 27 ; : 2 23 II 32 5 I 4.I , , , ; Cephei ** :::::: ; ; ; ;|* * ::::: 4 a. 30.8% 46'99 33 jº Polaris 35 4. 34. #:-º: #3; 39 5 I º: 2 23 I7° 22 57 Io. , is sº cºld , | * * ::::::::::::::: **::::: 4 a. 34.64 sys; , 28 Polaris , | * * ;I,3: # * * § 2 as 22-65 54." 73 , , ; 51 Cephei, º, I4o 8 §I ; § I77 24 #3. 4 22 35' 16 48 oz || , is , , |** ::::::::::::::: * '##|4 a. 35.7; 52 '73 May 3 | Polaris , 177 36 ; :- #3; .# 32 I 52 º: 2 23, 24'84 sº 58-73 , , |g| cºld , |* * ::::::::::::::::: **ś: 4 - 37° 53° 32 39 IPolaris 33 I27 24 :::::1 ; §: I62 41 §: 2 23 25'95 52'63 June . . . . ** :::::::::#|##| * * : ; ; ; sees 5I '74. 1, 9 || 2: , 3737 ::=#|##| **::::g|2 =3 so. 55 ° 97 Mean of §. Iºlongations 212° 52' #. 34 #. Mean 212° 52' 55.2% 33 3y 33 33 97 robable Error + ".62 "Cloudy; rejected in the mean. i OBSERVATIONS. 169 IBEN MIACDUI*. Date. Fº: Reading of se: cººd º IReading of R.O. Aºi, Resulting Star. and Col". of Star. at Elongation. Azimuth of R.O. 1847: O ſ ºf C F ºf O / // O / WP July 4 || Polaris E. 38 4 *:::: Iſº .# 197 6 ...: 2 46 39 of 161 48 29° 55 » 13 || 3, , 38 3 #: I'; .# 197 5 .# 37' 64 21 77 » 16 || > , * * :::::=";|;|* * : 37' og 36-40 , so | . , | **:::::::::::::::: * *:::#| 6a | yes Aug. 13 3) 3) 99 45 #3. + :::: ::::: 258 47 ::::: 27: 56 22 '84. , , ; cºld |* *:::: tº #: *** :#|s ; 37:1; 30° 32 33 14 | Polaris , 191 34 3. #3; # 35o 36 ...: 2 46 27' 19 25° 52 |scºpic |* * : 1...;|...}}|**::::: ; ; ;&ls 33' 47 | 1, 15 |Polaris ,, . 19: 34 ...?. i ź #3; 35o 36 .# 2 46 26.68 31-62 |s cºpic: , |* *::::::::::::::: **:::: ; ; ;89; 32’68 , 16 |Polaris , || 7° 4° #. #3; ##|#74. §§ 2 46 26' 13 32-33 , , |51 Cephei , | * 5° #: Tº: # 337 43 ## 5 3 38'91 32' 38 | July 20 |Polaris W. 79 23 35' to - 9'68 25'42 243 58 39'85 6 26' 4 o * ... ... " ...; ; ; ;|...;|...] ... ſº • 33 40-60 + 2.56 43' 16 46' 35 5 32 ° 35 22 ° 2 I » 14 || 2, 33 182 *::::: Tiš: *:::: 35o 36 i; 6 15 31 '98 33' 20 is , , |* *:::::::::#|##|**:::: G is 3-6, sº » , ! Polaris 3 * isé. I ; : I.3. #3; 35o 36 #: 2 46 26’41 27° 41 * 16 |& Urs. Min. , | *939 º: Táº; ::::: 337 43 #4. 6 I5 31 24 27' 55 Mean of Eastern Elongations 161° 48' 29".83 General Mean 161° 48' 29" 96 , Western 35 ,, , 30" I7 IProbablo Error + o”. 65 * Imperfect observation, Elongation doubtful: rejected in the mean. :*: iº - The bearing of the Referring-object at this station, omitted at page 81, is 161° 48' 21"'98 observed 181 times, range 8" 23. 170 PRINCIPAL TRIANGULATION. IBEN MORE S. UIST. IDate. Fºr Reading of Star. i. º: Reading of R.O. *::::::: Aºi.o. 1851 : • 234 as 8s 128-9s 5478 14; 33 3.25 . . O f ºf June 29 Polaris E. - J 7.56 | * 45 19-09 |305 41 34-69 July 3 , , 7° 34 25'83 – 14*79 I I o4. r I95 3o ;: 1890 45'11 1, 22 i. 2; , 17. 5 9:30 + 5°99 || 15:49 295 ## 15-24 41 °oo Aug. . . . . . , 1744744°7-1379 3o '88 297 44 #: Io'85 | 46° 14 5 || 51 Cephei , '77 7 50-83 – 4:96 |45'87 29744 #3; 5 5 16: o3 38°46 }} ,, . I’olaris , tº 38 26-67 – 15'85 Io'82 235 34 ::::: 2 45 Io'48 43 '87 , 6 , 96 24 15-oo – 4:23 10-77 219 zo §§ 2 45 Io' II 38-84 33 7 5 I Cephei , 98 44 I5' 5o — 1:37 I4° 13 219 20 #. 5 5 16:51 37° 13 , , poli, , 74 ºf 7-67 -2°33 |49'34 |*974 .# 2 45 9-60 38.76 , , s ); cºnd 17637 50-83 + 6-oy 56.9° 1974 ::::: 5 5 17:36 38-97 | . . pomi , 163 48 62.33 – 8-64 53:69 |* 45 : 2 45 9. 18 43. 57 , , |g| cºld 166 8 so 7 |+ o-29 |50'46 | * 45 ...; 5 5 17:8o 46-97 33 ,, . Polaris , 154 12 36-oo +13-27 |49-27 | *77 9 ::::: 2 45 8.68 45 ° 20 July 20 | Polaris W. 25 38 33' 17 |-|- 8-68 41 '85 154 5 ::::: 2 45 16: o3 37° 33 , 24 2, , 128 & 38 so || 6′oo 64.5° 256 35 º: 2 45 14° 78 37:30 Aug. . , u, Min. , 18; 44.76-17 -18°4° 37'73 |*974 ‘. . 6 17 29.07 4o'76 33 ,, . Polaris 3? 16o 44 43’50 –21 '96 || 21 '54 * #: 2 45 Io' 66 | 48° 22 5, 6 || 3 Urs. Min. , 103 35 53'50 -26°46 27°oq 235 34 #3; 6 17 28.65 49° 23 33 ,, . Polaris 35 Io'7 7 67' 50 – 15-86 51-64 235 34 #3; 2 45 Io' 29 4o '95" , ; ; Urs, Min. , | *7 * 3** -** ises is as ...; 6 17 28 is 42 '83 33 ,, . Polaris , 79 24 22 67 – 8'39 14:28 207 51 .# 2 45 9-88 46' 39" , sºvº. . . * * *- : * * * * （#|s ºn 40°48 35 9 || 8 Jy ,, . 154 46 3:33 * 15° 19 286 4.5 ::::: 6 17 27' 40 37 °oo . ! * Mean of Eastern Elongations 305° 41'41"'44 . . . , . . . . Western … , º, , 42" os General Mean 305° 41'41"'70 Probable Error + o”: 56 * Great motion during this arc. . OBSERVATIONS. 171 * * * BEN NEVIS. Name and | - - Date. Blongation of Reading of Star cººl ‘. IR •. Computed Resultin * tº • g IReading of R.O. A º § - - Star. *.*.*.*.* ºr ºilo Aº is: f // 8 C F // O 9 ºf O || PF ug. 5 5 I C * T. 7 30' oo — 8 5 I 21 I 58 I 8 5I Cephei E. ::::: * , § ; : 5 I 5 : 5 i 15' 16 81 52. 21'o6. 2, 2 I Polari I22 45 35 ‘80 + 2 °49 || 38' 29 || 2 I 52 I4' 50 mº | 1S 33 41 ° 20 – 17' 67 3. 5 :#; 2 45 4 I 5 I 32° 33’ »; 24. 33 182 46 6' 2.0 |+ 14° 12 20° 32 || 81 52 49 - 70 33 185 I #: º-s, .# ; : 8 65°45 2. 45 39'90 2O '59 3 tº 9 * 40 – 4. ‘7b 54." I º 3 33 5 I Cephei 2? 8 5 #. ††, #: 8 52 ; : 5 I 2.2 ° 45 18 Io } IPolari Iö2 4.5 bi 20 ‘47 b7, b7 I 52 46°40 3. 25 Polaris 33 84' oo —21 64 62: 36 5 É. 2 45 39°35 3o 48 3. 6 I72 39 72 Io – 2 5 60 - 5 I 46 • A - - " " ' "...#######| |...}}|.. . . . 2 I72 39 66 '20 |+ o' 69 66.8 I 46 43' oo - :: 27 3, 55 82 “oo T.: ;: 7I 4 #3. 2.45 38-26 27:28, 2, 28 33 33 148 53 42 50 — 8-88 33.62 48 o 13'55 º ºf tº ºt 33 °oo |— 9° 2 I 23” 79 I9'45 2 45 37'71 25° 5 I a , 51 Cephei , '5' 9 5.79 + 3.82 19:52 48 o 7:35 6 • 6 S I79 23.80 -13 53 || 10-27 24.83 || 5 || 23 7 23:09 ept. I2 2 33 31 2 I ‘oo +24'42 45°42 76 22 29°os. º } * I75 #: i. 3 * 32 #.g. ...; 5 1 27° 17 20 75 I * 2 b 4o * 22 I 5 ° 02 I 2 * O 33 3 33 33 ::::: i. 2.É. #3; 7I 53 ſº 5 I 27° 33 || 1971 I4 | Polari 172 45 16:80 +27.41 44'21 7I 52 23.6 - * ~ 6. 33 4 l’Olaris 33 4. |-13. i4 | ...; #: 2 45 27°66 | . 26°88 * } t * 175 I 8: 70 +17° 99 26. I 52 18' qo A. » 5I Cephei , 37' Io — 7.3% . ...; 7I 5 ...}. 5 1 27' 50 . 23'54 ug. 24 8 Urs. Min. W. 173 47 51.99 - 3:19 47.81 8+ 52 53.99 * º ~e I 39-oo H-13.9% A-39 ::::: 6 12 48.44 18: 79 , 28 Polaris , 167 8 32.70 - 9.2% 5:44 || 71 46 52:49 ſº 20° 36 I39 55 *:::: I tº #4, is . . . 2 45 37°43 20 '3 2, 6 Urs. Mi 5* bo tº • 2 .. tº * : S » :, & Urs. Min, , 68 ::::: T,3: }: 48 o ...: 6 12 47' 19 22 of Cpt. 12 168 17 17: bo +23 4.I.' 6 22 28' I , - . * | » . 33 ... + ; : ::::: 7 jº 6 12 43 89 - I5 °og » : A I72 24 32°6'o. --20° 31 52 '91 6 22 20' 6 º ſº 33 " " ||...;; #| || ##|- s 1924 | are: I 3 || 8 3 163 47 48' oo + 14° 13 2 * I I O 7. º • ey » I3 8 , "| 8, , #3: I : ; 7' 53 ...; 6 is 43.7% 26:26 » : * , I67 55 25' 90 |+ I '79 27° I O " tº ºw º 33 3. 3. 33 6 42 °40 – ; #: 7I 53 £3; 2 5 18 79 | 17’ og 3, ' Polari I67 I 5 I 9o |+ 1.4.” IO " I S2 • º tº ſº, ſº 35 OlariS , , ...; tº; ...}}| 7 | ##|- 4s aros I5' 95 33 I4. | Urs Min. 33 163 47 2 20 + 17' 27 | 19:47 7+ 5° 49' 5 || 6 12 43. 52 22 81 | 3o '90 – 7' 27 23°63 3.53 9 tº 43.5° 23 35 23 a 33 33 167 54. 28.19 +22:39 43.49 71 52 17:32 2. 5 18° 33 22 ° 32 *E*- : 5o' oo – 5 Io 44 ° 9o 37° 4o . - Mean of Eastern Elongations 81° 52' 24" 23 3} Western 53 General Mean 81° 52'22"'51 Probable Error * Cloudy and misty. * Cloudy. * Very misty; partial sun. * Very clear in all directions. + o” • 60 Y 2 172 PRINCIPAL TRLANGULATION. BLACK DOWN. TName and Computed IC ted Date, Elongation of Reading of Star. ºf i. Reading of R. O. Aſſº; sa. Resulting Star. and Col”. of Star. at Elongation. Azimuth of R.O. 1848 : O f fy - O f ſy C f // Ç R Fº Tr * 5 139 7 35' 67 |+ 5°o2 4o 69 || 93 18 9°oo , Nov. 8 ' Polaris E. #: †† ; : 14.33 || 2 21 33°71 || 316 31 59' 55 I27 I2 12" oo + 8° 43 20°43 41 22 43° 27 tº -- 3y IO 3y 23 29°33 -H. 8. 17 3.3. 8 43°77 32 65 47' 20 º 94 3 58' 67 |- 9 'oo 49' 67 || 48 I4. 44' 77 * * * * * 33 I3 32 33 8 §§ + }. 73°73 *:::: 31 o? 7o 90 * 7 53 37' — 3 II | 34° 22 || 42. 4 Ib' 83 * * * 3? 2 I 33 35 6 #3; Tišº #3; * 8 oo 27 o8 57' 57 º 9 13 41 67 |+ 12 - 14 53°81 || 23 24 20'33 * * . 33 24. 35 39 42 : oo + 2 °33 || 44°33 3.; 25-78 58-71 51 34 71 '67 – 16*68 54°99 || 5 45 47 '83 • * : * ~ ºf ºr ſº "sºº" 9) 2} §§ +23° 5o 7I 5o 24' oo 24' 40 57 of { * > Ioo 39 47 'oo |–12 22 34°78 54 50 37° 33 * * . Feb. 9 93 33 47.67 + 8: 15 55'82 30 °oo 16' 50 64'87 Ioo 39 57'33 – 3 '74 53'59 54 5o 33°6 i. • * ~ * 33 IO 33 33 42' 67 — o:76 4I '91 54 5 §§ I6 78 6o 53 159 17 69°oo — Io'oZ 58° 93 II3 28 52' 30 tº my gº i. y; I3 ?? 3y 69' 33 + 3 55 72-88 #: 17° 73 - 63 I2 4o 44, 66-67 – 2 °57 64’ Io I 74 55 44' 3o * tº | 39 I6 JJ }} 3.3% tº- .# 59' 65 8 40' 30 18° 52 58'94, 24 1 57 oo – 5'78 || 51 22 I58 12 35'70 tº tº gº I • * 33 17 35 33 6 57°oo * . .# 55 ° 45 3.; I8 83 61 36. • 3 12 33.67 – 12 18 21 “49 17 23 7' So • tº s "sºft 23 33 ; + 3.3. 3.7; 8 3. 2O 57 59' 36 i. * I44. I6 - 67 – 7 ° sº 283 o 53° tº ſº m Nov. 7 | Polaris W. 7 3.3% -- 3% 13% #.3% 33 ° 95 64 13 I5 73 53 5o'67 + 3 oz 53' 69 212 47 31' 17 O " 6 3y 2} 33 6 42 “oo :*::3% 54 ° 97 20.67 3 32 1:27 4 3o 47° 33 + 8° 21 55' 54 203 24 16. I ":3 24 72 33 56: oo — 3 32 52 '68 3 24 jº 25' 58 58'oy: ja.”% 147 16 33’33 + 4'97 38-30 || 286 9 54-84 tº gº ºf ſº 33 33 6 {.. — 5'79 § 52 50 I4. os 59'86 i * 95 56 53' 67 + I 5 °49 69' Ib | 234 50 19° 5o Feb. 8 23 33 6 95°oo —18.8% 76' 95 5 ...; 16:42 60.36% 5 46 56-67 – 5'81 5o '86 I o 2 I 8 33 II 33 33 68 #: + II '71 57'71 44 4 §§ I6' 94. 64' oa. 168 14 12' 67 |+ 1 - 99 || 14-66 30 • 5 I i. • £º 33 I2. 33 - ” 20'33 + 3’ or 23° 34 7 7 #3; I7' 25 66-68 I54 35 32°33 – 12 5o 19 '83 293 28 48-6 i. a º 3. , 39 2 39.97 - 9:33 30-34 || 1 8 - 76 | 3, 17 | 3. ## 1 #3; #|* * : I8 6o 61 “40 3. 27 || 2: , #37 tº 28:22 - 8:30 19-io || 276 7 44-84 • * tº ſº tº y I5' oo + 1 I 35 26-35 41 ° 17 22 - 31 57°97 Mean of Eastern Elongations 316° 32' 1" og General Mean 316° 32' 1". 55 33 Western 33 , , 2" os Probable Error + o” 52 * Referring-object in haze: rejected in the mean. * Referring-object in very bad light; very unsatisfactory. * Referring-object in haze. * Referring-object difficult to observe. * Unsatisfactory, in consequence of clouds. • The star was not satisfactorily observed, the wind being too strong for the axis light. * Referring object was not observed for two hours after the star, owing to mist, .--1 is º OBSERVATIONS. I73 BURNSWARK. Name and Computed Corrected Computed lting Date. Plongation of | Reading of star. ºil ſittaling Reading of R.O. Azimuth of star , "º": Star. ding o aſºn. of star. § at Elongation. Azimuth of R.O. | º 1847: O f // O f Wr O P Py C f ff March 28 8 Urs. Min. E. ro2 46 57-40 |+ 4'oz | 61 °42 121 41 20' Io 5 57 41 °47 204 52 o' 15 ” ” A , , 98 49 47' 40 + 5°77 53' 17 | 121 41 19-40 || 2 o 38 '66 4'89 2, 29 , , , , 95 22 I4'8o + 4° 37 19' 17 I 18 13 47' os 2 o 38' 89 6-77 ”. | 8 33 ,, . 99 I9 II 20 |+ 12 25 || 23°45 I 18 13 46'55 5 57 41 °47 4° 57 April 1 |, . , 279 25 6'8o + 5°o2 II '82 289 19 44. Io 5 57 41 ° 29 I 3 '57 ” x > | A 3. ,, . 266 28 5'8o |+ 3 ‘79 9'59 289 19 42 - 30 2 o 39' 63 I2 ° 34 33 2 || 3 35 , 267 47 53*60 |+ 2 44 56°oq 286 42 26-80 || 5 57 41 ° 29 I2 oš * 2: . A 2, ,, . 263 5o 49°oo + 2 - 54 51°54 286 42 23'55 2 o 39.72 II 73 » 5 || 3 , ,, . 85 51 13 4o |+ I 48 14'88 Io4 45 45 'o'; 5 57 40 '81 Io '98 33 2, 7. 33 35 81 54 I2 20 + o' 95 13' 15 IoA 45 44° off 2 o 4o’ og Io '99 3) 8 || 8 35 ,, . 264 9 37°oo + 3-62 | 40-62 283 4. 9.25 || 5 57 40'45 9 o8 35 9 | A 2, ,, . 269 12 36-40 |+ 2 - 30 || 38.70 283 4. Io. Io | * * 40° 58 II '98 * > |* , , , 78 47 50-40 |+ 1:15 51.55 97 42 20:50 5 57 40°28 9° 23 3, IO | A 2, » 74 5o 52°40 – I '88 5o 52 97 42 19:45 2 o 40° 70 9:63 » 12 || 8 , » 76 I 35°oo + o- 21 35’21 94 56 3-05 || 5 57 39°75 7' 59 2, 13 A 2, » 72 4 31 ° 20 + 1 ‘72 32 '92 | 94 56 I'3o 2 o 4o '98 9-36 9, 17 | 8 , » 245 I4. I4' 60 i-F 1 - 30 15' 90 264 8 42 Io 5 57 38°70 4 ° 90 ,, 18 X 33 ,, . 241 17 16' 60 – 2:38 14:22 264 8 4o. 9o 2 o 41 ° 16 7.84 2, 19 || 3 , ,, . 64 3 o' 20 + o- 22 o'42 82 57 28:75 5 57 38' 22 6° 55 » :, . A 2, , 6o 5 58' 8o + 1 '73 || 60'53 82 57 28°35 || 2 o 41 ° 33 9° 15 2, 3, Polaris , 24o 43 21 60 |+ o' 16 || 2 I '76 262 57 28'95 || 2 37 59' 47 6.66 » 21 8 Urs. Min. , 242 17 33 °oo — 2 : o3 3o 95 261 12 I 15 5 57 37-70 7. 9o » 3, A 35 , 238 20 33' oo — o' 36 32°64 261 12 2 : oo 2 o 41 ° 26 Io 62 33 3, Polaris , 58 57 55' 40 + 2 - 16 || 57'56 81 12 2.75 || 2 38 o' 52 5'71 • 23 & Urs. Min. , 53 58 29'8o |+ 3-88 33°68 || 76 49 58.85 2 o 41 ° 14 6' 31 ” | 8 , ,, . 57 55 27:20 + 4'25 31 “45 76 49 58° 45 5 57 37' oo 4°oo Mr. ** | * * , 222 20 61 °60 – 4'86 56'74 241 15 28' 55 5 57 36' 64 8’45 *y 4 ||, . . . ." § 12 69-60 + 5.04 || 75.6; 27 # 45-?? | 3 # 33-14 2 - 65 Mºrai, º ſº. …" 33 4 16 16-80 |+ 2 - 38 19° 18 27 7 45' 95 || 2 o 49' 51 7:28 Iarch 28 51 Cephei W. 92 I 44' oo + 3:46 || 47.46 | 12t 41 20 oo 4 47 28 16 4' 38 2, 29 29 33 88 34 6' 60 |+ 5.5o 12 io || 118 13 46' 30 28 - 20 6 oo ”, 31 35 , 259 4o 2' 60 + 1 30 || 3 9o 289 19 45' 35 28° 23 13° 22 April I , , ; 257 2 45° 20 + 4' 55 49' 75 286 42 26°75 28° 28 8-72 2, 4. 23 , 75 6 6' oo + 1 - 23 7'23 Io4 45 45' 30 28.65 9°42 » 8 23 , 253 24 34' 4o |- o' 27 | 34° 14 283 4. 9°75 29' 12 6' 50 2, 9 33 , 68 2 47 'oo + or 34 || 47° 34 || 97 42. 20' 65 29:26 4 °o 5 33 I 2 35 , 65 16 32°40 - 2'47 29° 93 94 56 5' 20 29' 72 5 ° 55 2, 17 35 , 234 29 8' 2.0 – o '79 || 7' 41 264 8 42 '85 30° 69 4 * 75 ” IQ | Polaris , 55 27 29' 40 + o' 71 || 3o II | 82 57 32 °75 || 2 37 59° 73 2 '91 33 * | 5 I Cephei , 53 I7 54" oo + o' 39 54°39 || 82 57 29' 20 || 4 47 3I of 3 * 74 2, 2 I | Polaris , 53 41 57' 60 |+ 2 71 || 6o 31 81 12 2.75 || 2 38 o' 5o I '94. ” ”, 51 Cephei , 23: 32 23.8o |+ o-35 | 24, 15 261 12 I-55 || 4 47 31'47 5 ° 93 ” 23 , » 47 Io 21 “40 + 2 - 66 24'o6 76 49 58: 65 3I 97 2 - 62 M. ** 33 2, 2 II 35 53' oo — 4'82 48* 18 241 15 28' 8o 3 I 97 8.65 ay 4. yy » 357 28 3' oo i+ 5'44 8°44 27 7 46’ 65 35' 64 2 * 57 Aſcan of Eastern Elongations 204° 52' 8": o3 General Mean 204° 52' 7". 20 33 Western 33 35 33 5”.68 Probablo Error + I74 PRINCIPAL TRIANGULATION. ETUTSER HILL. 1844: * 17: 18 KG7 -27-98 31-69 98. s sºoo º, O sº I ** *...; Hººl. ##|******* Jan. 20 , , , 59 58 #. f §§ ...; | 5 45 64' 67 55 ° 34. 51:45 " * * * | . . ; ; ; ; ; ; * * 3, 28 , , * * ::::::::::::::: **::::: 56’ II 44°29' , , , , , . " ":::::::::#|##|** 3: 56-26 sº Feb. 1 | y, | * * :::::::::::::::: * ~ : 56'85 52 '8o . , II | y, , 113 37 § f : #3; 39 24 #: 59' o? 52 51. , 4 , , | ** 3: ; ; ; ; ; ** {:}| Go-o; st-se pº", xUrs. Min. w. * *::::: - }; ; 98 5 .# I 49 29° 78 59' 5o *... Polaris 3y 64. 38 #. + §§ :.. I75 I3 #3; 2 23 55 ° 34. 48°24' 2, 21 | y, , is “ ſº tº 5: * * : 55 ° 34. 54-88 , 24 | y, , 16757 É.; †: ; ; 98 32 ...; 55 ° 55 56 of: , 26 || || , 146 * #. +...; ; 76 37 ; 55 '71 59' 49 3, 27 | y, , 46 29 ; * ...; §§ I57 *::::: 55'87 56.94 IFeb. 2 , , , 166 is §§ t; ::::: 96 47 ...; 56'98 54-56 , , , , |**::::::::::::::: * : ##| sº sº, , , , , , | **#######|**; sº, sº , 7 | * | ** is tº # * > 3; 57° 97 5I 5o Mean of Eastern Floration. Io8° Io' 54". 61 General Mean 108° to 54"'92 35 Wostern 93. , , 55", 13 Probablo Error + o''' 55 * The level out of adjustment. * Rejected in the mean. * Star clouded from 19° 27' to 24" 13'. * Weather stormy. *. * Strong wind caused the light on referring-object to be unsteady. "The light on referring-object unsatisfactory. * Wind very strong, observation unsatisfactory. OBSERVATIONS. - f75 CHEVIOT. Name and + C ted C ted Computed in tr Date. Llongation of Reading of Star. º i. Reading of R.O. Azimuth *- Aºi.o. Star. and Col”. of Star. at Llongation. 1846: O y ºf 8 O / // O 'F ºf – Jul ari 5. 164 14 16:40 + 9' 18 25'58 227 43 40'90 a º º uly 4 || Polaris E. - 54'40 – 15' 60 | 38'8o 33.3% * 4° 20'79 246 9 29' 20 August 2 33 35 49 48 2-80 |-|-10-81 || 13 61 113 17 5.9% I4 - 17 33°79 §: f .# #.7% 8 47° 70 IO. S. § “2O † 4." Ib II 8 4o 2 I 3o º º 33 3 3) - 33 55 É. *-* 3.3. 66-98 19'8o I3 83 28 - 8 I 56 6 12 20 |+ 5°79 I7 "99 I 19 35 42.60 º º 23 4. 33 33 39' 6o º- *::: #:# 4. I*2 o I3 46 , 29 “O4. 8 } '8o |+ or 96 || Io'76 | 121 32 34.70 * º 93 5 33 33 58 3 23: + o' 5o 20' 90 32 ° 9o - I 2 98 - 3o 96 , , |51 Cephei , | * '3 #: f : #: **::::: , ; 4:19 28° 24 •: 59 9 69°40 – 4:38 56' 02 || 122 39 22:60 º ~~. 33 6 | Polaris 33 68-80 |+ 1 . Io 69-90 19.70 | * 4o I2 58 30° 77 I8 2 29 6"oo |+ 5' 17 | 11 - 17 | 65 58 38.80 240 7-51 | 3o og 33 33 33 É. º- o “44. 21-76, 39'30 - * ſº - * * 6 º w º º ſº - , , || 51 Cephei , | + 39 §§ † :: :: *; sº ##|4 5, 9:25 34’ or 19|Poui, , |* *::::::::::::::: **::::), is 6'98 || 3:06 358 32 45° 6o -- 7 oz 52 '62 62 2 20 °oo º º 3, 2 I 53 33 48°60 |-|- 4. s: 6 20 '40 2 4o 6' os | 33° 5 I 7 51 9:20 |+ or 63 9°83 I 20 39 Io º * » 24. 2, » s: 5 17:60 — o' 86 16'74. 38° 30 2 40 4. 48 | - 29' 90 * , |51 Cephei , | * * ::::: – 3:4. #: 61 20 #: 4 51 I 23 33° 43 » as |Points |**:::::::::::::#| * * ::::: , ſo sº 29' I4. » , |51 Cephei , |35° 39 ::::: I ... [...] ** {{..., |45 it'ss 33 °3o , 26 Polaris , 354 44 #. + †† #3; 58 I 4 ... 2 4o 3:45 || 29 °49 . ~ . . 6 5 & 65 - 8 • I.A. | 66." 8 I 4, 23 7o º • * * ” 5 I Cephei , . 35 ##: + ; ::::: - 5 *::::: 4 51 II '87 32 °29 Sept. 2 , , 337 35 54°60 – 15:20 39°40 || 38 53 72°5o 13.75 | 42.88. . 3. 33 I6'oo |+15° 93 31 ° 93 57 Io . - 33 9 305 35 27: 8o — o' 15 27°65 6, 53 48' oo I5 °32 29°43 , ” 28' 60 + 3 '92 || 32° 52 40° 4o 3. * 307 56 32°20 – 7'o'8 25 12 || 9, 14 43' 20 º • 8 I to 33 33 7 29'8o — I 19 28-61 #. I5' 48 27 - * 308 54 65°oo – 9 'o6 55'94 | Io 13 19'8o * - 3 I • OI º i. 33 - 33 §§ f *::: .# 32 : I5'79 3 I 6 Augus * 49 22 38' 8o o' 98 || 39 '78 I2 I * IO º I • 66 4August 5 8 Urs. Min. W. 8 3. T *:::: $7.3; 6; 58 34. Io 6 o 18° 59 3 » A 8 48 So ‘78 52 '5 5 58 39'2O ºr * * - 3 3 - 2c - is 23 95 33 353 * 62 - 8o *. %; 55’ II 42 "Io || I3° 5o 33 se » 24 . . 349 Io 50°oo |+ o'o6 || 5o'o6 61 20 40° 5o I 1 - 37 32-61 22 75 33 61 oo — or 43 .# w : IO » - 347 47 55 °8o |+ 4' 36 6o 16 || 59 57 48° 5o º e * | * * * 7o 20 – 3:38 | 66'82 48°60 iro, is 99 * 26 , , , 346 443.39 + i. 13 |44:33 58 14, 23:30 Io-84 29° 53 " ' " ? - -----.... --- . - 47 '80 – 4: 17 43' 63 ... 25° 40 . . . . . - * >> | \, , , ,, ..., | 350 3 39'8o |+ o- 20 4o' oo 58 I4, 25.5o 2 I 13-91 29-66 - - . . . 42 “oo |+ o' 16 || 42° 16 23 °8o . Sept. * * , , , , 32° 44 36.42 -12-17 | 34:23 || 38 53-7:22 || 6 o 9-07 32 oz * * 3 Io 20 + II .o:3 || 2 I 28 . . . . 56' 5o || - -- '*jected in mean : Star not observed until 20" past elongation, owing to clouds. . 176 PRINCIPAL TRIANGULATION. CHEVIOT-continued. 1846: § ... c. ..., | c...., | . . . . . . . " ' " | * ' " Sept. 9 |x Urs. Min. W. 298 42 ;: † : ; É. 6 53 #: 2 I 6'92 || 246 9 30'85 , to , , |* *::::::::::: ##| * *::::: 6 o 7.3; 28.2. , , , , , |* * : I.3. 3.; * * : * : 6-48 || 374, , , , , , |**::::::::::::::: * * : 6 o 7.1, 32 ° 92 • * * * * *:::::::::##| "...º." - " sº , , , , , |* * : ; ; ; ; ; ; * * ';|2 5-39 28-36 . . . . .” “:::::::#|##|** : * * * * Mean of Eastern Elongations 246° 9' 30" 71 General Mean 246° 9' 30" 63 y? Western 53 » , , , 52 Probablo Error + o” 24 COWHYTHE. Name and Computed Corrected Computed Date. Flºgº of Reading of Star. ºl. º: Teading of IR.O. *::::: Aiºio. Wy C F // O / // O // bºrº, Eliº º-pºil;|** ##| sº sº. , as , , | **::::: . . ; ; ; **::::: 29'ss || 33-9: * * *|††:#|...; "| * Jan. Io 33 33 9 #. + 2.97 9:39 # 27.80 35' 66 , , , , , |* * ::::::::#|##|**:::: arse ºrgs • *| " " ||...}}|..}}|...";| * * » 14 | y, | **i; ; ; ; ;|##|* : ; 27.8o 38°58 *| " . . . . ; ; ; ; ; ; * * Dºo poni w "" ; ; ; ; ;|**:::#| sº ºss I 2 IO I 3 * OO * tº * "sº 33 33 . .# +: ; 22 I 35 # 29' 25 38'90 Jan. I2 3 * 33 ::::: I : ; 17o 24 33.3% 27.8o 37.62° , is , , | * *::::::::::::::: * * : *so | 3336 , is ºur Min. , |* *::::::::::: ; ;|* *::::: 6 a. 36-s: 43 o8 wn- Mean of Eastern Elongations 66° 27' 36”82 General Mean 66° 27' 36".91 33 Western 33 , , 37" of Probablo Error + o”. 52 . #. jº.delay occurred before the star could be found on the 2d arc. + : i | § OBSERVATIONS. 177 *— DUNIKERY, Name and C ted c mas C d Date. Eination of | Reading otsur l'º"; Radiº of R.o. Aiºs Resulting Star. * ...º.º. ººlºo 1844: O F // O / ºf Af If Oct. 2 I | Polaris E 69 22 52 '90 . 6.73 59-63 151 39 6'8o O f • 26 s: f º . ...Ald e 6o oo T 6'88 53 - 12 14:20 | * 25 o' 2 4 4 I I 4’39 ; 22 69 22 49' 60 + 6'83 56'43 | 151 39 7'90 it. º 33 º 2O & 2 ° 2 O 3’53 b5° 73 I5 I 39 3’ &o • * A * tº 33 5 I Cephei , 6 #: –33; #:... ° 3. |4 22 54-06 9' 49 º 5 ‘70 – 5' 30 b3 34 2 & 2 O * SO 2, 23 Polaris 59 61.60 |+ 3 '86 §§ 7 23 #: 2 24 59' I4. I4° 19 tº go |+ I 36 57° 26 87 23 17. 33 » 5 I Cephei , 7 4. #. f 1.33 53 ° 32 7 23 ...; 4. 22 53 ° 9o 17' 51 Sr. 66 28 46' Io i+ Io' 30 56-40 || 146 47 4'80 w . Nov. 17 32 3) 6 53'40 – 7 oz 46' 38 7 13.63 || 4 22 47.84 8: 15 tº I 32 18:20 |+ o' 71 18, 91 151 2 8o mº º Aº gº º sº º Oct. 22 |8 Urs. Min. W. 65 8 29-70 –10:48 º: 5 I 39 12.60 || 5 °5 33 75 14'89 3. A , 5 7'90 – 5' 39 2 51 151 39 Io' 20 * * £ 2, 23 "| is : I § § s * ... . . 49 53:68 16.67 33 24 Polaris } 59' 7o 26 67. 9 7 23 I7' 40 * º ey tº * * . " ... ; ; ; ;|...;|, ... . ." tº † * I F * 22 I I4.0 . & e ov. 17 | 8 Urs. Min. , 2.É. tº: : ; 4b 4 ; ; 5 25 4o 66 IO "2 O 60 15 5:20 |-|- 16:46 65-66 146 46 63 do W 5 55 ° 20 |-|- Io' 46 b5 4b 4b b3 9 e 3) 3 y 33 33 59 4 º: – 6’ 6S ... 6 75.36 49 53°7 I4. O4. 8 Polari I Ib 20 + 2 59 Iö '79 I40 47 23' 4o º • * ~ * » : olaris 33 6o :6 ::::: + 3.; º: 46 4 34.36 | * *444 98 28° 59 º . Mi XO I.A. * IO 2 '98 || 17 os I4b 47 2 I Io º º 3. 2 I X Urs. Min. , 59 4. ::::: -: # ...}} 6 26. oo 49 53°74 I 3 '8o ari . I 3 I '8o |– 6 ‘bá. 25 Ib I4b 47 27° 4o , * i. * 22 Polaris ?? 19° 50 |+ 6' 2 I 25'71 21 - 30 | * 24 42 '91 I6' oo Mean of Eastern Elongations 84° 41' 13". 64 General Mean 84° 41' 14” 46 *-__ 29 Western 55 , , 15" 17 Probable Error + o'-64 * Rejected in the mean. IDUNNOSE. Name and C ted Corrected Computed º Date. Fºrgºn of Iteading of Star. i. j Reading of IR.O. Ajºsar Aºi.o. º * and colº. of star. at Elongation. 1844: O f // —r— O / If O 1 ff O f ºf Jul I º 4 65 zo 42 '70 – 8: 52 34° 18 2 8 41 ° 4o º - * Y IS | Polaris E. 37' Io – 3 3o ::::: 4. #: 2 24 5’ or 339 I2 I4 ° 27 5 y I6 3. 8 22 23.80 – 18-29 5' 51 165 Io 21 go iº * 3. $2. 6 *:::: – I 29 24’ or 24' 60 4 * 74 I 3 '23 3 * 2 I y 2 22 53' 60 |+ 9° 48 63 c8 219 Io 55 ° 3o º * * * * * * * 3. 33 6 5o 60 — 19:38 3 I 22 59' oo 3 64 I 3 64 , 20 | Polaris W. 166 59 13’90 – 4:37 9°53 148 35 38' 20 i. I4 qq.” - 2-80 |+ 19.31 22-11 3 I ‘40 3 ° 99 4 '99 2, 2 I 3? 153 29 58' 90 + 7.81 66-71 135 6 15° Io tº ºr 8° 56 33 53 40 |+ 9'8o - 63' zo I9' 5o 3 '79 5 3 2 23 5 * ,, . 57 34 4. -º $44 3.3% 219 io 53.52 3 : 36 Io ‘84 º- - 36:90 |+ 1-24 38-14 49:40. l Mean of Eastern Elongations 339° 12' 13".71 General Mean 339° 12' 12"'59 33 Western 33 , , II"'46 IProbablo Error + o”: 61 --- * Levels we º tº º Yºº not read until the termination of the arc; observation not satisfactory. * Much motion. Z 178 PRINCIPAL TRIANGULATION. DUNIRICH. * | * | Release, ſº menºno Aiºia. Alºño Star. and Coln. ofsaf at Elongation. - º sº * * 6; ; ; ; 4 8:1, 45.4; is; ; 43.77| ...'... . ept. I5 | Polaris E. §: º: 3.94 I? I ::::: 2 38 II '90 242 28 64° 14 - 2, 17 }} 35 º 42 43 ... º § 3 I 33 4:::: Io. 78 59' 16 , , , , |* 33 #; I ?:, ; ;|** {3} 7'47 48° 57 , , , , | * * : 13; ##|**::::: 64; ass; oil 9, , , |**:::::::::::::::: * * : * 37 sº 54." II » II | y, | | 6’ 4. 3. + .# ; * 3: ; ; ; ; ;1.8; 55 ° 73 , , s: Cople , . * * ::::: -...} :#|**::::: 4 g. i. 5; 55° 31 , so Polaris , . * * §§ tº: ::::: 126 56 §§ 2 37 48.83 57' 57 2, 23 2. 15819 ;: f : .#3; * * §§ 2 37 46'89 58' 29 , , ; cºpic: , | * * ::::::::::: ##| **::::: |4 s, io9s 61-43 p? 26 Polaris 33 98 *::::: Tºš #3; I57 57 §: 2 37 44-82 62 92 , , |g| cºld , * * :::::::::::::::: * * *::::/4 sº toº 59' O2 , 28 |Polaris , . * * #3: + 3.3: ... Io8 44 ::::: 2 37 43°4o 56 o8 , 29 , , | * * :... . ; ; ; * * ::::: a 37 4-8. s?-14 sºrt aſ a Urs Min.w.. " " ... I'; ...}}|**::::: 6 o 492. 32 19° Oct. 9 Polaris 33 Io8 26 #: i #. #: I73 33 : 2 37 55'79 52' 35 3} II | 8 Urs. Min. , 54 * ... *:::: #. I22 32 §§ 6 o 49°96 5o '74. , , Polaris , | * * ; : :#|##|** #|- 37 sess 58' 28 • * : " ...:#F####|...}}|...] ... 29 || " " 43 Io + 3 64 46-74 :::::: - 37 48-53 56'70 , as | Un Min. , |**:::::::::: ; **::::: 6 o sº. 54.21 , , |x , , | * * ::: ; ; ; ; * * : * c 3-7, 6.1% , 26 || | * *:::::::::::::::: * **ś|s a sess 55' 08 , , |x , , | * * ...;|...: ; ; ;7 * : * c 3:4. ss's, , , Polaris | **::::: I ##|##| * * : * 37 4-46 | 6′ss 23 29 || 8 Urs. Min. , I7I 4 3. I*.*. 13% 59 34. *::. 6 o 53' 20 61.78 35 "Mean of Eastern Elongations 242° 28' 56” '69. , Western , 57" off General Mean 242° 28' 56”. Probable Error 5 + o”.63 \r:.. i * Rejected in the mean. i| OBSERVATIONS. I79 EASINGTON. Date E." Computed Corrected Computed * º gºn of Reading of Star. Level | Reading | Reading of R.O. |Azimuth of Star Resulting º and Col”. of Star. | at Elongation. Azimuth of R.O. 1846: O / // O / // O - Feb. 27 | 8 Urs. Min. I 2 6 57°oo – 8 Io || 48° 9o 124 52 45° 70 // O J // in. B. 8 33 40 + 16° 58 §§ 4 5 #4. 5 53 2-80 | 128 38 55'81 » A I78 I2 54° 20 — II '88 || 42° 32 || 3o4 52 47° 7o 35 33 33 :::::::::::::::: *** {..} : 59 is is 67° 35 33 28 || 8 3 y , 179 19:49 |+ 2.22 || 2:49 || 3or 47 19:39 5 • º 3I 4o |+ o' I2 3 I 52 19.70 || 2 53 3°oo 56° 04 March 1 |, 33 174: 27 51 ‘oo + 6' 62 57-62 297 13 56' oo 33 7: -º- .# *:::: 61.60 || 5 53 3'3% 58'90 » , | x - 17o 34 2 6o |-|- 4' • 46 || 2 tº Pº tº s r - y 3 * 33 ë. -º-º: 6.75 iſ: 97 I3 #. I 59 I4 II - 61 : 50 3 171 21 60-40 |+ 6'99 || 67. 2. 8 5 oo - 35 3 3 y y? 6 7. – 3 92 .# 94. 3. 5 53 3’ 72 59° 74 y » I64. 2 I 18' 20 -- 3 - 63 2 I '83 28 2 & " ?O • 3. 5 | is 25 6 38' 2.0 — 3. ; : 7 7 .#. 5 53 4'o6 60°44 3. 3y Ibo 27 24 20 + 3 2.7 ° I * CO " " "|... :::::::::::::::. . ;| < * * , 6 || 8 }} Ibi 44, 35' 4o |+ 3 + 72 • I2 284. 20 42 oo 33 - 35 #: - §§ #. 4 3 ;: 5 53 4'23 55 '26 . A. 3. I57 5o 56' 60 – 2 - 20 ‘4o 284 30 Ao’ 39 33 35 y? #: - ... ##|**::::: sº 16:34 57' 21 - } J) 145 44 59°oo — I 4o 57' 6o 272 24 52 '50 g - - 33 7 , 33 8 75°oo — o' 93 %; 72 24 §§ I 59 16" 7o 62° 41 8 || 8 138 38 28' 2.0 – 2 of 26’ I 5 || 261 24, 27° 7o - 33 j} 3} 4o 6o + I 23 .# 4. #: 5 53 4. 75 58. 36 A. r I34 44, 35°oo |+ I 75 36' 261 24, 28' xo - 33 37 33 35 a #: i. :::: §§ 4. .#. I 59 17' Io 61:38 - 3. I23 I4 66°oo |-|- 3: 74 69' 246 o 63 - 3o 33 9 33 J} 78° 4o |— 㺠## 4. §3. 5 53 4 ° 93 58-56 • s, a I 19 21 22 6o |— o' 27 22 33 246 o 64'40 - 3 y 33 33 8 20° 4o |— §§ .# 4. §. I 59 17' 50 62-78 1, 3, Polari II9 58 3' 60 |-|- I 52 • 12 246 o 63 Ao º . Ola I’lS 53 9 oo |+ 2 °oo { #: 4. §: 2 36 2 26 6o '45 ,, . 12 & Urs. Min. , 116 26 32.42 # 2.69 || 33:23 239 12 25.30 • * 6I • - * 33 20 – §§ 31 78 31 6o 5 53 5' 32 I 53 35 x II 2 32 47' 20 – 6 78 40'42 239 12 26-30 ſº .*. 33 33 35 39-40 |+ 9 24 || 48°64 39 #: I 59 18 69 60 '81 ,, . 8 3. II2 54 52 '20 - 2 9o 49' 30 2 O AL3 ° 30 º - 33 33 ; : T : ::: * *::::: ; ; 5:45 59 ° 99 | * 18 |, ?? , 99 35 68:22|-- 6'51 61-69 222 21 62 - 20 6. 6I • ; : [+... . . ; £3.75 553 °9′ I og ” 23 |, - 90 4 49' 60 |–12 '42 | 37' 18 212 5o 42°60 º º - " " sº is 3: tº: #; *::::: ; ; 6'ss 60-83 by 35 | A 33 Io 5b "40 - 5 - 29 || 51 II 212 5o 39°oo º c- 3. 33 8 5.o. oo |+ 7' 16 || 57' 16 5 #. I 59 22:36 65. 72 2, 24. 3 3 * 78 35 34° 20 + 5°41 || 39' 61 201 21 3o 6o º ... 33 #. — 16:83 28°37 3. 5 53 6' 35 62 - 2 I » 26|, 74 44 62 “40 – 6' 58 55'82 I o 56° 3o " - || º 33 64'4o |+ 3’53 || 67'93 97 3 #: 5 53 6' 22 58'95 33 » 7. 33 7o 51 20°oo — 9 14 Io:86 I o 6o 20 tº º 3. 33 I9' 60 — 3.; 18.78 97 3 33.70 | 59 °3°7 67-70 ” 27 | 8 . , , 7o 33 13°60 — o' 58 13° oz | 193 19 Io' 90 ſº sº » 3 66 17' 40 + o' 69 18’ og 93 IQ .. 5 53 6' 18 60° 57 ” , | * , 3. 39 28°40 — 5' 52 22 '88 193 19 Io'90 ſº * 28 || 8 32 . #: [+...; #: 9: " ...; so 23:29 64-77 33 33 , 59 57 34:80 –Io-48 || 24:32 182 43 28° 4o * tº 35'20 – o '47 || 34° 73 ...; s 53 6.18 63: 56 Z 2 18o PRINCIPAL TRIANGULATION. EASINGTON.—continued. Date. Fºr Reading of Star. º: º IReading of R.O. Aſſºa. Aºi. O º nd Col". of Star. at Eiongation. Azimuth or 1.0. **lºua in E * ::::::::::::::: **:::: . . . . . . . . April 3 || 8 33 33 49 20 ::::: I'...: #: 172 6 ##. 5 53 5'83 56' 20 , , , , , ; * *:::::::::::::::: * *::::: so zºos 70-68 Feb. 25 | Polaris W. '77 ; : – ...; | #% 3**::::: 2 35 37-so 55 ° 97 , as , , |* 37 g.: I # tº: “*::::: * is see ss as J) 27 5 I Cephei , I7I 29 ſ. I: | §§ 3O4 52 : 4 43 40' oo 61 - 66 » 28 , , 168 24 ::::: II ...; #; 301 47 #: 39° 71 59' 35 March 3 , , |**::::::::::::::: * * : 388, 6o' 19 , , , , sº is :::::::::g|##|**::::: 38-65 59' 56 , s , , , |**:::::::::#|##|* 7: 38,46 & , , |* 7; tº; ; ;|**::::: sº, sº , s , |* #: ; ;|##|**::::: 37.8% 58° 45 , 9 33 , 112 38 : + £4. §§ 246 *::::: 37.68 57° 12 23 II Polaris 35 Io'7 57 ;: – : .# 239 I2 #. 2 36 4' oë 54° 58 i , 12 51 Cephei , | *5 49 §§ + ...; ## * * : 4 43 37' I 3 58°43 31 ,, . Polaris , 104 25 3. – ... §§ 235 4o #: 2 36 4' 54 61 '91 , is; copic: , ; * * g.: I }}|...}}|**::::: 4 is 36-97 59° 22 , iſ Poui, , " "::::::::::::::: **::::: * is 7-17 | Gros , iss, cºpic | **::::: ; ; ; ;|** ...;|44; 36's 60° 95 * * * * ... :::::::::::::::::::::: * * 2, 24 | y, , º sº; +,&#|##|**::::: 36' 15 59-76 , is , , | * *:::::= #|##|*, *ā; ;&ls toº , is . . . * *:::::::::::::: * * : 36. 60° 55 , , , , | **:::::= #|##|**::::: ;62. 39:29 Mean of Eastern Elongations 128° 38' 61": 28 General Mean 128° 38' 60"'49 53 Western 33 » , 59" 32 Probable Error + o” 30 | OBSERVATIONS. I81 FAIRLIGHT DOWN. Name and Computed Corrected Computed tº Date. Elongation of Reading of Star. Level | Reading | IReading of IR.O. Azimuth of Star Resulting Star. and Col". of Star. at Élongation. Azimuth of R.O. 1844 : 8 * -- . ." ſº • 6 § * ſ £6 C f ºf O / // Scpt. II | Polaris E. 4 57 4.92 - 3.35 2.93 '7° 37' 57.37 2.24 30-30 |276 5 11.5o 16: oo — 2 71 || 13 29 48.67 3? I3 35 35 23 II 50' 67 + 3.54 57.3. I 16 52 5.99 29' I4. 12 65 - .# † 3.7% 7. $3.3% 177 14 20 b7 * 14 28 8 I 9o 55 20' 07 i. # 33 I9 35 35 / #: *º- º: 36: 42 6 6 2O 33 25 81 I3 69 I4 2 I b7 – 4' 54 I7 " I 3 2 4 * OO † * » 20 2, 33 9 5 ...? it ...; 3.; 2.É. 25 ° 23 II 24. * 144, 31 57 33 — o' 65 56' 68 58 12 42 67 º i. 33 24. 33 35 3 54." 33 |+ o' of 54'36 43' 67 22 85 Io 5o Io'7 13 13° oo — o' 17 | 12 83 20 53 59' 67 * * 39 25 33 33 1-67 H. 9' 40 I I of J 57' oo wº 22 28 8 : 66 26 7I 38 30°33 – 6 oz 24° 31 165 19 16:33 2 I 6 9° 20 23 35 33 6 #. + o- or 3; 31 I4 oo 29 3b 52 38 oo — 7' I o' 8 I I go 21-67 ey ºr s . . 53 27 3 25 6 ::::: 4. ... #: 3o 33 I2 * OO 2 : * IO 5' 77 27 26 18° 33 + 2 - io zo. 43 121 II " OO º * 33 28 35 33 *::::: I 2 27 : 7 Io' 33 20° 47 8 95 , so , |* * ::, ; ; ; ; ; * * : 9's iro, Oct. 4 , 5: 3 ::::: |- 9:7; 57.94 14444 53:33 I6'82 II '92 3. *.*.*. 59 ° 4. I #3; * † 94 59 57° 33 - II 38 45 ‘95 I3 29 47° 33 º * Sept. Io | Polaris W. 6o 67 |+ 9 'o.1 §§ 31 67 30-62 II' os Io2 24, 20' 67 |+ 2 o4 22 71 || 20 54 I 5o * sº 2? 25 33 35 6 I7' oo |+ 5° 44 22 '44. o' 83 2 I 93 I6' 66 66 49 52 17 – 6' 52 45' 65 165 19 19° 33 ſº 3, 26 , 39 41 67 |+ 2 52 ižº J I4 ° 33 2 I 42 10:49 22 37 39°33 – 4° 18 || 35’ I 5 121 7 II ‘oo tº ſº 33 29 33 33 J 35' 67 + I '84 37' 5 I 9° 33 I9° 55 I4 ° 29 Mean of Eastern Elongations 276° 5' 11" or General Mean 276° 5' 11.57 º , Western , ,, , 13" 12 IProbable Error + o” 5 I GAIDS HILL. Name and ſº Computed Corrected * Computed IResulting Date. Fºrgiº of Reading of Star. afé. º Reading of IR.O. *::::: A.ii. of R.O. 1845: O '6 // 60° ob C F // O W ºf o t / . Sept. : Tº 54. 5 I ’20 – 9 12 O * O 177 39 30' oo - ſº I SO " Sº I * 19|s Cephei E. ** 3: ...; ; ; ::... 4 24 39.34 397 tº 3°5. 26 27 Io 45'20 |+ 1 '87 || 47 of 149 58 I4°oo O * CO 5o 26 53 4 º' 55 33 60 ° ſº t * 2 O 3o 9 o “40 – 4. ‘99 || 55 4 I 7 g » 27 23 49 63.60 |+ o-38 63.98 || 146 37 26°oo 3o '98 54' 61 » 35 46'8o + 8 '95 55 ° 75 6 2 I " OO . 2 2. 13 43 51 ‘8o |+ 1 − 27 | 53° of I36 31 23 ‘oo o? 53 “I 3 3. x- 9 33 33 69' 60 — 5: 57 || 64’ og 13:33 3 I g - : 1 Oct. 4. 25 o 3 38'20 |+ 4:15 42:35 | 122 51 28' 8o 31 o8 66° 39 93. 46.40 |+ 13° 23 59' 63 23.8o l I82 PRINCIPAL TRIANGULATION. GADS EIILL—continued. Date. Eği Reading of Star. Cººl º Reading of R.O. a.º. sa. Aºi. O. Star. and Colº. of Star. at Elongation. ſº | 1845: * º § 18.60 + 5°38 || 23 '98 118 1; 44-86 C F // O / // Oct." 5 || 51 Cephei E. 355 ° 23'oo + 19 65 33°65 3.43 4 24 31°08 |307 II 46'36 , , , , |343 :::::::::::A; ; * *::::: *es 50'o6. , , , , |*37; ; ; ; ; ; ; * *:::: src; 43.38 , 10 | Polaris , | * • ?: Tâ’i, #3; 7 * :... . . as 27.4s 49' 53 , 11 || 51 Cephei , | ** *::::: I gº ºft| 7 º' #: 4. 24, 30 ° 90 47° 57 º * * 2 I 2 I " OO - 99 I3 33 33 . #: tº: §: º 49 ; 4 24 3o '77 52 ° 5o 35 14 | Polaris 25 2b I 55 ::::: T #: #: 2b 4 I §: 2 25 25' 17 49'o6 | , , |g| cºld , |* *:::::::::::::::: * * ... 4 24 30-7: 50° 35 , 16 . , 35 * 42 #: – ; #: 198 29 : 30-61 50° 47 3, 2 I 2, " | 6 27 #: – #: .# º #. 29' 98 5o' 20 2, 23 2, , **:::::::::: ::::: ź. 29' 66 47 '54 , 24 Polaris 22 61 22 #: I#3; #: [86 8 §: 2 25 I 9°os 52 '82 ,, . , || 51 Cephei , 57 °7 ; : I; .# I8o *:::: 4. 24. 29° 50 49° I4. , as , , , ; * ::::::::::::::: * * : 4 + 29.34 40-6, Sept. 19 & Urs. Min. W. 45 o 33. I': ;: I77 39 3. 5 27 12 26 45' 78 , 26 , , , . " '9;... . . . ...; **'. s 27 11:7; 45-c. , , , , , | * * : ; ; ; ; ##|***::: so 4.69 || 48-9. , , , , , || 3 *::::: ; ; ; ; ; * 37: ; 27 to:6; 46.18 , , , , , '73; ; ; ; ; ; ; *37:...; so lºss 4. I '95 , 28 |* , , | * * *%.: I, § § I36 31 ; : ; 27 11-67 49° 73 | , 29 |x 7” #####|##|**::::: , so lºss 5 I 93 : Oct. 5 || 8 33 , 345 36 £: T .# .# I 18 15 ::::: 5 27 II '71 39' 12 , , | x , , 349 °3 § - § #}; 118 15 #: so i2-83 46.68 7| " " |*::::::::##|##|* *;|s a res. 49.28 ?) 8 || Polaris , 325 Io ;: L.; ::::: • 94 47 ;: 2 25 28° 41 56-81 , 9 || Un Min. |**::::::::::::::: **;|s a tº seas | |**#: #|##| * *::::: so irºs was , is |* *:::::::::::::::: * * ::::: ; 27 tº ses. * This star was observed with an accidental collimation error of 58"x40. ; : OBSERVATIONS. - 183 GADS HILL–continued. * * | *s-, i. º Raisºno Aiºla.º.o. 1845. O / // . ===H-H. Oct. 11 | x Urs. Min. W. 39° 45 #. i,j}: #3; 75 47 #: I Jo II 41 |307 II 45° 23 |* |**::::::::::::::: **:::::: * * * is a Urs Min. , |* * *::::::::::::: **::::: ; ; 12.19 49' 47 * , |x , , |** 3: ; ; ; ; ; * * ::::: so iro, 49 so 3y 3, Polaris 33 263 II #. #3: #: 32 49 §: 2 25 26°oo 49' 39 , 14 Urs. Min. , | * * ::::: I': ; ** 3: ; 27 2.35 | 49-36 , , |x , , |**:::::::::#|...;| **::::: , so loss | Ass , , |Polai, , |* *:::::::::::::: **::::: , ; 4.89 44 ° 23 , 16 || 8 Urs. Min. , °5 5° º: Tº: :::: 198 29 ; : 5 27 12-67 45°48 , , , , , | **::::::::::::::: **:::: , sº toº 47° 19 as , | * * :::::::::::::::: * * : ; ; 3.6, 49'78 • *|, , , | * * : I';|##|* *::: ; 27 is so sºlo |x , , | * *::::::::::::::::: * *; ; ; so 9:40 43-94 as , | * * : ; ; ; ##|** : ; ; 13'ss 48.8o , , |x , , | * * :::::::::#|##|** {{#| so 9:29 56° 50' Mean of Eastern Elongations 307° 11' 50"-83 General Mean 307° 1 1' 48"'95 , Western , » , 47"'72 Probable Error + o"' 38 GOAT FELL. Date, Fºr IReading of Star. cº º Reading of R.O. Ašša, Aº Star. and Col". of Star. º' Azimuthorno s.” + C F // O } // o . A ſy O / // ºpt 5 | Polaris E. 97.4° #: Tº: ::::: I 18 5 4: 2 37 22:57 |233 I 56-78 " * , , " ":::::::::::::::: **::::: aros ºsſ » I3 , 172 25 #: † : ## 42 50 #: 17' 69 61 '77 ” 14 || 51 Cephei , IoG 15 §§ f {:}; ; 154. 25 §§ 4 52 34° 72 58-69 º” 16 , ,, . 49 49 39.69 -16:94 22:36 || 77 58 56.7° 35.6% 61 °65 30°40 |+ 5°45 35'85 55° Io 184 PRINCIPAL TRIANGULATION. GOAT FELL–continued. | Name and Computed C t d Datc. Elongation of Reading of Star. º 'i. Reading of R.O. Aºsa, Resulting Star. and co". of Star. at Elongation. Azimuth of R.O. 1852 : 16: f // | 6-8 O y my O / ſy O ºf Sept. •: * 2 o 9o:20 –16'89 73°31 32 25 57' 25 pt. 17 | Polaris E. 164 16 : tº: .# 32 º #: 2 37 15: o3 233 I 58' 86 y y {º oo — 19:82 19' I 9 Io * * J , 5 I Cephei , 96 56 12 50 t *::: 2 I 35 IAl” 2. I 4$.75 45° 35' 15 63-81 • * * OO – 22 * I & " O2 * CO 3} 2 I | Polaris 35 3. – 33. #: 47 ...; 2 37 I2 51 62'41 122 24 62 “Alo – 3 6 8. I 28 I 3, 27 | y, , * *::::::::::::::: * *::::: * * *s. 53 '88 * . 12 5 4o I 5 6o – 2 '66 † * * ALO 3y » 5 I Cephei 33 5 4 #. + Io' 36 .# I73 49 ; : 4 52 35'88 57: 18 Oct. lari 2 38 71.40 – 9:41 61-99 53 3 50.79 º iº i 5 Polaris , , 46.42 + 5.39 51.79 .#| - 37 3-16 54' 56 32 8 , 13° 397.73 - 7.3% $2.33 28 51 '87 † }} 3. 34' oo tº: 46.86 42.6% | * 37 Łoś 54' 67 I I 79 5o 21 “40 – 9 '86 I 1 - 54 130 14 71 ° 30 * 3? 23 33 82 5 ::::: i-H. }}. #3% ; 2 36 58° 91 52°46 3. * gº tºº • 30 I ?O I • 2 O 33 , 51 Cephei º 47 I4. ##. + 14 II ##. 3o I4. ; 4 52 35 °5 I 51 '8o 17 | Polari J. I4. 75' bo — I ‘43 || 74° 17 | 97 39 bi ‘40 º 3 y 7 OI:ATIS 3 6 53 ° 5o —H. I 8o 55 ° 30 63 5o 2 36 54. 83 52 55 Dec. I , , 167 56 #: + 5' 59 50-61 38 22 32.É. 2 36 27:49 67.86 tº 2 / " bo ºf * Sept. 10 |Polaris w. '47.49 %. t; ## 23 29 #: • º 95 2. I #: + §: 3:... 54 ;3.; 2 37 19:86 58-70 * >> . Min. – fl. " 4 * 33 I54 25 23°45 . 14 || 8 Urs. Min. , 81 14 ;: tºmº .. º: 6 ź. 6 I 23-50 61-77 ari – T * 29' 30 I 3b 5 * O.O 33 ,, . Polaris 32 38°30 – 4 75 33° 55 53 : 2 37 16.67 60-80 ,, 16 33 33 48 2 23.22 -- 4'46 18' 74 Io.3 41 34'8o 2. 6. 18 55 ...: + ; : 77 58 33.3% 37 Ib" Io 55°38 * tºº ; §§ S & " I O , , | 8 Urs. Min. » r 56 §§ -- ; 41-19 7 5 ;:6. 6 1 23:28 56°35 22 tº – 7:48 51 32 8 * ALO 33 33 2. 3} 33 I53 2 #: |-- ; : *:::: 77 5 #: I 59 54" og 6o 81 3. I 3 22 33 2 2 — • 2 32 ° 9 32 2 : O * I O * * * 3, 17 ... ;-); ##|... . ; : 6 23:14 54." II ,, 2 I 33 33 17 ºzo -1697 45°23 147 20 06’20 | 6 22.06 6 - 2 27 | Polaris W. 7° 3 ; : + 3. ##| iss *:::: 22 '9 50° 22 33 Ol:ll’IS i. rv - 3& 26 42 58 ‘I 5 ū * ... "...# =####|...;|.” ... ." 33 2, 6 UTS. I\ll Il. , jº – 4'83 18: 27 173 49 38 90 • * 3? 33 5' 70 — 5: 24 50'46 173 49 36' 50 * Y- 35 33 I 33.62 # 8- 16 46.76 36-30 | * 59 50° 16 57° 73 Oct. I I | 8 , , 7 tº 49.42 - 3.87 45.53 13° 15 $.2 || 6 || 23.8 †. A. is is # ; : ; 32.É. ; }; 5 59 '91 39 3. y f 28 ° |— 5 12 23 °o I 3o I * Oo nº 3. 33 y I6 - 8o H. 9'51 26’ 31 7. I 59 46' 56 53 ‘Iz Mean of . Elongations 2.33° 1' 57”83 General Mean 2.33° 1' 57"'98 }} CŞtern 22 ,, , 58” 16 Probable Error + o”.48 iš'| -- fº:* OBSERVATIONS. 185 wº HART FELL. Datc. #. Reading of star. º º; IReading of R.O. *:::::::: Aºi.o. 1846: O / // O f ºf O f ºf O 1 ºf ost |s cºld E. º 9 #: ; ; ; ; **::::: 4 so 46.36 |350 so 9.39 9 , |* *; it #: ;|* *::::: 49-48 || 8.6% is , , |**::::::::::::::: * * : 46.1. 4 is *::::: Polaris 3? 259 2 I #: + ...; ::::: 67 3 #: 2 38 41 '88 4-62 Jan. II 8 Urs. Min. , 25 I I 3.; T ; ::::: 55 2 I : 6 o 6' 59 12' 66 tº , 24° 49 #: + : ;: 47 Io §. 6 o 7'22 8'96 Feb. Polaris 33 189 56 ...; + ;: ; : 357 38 #4. 2 38 39° off 4° 73 33 6 8 Urs. Min. , 187 54 : + # #3. 352. I 5 É 6 o 20° 52 17° 32 7| |* * ::::::::::::::: * * : * : *s, *is * * * , , | * * *:::::::::::::: **ś| 6 c are iss; | . , |**::::::::#|##|* * : . . .3-3. I9'99 *| |**::::::::::::::: * *::::: * * * * Nº", , , w, sº *; f:3|##| * *::::: ; ; ;3-6, I2 °4o , , , , , |**::::::::::::::: * *#: . . .94s 5' 12 3) ,, . Polaris 33 306 9 ... † :::: § I 19 8 #: 2 38 58'94 3.66 to || Us. Min. , |* * :::::::::: ##|* * §: s 59 sºo. I2 °53 Dec. 1 | x , , 30, 20 §: – ; §§ II 3 º #: 2 o 41 °61 4'78 32 , ſpolaris , 300 42 ::::: – .# #: II 3 41 ; : 2 38 47' 17 I 1 '75 35 2 | X Urs. Min. , 298 30 º: + ; i: IIo 50 #: 2 o 42°91 I2 '99 * , |Polaris , |*7 * g.: ; ; ; ; ; ; ; * * ::::: a 33 45-64 || 3:69 * 22 3 |x Urs. Min. , | *97 5* i. T 3.; ::::: I [O I2. #: 2 o 43' 16 11-77 " . Poui, , |* * ::::::::::::::: * *:::::), is sº, 8'93 ". 4. A Urs. Min. , 296 27 : †"...# .# Io8 48 ::::: 2 o 43°39 11 65 " ; , , , |**:::::::::::::#|* 7 ##| 3:6; 13-76 7|, , , |* * g.: ; ; ; ;|**##| 4 is tº is . Io , 291 18 24'40 -18°47 5'93 || 103 38 67'8o * 33 33 5'8o |+ 7'95 13-75 57°oo 45.22 7° 34 » . . 12 || 2, 33 35 256 56 £2:80 + .33 62 : o3 69 17 53.79 45 ° 92 Io'36 ?? I3 || Polaris 256 18 §: f *::: §3. 69 17 §: º 2? 64'8o |+ 3:37 | 68. 17 #.; a 3843-4; 13° 25 A a 186 PRINCIPAL TRIANGULATION. * *Referring-object could not be observed for 1, hours after the star, owing to mist. * Morning cloudy, and mist about referring-object made the observation unsatisfactory. HART IFELL–continued. Name and Computed Corrected Computed † Datc. Elongation of | Reading of Star. Level | Reading | Reading of R.O. Azimuth of S Resulting Star. {\{[11] ºr Of Star and &. lm. . Cà (1111ſ. O ..". Azimuth of R.O. 1846: O ºf - 8 8 6. f // O / ſy C ºf •: 2 IC) * cº 28 ° & S 7 3 II 30 Dec. 4|Poui, w.” + ...; tº; ; ; ; : 38.42-06 |350 zo 9:39 3 249 4o 56°oo + 4-82 | 66'82 62 39 54°20 g • ºsº | " 33 㺠T -; 31-62 58°30 41 - 18 I2 °35 Jan. II 242 22 46:20 — 3 78 42°42 55 21 39'50 36.86 I : * 76 33 35 #... it 3.; 44.3% Ž. 5 °7 tº * A (Y | -- E * * ALO 2 I 30 * SO º i º 234 11 11.60 — or 32 II 28 47 Io 7'90 º ,, 12 | Polaris 33 18 6o |+ o' 44 || 19 “O4. ź. 2 38 36.86 15.63 º º 8. º e * OO ſº º , , s: Cople. , |** ::::: + 3.; ::::: 47 Io 7.43 |45° 9” 1o 17 º 8. — o' 26 º 2 58 ° , 13 | Polaris , 237 35 1: jº-º: ...; º 5o 33 #: 2 38 36.86 II 23 4 184 39 34° 20 – 3' 33 3o'87 357 38 25' 50 e tº Feb. 3 33 33 16' 40 + II 'oZ 27°47 3 18-70 39 2 I I3 72 182 Io 32 °8o |+ 4' 38 || 37° 18 355 9 3o' 40 • 28 II • 32 35 93 44' 6o — o' 75 43'85 - 32 ° 9o 39°3 75 6 18o 28 66-60 – 12 o8 54' 52 353 27 53°4o --- •88 33 3) 33 6 6o 8o + I2 ° 92 Žá.4. 53 '79 39 55 9 17q I6 22 6o • 60 26°2 352. I5 II '90 & * 33 7 Jy 33 79 25° 4o + 3.; ::::: *::: 39°95 9 94. , , ; cephi , |* *::::::::::: ; ; * º 1. 449 56.33 12.78 • 8 º º º 6. , a Poui, , |* * ::::::::#| ##|**::::: * is 45% 7' 16 357 12 52' 60 — 2 29 || 5 o' 31 35o II 50° 9o * d 33 23 23 39 54" oo |+ 6'29 6o 29 #: 45 46 Io' 14 º 175 I 59' 49 |+ I II 6o' 51 o II 61 °oo 23 32 5 I Cephei 22 ; tº- 3 * 12 ; 35 61 Io 4. 49 49' 65 I2 ° 90 172 8 57°80 + 2 53 60°33 || 347 19 15'50 , 24 | y, 23 96-40 - 3 ‘99 92°41 9 § 49' 47 9-86 Mean of Eastern Elongations 350° 20' 11": 50 General Mean 350° 20' II" II ,, . Western º ,, , Io"'96 Probable Error + o”. 38 LEITH HILL TOWER. Name and Computed Corrected Computed Resulti Datc. Flººn of IReading of Star. aft. ...; Iteading of R. O. *: i. A.iii. §o. 1844: O ſ ºf O y ºf O / // o f w Mar: 6 Polaris E. 56 38 ::::: Tºº 95 45 §§ 2 25 I2 °43 22 I 32 44'43" * d 8 6- g [. jy 8 35 23 39 30 .# sº 78 37 §§ 13°23 | 53 '90 8 º tation. º 2, 2 I , * *...; *3 37 3.; 19:30 55-64 | t OBSERVATIONS. 187 LEITH HILL TOWER—continued. Name and C d 1C ted Commuted Date. Elongation of Reading of Star. º i. Reading of R.O. |Aiºur A.º.o. Star. and Colº. of Star. at Elongation. 1844: C F ºf O y ºf O F // O ſt | March 24 || 8 Urs. Min. E. 45 49 57'99 8 I 47 24' oo 5 26 43' 12 221 32 62°46 8 93.3% 47° 33 O tº 7 4 19°oo tº wº * *9 , , * ...; 37 4. |s 264-96 51-13 » 30 Polaris , 127 55 #3; 167 3 §§ 2 25 23 76 º 54°og” , 31 8 Urs. Min. , | **3 *5 *:::: I49 2. I :#; 5 26 42 '8o 53' 30" , , Polaris , | *** *3 #. * º *:::#| as 24-36 47°ojº Anri in. 7o 20 59°oo Iob 27 2 I 33 • 6 * | April I & Urs. Min. , 6 2:3: 6 $3.3% 5 26 42 64 58°30 , , ,, . Polaris 35 7 19 ; Iob 27 †: 2 25 24°88 49° 2 I , 2 || 8 Urs. Min. , 55 ° 43.7 91 64° 33 l ; 26 42.6 • 8 TS• Mil Il 5 I 59 *::: | 6 #3; 5 2b 42 'bá. 49° So •: * 33 I b 43° 33 * * * * * * ,, ..., | Polaris 53 24°oo 9 46° 33 2 25 25-36 56 oz slº Uri. Min. , | * *; ** {:}|s 264-48 57-65 j IALO I & 22 ° 2 24, 32 ° 83 tº • * ~ 33 5 8 Urs. Min. , | * ić 68 8 34' 67 5 26 42°32 s 4o tº 131 2 18: 50 |+ I 20° 18 17o 9 5 I 33 * 33 8 Polaris 33 6 25'83 **:::: #: 6 48°oo 2 25 28:75 48°69 † 9 30 31 oo – 2 28 28 ‘72 | IoS 30 41 ° 33 * , || 8 Urs. Min. » 66 44' 33 – 12 °7o | 31 63 6 §§ 5 26 41 '88 53 “O4. ſº 29 9' 33 – o' 33 9°oo Ios 3b 47' * • * 33 9 | Polaris 35 9 11 : oo |+ 5° 51 | 16° 51 86 #. 2 25 29' 35 62°43 46 53 31 °oo – 5'99 || 25" or o 43 b7 • £2.6 33 IO 3 * 23 6 {{...}} + ...; 2 I 45 #: 29 75 49 69 34 36 I 3 '67 — o' 36 I3°31 | 73 43 33 ° 97 º º j} II 3? 33 17°oo |–12' 60 4 * 4o 6 §§ 30 °31 57' 63 i. 32. I 5 4' oo + 3 °49 7' 49 8 21 18-67 *. 33 I6 • Urs. Min. , . 4 * 33 + :::: §: 6 ::::: 5 26 4o I6 49 58 i. 29 13 73°oo — 5'99 b7 or 8 21 26-67 2 • * $ 8. 2, 17 | Polaris 33 8 54°33 |+ 5° 58 #.?. 49 I4. ...; 2 25 33 18 48° 22 I 3 47° 33 - I 5' 75 3 I 5 9 I4 50 °oo i. » , || 8 Urs. Min. » 37.67 — #. 33 ° 45 49 I4 #3; 5 26 39°84 55'83 i. Io 7 9°33 – I 3 7. 97 9 I4 3b* ey * . ſº 3, 19 Polaris }} 6 7° 33 + Io: o3 17° 41 || 6 25°oo " 25 34” I4. 52'28 169 9 28-oo |+ o-60 28.60 28 16.46°oo 6. . . - I » 23 35 3? 8 19'67 f 8-27 £7.3; 39°33 3b ‘os 50 ° 45 58 43 55 ° 33 |+ o’ I 5 55 ° 4 97 51 I 3 '33 i. • 6 J3 25 23. 25 48.67 + 7 ‘oo 55’ 67 5 °33 36 85 5o b1 2, 26 53 1 21.67 – 2:46 19:21 92 8 36°oo 37° 33 46°45 3} 23 I2 5o -- Io' 39 ... 64. 46 24 ° 33 8 25 38 72' 33 – 16' 30 56°og 64 46 21 "33 tº i. | " 2 y; 35 58.67 + 3 '85 62 52 9' 67 38' 13 54." 35 Feb. 20 | Polaris W. 33 20 8°oo 77 18 21 : 33 6-73 60°43 I7° 33 18° 33 * Referring-object very hazy. & { } * G . to the star taken at midnight. Referring-object not before six in the morning owing to mist. 6 e ºring-ºbject not observed for one hour after the star, owing to mist. Iłeferring-object very indistinct. A a 2 I88 PRINCIPAL TRIANGULATION. LEITH HILL TOWER—continued. | | - Date. º: | Reading of Star. º: º: IReading of R.O. *::::::: Aºi.o. 1844 : : o " o " " o m o m | March 3 || Polaris W. 69 9 ::::: | II 3 7 33.3% 2 25 I 1 - 23 22 I 32 63 Io' 1, 5 1, , #47; º; is #: 12 19 53 '98 , 9 || , , '7" + ... * * :... 13-9s so-o; , to , , | * * ::.. * *::::: 44; sº-ge » 2 I 2, , 64 24 #; loss. #3; I9' 57 45' 76 2, 23 | y, , 37 48 §§ 8 I 47 ; 20.65 55 ° 35 , 28 , , '73 #. 37 * : ; 23:04 54.63 3, 29 2, , tº 4 ; * : #: 23 ° 53 49° 30 2, 30 93. 3? IoS 22 %. * * .# 24. ‘O4. 52 '79 62 29 6.67 IoG 27 21: 33 3, 31 33 }} 33' 67 40' 67 24'64 46' 19 April 1 | y, , * *::::: 9: " : 25° I 2 52.88 2, 3 | 2, , * : ; a tº 26 o8 60.09 2, 4 | * , II 52 ; 55 5o §§ 26. 56 52 “o: , s , , is “; **::::: 27.03 || 51.6, , s , , * *:::::= };|**; ºn 99. 3, 9 22 , e : ; ; ; ; ; 86 o #3; 29'59 55.31' , is , , , -943 ::::: ; ; ; ; ; ; **::::: so-o; 51-20 2, 17 | y, , : " :::::: Tº: # * * §§ 33° 42 58.85 ,, 23 | " . ... is is #: 7 ; ; : 16o 44 ; 36:25 56.76. , , , , | * *; it; ; ; * *; 37.67 sº Mean of Eastern Elongations 221° , Western 33 33 32' 52". 61 , 53"'92 General Mean 2.21° 32' 53” 17 Probable Error + o''' 43 * Much motion. • Storm acting on axis light as well as on the light of the referring-object made the observation rather unsatisfactory. * -| º- i : OBSERVATIONS. LUNDY ISLAND. Datc. Fº Iteading of Star. º º Reading of R.O. *:::::::: Aºi. O. : 1845: O / // O / Af O 1 ºf . O F // Feb. 18 || Polaris E. 99 44 ; I }; #3; ** {..., |z 24 36:49 |194 as 68-91 March 11 , , 61 37 .# + .# *::: 73 38 ;: 44'87 65:63 3y 12 8 Urs. Min. , I43 59 3.3. – : 3.4% 152 58 #. 5 26 30' Io 66 oz , is , , |**::::::::::: ||...; "3 * ::: sº 63' 15 a , , | * * : ; ; ; ; ; ; 7 º' ; 30.6, 63.9% April 6 | **:::::::::: ;| **:::: 29.4| sº , , , , , | **:::::::::::::: **:::: so 4-6, 63' 37 3) 7 | Polaris 32 29 57 ... I'...}. #3; 4I 58 #: 2 24 58' 28 66.46 ... March 12 | Polaris W. 136 7 º: – : § 152 58 #: 45-59 61' 31 4 | *; ; ; ; ; ;|**::::: 46'ss gros |April 6, , , | * *:::::::::::::::: **::::: ;so, 98'ss Mean of Eastern Elongations 194° 26' 5" 56 General Mean 194° 26' 4.99 , Western 33 , , 2"'69 Probable Error + o''' 43 * Rejected in the mean. MORDINGTON. 1846: C F // º * ... . O / // o m |Marci 3 | Polaris E. * * : E § §§ ** ...; 2 4° 597. 148 aſ 45-97 , is | Urs Min. , | * * ::::: I tº ##| * * :#;|6 4 192: 38' o2 , a | . , | * *:::::::::: ; * * ::: , ; 9.1 41 ° 94 as |* , , | * * *::::::::: ; ; ; ; ; 4 soas 38.1% " * | * , | * : ##|..}}|:#| ##|- s 9:45 36'44 » , ! Polaris 33 61 38 93 - 20 — I I 98 81 - 22 $3.49 2 4o 67' 20 39°43 - 45 ° 5o |+33*47 78° 97 4 I 25 , 24 & Urs. Min. , | *5 47 #: + 3. #: 168 Io ## 6 4 20°28 4o'59 I90 PRINCIPAL TRIANGULATION. MORDINGTON.—continued. ~ | * --- *** -ºlº-...--> Star. and Col". of Star. at Elongation. Azimuth of R.O. Mºi, Polari sé 26 sºoo – 6 is 27.82 sº s: 146; O / . O / . 4\, . . º ill’IS W. 23' 30 + 6'79 3o og 17.56 | * 40 61 ‘os 148 27 46 of , is |si Cephei , | * * :... I : ##| * * :##|4 s. 37.73 || 33:9. , 14 |Polaris , 4° * ... I: §: " * ::::: to 6.4s 40° 14 , a. s. come # 3 #: ...}}|##| * *::::: 4 - 36.7, 38-90 33 22 | Polaris 33 56 16 #: I: #: 27 25 ; 2 4o 66'93 42-86 , , ; cºld # 3 #1; ; # * * ::::: 4 - 36.6% 41 ‘77 , , , , | * *; ; ; ; ; **::::: ; ; ;67; 35°oy | , as Pºui, , , , ; Hºº: " "::: * * *s, * , , , , |**::::::::#|##|**::::: 69-6, 4-6, , as , , | * * ... I #3; ##| * * ::::: 79.14 | 40 oz , , , , |* *::::::::#|##| ** {3}| ſize 46'34 Mean of Eastern Elongations 148° 27' 40" oš General Mean 148° 27' 40". 51 33 Western 32 ,, , 4o"'8o Probable Error + o”. 51 MORMONTEI. Name and º Computed cº Computed † Date. Elongº of | Reading of Star. aſſº. º; Reading of R.O. º Alºño. rºº’i, IPolaris E : 4; 33.67 + 4.47 ||38.14 si sã žool . . . . . . $CO. tº 60-67 —20:52 4o. 1; 14.3, a 48 14 to 84 55 44-29 * * * * | *::::::::::::::: *::::: * * |Mar 19 | * * ::::::::: # * *:::#| 26:6; sº ,, 18 |Polaris W. 145 20 #: t # ;: 233 *::::: 25° 77 48° 34 , , , , |* *::::::::::::::: **::::: *s, * , a. , | **ś-43; ##|**::::, so so", Mean of Eastern Elongations 84° 55' 45" 58 3) Western 33 , , 48 * - 80 General Mean 84° 55' 47". I9 Probablo Error + o”: 56 | : i ſ OBSERVATIONS. I9 I MOUNT BATTOCK. Name and Computed comes Computed º Date. Elongation of Reading of Star. Ilevel | Reading Iteading of 18.0. Azimuth of Star Resulting Star. and Coln. of Star. at Elongation. Azimuth of R.O. 1847: - O / Pf 8 O 6 ‘8 C F // O f ºf Mſ; in T. 4o 53 39°oo – 4 72 34" 2 97 Ib 5’ 83 * Hº º g ly 30 | A Urs. Mim. E. 64’33 — Io' 16 #: 6 #. 2 6 28.62 || 238 28 50' 56 3) 25 sº 4I 33 I 3 '33 + II 27 24° bo 97 I "oo * º - Polaris 33 ić — 16 or 29 '99 6 17-17 | * 46 3' 48 47: 77 139 43 55°oo |+ I4°29 69°29 || I5 26 51°33 . º * June 1 3 y 33 Ioo 33 –Io'49 | 89'84 61' 17 | * 46 4' of 4o'71 * gº I27 tº O 3 ; * I 3 * . o8 I 3 I O " Jy 2 | A Urs. Min. , 5 #3; f 3.43 #:; 4. I 3 ::::: 2 6 27.81 43 69 • I28 3o 20 °oo + 5° 49 25'49 4. I3 6' 5o º º }} ,, . Polaris 33 4. *:::: Iłż.; 27.84 6 #.; 2 46 4' 21 48°71 72 2 °33 |+ Ib'72 19 'os I27 4b 56' 17 º tº gº º }} 3o 25 33 8 .# + 13' 82 26' 15 64' 17 6-82 44 ° 39 45 28 48° 33 + 3 c5 || 51' 38 IoI II 33°oo º * * * July 2 | * gº 3 I ; – 4° 33 .# 6 : 6-67 45'90 J Polari W. “33 – I '73 56' 60 | 127 4b 5o 8 I 6-8 ſº une 29 |Iſolaris 52 2 § I'...: #: ::::: 2 4I 31 07 9° 44 64* II II 3 I 7 5o '4 º t 3° 35 6 8o 33 – 14 off 66-27 61 “48 6'82 43 ‘97 Jul 39 56 30°oo |+ 5°91 35'91 || IoI II 2.0'98 º . . . . uly I , , 33 56° 33 – 13 - 16 || 43.17 27-98 6-77 38: 17 37 2 33 22 14 24’33 – 17 17 | 7 - 16 || 83 28 68' 31 6.63 41-66 33 5' 67 |+ 9:21 || 14-88 5o 3 I - Mean of Eastern Elongations 238°28'45". 96 General Mean 238°28'44", 26 35 Western , ,, , 41" 28 Probable Error + o” 73 MOWCOPT. Name and Computed Corrected Computed •. . . Date. Llongation of Reading of Star. Level | Reading | Reading of R.O. Azimuth of Star Resulting Star. and Col". of Star. at Elongation. Azimuth of R.o. 1851 : C F ºf O / // O / // C F // April 10 |8 Urs. Min. E. 42 13 16-17 |+ Io' or 26, 18 || 137 9 36'98 || 5 4o 51 “43 28o 36 62°23 33 I5 2, 2, ,, . 67 49 5o'67 – 12 25 || 38-42 162 45 50' 67 || 5 4o 50°oo 62 - 25 33 I8 | x , ,, . 16o 1 53:67 – 11 og 42.58 .78 44 41.87 || 1 54 2'56 61-85 3? 2 I | 8 × ,, . I58 5 26°oo + 2 - 51 28' 51 | 73 I 38°25 5 4o 49° 15 58.89 » , | * , ,, . 154 18 28.67 +12:44 || 41' 11 | 73 37-88 || 1 54 2-64 59°4 I » 25 || 8 || , 97 42 24' 17 |+ I '37 || 25' 54 I2 38 36' 13 || 5 40 48' 14 58° 73 * 26 |, ..., ,, . 69 5o 58° 33 – 13 49 || 44'84 | 164 47 6'54 47 ° 43 69' 13 May 1 |, , ,, . I 13 5 18' 17 |—17'34 o'83 || 28 I 22 °33 46'14 67-64 | 3. 3 l ; , ,, . 9o 17 6o' 33 – 4' 53 || 55'8o 5 14 9'71 45 ° 5 I 59'42 ” ” |^ 3, , 86 31 Io'33 + 2 °os | 12'38 || 5 14 9'54 | I 54 I '71 58.87 33 I3 || 8 , ,, . 19 31 56°oo |+ 2* of 58' 05 II4 28 18°37 || 5 4o 41 °49 61 - 8 I ” ” |^ , ,, . 15 45 12-67 |+ o-'84 || 13’51 | I 14 28 19°33 | I 53 59'89 65'71 ſº » | 3 , ,, . 16o 15 56' 67 – 3-76 52 '91 || 75 12 12-62 5 4o 41 ° 12 60-83 39 I4. A 3) 33 I25 32 5o 17 -- 6. I6 56° 33 44 I6 7 og I 53 59' 65 70° 41 | I92 PRINCIPAL TRIANGULATION. MOWCOPT-continued. Name and g Computed Corrected * Computed Resulting IDate. Flºgº of Reading of Star. al £3. º; Reading of R.O. º Azimuth of R.O. 1851 : O y ºf O / WP O 1 ºf O / Wy April 18 51 Cophei W. 153 33 22 17 |+ 2.91 || 25 oš 78 44 45-29 || 4 34 13.72 |280 36 66.49 5, I9 J) , 58 35 51-83 – 6.70 || 45:13 | 163 46 55-33 I 3 '89 56' 31 2, 2 I 33 ,, . 147 5o 27°33 – 3 '73 23°6o | 73 ſ 37°42 I 3 '98 59'84. 2, 25 JJ }} 87 27 13: oo + 3' oo 16'oo 12 38 35'88 I 5' 36 64' 52 , 26 J). ... 59 35 51 oo – 6'52 44-48 || 164 47 7.67 I5' 62 67' 57 May 1 }} , 102 50 2-83 – 3:46 o' 63 28 I 23°42 16-97 67: o3 3 y I3 }} 25 9 16 57.67 + 4'21 61 '88 114 28 17' 54 2 I 13 54." 53 Mean of Eastern Elongations 280° 37' 2"'66 General Mean 280° 37' 2". 55 , Western 3 y ,, . 2", 33 I’robable Error + o”.63 IPRECELLY. Name and * Computed Corrected tº Computed Resulting Date. * of | Reading of Star. afé. º: IReading of R.O. *..." Aziº ão. 1843: O y ºf ; : ...al º º 68 6 2 I ‘oo — 3 * 17' 51 1973b I4°53 tº t May 29 | Polaris E. #: I }: #: 1.3; a 28 47°45 |z11 58 42.68 i. tº I R2 3 O II* - June 11 33 }} 123 o 15° 4o + 3 + 32 I & ‘72 52 3 ## 49'45 43'81' 8 • 7o |-|- 2 '86 52 '56 78 7 49° 73 t : , 16 Jy 23 48 37 #. – 2'54 53-56 55 ° 23 50° Io 49° 52 24 1 56°40 + 4'24 || 6o'64 || 53 31 56' 13 ſº * 9) 23 39 33 4. 63' oo – 5' 5 I 57° 49 8 63' 13 50' Io 50 67 I 52 24, 28° 7o |-|- 12 59 || 41 ° 29 | 18 I 54, 22 2 º 5, 24 | y, , is “...; tº:#|: *::::: 5o Io 43' I I 152 24 30' oo + 4'47 || 34°47 181 54. 22.8 * » 25 33 35 5 4. 33. — I I '82 34°48 54 ;: 5o Io 44 ° 55 29 Io 33 '8o |+ 8 oA 41 '8 8 Ao 24.8 º 33 26 3 y 3} 9 46'30 — 7'72 §§ 58 4 ...; 5o Io 39'87 : I35 2 I 41 °oo + I 4 I 42°41 | 164. 51 37.8 º 32 28 2) y? 6 46'80 4 -º # ##; 4 5 #: 5o' I4. 47° 78 i 133 56 30°40 – 2 14 28-26 168 23 62 - 50 º • Wº as $ May 28 , W. 8 . . . ; ; ; ;2.É * ...; 47 Og 48.85 7o 38 39° Io |+ 8 oz 47' 12 105 6 12.5o * > • * ~ * 3, 29 y? J} #. ſºme ºf º: 44' 44 2 I 6o 47° 37 43 '90 43 39 bg'40 – 11 16 || 58' 24 78 7 56.8o º • * ~ * June 17 JJ 19 6 ź. + 3 32 83 o2 52 °5o 5o Io 53 ° 93 - I 2 I "O º ſº I * . , 26 }} , 147 O 7 ° 93 || 53 'o'7 54 #: 5o Io 47 '94" Mean of Eastern Elongations 2 11° 58' 45" 25 General Mean 211° 58' 46". 38 , Western J) ,, , 48". 65 Probablo Error + o”.75 * Collimation error inferred. * Much motion in referring-object. ºſ i OBSERVATIONS. I93 SOUTH LOPHAM TOWIER. * | *|--|xº~~~}ºlº, 1844: C f ºf O f ºf O f ºf C f ºf Nov. 26 | Polaris E. 25 6 º: º #; 32 *::::: 2 28 41-64 190 Io 63.87 3, 27 | y, , tº #: 7 :#|;| **::::: 4. I ‘I 5 64-48 1, 39 2, 33 2 49 #: T.; #3; Io 31 ::::: 39'81 60° 30 . Dec. . . [**:::::::::::::: * * : *. 66-os , 6 , º, "...: Tº ſº; # * : * | 6′s . . . . . * * ::::::::::::::: * *; º; 56-38 , is , , |* 3: ...;|##|***: see, ºs, Nov. 26 xUrs. Min. W. *44 : Iº: ::::: s: 48 º: I 52 57'o6 63'87 |Polais , | * *:::::::::#|##| **::::: 2 2s +49 56'29 $3. 27 xUrs. Min. , I4 39 #: ić §§ 26 43 ; : I 52 57°27 55°27 Dec. 4 || Polaris , 339 54 #. T ź ## 352. 34. *:::: 2 28, 37.95 65'44 , , , Urs Min. , |***::::::::::::::: * *::::: ; ; ;sº 58'75 , s|, .. , |**:::::::::::::::: * *; ; ; ; ; 7o'oy , , |x , , 344 4 44.32 - 9.4% 37.7. 336 & 5.2 32 53-98 62 - 12 34°4o |+ Io' 27 44' 67 32 '8o * , , Polaris , 3°3 * #. Tºš ::::: 336 *::::: 2 28 37°46 61.96 , 6 || 8 Urs. Min. , 3°9 ** ##|I.3. #3; 324 58 º: 5 34 52 “o2 66 - 18 93. ,, . Polaris , 312 I8 #: II: £3. 324 58 ::::: 2 28 37' o2 61 ° 45 , is , , |* *:::::::::::::::: * * : 33% 65'79 5, 20 3, |**:::::::::::::::: * *:::: 32 ° 59 67'44 , , , , , |**::::::::::::::: * * : * | 6′s , as , , “ 7::::::::::::::: *** {:} sº | 66 as Mean of Eastern Elongations 190° 11’ 1": 38 General Mean 190° 11' 2"'68 33 Western 3) » , 3" 33 Probable Error + o” 59 B b I94 PRINCIPAL TRIANGULATION. WORDESLOW. Namc and Computed co rected Date. Elongation of Iteading of Star. L º i. i Readi f R.O C omputed Resulting ** . . * Star, aſºn. . § cading o i. * Azimuth of It.0. 1846: O F // - O 1 ºf f // * . O / Aſ April 20 8 Urs. Min. E. '59 37 48.49 -13.96 || 35.34 3* 33 39.3% g . . ~ 57° 4o |-|- 2 " I I 59° 5 I 25-30 || 5 55 32° or 57 51 16'73 , 28 » | 125 22 7 oo +15. 62 22 62 || 357 18 I2 '50 . . . y y 2 35 oo — 8 oo 27' oo 15-40 || 5 55 29-28 18:42 7. Urs, Mi 121 27 o' 20 + Io. 37 Io' 57 | 357 18 I5' to jºy Jy TS. Min. , 25 oo – 7 '89 || 17 II I4 ° 9o 2 o I5' 93 17'o'8 May 7 | Polaris 76 1 20:80 – 16:28 4: 52 || 311 14 63-40 tº " | 6, 2, §§ tº #% 53-30 | * 37 39'52 24” II iº 7 2I 64'80 – 2:08 62-72 299 17 63' 8o -- Jy 8 8 Urs. Min, 35 6 6 59 2C + 13 98. .# 99 I 7 ;. 5 55 25' 62 18-92 : A. 3 26 53 'oo — 5’ 65 47° 35 | 299 I7 65' 5o , º 33 p3 33 Jy 6 45 ° 4o †:#. 60° 53 7 §§ 2 o I4. 53 23 ° 25 J} ari 4. 4 37' 40 —26' 12 II 28 299 I7 63 4o ,, . Polaris 3 6 :::: + Io'24. 24 44 99 I7 ; : 2 37 39°97 2I '66 3. . Min. 3 2 I 53 '80 |-|- 3 I 56. 2 O S I * SO }} Io 8 Urs. Min. , 6 #3. + }; #}; 95 I7 #: 5 55 24' 60 16-22 59 25 48 °oo — o' • 23 295 17 63 - 70 » , ; * , JJ 6o 4 47 '60 ſº #: 7 .. 2 o 14 oz 18°44 J Polari O II oo |+ II 58 22 - 58 295 I7 64'40 * y 3} Ol{ll’IS J. J. 14.80 †:3: 33-33 8 7 ;: 2 37 40°83 I4°95 tº. i. 55 25 4. I* 20 + I '8 •o'7 287 2 I 48°60 32 I I sun. Min. 35 61 6o l— ;: §§ 7 ; 5 55 24 ° 22 20" og -: 5 I 3O 35 °oo -- 2 ° * 287 2 I 4.5 8o p3 3, A § 3. 33 #. i. .# 33.3% #: 2 o I3'93 16-8o I 53 Io 58-60 + 12.40 71 oo 285 7 8° 30 tº Wy 4. 8 93. y? 84.' 20 *gº. § #: 8 7 Io 5 55 22 88 I5*44. } 5o 33 46: oo + 16- 19 56' 19 282 29 45'90 º Q I5 Wy 33 6 28 56°20 ||-- §§ 56' 25 8 45 ° 3o 5 55 22 °35 II '73 46 38 29.20 + 10" of 39'21 282 29 43’ Io : ?? » | ?, ?, JJ 6 ... — or 3o 5 I Io 8 46-oo * 0 13 of I4 ° 93 i. 47 16 5.20 + 8. §o i4°oo 282 29 52'60 3 y ,, . Polaris 93. 8 15 20 + I I4. .# 8o 26 49-56 | * 37 42°75 18-63 48 4o 51.60 +17°53 69' 13 28o 36 60'50 r * 18 8 Urs. Min. , #. mº 4.38 66 62 ;: 5 55 2 I o8 I5' 5o j? , A 44 45 35-20 + 12'o6 47' 26 28o 36 66'40 , tº 3. 22 33 67' 40 – I I 59 55: 81 7:20 | * o 12" 28 24' 55 2, 2 I 22 1 57 20 + 8°74 65'94 257 53 16.80 | . sº 39 J} 76' 60 T 5' of 71 '54 18-49 | * * * '50 20:36 º 22 39 27 go + 7.5o 34°50 25 I6' do }} ,, . Polaris J3 58: 50 – 4-79 53.81 7 53 #. 2 37 44'83 17° 32 , 29 |xurs. Min. , 34' 5* ... it 2.33 ºš3 | *75° 34. 8. - 6 : I #### 23.46 | * * **59 21:36 33 ,, . Polaris 2 y 342 3 #. + 6:64 53' 64 217 5o 31 7o º 328 56 2 40 – 2 °62 59-78 39.36 ° 3747'09 2 I " I 2 April 20 |51 Cephei w. 3* 5° 53.42 T 8.7% 49:49 || 3: • 8o * prl 5 I UCpliel 36-40 – 1:30 #: 3I 33 #: 4 45 39'58 10.87 - - 13 - 28 23 ... - .22- - ). II4. 4 I 5 ' 20 + 13:58 | 18.78 357 18 I 3 ' 20 g i - 19-60 – 1-82 17.78. * I 5 70. 4I '82 14:35 May 8 , , 564° 5:32 – 5.95 47.35 299 1763:60 *. - 52 4 *:::::::::: #. 57' 20 4-5 °42 23° 34. o 38' 20 2 49 4o 20 S. I • 6 y; IO 93. Jy 48' 20 Tºš §: 95 17 # É 46' 19 I7'92 , II 39 33 44 44 39°49 - 3 of 39°44 287 21 4$ 50 - - - 46.s., || -----...s.º. 3. 46’20 — .# 45' 65 46-40 4b* 57 "18°33. 39 52 35' 20 + 8° 35 43’55 282 29 46. Io 39 I5 33 3y 44' 6o |-- I 62 46 22 40' oo 48° 30 12.87 Mean of £ºrn Elongations 57° 51' 18" 53 General Mean 57° 51' 18".o; 33 Wostern 53 ,, , 16"-28 Probable Error + o''' 4.5 OBSERVATIONS. I95 WROTEIAM. # s = Name and Computed con ted Com º * Date. Elongation of Reading of Star. º sº Iteading of IR.O. Aziº Star Aºi.o. Star, - and Col”. of Star. at Elongation. - | r | 1844: r 6: f 6% O / // O / W. O iſ Jul * - * | 162 5o 67°oo — I 3 'oo 54°oo 75 21 39°33 a tº • rºo I y 29 Polaris E. 5o'67 412.8 62.85 J 12-67 | * 26 12:44 274 56 40' 02 Aug. o 35 9' co — o' 15 8: 85 93 5 46' oo • 2 - || , sº Jºy & 4. 2} 39 16.67 + 3.2% 15:5; 37° 33 Io' 32 : 37°59 º, 7 87 28 39' 67 – 5'91 || 33°76 179 59 6' 67 56 7'74" 3 y 35 44' 67 º ; : 33. 6 2.67 9 3 I 17 Io' oo — 3 ‘o * O2 . I 4. º tº ſº * * 33 8 Jy 33 7 3 * 33 – 3:36 o:27 3 47 #3; - 9 24 4I 3 I 17o I 4o oo — 14° 13 25' 87 | 82 31 76. 3. 4. | 23 IO 3? 5 § .. + 17-78 23% 3 £3; 8' 31 - 39'32 148 5 36°33 – 2 94 33' 39 6o 36 I5'oo * • Q &s 33 I3 35 22 36: oo |+ 2 21 #3; 3 É. 7 16 41 -86. * * ... - I79 55 I7 "oo — 2 48 14' 52 92 25 57° 33 * º 33 17 9) 33 I8' oo + 9 : 18 .# ...) 45 °oo 5 : 56 35.88% tº: º, 18 59 31 oo – 4: 52 26-48 III 29 68' oo º a º 93. 23 3) 33 31 67 4. I 61 33: 28 3. 2.77 35' 39 , 28 » , 147 31 55' 33 + 6:26 61° 59 6o 2 35' 67 * tº sº ºn 3. : 3 6 75' oo —to: 2 64° 58 38°oo o' 47 34° 22 2 I35 56 35' 33 + 4'42 39°75 || 48 27 I l'oo º F & 33 9 2? 33 | 46-67 º 7' 23 i 39 °44 Io'67 O * OO 3I 23 tº , 107 o 61 °67 – 6' 54 55' 13 24, 23 46-67 * A s - 1, 20 Polaris W. 8 52 “oo |+ 8-84 60-84 34° 33 4' of 38.45 158 5o 20-67 — I off 19:62, 76 13 3-67 {} 2, 23 33 33 32.37 ± 7.2 3.4% o:67 2-63 37'99 I42 4o 17' oo + 2 - 40 | 19:40 6o 2 5 I ‘oo º • * ~ 33 28 y? 33 29' 33 |-ji: I2 " I 5 54." Oo o' 23 36 49 Mean of Eastern Elongations 274° 56' 37" 46 General Mean 274° 56' 37" 5o , Western 22 , , 37"'64 IProbable Error + o” 52 * One of the level readings altered Io divisions. * Level observations made before the star was commenced. * Referring-object not observed for half an hour after the star. * One of the cross levels altered East for West. YORK MINSTER. Name and ſº Computed cºnsº tº Computed Resulting Date, Biogºn of IReading of Star. Level, | Reading | Reading of R.O. Azimuth of Star Azimuth of it.O. tar. and Col". of Star. | at Elongation. | 1846: O F // O F ºf O F // C F ºf Jº's ºur Min. E. " ":::::::::::::::: * *::::: ; ; ; ;6|26, 26 so is Feb. 90 41 33 oo — 7. It 25'89 165 20 I5'90 º 99. 9 || 3, , , 53.39 -11.99 |44.7 ... , 37.82 48° 44 34°59 33 II 8o 25 28:8o |+ 5' 61 34°41 155 4 II Io 49° 34. 3o '95" * * * 59:20 –26’44 || 32 '76 I9' 3o » 14 , , 48 39 43°40 – 6'43 || 36'97 | 123 9 22 °oo 50° 54 28 - 66 3 y 35 61 “40 – 9 II | 52 29 23 ° 5o * Clouded over for several minutes. B b 2 196 PRINCIPAL TRIANGULATION. YORK MINSTER—continued. Name and Computed |Corrected Date. Elongation of Reading of Star. Level JR . º Readi f Computed Resulti Star. .*.*.*.* ºr Azīāo. pº'olua iſ 13 ºf 63.4° 4 8:13 ſess of 4; 33.3% ...'... O F fr CC, 2. Urs. Min. tº o' 53 • 30 9 rs. Min. W. 61 °6o |+24. 53 || 86' 13 26.70 | * 56 51 - 11 26o 26 23:06 , 30 | Polaris 124. 44 57' 60 |+ 7.62 65 22 207 45 I 3 'oo 1846: 95 61 °oo +12.8o | 73'8o 5. Io | * 33 33'51 26°o: Jan. I 3? 113 51 8' oo — 1.78 || 6’22 196 51 31 '8o yy 19 °oo + 18' 55 37' 55 I4 °30 33° 17 27'99 9? 4. JJ Io9 8 29°40 |-|- 18: 13 47' 53 192 8 4o'70 i 33 5. I; 29 |3}: 33°70 32°83 23°6o tº Io? 2 8' 20 + 16- 24. " 102 8 4.5 ° 30 93. 5 || 5 I Cephei , I79 25 É. †:# ...}} 9 ::::: 4 39 55'82 9'91"| 27 | Polari 9 25 28°6o |+ 12 24 || 4o '84 262 25 46' 20 Jy 7 | Polaris 32 75°oo — 14' 76 É.;; > #: 2 33 33' I 7 24'09 » 28 , 166 29 26.32 +2.29 38.89 69 29 38.9% y 6 73°oo Tº: 55'99 43'40 2 33 33°34. 20'37 y Cenhei I64. 23 I5°20 +2 o' 6o 35'8o 249 2 o “8o 3. 29 5 I Cephel , 55°oo |–2 I '98 || 33 oz 9 º #: 4 39 43° 43 25° 21 Feb. 7 | Polaris , to3 35 #3.23 - 2.58 53.42 18636 2.32 i 86°20 –II '75 74.45 9-šo | * 33 35' 34 27:27 39 8 33 ?? 82 20 7'oo – 2:09 '4-31 | 165 20 12'oo 8o 14 3. I?..., | *...* | 16. 2, #3. 2 33 35' 68 29°25 I Cephci , I2 ° 20 – 2 * Qo • 30 165 20 18." Io s a sºn ºf 3) 9 || 51 Ucphel 75 30 °oo — ... .# 25.90 4 39 38-27 25° 73 y Polaris 3. 4I 50-40 |-16-20 | 34° 20 ! I 58 41 53'50 tº 3. 3? y 72 3 ; : — 8-69 ; £3. 3., | * 33 35'98 35 °22 IO '40 -- Io" * I55 4. II " IO 39 33 33 6 81 °oo º .# #3; ::::: 36 I9 24*73 : II 7 27 9-80 |+15. 32 25' 12 | 1.5o 27 29'50 dº 95 9] 3? 50°oo *::::: 34 '90 * 36 70 36 53 25° off 3, 12 | y, 64 17 57.20 |+18 oz 75°22 || 147 18 14' ſo 6-8 33 95' 20 —16' 19 79' or 27.8o 3 7 27:27 5, 13 | y, 4o 9 17.60 – 4'82 | 12" 78 123 9 19. Io { } 3) 8 #: — 4" or ...; I9' 5o 37°21 25’71 38 3 15-60 – 4: 71 || Io'89 123 9 23°oo 35 I4 || 5 I Ceplici 33 33' 60 — 4° or 29° 59 26' 50 4 39 36.78 27° 73 ‘. Mean of Eastern Elongations 260° 26'28"59 General Mean 260° 26' 26". 63 33 Western 33 , , 26"’ 15 Probable Error + o”. §§ I | * liejected in mean. g . OBSERVATIONS. RESULTS OF AZIMUTHAL OBSEl?VATIONS AT STATIONS NOT INCLUDED AMONGST TIII). FOREGOING, Name. Azimuth of R.O. No. of Obs. Itange. Fº + Arbury Hill 185 co I 2. 5. 1'. 5 Bardon Hill 2I3 # : : ; o,81 Brandon • 126 I5 II.35 42 29°52. o,66 Bunwell Tower 183 2O 28.23 I6 2I-70 I.o8 Clifton IBeacon . 2 I 34. 22:58 2O 18:45 o,82 Corryhabbie º 2O4 4o I-59 17 I6.52 o.82 Cradle . . . . I3o 5o 37.59 8 I4-70 I'O4. Ditchling . . . 274. 23 Io'o6 7 Io-O4. o,76 Docking Tower 4o 47 2 I-26 7 8. Io o-70 Epping Poorhouse . 342 29 56.23 I4. I2 - 2C o°59 Frittenfield . 23I 8 35-44 6 IO-4I O'95 Goonhilly . . . 342 57 35. I4 7 8.47. O-73 Happisburgh . . I45 27 39:70 II I6. Io I'o6 Hensbarrow 78 25 49.82 17 25. I2 I. I 5 |Inkpen Beacon. 319 9 45-78 8 12.78 I • OI Laxfield Tower I45 54 34’ og I4. 22.77 I'o6 Lumsden I44. 53 59.95 8 I5-76 o,84. Mendip . II4 54. 24.9 I I4. I4-73 o.78 |Merrick . . 7I 27 6.48 I3 3I '59 I-50 Orford Castle . 68 49 23.65 8 7.98 o.72 Paracombe. . . . . 87 45 II-24 7 6.76 o:56 Pertinny . 3I 2I 43.70 8 I3-O9 O'93 Tyders Hill 3Io o 36. I2 8 II.89 o,87 Sayrs Law • II3 5o 2 I-61 II I2.35 O'74. Scournalapich . 351 58 35-I4 5 5'79 o-61 Slieve Donard . I3o 5 23-o'7 22 24°59 I-46 Stoke Tower 272 34 28.67 I3 18.75 I • I2 Tharfield III 38 39'58 I3 16.78 o.85 Tofts Tower . . 273 35 I4.96 17 I8-59 o°75 Walpole, St. Peter's . I94. 47 3I '91 6 5' 25 o°49 Wingreen . . . 85 58 44.84 18 15.86 o.72 198 PRINCIPAL TRIANGULATION. R E S U L T S OF O B S E R v ATI o N s MADE WITH THE ZENITH-SECTORS, FOR THIE LATITUDES OF WARIOUS POINTS IN THE TRIANGULATION,+ Date. * Stations. Latitudes Direct. . * Amplitudes. Latitudes Inferred. Instrument. O / // O / fM o , a y | 1802 || Greenwich . . . . s 28 38.52 47 { º 51 28 38.30 zºº. I802 | Dunnose" . . . . 5o 37 6.99 || 232 o 51 31:38.5° 37 6.72 55 33 1802 | Clifton Beacon . 53 27 30-44 157 I 58 51.94 53 27 3024 3y 33 1802 Arbury Hill • 52 I3 27. I3 I52 o 44, 49'o6 52 13 27-35 33 23 1806 Delamero • 53 13 18:47 | 84 I 44 40.29 53 13 18.59 33 39 1806 | Burleigh Moor . . . . 54 34 19:45 7o 3 5 4 I-45 54° 34 IQ-75 33 j} 1813 ICellie Law . ſº 56 I4 5o-33 273 *mº -- 56. 14 56.33 - 53 33 1813 Cowhythe iº '57 41 9.47 258 || 1 26 1894 57.41 9-27 33 33 1817 | Balta • § 6o 45 1.59 || 382 || 4 3o II-37 6o 45 I-70 33 33 1836 Greenwich". • 51 28 39-30 || – — * * 33 35 1842 | South Berule 54 8 56.85 III | 3 I4 Io. I2 54 8 56.8o Aiyºzºisºtor 1842 | Black Down • 5o 4. I 8.90 Io92 o 13 37.79 5o 41 8.89 33 53 1843 | Precclly . • 51 56 46-06 | 660 I I 59:59 51 56 46.27 33 53 1843 Forth Mountain 52 18 57.84 659 1 24 II:23 52 18 57.91 , 33 1843 || Hungry Hill . . 51 41 Io:23 294 i o 46 23:58 5I 4I IO-26 33 35 1843 | Feaghmaan ' ' ' || 51 55 22.85 393 | I o 36-17, 51 55 22.85 33 33 1843 Tawnaghmore 54 17 41'56 293 3 22 54.66 | 54 17 41-34 JJ 95 1843 South End of L.F. Base 55 2 38.78 || 334 4 7 52-06 || 55 2 38.74 53 55 1844 || Monach . 58 21 20.77 179 || 7 26 34,16 58 21 20.84. 95 55 1844 Ben Hutig . 58 33 6.44 479 7 38 1979 58 33 6.47 33 53 1845 | Hensbarrow 5° 23 I-15 286 o 31 45-55 5o. 23 1.13 33 32 1845"| South Berule" . 54 8 55-38 114 3 14 9-31 54 8 55.26 33 33 1845 Ben Lomond 56 II 26.41 624 || 5 16 39-59 56 Ii 26-27 33 33 1845 Ben Heynish 56 27 16.86 266 || 5 32 30.20 56 27 16.88 33 35 1846 Weck Down • 5o 35 51.19 || 55o o 18 55.26 5o 35 51-42 33 33 1846 | Dunnose . . . 5o 37 6.98 || 638 o 17 39.53 5o 37 7. I5 95 3 J. 1846 Boniface Down • 5o 36 Io.43 352 o 18 36.13 5o 36 Io.55 33 3 J. 1 The point observed from in 1802 was 6'5 feet south of that observed from in 1836. • The point observed from in 1830 was 50 feet north of the mural circles. • The point observed from in 1845 was 74 feet south of that observed from in 1842. ; : OBSERVATIONS. I99 RESULTS OF ZENITH-SECTOR OBSERVATIONS-continued Date. Stations. Latitudes Direct. ºf Amplitudes. * Inferred. Instrument. 1846 Port Valley . . . 5o 35 45-61 407 o 19 I-16 5o 35 45-52 Airy's Zenith.Sector. *4% Saxavord . . . . 6o 49 38.83 563 || 9 54 51.90 6o 49 38.58 33 3 : 1847 |Gerth of Scaw . . . 6o 48 56.27 576 || 9 54 9.75 6o 48 56.43 º f 1847 | Balta . . . . . . . 6o 45 I-68 73o 9 5o I5'oZ 6o 45 I-75 33 o 1847 Cowhythe . . . . . 5741 9-58 638 || 6 46 22.65 57 41 9°33 n 33 1847 | Southampton . . . 5o 54 46.68 | 8687 i-º-º-º: | 5o 54 46.68 º 33 - 1859 St. Agnes . . . . 49 53 32.99 411 || 1 + 13:32 49 33 33.36 Jy 39 185o Goonhilly Down 5o 2 49.93 431 || o 51 56-61 5o 2 5o-o/ 3? 33 1850 North Tºona . 59 7 15:49 427 8 12. 28.72 | 59 7 I5-4o 33 39 1850 |Great Stirling ' ' ' | 57 27 49:20 439 6 33 2-44 57 27 49' 12 35 33 The Latitudes Direct are obtained for each Station, by giving to the latitude resulting from the observations of any one star a weight equal to the number of observations of that star: the resulting latitudes given by different stars are then combined with respect to their weights. In the observations made with Ramsden's Zenith Sector, the amplitudes are obtained as follows:–Let r, ra as . . . . be the successive amplitudes of the stations A A, A2 Aa . . . . and let a observations of a certain star at A, give its latitude An, and b observations of the same star at A, give its latitude A, c observations of the same star at A, give its latitude Ar, and so on ; then we have these equations,— * ab rat, “ . . . . * * =^. - An weight = a-Tº- bc +,+, + . . . . * r = A, - A.; weight = 5 T- From which, by the method of least squares, r, ra za . . . . are obtained. The six stations first on the list, observed at between 1802 and 1806, are combined by themselves; the other three, Kellie Law, Cowhythe, Balta, observed at between 1813 and 1817. are treated separately. The amplitudes of the first set are applied to the latitude of Greenwich as determined by the Astronomer Boyal, namely, 51° 28' 38”. 30. In the observations made with Airy's Zenith Sector, the amplitudes are all taken with Southampton directly. f The Zenith-Sector Station was not in every case coincident with the Trigonometrical Station; the following table contains the con- sequent corrections to be applied to the observed latitudes. * Station. Correction. Station. Correction. Station. Correction. Clifton. • * * * * +- 6:03 Cowhythe . . . . . –6-41 I’ort Valley . . . . – 4-31 Arbury . . . . . —o'33 S. Berule (1845) . . . + o' 73 || St. Agnes . . . . . + o' 57 Delamere . . . . . . —o'o.3 || Precelly . . . . . – 1 'oo | Southampton . . . . . 4 o' 29 * † º is + 1 . Io i Hensbarrow . . . . + o- 71 || North IRona . . . . . – o' 21 | Kellie Law ar- S E C T I O N V. M EA S U R E M E N T 0 F B A S E LIN E S. To determine by actual measurement on the ground the length of one side of a network of triangulation wherefrom to infer the lengths of all the other sides, is not the least difficult operation in a trigonometrical survey. To effect this with all the accuracy necessary for the purposes of topography presents indeed no formidable difficulty; but when the ultimate end of the operations is to contribute towards the knowledge of the figure and actual dimensions of the earth, and when the problem is stated thus, To determine the number of times that a certain standard or unit of length is contained between two finely marked points on the surface of the earth at a distance of some miles asunder, so that the error of the result may be pronounced with certainty to lie between certain very narrow limits plus or minus, then the question requires and has always obtained serious conside- ration. In the first place, the representation of the unit of length, an abstract idea, by means of the distance between two finely engraved dots or lines upon the surface of a bar of metal at a certain temperature, is never itself free from uncertainty and probable error, from the difficulty of ascertaining at any moment the precise temperature of the bar, and also in a less degree from the circumstance that such bars or scales have in the course of time altered perceptibly in length. Omitting this last consideration, the transference of the unit of length or a certain multiple of it to a measuring bar will be affected, not only with the unavoidable errors of observation, but with errors arising from the uncertainty of tempe- rature of both bars. It is therefore necessary that the ratio of the multiple bar to the standard, as well as the coefficients of expansion of both, should be the objects of very numerous and careful observations. This multiple of the standard is however seldom used in actual measurement, but serves as a secondary standard for the examination of the rods or bars with which the actual measuring is performed. The construction of the measuring rods must then be such that they may admit of easy and direct comparison with the working standard, that they may be aligned with great exactness between the extremities of the line of measurement, that they may be made individually perfectly level, and that, with respect to the alterations due to variations of temperature, they may be either eliminated by the principle of compensation or any other mechanical means, or that the temperature of the bars may be precisely ascertainable at any given time. Compensation Bars. (1.) The compensation bars, invented by Major-General Colby with the view of eliminating the errors resulting from our ignorance of the exact temperature of the : * MEASUREMENT OF BASE LINES. 2OI measuring rods at a given time, are constructed on the following simple and beautiful Principle :-Two bars of different metals and different rates of expansion are laid parallel tºn 7? iA - IB Aſ - - J3' and close to each other as A B, A B'; these are firmly connected at the centre, from or to Which point they are free to expand and contract. At a given temperature they are taken of the same length, and in this state suppose lines A' A m, B' Bn, to be drawn through their extremities and perpendicular to their lengths, so that A m = B n ; make also the ratio of Am to A' m or of B n to B' n equal to the ratio of the expansion of the bar A B to the expansion of the bar A'B'. Now if we suppose both bars to receive an equal increment positive or negative of temperature and in this position lines to be drawn through their extremities, these lines will evidently pass through the points m n as already determined. This, indeed, is not mathematically or strictly speaking true, but the difference would be quite imperceptible. * (2.) In the actual construction the bar A B is of iron, the bar A'B' of brass, A' m, B'n, are flat steel tongues at the extremities of these bars moving freely on conical brass pivots, allowing them to be inclined at small angles with the lines perpendicular to A B, A'B'. At the temperature of 62°Fahrenheit the bars are assumed to be precisely the same length, and the tongues consequently at right angles to the bars. It is evidently necessary for the construction that in order to the fulfilment of the required compensation, the bars must always be of the very same temperature, but as they are necessarily subjected to constant variations of temperature it is also clear that they will not generally be of the same temperature unless they have the same rates of changing temperature. It was necessary therefore to ensure this equality, and two modes presented themselves, either to alter the dimensions of one until its rate was equal to that of the other or to produce the same effect by varying the surface of the one while the other remained constant. The latter method was adopted, and after a number of experiments, in which the brass bars were bronzed and varnished and remained unaltered, while the iron bars were browned (as the barrels of fowling pieces), lacquered, and smoked in different degrees, the desired equality was obtained. (3.) The compensation bar consists of two bars, each Io feet 1.5 inch long, or 5 inch broad, and 1. 5 inch deep, placed I. 125 inch apart, and firmly connected at their centres by two small transverse steel cylinders not quite in contact. At each extremity of the bars is a metal tongue (corresponding to the lines A'm B'n) so connected by pivots to the bars as to admit freely of any expansion, and yet to be quite immoveable otherwise. These tongues are each 6.2 inches long, and on a silver pin at the extremity of each is marked the com- Pensation point. This compound bar is placed in a deal box (resting more immediately "Pon two brass rollers in the bottom of it), and is kept from moving lengthways by means C c 2O2 PRINCIPAL TRIANGULATION. of a brass stay firmly fixed to the bottom of the box at the centre, and projecting upwards between the two small steel cylinders before mentioned. The long level for levelling the bars is fixed to the upper surface of the brass bar, and is read by means of a glass covered opening W., Pl. II., in the top of the box. The tongues carrying the compensation points project beyond the box, but are carefully protected. These points, it is to be noted, and not the bars themselves, lie in the line of measurement. . . . .# The complete set contains six bars, distinguished by the letters A, B, C, D, E, G. Each box when in use is supported at one-fourth and three-fourths of its length by means of strong brass tripods, having rollers oo (Plate II. fig. 2) on their upper surface. One of the tripods is provided with a tangent screw g for communicating a longitudinal motion to the bar, and both have screws f, for communicating a transverse motion, and an elevating screw e, for the final adjustment of the bar as to level. These tripods rest on trestles TT, which are of various lengths from 6 to 3o inches, and are selected as the nature of the ground requires. (4.) The interval between the adjacent compensation points of two bars lying in line is brought to exactly six inches by means of a compensation microscope which is constructed in the following manner: Two microscopes of two inches focal distance, lying parallel to one another, and six inches apart, are connected by two bars, one of brass and the other of iron, in such a manner that the outer foci of their object glasses are compensated points at exactly six inches apart. Through the centre of these two bars passes a telescopic micro- scope parallel to the other two. . The microscopes revolve on the axis of this centre or telescopic microscope in a vertical tube attached to the upper surface of a tripod with levelling screws, and screws for communicating motionin alongitudinal or transverse direction. The tripod of the compensation microscope rests on a three armed grooved stands s's" (Fig. 3, Pl. II.) carried by the brass plate tº ºt, screwed to the end of the box. To the - brass bar of each compensation microscope is attached the level, and on the other side is a small telescope moveable in a vertical plane for the alignement. The measurement of the six inch interval is effected by bringing one of the outer microscopes of the compensation microscope when in perfect adjustment, alignement, and level, to bisect the compensation point of one of the bars, and then bringing the compensation point of the other bar (by tangent screw motion) to be bisected by the other outer microscope. Seven microscopes, distinguished by the letters M, N, o, p, q, r, s, are thus required for a set of bars, so that between the telescopic microscopes of the first and last compensation microscopes of a complete set of bars arranged in the line of measurement, the distance is 63 feet. (5.) The end of each series of bars when used in measurement is transferred to the ground by means of a point carrier; this simple apparatus consists of a massive triangular cast-iron plate of about 15:5 inches side, with a short, flat, hollow cylinder of brass screwed to the centre of its upper surface, enclosing a moveable disc having a fine point engraved on 3.f MEASUREMENT OF BASE LINES. 2O3 its surface, this dot is adjusted to the required position by means of three small equi-distant screws passing through the cylinder. The point carrier is placed under the telescopic microscope, so that the dot shall be very nearly in the line of its optical axis, and the final adjustment of the dot is then made by means of the three adjusting screws. This dot forms the initial point for the next set of bars. - Standards. (6.) The Ten-Feet Ordnance Standards, designated as O, and O, are two wrought- iron bars 122. 15 inches long, 1.45 inch broad, and 2.5 inches déep (constructed for the Ordnance Survey Department by Messrs. Troughton and Simms, in 1826–7), supported at one-fourth and three-fourths of their length on rollers secured to the bottom of the wooden box by which the bars are encased, and having a slight pin attached to the box and passing into a small hole in the centre of the under surface of the bars, to prevent their moving longitudinally in the box. The mode of supporting them on rollers was devised to allow them to contract or expand freely from the effects of temperature, some of the preliminary experiments having shewn that the length of standards would be sensibly affected by the manner in which they were supported throughout their length. The precaution was taken of cutting away the ends of the bars to half their depth, to obviate the effects of flexure, consequent on the mode adopted for supporting the bars at two points only; and by this method, by which the dots marking the standard of length are placed in the axes of the bars, it is believed that no material flexure will exist, and from their depth and massiveness it is more than probable that, whatever it may be, it is not likely to vary in amount, which is, after all, the great desideratum in a standard InCaSure. - - - r Platina pins were then inserted at each end, and the distance, Iofeet having been set off at the temperature of 62°Fahrenheit, dots were engraved on them to indicate the standard of measure. On the upper surface of each bar, over the supporting brass rollers, were two cylindrical holes, made large enough to admit the bulbs of two thermometers, for registering the temperature of the bar, the metal and the bulbs of the thermometer being brought into contact by immersing the bulbs in oil of mercury. The bars are retained in their proper positions in their boxes by small pieces of brass at the top and sides, to prevent their being displaced with reference to the rollers. The ends of the bars are protected by circular brass caps screwed on to the ends of the boxes when not required to be used. - Sit-inch Standard.—The distance between the outer ſoci of the compensation *oscopes is referred to a brass standard measure 11.5 inches long, I-5 inch broad, **55 inch deep, supported at each end by small pieces of brass screwed on to the * surface, the standard measure being defined by dots engraved on silver pins, let into the brass, 6 inches apart. The distance between the outer ſoci of the microscopes was C c 2 2O4. PRINCIPAL TRLANGULATION. adjusted to the length between these dots, the temperature of the standard being ascertained by means of a thermometer having its bulb let into an orifice at one end. * (7.) Comparisons of Standards.-Extensive comparisons, given in detail in the “Account of the Measurement of the Lough Foyle Base” were made at Southampton in the years 1844–5–6, in order to obtain the relations between these standards and the following: Indian Bar B, Cape Bar B, Ramsden's Prismatic Bar, Roy's Scale, Messrs. Troughton and Simms' Brass Scale, and the Indian 6-inch standard. The first of these bars differs from the Ordnance Standard only in the dimensions of the section which are rather smaller, the second bar differs only in having gold pins instead of platina. Ramsden's Prismatic Bar is of cast- iron, 2 I feet in length; the section is an equilateral triangle of I.25 inch side. The 20 feet measure is divided into parts of 40 inches marked by dots on brass pins let into the bar; these distances were laid off at the temperature of 54° by Ramsden from his Brass Scale. General Roy's scale is of brass 42.8 inches long, -55 inch broad, and .22 inch deep, divided by lines, which are now much worn, into inches and tenths of inches; it has a vernier at each end, one dividing the inch into Iooo, the other into 50o parts. Messrs. Troughton and Simms' Brass Scale is 66 inches long, I-5 inch broad, and 5 inch deep; it is divided by lines on silver into inches and tenths of inches, numbered from o to 60; it is also divided into inches by a scale of dots on silver pins let into the brass opposite the linear divisions of inches, these dots were used in the comparisons. (8.) The following table contains the principal results of these comparisons; the third column contains the factor by which any results given in terms of the several scales are to be multiplied, in order to reduce them to mean feet of O, ; the fourth column contains the corresponding logarithm. - Standard Measure. Mean Teet of O1. Factor. Logarithm. Ordnance Standard O. : 9-9999972 o'99999972 9.9999999 Ramsden's 20-feet Bar - 20-ooo7656 1-oooo;828 o-ooooi66 Roy's Scale o-49 in. ' ' ' 3.3333368 I-oooooroş o-oooooo.5 Roy's Scale o–36 in. . . . 3-oooo.281 I-ooooog37 o-ooooo.41 Cape Bar B. . . . . . . 9.9998498 o.99998.498 || 9.9999935 Indian Bar B: ... . . ; 9-9999279 o. 99999279 || 9.9999969 Troughton and Simms o-60 in. 4.999992; o:9999985o 9.9999993 Troughton and Simms o–4o in. g 3.3333458 I-ooooog 75 o-oooool 6 Troughton and Simms o–36 in.. 3-oooool 8 || I-oooooooo o-oooooog §º o°49.99778 o'9999555o 9.99998o?. nCll:l Il O-111Cll NoLill 101:ll'C1 J5 • o-4999652 o'99993039 || 9.99996.97 (9.) The method of making these comparisons was essentially the same as followed in the measurement of the Salisbury Plain Base, page 217. If we suppose a y to be the coefficients of expansion of the two bars under comparison, 2. their true difference of length ——ºf *--- * Published by the Honourable Board of Ordnance, .---\ ** i i i MEASUREMENT OF BASE LINES. 205 at the standard temperature of 62°, whilst 62° + l\", 62° + k", and n, are the observed temperatures of the bars and their difference of length, then we shall have h, a - k, y + 2 + m, = o h, a - k, y + 2 + m, = o h, a - k, y + 2 + m, = o h, a - k, y + 2 + m, = o each comparison giving an equation: hence, by the method of least squares, (h”) a - (hk) y + (h) 2 + (h m) = o — (hk) a + (k’) y – (A) 2 – (km) = o (h) a - (3) y + r z + (m) = o The following table contains the coefficients of expansion obtained in this manner:— l Year. Standards compared. O, O Cape Bar B. Indian Bar B. Ramsden's Bar..] ºnto, *: 2. & Simms'. Comp. 1844 Q, and Cape Bar B •oooooº 13c - • -ooooo 5918 - • * * * IOI 1844. 9, and Troughton & Simms'-ooooooogg|. * * * * . . . . . . .oOooog'749|Ioo 1845. O, and Ramsden's Bar •oooooo 196|. . . . . . ooooo 5848 . . . . Ioo 1846 O, and Indian Bar B . •ooooo 5921] . . . . • -oooooo.13 . . . . 2O 1831| O, and Indian Bar B . . . . . . . oooooo 508 . tº º tº º 25 (Io.) The coefficient of expansion of the standard O, resulting from the whole of these comparisons, is somewhat different from that obtained by Captain Drummond, R.E., in 1827. In his experiment, the length of the standard when in a natural state was read by a microscope placed over each dot, one having a micrometer, and the temperature of the bar registered. The bar was then carried to an adjoining room, in which the temperature was about 120°, and, acquiring thus a considerable increase of temperature, was quickly re- placed under the microscope, and its length again ascertained. The mean of eight values of the coefficient of expansion thus obtained gave -oooooo;22; and it will be seen from the comparison made at the base line on Salisbury Plain, that the coefficient of expansion at that time was apparently intermediate to this value obtained by Captain Drummond in 1827, and that resulting from the comparisons at Southampton in 1844–6, as contained in the above Table. (II.) In 1834 a series of 54 comparisons was made by Lieut. Murphy, R.E., between two lengths of the Royal Astronomical Society's Scale and the standard O, by which it appeared that the former exceeded the latter by . oorg5 of an inch (see “Lough Foyle Base,” page [29] Appendix); and, therefore, since O, - O, - .oOoo34 of an inch, and since the Whole length of the Royal Astronomical Society's Scale is equal to 59.999712 mean inches of the centre yard (see vol. ix, page Ioo, R. A. S. Memoirs), therefore O, as I I9.997508 mean inches of centre yard of R. A. S. Scale. 2O6 PRINCIPAL TRIANGULATION. Measured Lines. (12.) The three volumes, entitled “An Account of the Trigonometrical Survey,” COIl- tain all the particulars relating to the measurement of the base lines on Hounslow Heath, latitude 51° 27', longitude E. o” 27', by General Roy, assisted by Lieut.-Colonel Pringle, R. E., in 1784, and by Lieut.-Colonel Williams and General Mudge in 1 791; on Salisbury Plain, latitude 51° Io', longitude 1° 45', by the same officers, in 1794; on Misterton Carr, latitude 53° 30', longitude o' 55", by General Mudge, in 1801; on Rhuddlan Marsh, latitude 53° Io', longitude 3° 30', by the same officer, in 1806. A base line, of which no account has been published, was measured, in 1817, by Major-General Colby, with the assistance of Mr. Gardner, on Belhelvie Sands, latitude 57° 15', longitude 2° Io', near Aberdeen in Scotland; of this proceeding there is no written account, further than the note- books used in the operation, containing the readings of the thermometers, &c., together with the result of Mr. Berge's comparisons of the chains with Ramsden's Prismatic Bar and the “Reduction of the Base,” by Major-General Colby. In the present work the absolute distances are derived from the bases measured with the compensation apparatus at Lough Foyle, in 1827 and 1828, and on Salisbury Plain in 1849, the others being considered as ` bases of verification. A general account of these bases will now be given, referring for the details of those previous to the date 1806 to the volumes of the “Trigonometrical Survey” and the engravings given in them; and for the details of the Lough Foyle Base, to the account published by the Honourable Board of Ordnance in 1847. Hounslow HEATH BASE. The measurement of the base line on Hounslow Heath, by General Roy, was the first operation of the trigonometrical survey of Great Britain. The ground was selected from the extraordinary evenness of its surface, its great extent, without any local obstructions to the measurement of a base line, and also from its advantageous vicinity to London and Greenwich. - * - The first measurement which was made in June 1784 with a steel chain of 100 fect in length, constructed by Ramsden, was considered merely experimental, and gave for the length of the line, after due corrections for temperature, 27408. 22 feet. - The bases which had previously to that time been measured in other countries, with the appearance of the greatest care and exactness, had been mostly effected with deal rods, whose actual lengths were compared with a metal standard; and it was therefore deter- mined to measure the base line on Hounslow Heath with such rods, very carefully con- structed of the finest material. The rods, which were 3 in number, were each 20 feet 3 inches long between the extremities of the bell-metal tips, by the contact of which the measurement was finally made; the lengths were carefully laid off by Ramsden, from General Roy's scale. - * Vols. I. & II, were first published in the Philosophical Transactions. - * | MEASUREMENT OF BASE LINES. 2O7 In the course of the measurement, however, it became obvious that the deal rods were affected by the variations of the hygrometric state of the atmosphere to a degree that was quite unexpected, and threw at last such doubts upon the correctness of thé operation that, before the measurement was even completed, it was considered a failure. In order to throw additional light on the subject of the expansion of deal rods, several experiments were afterwards made, which led to the conclusion that they were quite unfit to be used in the measurement of a base line. It does not, however, appear that the surfaces of the rods. Were prepared in any manner by oiling or varnishing, in order to diminish the effect of the humidity of the atmosphere. - The result of this measurement gave 274O6. 26 for the distance between the centres of the pipes which marked the extremities of the line, reduced to the level of the lowest, in the temperature of 63°, being that of the brass scale when the lengths of the deal rods were laid off. f - At the same time that it became clear that the rods of deal would not furnish a result that could be finally relied upon, it also became evident that the measurement must necessarily be repeated with rods of some other material. At the suggestion of Lieut.- Colonel Calderwood of the Royal Horse Guards, F.R.S., General Roy determined to remeasure the line with tubes of glass. • r, * * - These tubes, which were each 20 feet in length, were firmly secured in deal cases eight inches deep, of the same width in the middle, and tapering from thence in a curvilinear manner towards each end. Through two small orifices in the top of each case passed down- wards the bent tubes of two thermometers, whose bulbs were within the deal case. Thus the temperature of each rod was inferred from the readings of two thermometers. The manner of securing the rods in their cases was such that they were free to expand or contract to and from their centres, which parts were rigidly and permanently fixed in the cases. The ends of each tube were ground perfectly smooth and truly at right angles to the axis of the bore, and projected respectively seven and nine-tenths of an inch beyond the case, the former called the fixed, the latter the moveable end. Into the former end was tightly fixed a cork of the very best material, into which was inserted a small brass tube co-axial with the cork. Into this tube again was inserted, screwing into the inner end of the brass tube, a steel pin carrying a button at its exterior end. The inside of the button fitted very closely the ground end of the glass tube to which the outer surface of the button, made as nearly as possible a perfect plane, was parallel. The apparatus at the other extremity of the glass tube was somewhat similar, except that the button, which had a spherical surface the radius of which was two inches, was moveable in the direction of the axis of the tube, by means of a spring acting outwards; and the pin, instead of screwing into the small brass tube in the cork, passed freely through it, and carried at its inner extremity a small ivory scale with a fine intersection cut upon it. Thus, two rods being brought into contact, and the fixed button of one being pressed against the moveable button of the other, the mark on the ivory scale of the latter was pushed backward until it coincided with a diamond line cut on the interior and tipper surface of the glass tube, whose length was so adjusted that, when the coincidence was perfect, the distance between the plane surface of the one button and the 208 PRINCIPAL TRIANGULATION. spherical surface of the other was exactly 20 feet of General Roy's Scale, at the temperature of 68°. Each case had at each extremity a pair of wheels, two inches in diameter, connected by a common steel axis, and also a pair of small cross feet projecting four or five inches outwards from the centre on both sides. By the turning of a screw, the axis of either pair of wheels could be raised or depressed with reference to the case, and thus the case might as required rest either immoveably upon its feet, or have its weight transferred to its four rollers and so become moveable in order to perfect adjustment in the measurement. Also from the upper surface of each end of each case projected upwards a small brass piece two inches long, by means of which, and a slow motion screw connecting them, the rods were drawn together to the required distance; that is, until the mark on the ivory scale coincided with the mark on the inner surface of the glass tube as before described. The final length of the base line, deduced from the measurement with these rods, when reduced to the temperature of 62°, and to the mean level of the sea, was 274O4- or 37 feet. The coefficient of the expansion of the glass tubes used in the reduction of the base, namely -ooooo.43, was obtained from a single observation made with a microscopic pyrometer, of the total expansion of a five foot tube for 180°, the difference of 32° and 212° Fahrenheit. The principal defect in this measure is probably the manner in which the rods were sup- ported, or rather left unsupported. Each rod rested on two trestles, one at each extremity, the same length supporting the extremity of two contiguous rods; it therefore is probable that the rods were subject to considerable flexure, and also that in removing from the trestles any one of the rods, the trestle which still supported the end of the contiguous rod would, from the change in the force acting upon it, be liable to some small motion. This last source of error was indeed experimentally investigated and found to be real, and produce an observable motion. + These considerations, together with that of the novelty of the method, demanded some verification of the result of the glass rod measurement; it was therefore determined by his Grace the Duke of Richmond, Master-General of the Ordnance in 1791, after the death of General Roy, to re-measure the same line with the steel chain, to which method General Roy had expressed his preference. Two steel chains of Ioo feet in length, designated as A and B, were constructed by Ramsden for this purpose. Each chain consisted of 40 links 2.5 feet long and half an inch square in section, the handles were of brass perfectly flat on the under side, so that the coincidences between the arrows at the extremities of the chains and the division of scales on the brass register heads were easily observed. The chain A was used for measuring, while B was preserved as a standard. # As in the operations with the deal and glass rods, the measurement was made in hypothenusal lengths which were afterwards reduced for inclination. The alignement of the base was effected with a species of transit instrument, which was constructed by Ramsden for that purpose. f At every Ioo feet, as measured off in the line of the base with a 20-feet deal rod, was driven a beech post or very stout picket having on its upper surface a brass register head carrying a graduated slider, moved in the direction of the line of the base by a slow- ! # . º MEASUREMENT OF BASE LINES. 2O9. motion screw. This post supported no part of the apparatus, but served merely to indicate, by a division of the scale, the extremity of one chain, and thus give the initial point for the next succeeding. The chain was laid out in a succession of five deal coffers resting upon trestles, the extreme points of support being within about ten inches of the extremity of the chain, or of the register headpickets, so that each handle of the chain rested upon the sliding scale of one of those pickets. The forward end of the chain was then drawn with a weight of twenty-eight pounds, while the rear end was drawn back by means of a screw which had its bearing from a post used for that purpose, until the mark on the handle indicating that extremity of the chain, coincided with that division on the register head scale which indi- cated the forward extremity of the chain in its previous position. The register head scale at the forward end was then adjusted by its screw, until one of its divisions coincided with the end of the chain, which division again became the initial point for the next chain. The appa- ratus for the ends of the chain can only be understood in all details by a reference to the engravings in the original account. Five thermometers were laid close by the chain in each position, and suffered to remain until they showed nearly the same temperature, which took generally from 7 to I5 minutes. When the sun shone out, the chain was covered with a white linen cloth, the ends of which were put over the openings of the first and last coffers to exclude the circulation of the air. The result of this measurement gave for the length of the base line, after the due correction for the inclinations of the several hypothenuses, reduction to the temperature of 62°Fahrenheit and to the mean level of the sea, 27404.24 feet, exceeding the result given by the glass rods by .21 feet or two inches and a half, and falling short of that by the deal rods by 2.02 feet; the coefficient of expansion used in making the reduction for temperature was . ooooofi25, which was deduced from the mean of nine observations made on the chain directly. -- The lengths of the chains were ascertained by comparison with Ramsden's Prismatic Bar. The length of this bar, 20 feet, was laid off at the temperature of 54° from his brass scale, which he had compared with that of the Royal Society and found to be of precisely the same length. In the comparison of the chains with the bar, the latter was supported in twenty-one points in a perfectly straight line, as nearly as could be ascertained ; part of the chain was then placed on rollers in a horizontal line parallel to the bar and a few inches below it, and whilst it was fastened to an adjusting screw near one end of the bar, it was kept straight on the rollers by a weight of fifty-six pounds. From the extremities of the 20 feet on the edge of the bar, two fine wires with plummets were suspended which were immersed in vessels of water, the wires hanging so as nearly to touch the chain. One end of the chain being then brought under its wire by means of the adjusting screw, a fine point was made on the chain coinciding with the other wire. This Pºrt of the chain was then shifted, and so the whole measured in five successive portions. ID (l 2 IO. PRINCIPAL TRLANGULATION. . . It is not stated that the operation was repeated more than once for each chain. The result, when corrected for temperature to 54°, gave for the length of the chains— - g A = Ioo-oog52 feet of the Prismatic Bar. B = 1oo-oo.485 * * * '3? . g 35 It is to be feared, from the manner in which the comparison as above described was made, and from the probability of their being the results of one observation only, that the lengths of the chains as thus obtained are affected with a large probable error; for it is now well known that in these matters the truth cannot be arrived at by a small number of observations. W It may be necessary to observe that the length of the base as given above is in terms of feet of Ramsden's Brass Scale at 62°. The extremities of this line are marked by iron guns sunk in the ground, the centre of the bore being in each case the precise end of the base. SALISBURY PLAIN. . This base of verification was measured in the summer of 1794, by Lieutenant-Colonel. Williams and Captain William Mudge of the Royal Artillery. . The measurement was, effected with the same chains that had been used at Hounslow Heath. Previous to the measurement, the chains were compared with one another, and were found to have the same difference of length as when measured by Ramsden subsequent to the measurement of the Hounslow Heath base. The operation was conducted in the same manner as at Hounslow Heath, with some trifling improvements in the method of aligning with the transit; the inclinations of the different hypothenuses were observed with the transit, which had a small vertical arc for the purpose. An examination of the chains after the operation showed that the measuring chain A had stretched #3 part of an inch. The final length of the base when corrected for the wear of the chain, reduced to the temperature of 62°, and to the level of the station on Beacon Hill which was one extremity of the base, was 36575.401 feet of the brass scale. Now the height of Beacon Hill is 669.5 feet, as obtained by levelling, thérefore the length of the base reduced to the level of the sea becomes 36574.232. The extremities of the line were marked by iron guns sunk in the earth, the centre of the bore of each marking the precise end of the base. MISTERTON CARR. º The apparatus used in the measurement of this base in 1801 by Major Mudge was the same as that employed on Hounslow Heath and Salisbury Plain, with the addition of a steel chain of fifty feet in length of exactly the same construction with the longer chains. ; |- * +4.g -- n-** º | MEASUREMENT OF BASE LINES. 2 II The resulting length of the base line was 26 342. 19 feet when reduced to the temperature of 62° of the brass scale and to the mean level of the sea;" after the operation the chains were compared by Mr. Berge, successor to Mr. Ramsden, with the Prismatic Bar, from which comparisons it was found that at 54°– A = Ioo.or Ioa feet of the Prismatic Bar. B = Ioo-ooo.48 33 33 - The 50-feet chain C was also carefully compared with the standard B, which gave— 2 C = B + ·oo786 feet. This chain only measured four lengths or two hundred feet of the line. The ends of the base were marked by two blocks of oak with square holes in their upper surface, these holes were run in with lead which was filed off even with the surface of the wood and the diagonals drawn. . The intersections of the diagonals indicated the precise ends of the base. These oak blocks are not now to be found. º, RHUDDLAN MARSII. This base line was measured in the summer of 1806 on an extensive and level piece of ground about four miles north-west of St. Asaph in Flintshire, North Wales. The measurement was made with the same apparatus and in the same manner as in the former lines; the chains were very carefully compared before and after the operation with the stañdard B. The final result for the length of the base, after reducing to the temperature of 62°, was 2451426 feet of Ramsden's Brass Scale. r - # ‘. . The extremities of the line were marked as at Misterton Carr with blocks of wood, but of these unfortunately every trace has been lost. - BELHELVIE SANDS. " . The ground selected for this base line is situated near Aberdeen. The same chains and method of measurement were employed as on all former occasions. The chains were compared with the points in the cast-iron prismatic bar both before and after the measure- ment by Mr. Berge, and the results of the comparisons gave, when corrected to the tempe- rature of 54°, + . . . . . . . . . A = Ioo.o'Iz7o feet of the Prismatic Bar - - B. = Ioo-oo547 23 sº }*** C = 5o-ool.27 33 , * A = Ioo.or. AI 2, - * -* º B = Ioo-ooog1. 32 23 - }* the measurement. C = 5o-ool 23 35' 33 *--- -m-mº —-r #. i * º 2 O = In the reduction of the base in the original account there is a slight error in the reduction from 5.4° to 62° ; the quantity should cvidently be 2' 172 feet. D d 2 2 I2 PRINCIPAL TRLANGULATION. The “Reduction of the Base” by Major-General Colby is as follows:– . Reduction of the Base Line. The apparent length of the base line, when reduced from the several hypothenuses (to mean level of the sea), according to the JFeet. Table, is º º º iº º º C & 265 I4.2653 The mean length of the measuring chain A, as found by Mr. Berge's comparisons with the points on the cast iron bar, pre- viously and subsequently to the measurement, was, when reduced to the temperature of 54° Fahr, IQo-org55 feet, whence or 355 x 261 3:5365 The mean length of the fifty-feet chain was 5o-ool 25 feet, whence •oor 25 × 8 ſº * {} º Ç •oroo The sum of all the degrees shown on the thermometers was 70699.5 + I314:25 $º 5 6 = 'o245 of a foot, which is the correction for 70699.5 + 1314:25, wherefore ( • OO 54° × 26518) {} # the mean heat at which the base was measured above 54°, the tem- perature at which the chains yº off . º Ç ſº •o245 • OI 2.27 X 2 Finally, we have of 237 I 2 5 × 8. = 2.1854 feet for the re- duction of the base to the temperature of 62° • {º tº –2. I854 2651.5-6.509 In explanation of the reduction of the thermometer readings to obtain the correction o245 feet, it should be stated that the 50-feet chain had three thermometers to record its temperature, so that two 50-feet chains had six thermometers, whence the number 6 in the denominator of the fraction whose numerator is I314:25, which is the sum of the readings of the thermometers for the eight positions of the 50-feet chain. The quantity of 237 in the last correction is the expansion in inches of 100 feet of the brass scale for 1° of Fahrenheit. The reduction to the mean level of the sea is included in the first term. This line was measured between May 5th and June 6th 1817 by the late Major-General Colby with the assistance of Mr. Gardner. To reduce these base lines into terms of Ramsden's Bar at 62° we must multiply them by the ratio of the length of a foot of the brass scale to that of the prismatic bar when both are at that temperature. Now both standards are equal at 54°, therefore if e e' be their respective coefficients of expansion, their relative lengths at 62° will be as 1 + 8 e to I + 8 e', or 1 + 8 (e – e') to unity, and using the values given in the original accounts, namely e = . ooooºo; and e' = . oooooo2, the factor for multiplying the bases becomes oooo328, also the factor for converting measures in terms of Ramsden's Bar into feet of O, is I -oooo.383. The following table contains the length of the old bases according to the different standards of measure:— * * | MEASUREMENT OF BASE LINES. 2 I 3 Length in feet of Date. IBase. IBrass Scale. Prismatic Bar. Ordnance Or. 1791 Hounslow Heath . 274O4'24. 27405. I4. 274O6. I9 1794 | Salisbury Plain . 36574.23 36575.43 36576.83 I8or Misterton Carr . . . . 26342. I9 26343-off 26344.06 I806 | Rhuddlan Marsh . . . 24514-26 24515-off 24,516-oo 1817 | Belhelvie Sands . . 26515.65 26516.52 26517-53 Lough ToyLE. (13.) The ground chosen for the measurement of the Lough Foyle base lies on the eastern border of the lake of that name in the north of Ireland. The northern extremity of the line is about two miles and three quarters south of the martello tower on Magilligan Point, in the county of Londonderry, the southern extremity is a quarter of a mile south- east of the church at Ballykelly. The ground is admirably adapted for the purpose, and is at a mean height of eighteen feet above the mean level of the sea. The measurement commenced on the 6th of September 1827 and was continued until the 25th of October, during which time several partial remeasurements were made in order to test the accuracy of the compensation apparatus and the stability of the point carriers. The results of these remeasurements were always very satisfactory. The measurement was resumed on the 7th of July in the following year and continued until the 25th of the same month, when it was suspended in consequence of the crops being on the ground. It was again resumed on the 13th of September and finally concluded at the south end of the base on the 20th of November 1828. The measurement was thus effected in three periods amounting in the total to sixty days, the average daily progress five hundred feet. The mean lengths of the bars applicable to these three periods in terms of the com- pensation bar A, were determined by numerous comparisons, and are as follows, the bars being individualized by the letters A, B, C, D, E, G : Bar. 1st Period. 2d Period. 3d Period. B = A-F33-o d A-F39-3 d A-H46. I d C = +38.3 d +41.o d +48.8 d D = + 14.2 d + 7.9 d + II. I d IP = + 9.o d + 16-8 d. +23.5 d G = + II.5 d, + 6.8 d + 9.4 d When d is one division of the micrometer and equal to 7: of a foot. The total length + tº ſº 24$400 *asured by the bars is then found by summation equal to 3966 A + 86696.8 d 2I4. PRINCIPAL TRIANGULATION. Similarly, by frequent comparisons of the compound microscopes with the Ordnance 6-inch Standard, and using their mean values for 5 different periods, the total length of the part measured with microscopes was found equal to 5208.5 O* + 23735-2 d’ – 708 feet O” being the length of the Ordnance 6-inch Standard at 62°: d' the value of a division of the micrometer = ± of a foot; '708 feet was the distance measured back from the dot marking the termination of the last series, to the dot on platina wire marking the south end of the base. This measurement was made with two beam compasses of ebony. The values of the compensation bar A, and the 6-inch Standard in terms of the mean feet of O, were determined as A = Io feet – 24-3 d Oºinth = o'5 feet – 56 d' The length of the base reduced to feet of O, at the temperature of 62° is thus found to be 4164o. 9228 feet, and the reduction to the mean level of the sea being : o355 feet, the length finally is 41640.8873 feet. - The base was then verified by means of intermediate points in its line by a Comparative Triangulation, which will be found in the original account. The conduct of this measure- ment was principally entrusted to Captain Drummond, R.E. SALISBURY PLAIN. (14.). In the year 1849 the base line on Salisbury Plain was remeasured with the compensation bars. As the old measured distance could not be reproduced with sufficient accuracy by calculation from the Lough Foyle base, Lieut.-Col. (then Captain) Yolland directed, with the approval 6f Colonel Hall, then Superintendent of the Ordnance Survey, the remeasurement of this line with the apparatus used in the measurement of the Irish base. This operation was conducted entirely by a party of the Royal Säppers and Miners under Serjeant Steel of the same corps, who was selected for the duty by Captain Yolland as a man quite capable of doing justice to this difficult undertaking. The north end of the base is on Beacon Hill, three miles west of the village of Amesbury; the south end near Old Sarum Castle, a milé and a half from Salisbury. The guns marking the extremities of the old base were easily found, and having retained their vertical position, and being very firm, it is highly probable they have not moved sensibly from the position in which they were placed in 1794. As it was found that the extremities of the line were not reciprocally visible, it became necessary to elevate the theodolite at the south end by a scaffolding 32 feet high. The choice of this point in the first instance as the extremity of the base line is rather singular, as, a few yards further on, a higher piece of ground affords a much more satisfactory terminus. The muzzles of both guns were | i MEASUREMENT OF BASE LINES. 2 I5 fitted tightly with a cylindrical plug of wood, the centre being very carefully marked with a brass pin. Over the Beacon Hill centre was brought the Ordnance 3-foot theodolite with its observatory, the instrument being centred in the usual manner with a plummet. The centreing of the Royal Society's, theodolite over the south end was a little trouble- Some on account of the height of the instrument above the gun; but, finally, by protecting carefully the plummet from currents of air, it was satisfactorily accomplished. These instruments served to align the base and connect it with the triangulation. The observer Was Serjeant Donelan of the Royal Sappers and Miners. * + tº: The party proceeded from the Map. Office, Southampton, on the 1st of May 1849, and pitched camp on Arrow Down, near Amesbury. The first three weeks were spent in tracing the line, clearing it of trees, furze, &c., driving pickets for the alignement and com- parisons of bars. The pickets were driven at short intervals at first, and afterwards the observer at the ends of the line, taking advantage of particularly favorable circumstances of atmosphere, selected those which were more exactly bisected by the vertical plane of the base, and the others were rejected. The pickets were from I-5 to 2.5 inches square, with the centre marked on the upper surface. The intermediate alignement was made with a portable transit instrument, the telescope of which had a magnifying power of 40. This instrument was brought into the base line by means of one of the “point carriers” left on the ground by the bars in their measurement, and the signal at the end of the base. As the point carrier was at a Very short distance and was bisected by means of a small straight-edge erected vertically and precisely over the dot, it is evident that the transit was by this means brought with the greatest precision into the base line; if the extremity of the line was not visible, the furthest picket was used in conjunction with the point carrier, and the final adjustment of the transit into line was effected by screws, which gave the instrument a lateral motion on its stand. The transit thus adjusted and scrupulously levelled, aligned the centre of the telescopic microscope of each compensation microscope (a brass pin being erected over that centre for perfect bisection), when the set of bars and microscopes were approximately laid on the trestles. Each microscope was aligned by its own directing telescope on a point marked on the transit at a distance from the plane of the axis of its telescope equal to the distance between the plane of the axes of a compensation microscope and the axis of its directing telescope. (15.) The method of measurement was much the same as described at Lough Foyle. Preparatory to the laying of a set of bars, a party of two men lay off distances in the line of the base of 5 feet and 5 feet 6 inches alternately, which points are to be the centres of equilateral triangles, of 17 inches side, formed by driving pickets thus,— . 216 PRINCIPAL TRIANGULATION. They then level carefully each set of pickets, and place on each a wooden triangular frame (R. R', Plate 11.); having levelled these triangles, they next place on each a trestle, selecting them according to length if the ground be uneven, so that their upper sur- faces may be in a horizontal plane nearly. A second party of two men then place on each trestle a camel or tripod, LL', which are aligned by signals from the observer at the transit, and carefully levelled, each in itself and with respect to all the others, so that the bars may require but little final adjustment with respect to level. The bars are then laid on the camels, and levelled individually by a third party. The microscopes M are laid by the principal operator, and in the meantime the whole is covered by a fourth party with the base tents. Suppose now the bars and microscopes thus approximately arranged to be in the usual order, A B C D E G. M N O P Q R S The principal first brings the telescopic or centre microscope of M over the point to be measured from (on the ground), aligns and levels the microscope, and brings the following dot of bar A under the advanced microscope of M. In the meantime one assistant has brought the telescopic microscope of N into the base line by signals from the transit, and another has brought the preceding end of the bar A into level with the following end. The principal then proceeds to the second microscope N, aligns and levels it, and bisects the contiguous dots on A and B, whilst the bar B is being levelled, and the microscope O, or rather the axis of its telescopic microscope, brought into the line of the base by the two assistants; and so on to the end, when a point carrier is brought accurately to bisection under the telescopic microscope of S. The principal then goes over the whole, and revises, if necessary, every bisection, level, and alignement. The bars then move forward to the trestles which are ready for them in their next Position. All the different operations here mentioned were invariably performed in the same order, for regularity is indispensable in the use of such a complicated apparatus. The measurement commenced at the Beacon Hill or northern extremity, and owing to the steepness of the hill for some distance, only one or two bars could be laid at a time. The slope has a maximum value of about II", and disappears at the distance of about 700 to 800 yards. This was the only troublesome part of the measurement as regards ground. Salisbury Plain is very well adapted for the measurement of a base, and a longer line might have been selected on it; but it is certain that little if any advantage is gained by the measurement of a base of more than six or seven miles, provided it be surrounded with very careful triangulation. (16.) The comparisons of the compensation bars with each other and with the standard O, were conducted in the same manner as the comparisons made at the Ordnance Map Office, Southampton, in 1845 and 1846, and described in the “Measurement of the Lough Foyle Base.". Two stone pillars (A A', Plate III.), about five feet long and one foot w | h; MEASUREMENT OF BASE LINES. 217 square, were sunk two feet into very firm soil, which was rammed as tightly as possible round them, leaving however the upper surface of the adjacent ground not in contact with them, so that the movement of the observer could have no effect upon their stability. To the upper surface of these pillars, the centres of which were ten feet apart, brass arms it', for carrying the microscopes, were fixed by vertical screws ss', clamping them to the ends of truncated brass cones sunk into the pillars, and run in with plaster of Paris. In order to ensure the stability of the bars when under observation, a strong wooden frame B C D, braced in the most solid manner, seven feet long, three and a half broad, and rather more than a foot high, and having a firm resting on the earth, was placed between the pillars and to the front, the length being exactly parallel to the line of the pillars. The end beams of this frame, b c, b'c', were made to act as rails, on which a strong plank E, seven feet nine inches long, ten inches broad and three inches thick, was made to slide in a direction trans. verse to itself, and therefore perpendicular to the line of the pillars. This motion was communicated by a lever d d", without communicating the slightest jar or shake to the apparatus. Equidistant from the extremities of this plank, and five feet apart, were placed the tripods F T' for carrying the bars, their elevation screws passing down through circular holes cut in the plank. The bar being then placed on the camels and levelled, could be brought by the sliding of the plank, with the greatest ease under the microscopes, the ultimate adjustment of its position being effected by the screws ff" e e' of the tripods, the bar having a longitudinal motion communicated to it by a tangent screw gg, working on one of the tripods. The microscopes a a', one of which had a fixed wire and the other a micrometer, were at the commencement of the operations brought to focus over the dots of the bar when perfectly level, and firmly secured in that position by means of their screws (acting on the supporting arm). In order to bring the surface, carrying the dot, of each of the other bars into precisely the same position or focal distance, the levers used in the comparisons in 1844–46 were also used in the comparisons on the base line. The arrange- ment may be described as follows: to each of the stone pillars was fixed a bracket 0 o', having a knife edge on its upper surface, on which as a fulcrum rested a lever !!!, the short arm being counterpoised rested with a metallic point on the surface carrying the dot, whilst the exact position of the extremity of the longer arm, which was six times the length of the shorter, was indicated by a fine line on a post erected for the purpose. Thus after one bar was finally adjusted, all the others were brought to exactly the same position as regards height and focal distance by bringing the outer extremity of each of the levers to its mark on the post. The standard O, was in every case first brought under the microscope, then the six compensation bars in succession, and then the standard again. The temperatures of the bars as Well as the readings of the micrometer were registered. The standard bar has the bulbs of two mercurial thermometers let into it, and the interstice being filled with oil, the temperature of the air is avoided. With respect to the constancy of the distance between the microscopes during the com. parison of one set of bars, it is probable that, mathematically speaking, it was always E c 218. PRINCIPAL TRIANGULATION. varying, especially with any rapid change of temperature, but within such a short space of time as one set of comparisons (reading of eight bars) would take up, it is probable that the variation would be of so small an amount as not to materially affect any results. Besides, care was taken in the selection of the days for observing, so that changes of temperature . within a short space of time were avoided, and the whole apparatus was of course protected by the base tents. The following table contains the comparisons of the bars with, the . standard O. s r 3. Observed * Date. MICROMETER READINGS. Temperature of Or. Te * 1849. | At Com- reduced t s O, A . B C D E G. O, Imencement. . At Close. said. | O O. Q May 17 | 77°o 93°5 154'o 159°o 107°o I42 °o 82°o 69°o 6oroo 59° 55 60° oz 23. 8 || 87°o 192 o 256°o 25% o 202 "o 243 “o 184°o 97°o 51 6o 52 “2O 51 '87 3) 3) o'o go'o 15o'o 152'o 98°o 138°o , 81°o || 8°o , 53°oo 53° 35 | 53 oš August 2 I48°o 84°5 I43 °o 143°o Io9'o 136°o 78°o 136.5 65. 55 68. Io 69'28 }} 3 92 “o 105 o 16o'o 164°o 118°o 156°o 97°o 94-3 61-60 61 “40 62 o4 » , 94°o 107'o 163'o 164°o 119°o 157.9 94.9 || 94.0 in 61:25 61 25 61-66 3? ... 94 o 106°o 164'o 167'o 117'o 158°o 97°o 95°o 61 off 61 Io 61 - 32 33 4 || 3: o 113'o 17i.o 173'o -126'o 163 o 197.9 | #3'o 51-26 51 65 51 '81 3 ,, . 15 of 116°o 173°o 173 o |-125°o 194'o 105.9 || 2:0 || 51 go 52' 65 52'21 J. J. , 46-o 116-o 163.7 1% o 122-o 160°o Io; 2 | 66 o 54-55 57'20 56° off » , 84°o 115-o 168.6 173-o 122°o 16o'o 103.9 || 101 o 59-60 - || 56'90 60-53 3 J. , 5’o 14: o 73°o 76-o 23°o 60°o 2.5 12.5 ºr 40 52 '70 || 62.2% 3 * ,, . 117'o 112'o 16; o 169'o 123°o 162°o 96'o 127°o * 63' oo 63' 90 63'58 Jy , 32 'o 12'o 63.0 76°o 22 °o 5% o 2.2 || 3:2 64' 60 65.15 65°oo J D ... 35'o iſ o 63-0 | 68-o 25.9 | #.9 ...?.9 || 33.9 95.42 65.15 65.49 32 26' 0 | 113'o 169°o 174°o 124.5 136.9 126.9 33 °o 53' os 53 ‘80 53' 33 ?? , 38.0 114-0 || 176-0 || 174°o 1249 | 16.2 2.5 || 54.9 54:35 55*40 54-88 JJ 93. 74°o 116 o 169°o 173: o | I 1919 157.2 1oz “o | Ioo'o 58-45 6o 35 59' 63 Jy ... 39'o 14: o 65 o 69°o 18:0 59.2 2.2 59:0 66 oo 66'95 66-87 3? .., | 158'o 112'o 163’o 168°o || 1:19.9 36.9 95°o 164'o 67-60 68°45 | 68-45 jj ... 133-0 | rio-o ié'o 167:0 | 18.9 92.9 98.9 173°o 69°35 | 69.3% | 73.3% 3 y ... 178'o 114-o 165°o 168.9 22.9 #55.2 | 97.5 178°o 70:30 76.36 jo-63 3 y ... 181 -o 112'o 166°o 169°o 119.2 158°o 97.5 | 181: 5 || 70’ 35 70’ 50 70-76 September 18 62.5 51 "o 131 ‘o 129.9 45.2 99.9 59°o 62°o 63: Io 62.5o 63.63 * 93. 51 °o 59 °o 141 'o 132 °o 81 °o 117’o 6o'o 48°o * 61' 15 * 61 °oo 61 ° 35' ! 3 19 ji o 26á'o 349'o || 333.9 285.5 | 325'o 269.5 || 109-0 || 43-66 45-o; 44.3% , , || 30-5 | 158:5 236.9 228.9 74.9 319.5 155-6 || 33-5 47-55 48.7; 47.75 º Jy 2-6 || 134°o 229°o 225.5 | 166.5 207'o 146-o é5-3 . . ;4.7% #2-#3 2 * 24. }} ... $1'o 144°o 225°o 2.18°o | 161 °o 202 "o 146.0 93 5. 55 ° 40 56° 15 55 ° 90 y . 99 o 179°o 256.5 254 o 202 "o 237’o 182-o 146.3 — 57 '85 58' 07 p? , 5.9 77.9 | #2.9 || 49.9 99.9 135°5 79° 5 57'o 59'oo 59' 56 59.4% yy , 39°o 79.5 | 199: o 149°o 99'o 136.6 $6.5 60° 5 59'85. 6o'o6. 6o 2 I sº 20 | 89°o 1835 | 261°o 253°o 261 -o 239-o 183’5 | 93°o 52 '5o 52 '90 || 52.62 y? , - 98'o 176°o 255°o 248 o 193°o 236°o 180°o Ioz “o 53'50 54°8o 54°oS 3 J. , 3'o 71 o | 153.0 145°o 93.5 | 129° 5 74°5 Io'o 54.60 55-oo 54°81 3y , 18°o 79.9 148°o 140°o 87.6 | 127-6 || 69.5 24.5 56.35 | #6-90 56'72 22 , 27°o 67°o 145'5 139°o 85-o 124'o 63-6 || 28-6 || 37:63 57'99 || 57 '83 3? 33 30 °o 64'o I45°o 135°o 86°o 125 °o 64'o 34°5 58' 20 58-60 58-69 22 , 33°o 69°o 145°5 134°o 82: o 121 : 5 | 66°o || 34.5 53.45 53:55 58.78 3 J. , 35°o 67°o 144°5 134.5 86.5 123-6 || 64°o 36°o 58' 36 58 ‘oo 58-45 3 y 21 58°o 176°o 257°o 256-6 || 1973 234'o 179°o 6o'o 49.5o 5o ‘oo 49°78 33 , 68°o 175°o 253°o 246'o 196-6 || 233 o 175' o 2 °o 5o 75 5I 25 50-70 79 , 83.5 74.9 253.9 243'o 134-0 |23: o 1735 | 33-0 || 52:26 52.9% #2.47 2 : , 96°o 169°o 248°o 236°o 187°o 228 o 172'o 166°o 53'95 || 55.30 54 * 54. October 18 63’o 63 o 138°o 124°o 75'o 116 o 60°o 67°o 61 °25 * 61 °42 * i MEASUREMENT OF BASE LINES. 219 MICROMETER READINGS, Observed Temperature of 01. Mean Temperature Date. *E-mºm- - reduced .# * - * r † : - to O, A. B C - D E G. O, rº t. At Close. Standard. October 18 68 so 55 'o' | 133 °o 116°o | 72°o 109°o 53°o | 72°o 62°85 63°25 63°27 $3 » 71 ‘5 57°5 136°o 116°o || 70°5 || 106.5 || 49°o 71°o || 63'70 63-65 63-77 n » 67'o 50-6 125'o 111 "o 71 "o 106.5 46°o 63'o 63.75 63' 15 63'58 y? 19 38°o roo. 5 || 180°o | 169°o | 122 "o | 161 “o IoI'o 48°o 54-40 55 ° 35 54'89 JJ » 55°o 93 °5 || 175°o 162°o I 17"o 155°o 95°o 68°o 56'95 || 58-40 || 57'79 }} » 82°o 92°o 175°o 159° 5 || Io& ‘o 153°o | 93° 5 85’ o 59' 6o 6o. 9o 6o 53 39 ,, . 104°o 91 °o 173 o | 158°o III: o 152'o 93 °o Io8'o 62 '85 63' 4o 63' 30 13 ,, . Io9'o 90°o 171 °o 159°o 115°o 151 to 96°o | Ioq'o 63' oo 63' 30 63' 32 32 ,, . Ior "o 91 o | 168'o | 161 °o IIo'o 147°o 88°o 96 o 63' os 62 - 40 62.83 . Jy 20 25°o || 71 5 || 152 “o 14o'o 93 °o 135°o 72°5 25°o 56' 55 56° 5o 56-63 Wy ,, . 26-o | 71 °o 151 °o I41 °o 91 °o I3o°o 74°o 25°o 56' 5o 56-70 56-70 ?? ,, . 27°o 68°o I52 “o I39°5 93 °o I33"o 2 °o 29°o 56' 65 57 ‘oo 56'91 3? , 36°o 69°o 148°o 136°o 90°o | 130°5 | 72°o 31 °o 57' 10 57-30 || 57:23 Jy 32 36°o 67°o 144°o 134°o 9o'o 126°o 69°o 4o'o 58' 15 58 ‘oo 58-38 }} , 42°o 65°o I44'5 | 136°o 89°o 128°o 70°5 44°o 58°35 58' 95 58-92 jp , 45°o 67°o I47°o 134°o 91 o 127°o | 68°o 43°o 58'85 58'90 59' 12 92 » 41 °o 64°o 146'o 135°5 91 o 136: o 71 o 41 o 58' 20 58' 55 58-66 29 22 12'o 206'o 286 o 275 'o 223-o 263-o 267'o Żo'o 41 '60 42 Io 41 '85 Jy » 36°o | 199°o 282 'o 272'o 223: o 263'o 205'o 48° 5 43'95 || 45' 03 44; 29 3 » 61 °o 201'o 281 5 271 ‘o 215 o 261 -o 204' 5 || 74-6 || 46:45 47° 75 46' 19 the four thermometer readings; m, The last column in this Table contains the mean of the thermometer readings of the standard bar reduced to the corresponding reading of the standard thermometer used in the measurement of the Lough Foyle Base. * (17.) These observations have been reduced in the following manner. Let X be the distance between the fixed wire of one microscope and that point in the other from which the readings of the micrometer commence; then if m be the mean of the readings of the standard (which was observed the first and last of each set); t the mean of expansion for 1° Fahrenheit of O, in micrometer divisions O. = X + m + (62–1) = A = X + m, B = X + m, m, the readings of the compensation bars ; a the Now put X – O. = y, O, - A = ~, O, – B = , . . . . G. - G = r. ; then each set of comparisons will give the seven equations following:— - o = m + air + y o = m, + +, + y o = m, + ar, -i- y o = mé + æs + y 22O PRINCIPAL TRLANGULATION. The quantity a', or the expansion of O, has been shown to be variable in the “Measurement of the Lough Foyle Base,” the earlier determinations giving an expansion of , ooooo 65 on unity, and the later -oooooo I. On using this last determination in the above equation for obtaining the differences between the compensation bars and the standard, it was obvious at once, from the resulting discrepancies, that the assumed expansion was too small. As no observations of the expansion were made about the time of the measurement, the best that can be done is to use that expansion which will introduce the least discrepancies. If, therefore, there be m sets of comparisons on the same day, or on two or three suc- cessive days, there will be 7 m equations for the determination of the 7 + n quantities *, *, . . . . tº y V . . . . . the quantity y being assumed different for each set of com- parisons. If we solve these equations by the method of least squares, and put p = the mean of the seven readings in each set successively, 77? the reading of the standard in each set, p., - the mean of the n readings of A, pº, - the mean of the n readings of B, and so on, a = the mean of all the quantities m or readings of the standard, 6 = the mean of the 6n readings of the compensation bars, then we shall have, the brackets ( ) signifying summation, o = 7 (aſp.-m) + 6 (6) (2–3) + 6 (º Hºmº (e) Jº a) - •= x + c, -, -}. O. e = 2, re-, -}. o = x + p. – º –9. 7? y = - p. -}(-)-; (a + 6%). y--º-;(-)-; (, sº). & * º a", = - m, - y r, = — m, - y = - m'. - y’ = — m'a - y’ &c. - - - * ſy ſ *- smºm, ” – 2,” = — m', -y = — m'a – y The value of the expansions of the standard bar thus determined, though it may not have the same accuracy as if direct experiments had been made for determining it, is ! MEASUREMENT OF BASE LINES. 22 I certainly more near the truth at the time than the old determination. Comparisons of the bars were made in May, August, September, and October. The comparisons in May are not sufficiently numerous to obtain a value of v. Twenty comparisons in August give 435o a = 39477 , a = 9 o'7 Twenty-one comparisons in September give 2677 x = 247 I2 , r = 9.23 Twenty-one comparisons in October give 4.755 a = 442O4. , a = 9. 29 Combining these we get the expansion equal to 9. 20 divisions of the micrometer for 1°Fahrenheit. Now one inch is equal to 12040 divisions, therefore, 9.20 divisions are equal to . oooo.37 of a foot, and the bar being Io feet long, gives an expansion of •oooooo.37 on unity. It seems, therefore, in accordance with these comparisons, that the expansion of the standard O. must have increased since 1846, and is approaching again its former expansion, namely, -ooooods. Using the coefficient of expansion as determined above, namely, -ooooof 37, the values of the compensation bars at the different periods of comparison will be as follows: MAY. AUGUST. SEPTEMBER. OctopeIt. Difference. Micr. Probable Micr. Probable Micr. Probable Micr. Probable IDivision. Irror. Division. IBrror. I)ivision. Iºrror. Division. Error, | A–O, +4' I O - O2. I +8.7 o.O31 + 1-3 o'oz7 | – 4:4 o-og8 B —O, 65.6 o-oog 63. I o-or 7 8o.6 O O2O 75°4. o-o27 C —O, 66.6 o.o.78 66.5 o:or9 || 72-6 o-o29 63. I o-o29 D–O, 14-6 o-oô8 I8.o o-og I 20-4 O-O24 I6-2 O'O34. IE – O, 53°3 o.OSI 55-7 o-o29 58-6 o.OI9 55-2 o-o26 G—O, - 5-4 o-o/3 -3-3 o-o27 + 2 - I o-o28 –3.O o.O23 I 12040 One micrometer division = inch. (18.) The compensation microscopes were compared with the Ordnance 6-inch Standard every week and adjusted if necessary, the readings of each being always recorded. As the microscopes were generally very near the state of adjustment in regard to the measure of six inches, the total correction of the base line is very small. It is to be regretted that these comparisons were not made oftener in the measurement of the base at Lough Foyle as it is probable that from the neglect of this in the first part of the measurement in 1827, àIl error of an inch as a maximum might result in the estimate of the length. The compen- sation microscope is a delicate apparatus and even uncareful handling will cause motion in 22.2 PRINCIPAL TRIANGULATION. the wires; hence: the necessity for frequent comparison with the dots of the six-inch scale. In correcting the length of the brass scale in the following table of microscope equi- valents the expansion for one degree of Fahrenheit has been taken at . oooooo?. MICRoscope EquivaLENTS. Sets. M O P Q R S From | To. Value. No. Value. No. Value. No. Value. No. Value, No. Value. No. Value No. | - I II |+o'53 || 4 |+o 27 7' 5 tºmº tºº. tºº tº ſº *m-. – — |- I 3 '53 5 * 5 12 || 38 -o-o: | 16 |+o'98 || 13.5 + º-º-º: sº tº-ºº: — 1 +o 26 4'5 — — — o' 27 17 39 || 88 |+2 - 19 || 48 |+2-71 24' 5 3.8o 22 -7°79 || 7 |-o'27 30°5 |—o’80 || 6 ||— o' Io 45 89 172 |–2 20 | 84 |+2 77 | 82 – 3 '86 42 +7°53' | 84 ||—o. 54 || 83 — I '85 77 |+ o'44 5o 173 297 –5-22 || 35 |+o:67 35 – 3-89 17°5 |+2.73 || 35 —o'97 35 —2:40 35 + 1.26 17' 5 208 240 ||—3 of 33 + 1 36 || 33 tºº-- — |-F2’95 || 33 — I Io 33 –o’83 || 33 — * 208 216 tº ºmit º — — 3 '48 4' 5 * º * tºmºmº sº * ºl tºº-ºº: tº-º-º: 2 I7 | – || — — iſºmº — – 9°473 o' 5 *…* Hºmºmº * = } * tº *º tºº tºº 218 24o * | *mº tºm — +28' 82 II 5 tºº dºº- * - hºmºsº | * *mº e- 208 231 || – || – tº mº º tº º gºmº iſºmº Hºmº — — — — |+ I 54 I2 232 | – || – || – || – || – * tºmº * º - – - — — 3 I I44 o' 5 233 24o || – || – tºº * *ºmº jº wº sº — — - — – o '92 || 4. 241 259 ||—3.73 || 19 |+2 - 18 19 |+ 3' 61 9.5 +3° 12 || 19 - 1 '42 | 19 -o- 18 19 — 1 - 21 9' 5 26o 268 ||—I '82 | 9 |+2' 52 | 9 |+ i. 65 6-5 –2°43 || 7 |+9° 9 |+o’95 || 9 |+ o' 5o || 4-5 269 313 ||—3' 16 45 + 1 .49 45 — o'29 45 |–8°oI 22°5 - 49 45 -o'64 45 + o'72 22.5 | 314 360 ||—3°29 || 48 + 1 '96 || 48 – 1: 16 || 45 +6'74; 24, -1 54 40 + I too 37 – o'43 24 36; 408 ||—3:47 49 |+1-31 || 49 – 1.93 || 45 |+7° 18' 24°5 -2.98 || 4 |+2'74 41 – 2:04 24' 5 409 || 456 |-3:61 48 |+o.43 || 48 – or 63 || 48 |+6'75 24, -1.95 45 +2 '75 40 — or 99 24 A5% 463 –3. 12 || 37 -o-; 37 – o'3% 37 |+6.6% 8°5 -2.36 37 |+2' iz 37 – 1:57 | 18.5 434 #74 ||—2' 12 | 73 –o.7% #4 + o-26 82 |+6.9% | 4 |-2: 14 82 |+2'oZ 82 – o'3? 41 #75 | 621 ||—2'95 || 3 |-1.61 || 48 |+ 1.41 47 |+5'98 | *4 - '79 || 45 |+2'22 || 45 |+ 1.73 24 6% 638 –4.66 || 7 ||—o.70 || 7 |+ 1 ió | 7 |+5'66 || 8 |-2°02 || 16 |+2.06 || 3 |- 1.6% 3.5 3 $ * The microscopes P. R. not injurcd. • The result of some accidental disturbance of the wire plate screws subsequent to June 18th. fell from their feet to their sides when the box was being removed down the hill, but were down the lid of its box. 4 Applics to set 232 only. Microscope S was disturbed between 231 and 232; after 232 and before 233 it was compared. This value applies to set 217 only. Between sets 216 and 217 microscope O was deranged by the wind blowing A change took place in P between the evening of the 18th and morning of the 19th of August. *- 9:02:06 Micrometer divisions = one inch. (19.) The following Table contains an abstract of the number of bars and microscopes, used in the measurement of the line, MEASUREMENT OF, BASE LINES. 223. * * IBARs. MICROSCOPES. I)ATE. SETs. - - - - - --dº - * - - -ºr - - - a- + º-, * ** * - w - - - ** A. IB | C ID E G. M N O P : Q R S May 23 to 24 I to 4 4. 4 | – || – || – || – 2. 4. *º tºmº ºmmº tº- 2 37 24 5 I I | – || - I - I - I o' 5 ºmº- -º- * -º-º: o' 5 23 25 6 and 7 2 | – | – || – | — - || – I º-ſº tº- ºmmunº - I 33 53. 8 I | . . I *-*. I am- tº- + º-º-º-º: I o' 5 º º tºº tº- o' 5 2, . 26 9 to 20 12 || – | – | – || – | – || – || 6 ſºmº tº- *º- tº-º 6 ºx 3o 2 I to 24 4 || | 4 || – || – || - || – 4. 2. ºmmºn tºm- tºmº ºmmº 2 23 23_ 25 I * *º - º tº- ºmº o' 5 -º-º: tº- - tºmº * --> o “5 33 31 26 to 2 4 || 4 || - || – || – || – 4. 2 4-mºm- *m- .* tº- 2 June I 3o to 37 8 8 8 — — — 8 4. -º- tº- 4. --- 8. 22 2 || 38 I - 1 - 1 - H - I - I — o' 5 *m-. ºmmº- O 5 — — j} . 4 || 39 to 49 II | I I I I I | – || - || – || II 5 * 5 ºmº * - 5 °5 — I I 3, 6 | 5o I | - I | – | – || – I o' 5 ºmmº tº- o' 5 — ſº º . . ~, r. -7° 51 to 53 3 } ... 3 3 - || – | —-- 3 - I*5 tº . — -- I 5 || – || 3: . 33 3? 54. I I I I 1 - || – I o' 5 I tº- o° 5 — I 33 8 55 I l — I — 1 - 1 — I o' 5 º *mºnº o “5 — * 33 3? 56 I I I I | - — I | o' 5 I ºmmº o' 5 -*- I 33 9 57 I I I l - 1 - 1 — I o' 5 E- tºº o' 5 — I 33 33 58 to 61 4 4. 4. 4. *Exº - 4. 2 . 4. -. 2 . tº-yº 4. 33 35 62 I -º- º-ºº: - ºmº tº- º o' 5 ºmºmº tºmº o' 5 --> ºmmº 33 II | 63 to 66 || 4 || 4 || 4 || 4 || – || – || 4 || 2 || || 4 – 2 — 4. 73 I2 67 I I I | - I - I - I o' 5 tºº tº- o' 5 — I 33 33 68 to 69 2 2. 2. 2 || - || – 2 I 2. sºmº I *º- 2. 33 •y 7o I | – I | – || - I – I o' 5 ºmmº ~ o “5 — ºmº 33 33 71 I I | I | – | – || – I o' 5 tº-ºxº — o' 5 || – I 33 I3 72 to 75 4. 4. 4. 4 || – || – 4. 2 4. º 2. *y 4. 32 14 || 76 to 79 || 4 || 4 || 4 || 4 || – | – || 4 || 2 2. º 4. - || 4. 33 33 8o I I I . I I ºm- I o' 5 o' 5 I I =º- I 3} I5 8I I I I I - || - I o' 5 o' 5 t- I *m- I 23 33 82 to 92 IO IO IO IO IO IO IO 5 5 Io Io IO IO 33 2 I 93 to IOA. I2 I2 I2 12 I2 12 || 12 || 12 6 I2 . "I 2 6 ſ : Iz 33 25 IoS I I I | – || - I I I o' 5 I ſº- tº-º- o' 5 August 16 || 106 to 264 || 159 159 || 159 I59 I59 I59 || 159 I59 79° 5 || I59 I59 I59 || 79° 5 33 22 265 to 344 || 8o 8o 8o 86 80 80 8o 8o 8o 4o 8o 8o 4o ?? , 345 and 346| 2 2 2 2 || -- 2 2 2 2 ... I 2 - I 3? 24 347 I I - || – || - I I I º o' 5 mºmº *m- o' 5 33 * | 348 and 349| 2 || 2 || 2 | – || – 2 2 2 2 I ºmº. º- I 3? 39 35o I I - -] — I - I I I . ſº o' 5 tºmº ºmº o' 5 33 }} 35 I I I I | – || - I I I I o' 5 *º- -º-º: o' 5 33 * | 352 and 353 2 2 || 2 | 2 2 2 2 2 2. I 2 2 I 33 25 354 I I I I | - I I I I o' 5 I º- o' 5 3} 33 355 I I I | – || – 1 || || 1 || | 1 I . :o 5 - — ; o' 5 33 33 356 I I | – || – || – I I I sº o' 5 º --- o' 5 33 33 357 I . I I | – || – . I | \, I . I I o' 5 º - o' 5 3} » 358 to 383 || 27 | 27 | 27 27 27 27 | 27 27 27 I3°5 27 27 I 3 '5 39 33 #. 3. 3 || 3 || 3 || – || – || 3 || 3 || 3 3 1.5 ...— . . — I'5 33 3 O 4. 4. * * -º- mºs 4. tº-sº 2 º * 2 |- September 1 390 to : | . I6 I6 | . I6.: I6 | 16 ſé I6 ić I6 |.. 8 I6 I6 8 39 33 406 - I | . I | I - || – I I I I o' 5 sºmº - o “5 33 » 407 and 408 || | 2 || 2 | 2 2 2 2 2 2 2 I 2 2 I }} 4. * • I | I*} : I H — — I I , I I ::, o' 5 &mmº ºm- : 33 }} IO to 4. I4. 5 2 * 5 5 5 º |...] ; ; ;| | | | | | | | | #| + | = }; 33 33 o 418 || †-º: I 5 3 | - » 2, 419 #| | | | | | | | | | | | | | | | ...; | | | }.} 224. PRINCIPAL TRIANGULATION. Abstract of the Bars and Microscopes in the Base Line Measurement on Salisbury Plain–continued. BARS. MICRoscopes. DATE. SETS. - September 4 |420 and 421 2 2 2 2 || -- 2 2 2. 2. I 2 tº-mº I 3 y o: 422 6 I I I | – || - d d I I o' 5 tº | = nº o' 5 5 to Oct. 5| 423 to 565 | 1.44 || I44. 144 I44 144 I I I44 I44. 72 I I 2. Oétoic 6’ 36é to 391 || 26 || | | | 36 26 26 26 || – || 26 26 I3 # # ſ: JJ Io 592 to 666 16 16 | 16 | 16 | 16 || 16 || 16 || 16 I6 8 I6 I6 8 9) y? 607 I I I | – | – | I I I I o'5 | – || – || o' 5 Jy Jy 608 I I | – || – | – | I I I tºms o°5 — — o° 5 yy J} 609 I I I | – || – I I I I o' 5 - — o' 5 Oct. 12 to 16 || 610 to 635 | 26 26 26 26 26 26 || 26 26 26 I3 26 26 13 }} I6 636 I I I | – || -- I I I I o' 5 º-ºº: º o' 5 3) 33 637 I I I I I I I I I o' 5 I I o' 5 J D 33 638 I I I I ºmº I I I I o' 5 I tº immº o' 5 641 595 602 || 558 528 569 596 || 597.5 48o 372 565 521 352-5 Summation of the Measurement. Between May 23d and August 2d we have, putting S for a complete set 176 S + 82 A + 62 B + 51 C + 22 D + E + G. Where the values of the bars are A = O, + 6-40 d. B = O, + 64.35 d. C = O, -H. 66.65 d. D = O, + 16-30 d. E = O, + 54'50 d. G = O, + 4’35 d. Between August 1oth and September 18th 209 S + 27 A + 27 B + 20 C + 8 D + 27 G. Where the values of the bars are A = O, + 5°oo d. B = O, + 71.85 d. C = O, + 69.55 d. D = O, + 19.20 d. E = O, + 57.15 d. G = O. — o-60 d. Between September 21st and October 18th 116 S + 31 A + 5 B + 30 C + 27 D + 26 E + 31 G. Where the values of the bars are A = O. — 1.55 d. B = O, + 78.ood. C = O, + 67.85 d. D = O, + 18.3o d. E = O, + 56.90 d. G = O, - o'45 d. So that the whole distance measured by the bars is equal to 3484 O, + 123956 d. MEASUREMENT OF BASE LINES. 225 And the value of one division of the micrometer is Hº of an inch, so that the above distance is equal to 34840-8579 feet of O. The summation of the distance measured by the microscopes is 3484 (6-inch Standard) + IoI d. The micrometer divisions are equal mºrs of an inch; so that the above is equal to 1742-ooog feet of 6-inch Standard, which, converted into feet of the standard O, by the factor .99995550, given at page IoI of the “Measurement of the Lough Foyle Base,” is I74I-9234 feet of O. The whole measured distance is therefore 36582 .7813 feet. From this must be deducted 4-2938 feet measured back to the extremity of the base from the point carrier at the extremity of the 3484th bar. This measure was carefully made with a beam compass. Reduction to Mean Level of the Sea. (2I.) If h, be the height of any bar above the mean level of the sea, the correction to it is—Io. 5 #: so that the whole reduction to the mean level of the sea is X (hn – Io.5 % ) feet. * The quantity > (h,) is obtained from the levelled heights and the recorded differences of heights of the different sets of bars; it is equal to 1254220.38 feet. The logarithm of the radius of curvature for the mean latitude (51°. 8. 21") and mean bearing (28° 29' 16") of the base is 7.3206329; hence, the reduction to the level of the sea is — . 6294 of a foot. The following Table contains the height above the mean level of the sea of each set of bars used in the measurement. Ff 226 . . . PRINCIPAL TRIANGULATION. ABSTRACT of THE HEIGHTS OF THE SUCCESSIVE PARTs of THE LINE ABOVE MEAN LEVEL OF THE SEA. No. of Set. IIeight. No. of Set. Height. No. of Set. No. of Set. 671 or 668° 44 666" 14 6.63" 24 66o'o6 657°oo 654°50 651 ° 97 0.49° II 645'98 643° 27 641 ° 33 639°33 636'60 634°43 632°64 630' 61 628' 55 626'91 624°52 624°92 62.4° 17 621 ° 29 618 62 616'34 614°44 61.2 ° 15 | 61 o' 34 608 13 606’ off Gos' 35 6oo' Go 597'56 59.4° 9o 592 16 589'57 586-78 584.” 18 583' 12 58o'46 578: 12 575'69 573° 26 570-86 568 or 565°33 563' os 50 o' 5o 5.57° 54 554°64 55 I ‘94 55o '73 547 ° 92 545 'o6 542 °58 530°76 536'99 534' 01 531 ° 22 528° 24 525 26 522° 26 520'38 517° 13 514°o:3 51 o’94 507' 57 504.86 501 - 28 498°o:3 495' 26 492'96 1.17 I 18 I 19 I 2C) I 2 I I 2.2 I 23 I 24 125 126 127 I 28 120 I 30 I31 I 32 I33 I34 I35 136 I37 138 I39 I4o I4 I I42 489° off 485'96 482 '82 479° 59 476° 52 473°37 470 ° 20 467 96 464'93 460° 93 458 ‘97 456°45 456'94 456'43 453'29 453°82 454".30 45.4° 18 453° 55 || 432° 3 I 453° 7'o', 453' 6o 452 °35 451 “43 45o'77 45o" o!) 449' 62 449' 39 448' 76 447°63 449'86 45 I '83 455 ° 23 457 Io 457'79 458° 57 459'82 459' 49 46o'o6 460°44 46o'oſ) 460° 25 459 ° 4o 458'85 458°84 458°39 458° 51 459 °48 461 ° 24 462 “72 463°45 464° 37 464 9o 465°28 465° 5'I 465 65 465°45 465° 21 464'87 464°48 463 7o 462 ° 93 461 ° or 459 °54 459'81 455 ° 91 454 * 19 452 °53 45o'86 449' I 7 446' 68 444"92 146 I47 I48 149 I 5o I5 I I52 I53 I54 I 55 I56 I 57 158 I59 16o 161 102 163 218 219 22O 22 I 222 223 224. 225 226 227 228 229 23o 231 232 233 234 235 236 237 238 239 24o 24. I 242 243 244 245 246 247 248 249 25o 25 I 252 253 254 255 250 257 258 259 26o 261 262 263 264 265 266 267 268 269 27,o 271 27 273 274 275 276 277 278 279 28o 28 I 282 Height. Height. No. of Set. No. of Set. No. of Set. Height. 329 33o 334 335 336 337 338 339 34o 34 I 342 343 344 345 346 347 348 349 35o 35 I 352 353 354. 355 356 357 358 358a. 359 so 37o'8o 369° 96 369° 97 370° 23 37 I* 53 372' 62 37.4° oz 375 ° 99 376'83 376-71 376'72 376' 57 37.6’ 63 376° 56 374° 72 374° of 3.73° 18 371 ° 99 369: 76 368 oz 367° 13 360° 19 365' 30 364°oo 363'29 362.66 362° 35 361 ° 46 361' 16 360° 26 360° os 359° 44 358-81 357 ° 95 357' 68 356'85 356° 14 355’ 63 355° 59 355 ° o!) 354" 24 353° 35 352 ° 49 35 I "55 35o "99 350° Io 348° 55 347°61 346’ 67 344°89 343" I I 341 ° 52 339° 53 337' 62 335°oo 331 66 3.28° 12 324' 62 321 °38 317° 99 314' 56 3 II* 24 3oſ)” 2d 31 o'oſ) 313° 37 3.16-78 320°o.4 323:38 326°55 329' 17 33o" 73 331 ° 94 332 °86 333°86 333' 68 333°7 I 333°69 332 °83 332° 58 332°56 331 '66 33o'8o 329°94 329°38 328' 81 3.28° 27 327° 73 326°os 325 °43 324'89 323" 25 321 * 71 320°86 3.18° 49 316' 36 313° 22 309° 98 300 °59 303° 26 3oo'o6 296-77 293 78 29 o'44 287 °55 287 og 287 ° 42 288°68 289°57 290° 46 290° 95 290'85 290°31 288-63 286-71 284. 18 28.1° 57 278-72 28o'o'; 282°48 285'96 288-8 I 29I '94 295" I5 298. 11 3ol. * 58 3o4" 69 3o'7' 65 31 I ‘oſ, 313°78 316" 79 31.9°47 322'48 325 4 I 3.28° 61 331 ° 91 335 ° 27 337 ° 99 34O' 23 342 °4 I 345°42 3.47° oz 3.48° 23 348-81 3.49° 53 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 45 I 452 453 454 45.5 456 457 458 459: 460 461 462 463 464 465 466 467 468 469 47o 47 I 472 473 474 475 476 477 478 479 48o 481 482 483 484; l 485 486 487 488 489 490 | 491 492 493 494 495 496 497 498 499 5oo 5o I 502 503 504 505 506 5o'7 5o8 500 5 Io 5 II 533 534 534 535 536 537 538 539 55o 55 I 552 553 554 * * * 5 5.5 559 572 Height. I 43 I44 I45 164 165 166 167 168 169 17o 171 172 I73 I 74 I 75 176 177 178 I 79 18o 181 182 183 184 185 186 187 I88 189 190 I9 I 192 I93 I94 I95 196 197 198 199 2CO 2O I 2O2 2O3 2O4. 205 206 207 208 209 2 IO 2 II 2 I 2 2 I3 2I4 2 I 5 442 '89 440' 67 438-89 437 °oo 435' 13 433°68 432° o'7 43o" 28 428'95 427°39 425'96 423° 50 42 I*32 419' 14 417° 7'o 416'40 413 '89 412° 30 41 o' 72 . 409° 33 408-71. 407 o8 405" of 403°54 402 "'74 401 7o 4oo '83 398-25 396'47 393'5o 393 ° 97 393 "o.4 391 °42 380° 72 388-82 387 ° 93 387' 25 385-78 384-32 382 '71 382 23 380° 72. 379 'o6 378 Io 376'82 376°37 376- 17 376°34 375 ° 79 376 of 377 ° 25 378.62 379°39 38o II 38o' 74 381 - 10 381 ° 45 381 - 76 382 - 1 I 382 - 29 382 - 54 382 '86 382 - 38 381 - 8o 382 °oo 381 - 32 38o. 62 38o" 31 38o 18 38o'o6 216 38o' 13 * 380° 11 283 284 285 286 287 288 289 Height. 380° 47 38o' 95 381 °52 382 o8 383 - 66 38.4° 12 38.4°42 385 '54 386' 16 386°33 386.86 386' 94 387: o3 387' 24 387' 28 386-91 386'83 387' 26 387:66 388° 35 389 of 38.9°o.4 38.9° 56 390 - 61 391 64 392 ol 392 - 67 393-64 394" 74 395'8o 396'83 397° 75 398.62 399 °32 399°89 4oo" 32 4oo Go 4oo' 71 || 4oo" 33 4oo' of 4o3 °o:3 4oz 63 4oz " I 7 4o I '92 4o I "55 399 ° 93 398-09 397 ° 25 396-87 395' 60 393°52 392 ° 22 390 °51 388° 53 387' 64 387' 66 386°35 385'84 385 68. 385*49 384-40 383 57 382 - 80 382 °47 381 ° 23 38o '82 379° 23 378°77 376'98 375 ° 45 37.4° 55 372°84 No. of Sct. IIeight. Height. | 361 362 363 364 365 366 367 368 369 37o 37 I 372 373 374 375 376 377 378 379 38o 381 382 383 384 386 387 388 389 390 391 392 393 395 396 397 398 399 4OO 4OI 4O2 403 4O4 405 406 407 4o8 400 41 O 4 II 4I 2 4 I.3 414 4 IS 416 4.17 4.18 419 42O 42 I 422 423 424 4.25 426 427 .428 429 43O 431 385 3850. 349°94 35o' Go 35o' 47 35o° 42 35o 18 35o'o6 349'87 349° 18 347°64 346’ Io 345 ° 27 343°7 I 342°81 340° 47 338°94 337° 3I 335-76 333' 67 331 °36 320° 21 3.28° 27 327° 38 327' 69 327-98 3.28° 76 33o°37 33o° 9o 331 ° 25 33 I "3o 33o'46 3.29' 61 328-76 3.28° 25 327°39 327°30 326'86 325°84 324'89 325 °54 325'90 326°51 327-78 329°71 33 I "OS 33 I '95 333 ° 4 I 335° 16 336' 62 339°35 342' 3 I 3.43° 52 344° 23 345-46 346-78 3.47° 35 347 ° 23 347°83 348' 29 3.47° 7'o 346" 72 344' 61 344° 26 343" O.4 34I 24 339°88 338° 21 335 °47 332 °83 330°34 327°5 I 3.25° 40 3.24° 45 $74 323°52 32.2° 55 321° 49 320'99 320” os 319" Io 3.18° 30 317° 96 317° 52 317. 67 317° 16 316' 63 316' 17 3.15° 28 3I4°32 312" 42 312 °36 311'88 3 Io' 99 3.09° 31 308°37 307 ° 44 305'99 3O4° 40 303' 69 3oz 65 3oo' go 299-89 297: 71 295' 67 203 78 292 ° 24 290°36 288 - 12 286 52 284° 41 282 - 17 28o' 59 279' 64 277-77 275-81 27.4° 74 272 °47 27o°54 268.78 266: 29 203'85 26.3' oſ, 26.2 °82 262°35 263 21 26.3' 17 262 - 64 261 ° 90 261' 14 26o 36 258-67 256' 95 255 ° 25 254° 26 252°38 25I 55 249°45 2.47 '83 246' 17 244° 23 242 "3o 241 ° 29 239°75 238-21 236'43 23.4° 43 575 576 577 578 579 58o 581 582 583 584 585 586 587 605a 606 61.2 613 Mean Height = 360°oo feet. * . i-- MEASUREMENT OF BASE LINES. 227 The final length of the line stands therefore thus: SALISBURY PLAIN BASE. 1849. Measured with Compensation Bars . . . . . Measured with Compensation Microscopes . Measured back with Beam Compass . . . . . . — Reduction to Level of Sea . . . . . . . . . — 3484o-8579 Length of Base Line in feet of O. . . Log = 4.56321827.08 36577.8581 Ff 2 S E C T I O N VI. PIR IN C II? L E S 0 F C A L O U L A TI O N. In a triangulation in which the distances are short and the triangles very small, the necessary calculations can be made with very little labour, as the terms of the formulae employed depending on the higher powers of the distances become insensible; but when, as in the triangulation of Great Britain and Ireland, the distances are long, often approaching to and sometimes exceeding Ioo miles, it becomes necessary to examine into the sufficiency of the formulae employed, and to make sure that the small terms neglected cannot lead to any final defect. The present section contains an exposition of those principles upon which all the methods of calculation are based. * § I. 1. Let a and b be the semi-axes of the spheroid, so that the equation of the meri- dian is, – " . " — , = . w = i, 4 #, - 1 = 0, z and y being the distances of any point in the meridian from the polar axis and from the plane of the equator; then, if x be the latitude of the point 4 y, dw (dw' ... dw’\} du — ſaw” , dw’N } * = | * rººm. COS X * = ºn- * tº. da: da:' ' dy” OS dy da: ' dy” Sln A # = (; ; ;) % = (+, + )'s a’ º ( a 4 + U. # COS A b? aft -- 54 SIIl 2, Multiply these last equations by a and b, and by r and y, and add: ſº a;2 2 * † i. a” cos” x + b% sin.” A = a; + #. = (a, cos x + y sin A)” and by substitution in the preceding, a” cos A b” sin A QC -: I–– - (a” cos’ A + b sin” X) 3/ (a” cos” x + b sin” x) or, if we make use of the excentricity, and put I – e'sin' x = A', then the values of a; and 3/ are, -- * -º – 0. * 3C = - COS X. y = < (1 – e’) sin a (1) % If a be the radius of curvature of the meridian at the same point, then g d2 = d s, s being the length of the meridian curve, and we have ; -i PRINCIPLES OF CALCULATION. 229 # = – in a # = co, a multiplying these equations by – y and v, and adding *ā; T J J ** JR [. ECOS XT) ºn XT * T (ºcos; ATVsin;Tx); dy da: , & #) But expressing the ratio of a to y, we find d // l,” -— f *- 1 - - * 2. dź. %) a” SGC g = a” b” , = * (I — e”) (2) (a” cos’ x + b sin” x)* Ağ The logarithm of A, which is a quantity of frequent occurrence, may be obtained as follows: if we put _ a - b - 77 = a + b then it follows that - (I + n) A = (1 + n’ + 2 m cos 2 x)} (3) = (1 + n = ***)} (1 + ne-ºv-jº log (1 + n) A = M {n ( * v- + s-ºxy-5) * === (ev- + s–4 ºv-7) + . . ..} log A = — log (I + n) + M (acos 2 x -ºcos 4 x+...) . (4) the term of this series in nº can only affect the tenth figure of the logarithm, and is con- sequently not required. The portion of the normal to the curve at the point a y, intercepted between that point and the minor axis, is evidently equal to a sec x, so that if we call this quantity N, N = *. A 2. If the ordinate of the point v y be produced to meet a circle described upon the major axis of the ellipse as diameter, and a straight line be drawn joining this point of intersection, with the centre of the ellipse, the inclination of this line to the major axis is called the reduced latitude; and if we designate it by u, the following relations exist between u and A – (5) cos A = A cos u (1 – e’)* sin x = :} A,A = (1-e')* Where A, is the same function of u that A is of x. 23O PRINCIPAL TRIANGULATION. § II. On the mutual relation of two points on the surface of a spheroid. 3. Let x, a be the reciprocal azimuths” of two points PQ on a spheroid, k the chord line joining them, or their rectilinear distance; M. P., the angles made by the chord with the normals of P Q, so that go” – p., 90° – pſ, are the mutual depressions of these points, x, x', w, their latitudes and difference of longitude, and 2 - — I = o 52 the equation of the surface: then if the plane of v z be made to pass through P, the co-ordinates of P and Q will be = + (I–e”) sin A & 3 = ~ COSA 7/ - O 2. A 9 = a’ ={cos X' cos w 3)' = ... cos x' sin w z' = . (I–e”) sin X' : % Let now fgh be the direction-cosines of the normal to that plane which contains the line of the vertical at P and passes through Q, and whose inclination to the meridian of P is a ; let also l mºn, 1 m n', be the direction-cosines of the normal at P, and of the tangent to the surface at P, which is contained in the plane passing through Q: then since the first line (fgh) is perpendicular to each of the other two, and to the chord line k whose direction- cosines are proportional to a -a, y' – y, z – 2, we have these three equations:— f(+/–2) + gy + h (2'-2) = o fl + gm + hn = o fl' + gm' + hn' = o Now if we eliminate fgh from these equations and substitute the following values, ! = cos A 771 E O n = sin A l' = — sin A cos & m' = sin & n' = cos & cos A there will result The substitution of the values of a z, v 3)' 2", in this equation will give immediately the value of cot & ; and if we put & 3", for the corresponding azimuths on a sphere, or on the supposition e = or the following equations will exist: * In the figure pago (236) let PM, QN, be the normals to the surface at the points P, Q, meeting the axis of revolution OC in M, N. Join PQ ; draw MH, NK parallel respectively to QN, PM, and join PH, QK. Then a, the azimuth of Q at P, is the inclination of the planes PMQ, PMO, and 2', the azimuth of P at Q, is the inclination of the planes QNR, QNO. The inclination of the planes PMH, PMO, is the azimuth g in equation (6); the inclination of the planes QNH, QNO, is equal to gº in the same set of equations. The angle QPM = p, PMN = p.'. y . ; yº | * | PRINCIPLES OF CALCULATION. 231 ** # * , a cos x Q COt cº — COt & = e” Q § cos x' A / cot &’ — cot º' = — e” COS X. Q. r (6) * - cº - sº k = -s. .” r - r cos A A' | . A' sin A — A sin x' = sin w Q 4. These azimuths” may also be obtained in the following manner: from Q let fall a Perpendicular upon the meridian plane of P, and from P let fall a perpendicular upon the meridian plane of Q; then the following equations will become evident:— º º Q. º k sin pº sin c. = z cos X' sin w :-- ... -:... ..., 4 - (7) k sin º' sin & = + cos x sin a A Now in any surface, w = o, we have k’ = (a' — wy” + (y’ — y)* + (2' – 2)” , - A du – A * ... (- - - * - COS _º *); + (y w);+(s 2); M = # (; +; +%)' da,” dy” dz” * f ._/ du ,-,\dº ’ — du cos w = (a. a.) dº' + (y w); +- (z z) dz’ Spſ - k (# -- du” +4. # 㺠' d', ' ..." * •24'---~ : aca' 22' In the present instance therefore, if we put I — # –% = U, * — a 2/z' — z\” # = 2 U – e’(*#) cos p = # A U k cos p' = #A' U * From the convexity of the earth, the supposition of two points on the surface being mutually visible is imaginary. If, instead of Q, a point S vertically above it, at the height h, be observed at P, then the influence of this upon the observed azimuth may be thus ascertained:—Join S with M, the foot of the normal at P (see figure, page 236). This line, being sensibly parallel to QM, will intersect the meridian of Q at the distance h x sin MQN from Q; but if s, a, be the length and azimuth of the line, 2, the mean latitude, sin MQN = e2 ; cos a cosº X. The influence of this small meridian distance on the azimuth at P is equal Å X sin MQN × sin a -i-s, or == e2 # sin 22 cos” x. This quantity is very small; in the latitude of Great Britain its maximum amount is about an eightieth of a second for every thousand feet of height. 232 PRINCIPAL TRIANGULATION. By putting v" for the third side of a spherical triangle, of which two sides are 90° — w, 90° — uſ, and the included angle o, and using a subsidiary angle q, such that y 1. – ºf 7t' cost f : 2 2. iº • ?) * . Sin q. Sin - = e Sin 2. we obtain from the preceding three equations and (7) the following set, • QX ^ k = 2 a sin cos t r) ... ?) cos w = A sin; see 4 8 cos p' = A' sin º sec q> (8) sº iº º Q. * Sin pº Sin & = 7. cos uſ sin w t * -- ... / ---- --/ (Z i. Sin pº sun & = + COS it Sin w /. 2 These equations determine the distance, mutual depressions and azimuths of any two points on the surface of a spheroid.i. 5. Hitherto we have considered only the chord or rectilinear distance of P and Q, we proceed now to obtain the distance as measured along either of the curves formed by the intersection of the vertical planes at P and Q with the surface. If we take the curve formed by the plane vertical at P, and measure w along the tangent to the curve at P, and y parallel to the vertical line at P, then the equation of the curve is 6? 2 * ; : 2 e I — e” , sin a cos x cos 2 + y” (1 + I – 6 I – c’ cos’ A cos" c.) – 2 ay a" (1 + º tº gº -" * . * * * By substituting the values of a, a , 2, 2’, in terms of it and u' in the value of U, U = I - cost cos w'cos & — sin it sin tº tººk . - I = I - COS v = 2 Sin2 – v. . 2 * t The direct distance between two points on a spheroid whose latitudes and difference of longitude are x, x', w, is most readily calculated by the following formula :—Put tº & Q* = cos x cos X'sina 2 I — e” X'—X tan d = − sin p Q A*o 2. then k 2 Q #=(xãº"? which is very convenient for calculation when tables of log A are at hand, and is true to 9 places of decimals for a distance of more than 2°. As is the value of A corresponding to the mean latitude of the two stations. | - i r PRINCIPLES OF CALCULATION. 233 From this equation we may deduce the value of the radius of curvature of the vertical section at the point P, for it is the limit of the ratio if R be this radius, 4;" +, as a and y become zero; therefore 23/ I — A e? # = (1 + H, cos” a cos’ x) (9) which gives the curvature of the surface for any latitude and azimuth. We may write the equation of the curve in the form r +fsin' 6. r + 1, sin 26 r–g sin 6 = o and then assuming = 2 r + 3 r + y^3 + . . we shall have, by forming the values of sin 0, sin 2 %, sin' 3, and substituting them in the equation of the curve, I 2 h a = . ; = + 9 9 I + 6 f-- 24 hº 6 gº 'y = * d 6. 2 ſº 4 Also, since ds' = dr" + r" d 6°, we have #. = 1 + # (#) — , (#) * (19 M* d6 * = r + ſ^(; (Fº)-;(º)) r:# = < r + 2 3 r + 3 + r + . . . . Substituting this last equation in the preceding, we obtain s in terms of a 3 y . . . ; and finally, by substituting for a 3 y their values given above, 7-3 3 rº 3f r\ r" s = r + º-, + +, + (h + 424 -) : 6.9° 4o gº (h {}); J:3 3 k? 62 A3 º 2.É. * 3: R. Ta E. cos a sin 2 x + . . . . . (10) s = k + in which last equation k is the chord PQ, and s the length of the elliptical arc. Similarly, if s be the length of the elliptic curve formed by the plane which is vertical at Q and passes through P, x' the latitude of Q, and 180° – c' the azimuth of Pat Q, }:3 3 #3 e” hº ' = k + –tº– *sºmºmº *-* ºms * * * * : R* * : R* * ##, COS 2' sin 2x'+ tº Q & º - (11) these curves may be taken as equal in length, differing only from the shortest line by a quantity quite imperceptible for arcs of only a small number of degrees in length. - G. g - - * 234 PRINCIPAL TRIANGULATION: 6. The term in e' k in either of these series is very small, it may amount to 2 feet in 500 miles: we may therefore reject both the terms in 6', and consider the remainder of the expression in either equation as the true length of the curve. The term in e' K' will, however, disappear by adding the two equations, and if R, be the radius of curvature of the surface for the mean latitude x = } (x + x'), and the mean azimuth a = \, (2 + 2), the length of the curve will be - - Å2 + 3” (I +”) + s = k + 24 F.” 64o lè; º C. C. (I.2) Where n is a function of 2 and A. As in every case of actual calculation, we may put m = o, it follows that - log(;)=#(#) { *#(#)} (13) M – log; = 2,2575731 7. We shall illustrate these formulae in the calculation of an exact spheroidal triangle which may be useful in the examination of approximate methods of calculation :-Let it be required to find the relative distances, azimuths, and depressions of three points A B C, given by their astronomical positions as follows:— A, - 52° o' w, - o° o' Aa - 52° 3o' to2 = 3° I5' As = 53° 30' w; - 4° 30' Let the chords AB = k, B C = k, C A =k, the corresponding curve distances being c, a, b. Let the azimuth of AB = y, of B A = ?', of B C = a, of C B = a, of C A = 3, of A C = 8. Let also the complements of the depressions (P), reckoned in the same order as the azimuths, be º Pº, P., Pº', P, Pº’s. - - * Let the semi-axes of the surface be 20923713 and 2085.381o feet; then we have log a = 7.3206387544; - log b = 7-3191854.123; log e = 8.9120804964 log A, - 9.9999986767; log A. = 9.999986.3878; log As = 9.9996619836. If u, u, u, be the reduced latitudes, then, since a tan x = b tan u, we find, u; = 51°54' 34"-9900 * = 52°24'26",4893 u, - 53°24'29".7927 and if v, be the third side of a spherical triangle, of which two sides are 90°-w, and 90°– u, including the angle w, - w, ; v, v, having a similar meaning, we shall find by spherical trigonometry log sin : := 8.0387.964746 log sin # = 8.4341719716 log sin ; - 8.2537431052 The subsidiary angles & equation (8) are next found, giving * * * - log cosé, -9.9996695536 log cost, -99998769943 log cosº, -9999967682, PRINCIPLES OF CALCULATION. 235 The rectilinear distances of the three points are now derived immediately from the equation * ' . . . . g a * . . . . . . . . . 1 - . . º ty k = 2 a sin; cos ºf adding the corresponding logarithms, there results log k. - 5.660.1287778 logh, - 6.0557.1681.59 logh, - 5.8754027.338 Also from the equations cost. - A sin; see #: cos p' = A sin; see # by adding the corresponding logarithms, we find 90 – 2, - o' 37'32"-4392 : 90 - P. = 1° 33' 15",4660 - 90 – e. = 1° 1' 32".5164 90 — w;" = o' 37'32"-3136: 90 - P.' = 1° 33' 15".9389 : 9o — pa’ = 1° 1' 32"-4102 which are the reciprocal depressions: the first line gives the depressions of C at B, A at C, and B at A ; the second line the reverse depressions, namely of B at C, C at A, and A at B. - * - * Equations (8) give a cos w' . & COS 7% . sin & = −. IIl () sin ox’ = k sin p. Ł from which we have finally, counting the azimuths from north round by east and south, « = 36° 31' 19".744 8 = 24.3° 1' 21".577 y = 74° 38' 48", 125 a' = 217 31 I3 '793 3’ = 59 26 22 -812 y' = 257 13 o 21 I If R, R, R. be the radii of curvature for the mean latitude and mean azimuth of each line, - . . . - log R, = 7.3208918 log R, = 7.32130II log R, - 7.3214816 whence by means of equation (13) we get log} = •ooooo36311 log}= •oooo 532748 log = •ooooz31964 C h, and thence log a = 5.660.1374089 log b = 6.05577.00907 log c = 5.8754027.338 The angles and sides of the spheroidal triangle are, therefore, A = 13 13 2334 a = 457232.83 feet. B = 139 18 19.533 b = II37025-2O >, C = 25 30 7,784 c = 750589-93. , Dalby's Theorem. 8. By a series of reductions from the equations (6), the following result may be obtained:— r * + 2 = ′ + k +: a 6'-xycoºxinx • (4) 236 PRINCIPAL TRLANGULATION. A short computation will show that the small quantity on the right-hand side of this equation can never amount to even the ten-thousandth part of a second, which is, prac- tically speaking, zero; consequently the sum of the spheroidal is equal to the sum of the spherical azimuths, whence we obtain the following important theorem:—If x x' be the latitudes of two points on the surface of a spheroid, a their difference of longitude, 2 o' their reciprocal azimuths, Aſ — A cos — / Cº) 2. &’ + cz f dº # tall 2 fººms —H. COt 2 (15) SIII r) * 9. From the inaccuracies of the results obtained from the use of this equation in the determination of the difference of longitude of Beachy Head and Dunnose, in the first volume of the “Account of the Trigonometrical Survey,” and the imperfection of the demonstration there given, doubts have been thrown upon the truth of this equation, and therefore the following proof is here given : Let PQ be the two points, their verticals intersecting the O axis of revolution OC in M, N, Draw MH, NK parallel to QN, PM respectively, and join QM., PN, QP, HP, QK: II. then the spheroidal azimuths are QPMO and PQNO ; the Q. Ö former exceeds the corresponding spherical azimuth HPMO & by the angle QPMH, while the latter is less than the corre- sponding spherical azimuth KQNO by the angle PQNK: therefore the sum of the spheroidal azimuths exceeds the sum IC C of the spherical azimuths by the excess of the angle QPMH NL above the angle PQNK. Let now D be the distance of the parallel planes PMH, QKN, and let U, V, be the lengths of the perpendiculars from Q upon PM and from P upon QN respectively, then, if E be the quantity in question, sin QPMH = #. sin PQNK = R ... E=D(;-&) sºmºrrºw- * This equation has been the subject of considerable discussion, and has been characterised by a high mathematical authority as the “greatest delusion that has ever prevailed in practical mathematics.” In a series of papers published in the Philosophical Magazine for July, October, and December 1828, Mr. Ivory denies the truth of the theorem, and maintains that the longitude obtained by this method should be multiplied by 1 + , e, cosº (a + X). Dr. Tiarks, in the same journal for the month of November, proves the theorem true; and in January and February of the following year Mr. Ivory corrects his own error, and proves the theorem generally true for other surfaces of revolution. : PRINCIPLES OF CALCULATION. 23# But D is less than MN which is equal to e (sin x' – sin »), taking the semi-axis of the spheroid as unity, and neglecting higher powers of e, therefore D is less than e” k, and consequently, since U = k sin p, W = k sin p!, D - e” (sin pº’ — sin p.) < :*k (2–2) because cos p = # k approximately. But since from equations (8) A' cos p = A cos p', we have A' (1 + (g' – p.) tan p.) = A * 2–1 = }} (A — A') but A — A' is clearly less than , e, k, and therefore I tº { * 3 E * : *k, which for a distance k of 150 miles is less than . oooo; of a second. § III. Theory of Spheroidal Triangles. Io. In order that a spheroidal triangle may be rigorously defined, it is necessary that the nature of the lines joining the three points forming the vertices of the triangle should be expressed. It is evident that if we take two points A, B, on a spheroid, and make one plane to contain the vertical line through A and to pass through B, and make another plane containing the vertical line through B to pass through A, these planes, being inclined to each other at a definite angle, will cut the surface in two distinct plane curves. A variety of curves, very nearly plane curves, may be drawn between the two points and contained between the two plane curves just mentioned; such, for instance, is the curve which may be theoretically imagined to be traced in measuring a base line, in which the plane which is determined at each point by the direction of measurement and the vertical at that point, passes through the extremity of the base measured to. If we designate by P and Q respectively the curves formed by the intersection with the surface of the vertical planes at A and B, then the curve line just considered will touch P at A and Q at B. If a line were traced in such a manner that at every point in it the sum of the azimuths of the fixed extremities should be exactly 180°, or, which is the same thing, that the point should be apparently in a direct line between the stations, the curve so formed, being the intersection of a hyperbolic cylinder with the spheroid, will also touch P at A and Q at B : it has also this property, that it is nearer at every point to the straight line joining A and B than any other curve, but yet is not the shortest line that can be traced on the surface. If we suppose the celestial zeniths of A and B to be joined by a great circle, and take all those points on the surface which have their zeniths in this great circle, a curve different from either of the preceding will be formed. This curve has been sometimes confounded 238 - PRINCIPAL TRIANGULATION. with the geodetic or shortest curve between A and B, it is, however, a plane curve; for since at each point in it the normal to the surface is parallel to a given plane, the tangent plane to the surface at every point must be parallel to a given line, and therefore generates a cylindrical surface whose line of contact with the spheroid lies in a plane passing through the centre of the latter. The curve does not, however, lie between P and Q. 11. But the curve which has generally been considered in reference to spheroidal triangles is the geodetic or shortest line. A distinguishing property of this curve is, that at every point the sine of the azimuth of the line is inversely proportional to the distance of that point from the axis of revolution. It lies entirely between P and Q, and, if we neglect quantities of the order e 63, 6 being the distance of A and B, makes at A an angle with P equal to the angle it makes with Q at B, each of these angles being equal to one third of the angle of intersection of P and Q. The difference of length of the geodetic line and either of the curves P, Q is *. 2 S a 8 2 2. 360 € a; COS" A Sin 2a) where 2 is the azimuth of the line, s its length, 2, the latitude, and a the semi-axis major (Bessel, Astronomische Nachrichten, No. 330). This quantity is so minute as to be quite inappreciable; therefore, as far as length is concerned, either of the plane curves P, Q may be taken as the side of the triangle. * 12. The greatest distance apart of the curves P, Q may be easily obtained thus: if x be the mean latitude of A and B, 4 the difference of latitude, the distance apart of the intersections of their normals with the minor axis is, neglecting e, - 2 ae' sin #3 cos x : let now a meridian plane be drawn bisecting the chord AB, and let the portion of this meridian intercepted by the curves P, Q be 4, then it will be evident, by considering the lines of intersection of this meridian plane with the two vertical planes at A and B, that º • I —: = 2 e” sin - 2 a vers # 6 ; : cos’, and since we may put with sufficient approximation cos & = sin , b, a being the mean Q, tºº -- azimuth of the line, 2 - a cos’ A cos & S * = 6? a s the greatest distance of the curves is a sin a, and therefore equal to * ...a S? 2 * ~ * — e” —- COS" A S11, 2& I6 a” This quantity is So small, that for a line of Ioo miles in length, inclined at 45° to the meridian in the latitude of Great Britain, it will.only amount to half an inch, whilst for a line of 50 miles it cannot surpass the sixteenth part of an inch. - PRINCIPLES OF CALCULATION. 239 13. We now proceed to find the angle subtended at the point H of intersection of the vertical line AH with the axis of revolution, by any given distance s measured from A along the curve of intersection of the plane AHB with the surface of the spheroid. Let P be the extremity of the arc s, and let the required angle AHP = 0. Let also o be the azimuth of the plane AHB, a the latitude of A, and p the angle between HP and the plane of the equator; put HA = v, HP = r, then from properties of the ellipse it may be shown that - 2. r” — v" = — I — e” ('sin 4 — v sin A)* From this equation we may obtain, neglecting quantities of the order e (3 – ?)", 2 ty 7° E J - - 2 I – c’ (sin & — sin x)” also, by spherical trigonometry, sin q = sin à cos 0 + cos A sin 6 cos & and by substitution in the preceding equation We get 7" * ;= 1 + P 6 + Q0; 4. tº a tº I cº P = — - cos a cos’ x 9. (16) 2 I — cº I e” - Q = + a cos & sin 2 A 4. I — e * which determines the nature of the curve. Now _ ſ”6 dr” \# I ſº 0 dr" •=ſ. (r' ++.) = r 0+ #J, #, + + (#) = 2 v Pa 9” + 6 v PQ 63 27 \dé •'. := 0 +; P G + 2 period 160°4. (17) and by reversing the series, 9 =#–; G + 2P); +... g (18) v 3 U --> 14. We must now find an expression for the value of a perpèndicular from the extremity of the curve s to the normal v, in terms of s and its ratio to €. the mean radius of curvature of the surface at A. We have already shown the value of the radius - 3 º .3.1: of curvature on the meridian to be a (1 – e’) AT â, and that perpendicular to the º is equal to the normal, for if an indefinitely small arc be drawn perpendicular to the 24o . PRINCIPAL TRIANGULATION. meridian the normals at its extremities will intersect on the axis of revolution; therefore if g be a mean proportional between the principal radii of curvature, , a” (I – e’) g = (1 — e” sin” x)” The perpendicular in question is equal to r sin 6 = w (1 + P 6 + Q 6. +. . . ) in (; – ..) 3 vº omitting the higher powers of eº; continuing the reduction tº S3 sº r sin 6 = s — 2-3 vº (1 – 4P) + 2-3-4-5-v" * g º º e sin: = s — S$ tº g tº ſº , + ---., - 2-3-g 2.3.4°5'g" * • S 3 / I I – 41° sº I I r sin 6 – o sin – = - (-t- — 2. - – - ) + sºn; = g; (; 2. ) + 2°3'4'5 (i. #) S * = — — cº Cos” A. COS 22 + . . . 2-3-g * . . S e” s? - r sin 6 = g an; ( i lºº zºos”. COS 2a) - (19) in which expression terms of the order e s are neglected; also, if terms of the order e” sº be neglected, as they may, g may be considered evidently as belonging to any point whose distance from A is of the order s. 3 15. Let A B C be three points on the surface of a spheroid, a b c their mutual dis- tances, which may be considered as measured in each case either along the shortest line or along one of the plane curves. Supposing all azimuths measured from north round by east, let y y’ be the azimuths of B at A, and A at B, c. 2' the azimuths of C at B, and of B at C, 9 @ the azimuths of A at C, and of C at A. - Let H K be the intersections, with the minor axis, of the normals of A and B, and let B K C = 0, A H C = 6', K C = r., H C = r", H A = v, K. B = v'; let also h be the perpendicular from C upon the plane which is vertical at A passing through B, h' the perpendicular from C upon the plane which is vertical at B passing through A; then h = r" sin 6' sin A ; h’ = r sin 9 sin B sin A r sin 6 (20) sin B T h’ r" sin Ó' * -- * From cquation (19.), if we take g for the centre of the triangle, r sin 6 = g sin # (1 _ e” gº cos “Ao cos 22) g 6g” * * - /h/ ... b 62 b” - r'sin 6' = g sin #(, ~ 6. cos ºxo coS 26) sin “ - in A / º ..". # == % —; (1 iº ; , (a” cos 22 — bºcos 2,3) cos ”.) (21) SIIl g | PRINCIPLES OF CALCULATION. 24.I. in which A, is the latitude of the centre of the triangle. If e = 0 * } ... b tº . (I sin A sin = sin B sin - g g 16. It remains now to find the ratio of the perpendiculars h h’. Taking the point A on the plane of a 2, let the equation of the vertical plane at A passing through B be a: , 3/ Tºw + **_ J 9 then if a y 2' be the co-ordinates of C, and a the latitude of A, – (; +} + i) (; +} + i). = I i. + h = * — I . I _ _- I ; : = (+, + k) cot f T ve” cos?, k T ve" sin x * g T \f. #) y a’ y’ 2’ •. h =(1– - - - - #) ºvcos x sin a siny f' g ſt A similar expression gives h’. If now we put a g’ for the spherical azimuths corresponding to Y y', we shall find, after some lengthened reductions, h sin y sin a' (1 + Qc") -: , E →-- 6. h' T sin y'sin a ſº º º f Q = (sin A' — sin A) {###! COS X. — sin a cos^ -- sin (a' - B) cºx} sin c sin A sin a sin B sin c sin B from which finally Ji e°C’ . f = 1 - 4g. sin 27 cos’Ao cot C (22) This same result may be obtained, and more readily, thus: Let a plane pass through the three points A, B, C, intersecting the surface in an ellipse of very small excentricity, and which may for the present purpose be taken as a circle; the centre of this circle will be distant g. c. cot C from A B, so that if p be the inclination of this intersecting plane to either of the vertical planes at A and B, cot u = - #cotc. also, if i be the inclination of the vertical planes to each other, i = < * sin 2) cos’ A But the ratio of the perpendiculars is determined by the relation h = h/ (1 + 3 cot p.), and if in this expression we substitute the values of i and u, equation (22) is reproduced. H in * 242 PRINCIPAL TRLANGULATION. 17. Having now obtained an expression for the value of the ratio h : h, equation (21) becomes by the substitution of this expression sin sin A º sin B (I. g c” cos’ Ao 2 - 2 — 3 - si * } sº #(; +*.* (– a cos 22 + b cos 28 # * sin 2, cot C) S1 II - g Now in the small quantity within the inner bracket we may neglect all quantities of a smaller order, so that we may take C = — a + 3 + 180° B = — y + cz — 180° A = — 3 + y + 180° supposing C to be on the north side of A B and intermediate to A and B in longitude. By means of these equations the quantity within the bracket may be transformed to º (sin 2) cos (c. – 3) + 2 sin (e + 6)) - 2 sin C Hence we have the following set of equations:— sin A tºº sin a sin B T sin b sin B sin b { + pta (e. (3 — y) sin 22 + 2 sin (3 + y))} (23) sin C T sinc sin C sin c { + ºbſcos (y – c.) sin 23 + 2 sin () -- •))} I + ºr (cos(a – 3) in ay 4. a sin (a +3))} sin A T sin a where c” c nº cos” A 12 sin C O pſ = the unit of length being the radius of mean curvature. 18. From these fundamental equations of Spheroidal Trigonometry we may deduce the errors of the two sides a and b, as determined by Spherical Trigonometry from a given side c, and the angles of a spheroidal triangle A B C ; they are in fact * ea = - p. ab {& – c.) sin 23 + 2 sin (y -- a)} e, H + p ab {cos(6 — y) sin 22 + 2 sin (3 + 7)} which again may be put in the form ea = — w a b k sin (2) + 4) 2 e, - + p a b k'sin (2) + 4') (24) f PRINCIPLES OF CALCULATION. 243 in which k = (4 cos" A + cosº B + 4 cosº C): k' = (cos” A + 4 cos” B + 4 cos’ C); k sin (p = cos B sin 2A – 2 sin B — k'sin q' = cos Asin 2B – 2 sin A. I9. We have now reduced the expressions for the errors in the solution of spheroidal triangles by spherical trigonometry to their simplest form, and it remains to examine the limits within which these errors are confined. If we take any triangle of which the sides are a b c and the angles A B C, having also a mean latitude Ag, and place it with respect to the meridian in such a position that 2 y + q = : 7 Ol' = #7, then the resulting error of the side a, as calculated by spherical trigonometry from the side c, is e” abe — — —s cos" X. •k I2 sin C O if the same triangle were so placed in azimuth that 2 y + b = :* OT = #7, then the side b would be affected with the greatest error, which is equal to c” abo Iº sin C cos’ \'s •k’ Therefore a limit to which the error can never amount is (since k < 3) For Great Britain the limit of error may be taken at e” abo -- Iz sin C which depends solely upon the length of the sides and the acuteness or obtuseness of the angle C. * - In order to obtain an idea of the actual magnitude of this quantity, let us suppose a triangle of larger dimensions and more ill-shaped than any that would probably ever be actually solved, for example A = 21°, B = 146°, C = 13°, a = 124 miles, b = 196 miles, c = 80 miles, then the error in calculating either of the long sides from the shorter side could not amount to 1.6 feet. If we had taken a triangle of the same shape but smaller dimensions, say 93, 147, 60 miles, the limit of error would be found to be under 8 inches; but even this triangle is more unfavourable than any in the triangulation of Great JBritain. - In general the spheroidal error varies as the square of the cosine of the latitude, it increases with the departure of the triangle from the “well-conditioned” or equilateral form, and in two similar triangles the errors are as the cubes of the homologous sides. g H II 2 244. PRINCIPAL TRIANGULATION. The following Table exhibits the greatest errors that could result in the calculation by Spherical Trigonometry of several large triangles:— Angles. Sidcs in Miles. | Error in Feet in No | A. IB C C. * a b | I 30° 39° 111° 64 79 II9 •og •o9 2 59 92 2 IO4. 122 59 • 22 • 20 3 85 || 42 53 I43 97 II6 • 20 •27 4. 3o IIo 4O 94 176 129 '50 •4.I 5 || 23 I4O | I7 90 146 66 • 57 '54 6 35 II 8 27 I2O 184 95 •8I •71 7 17 | 138 25 13o 303 194 || 3:46 || 3:19 8 II2 4. I 27 324 228 I62 3-83 4:36 9 17 I53 IO I9o 302 120 7.82 | 6.67 Legendre's Theorem. 20. Having now proved that the errors resulting from the solution of spheroidal triangles by Spherical Trigonometry are inconsiderable, we proceed to consider the solution of spherical triangles. In the earlier operations of the Trigonometrical Survey, the triangles were calculated by the chord method; this has been for many years discontinued, and in place of it Legendre's theorem has been exclusively adopted. This simple and elegant method, though of less primâ facie accuracy than the chord method, is sufficiently near the truth for calculations of almost any degree of exactitude, and is of very easy application. In large triangles, however, the accuracy of the result will both depend on the value of the spherical excess adopted, and on the shape and magnitude of the triangle. If we put tº for one third of the spherical excess adopted, then a, the correction to the side a calculated from the side c, will be sin A sin (A — p.) # = sin - (sinc ſº - C ----- sin C sin (C — p.) and expanding into series the quantities sin a sin (A — p.) sin & gin (C-E) and substituting for cot C – cot A its value a” – c’ I =&##e) #3 ( * I 2. PRINCIPLES OF CALCULATION. 24.5 there results — , º' - a .,, º' – d’ (, — 30° - 7° * = * in C a 6 ( 6o ) a ſº I º 2 6p. 3a* tº 7c. - r) = ga (e. •) (#o + 4*.* - 1) (25) If now we calculate p. by the formula PL = # #sin C (a) (r being the radius of the sphere which we have hitherto assumed to be unity) the errors of the sides a and b thus calculated will be - sºme * - n” 3a* — 7c” ea = — a (c” – a”) Tāāa T (26) l,” * = -1 (e–w)*.* If C' be the angle C reduced by of the spherical excess, then sin C" " , a”-F bº- c. sin C T I2. and consequently if p be calculated by the formula I ab ..., r, - P = 3 = sin C (3) the errors in a and b will be 2a1 + 50° -- 2c” ea = a (c’ – a”) 360 2. 2 or 2 (27) c. = b (e–V)* ++* - Again, if the true spherical excess be used, sin ‘sin : sin C sin # = — C COS o a” -- b” , c* a sinc( – #####) 2 2. a sinc(; + tºtº) (y) ..". Pt - * ºmº : if this value of p, which is true to the order of terms included, be used, the errors in a and b will be - a” º 5b” -- C2 ea = — a (c” — a”) * 2. º sº (28) €6 = – b (e–V)*=#t.— 5 a” + cº 720 246 PRINCIPAL TRIANGULATION. These errors are rather smaller than in either of the preceding cases, and may be altogether neglected even in triangles of sides of 200 or 3oo miles. This supposes the spherical excess to be true to terms of the order of cº. 21. To take a numerical case, suppose the side c = 60 miles, a = 220 miles, b = 180 miles, then, using a radius of 4,000 miles, a = • OS5 b = 045 c = or 5 * 1.2 b 360 (c º a’) := - 9-036 feet, 360 (c’— b”) = — 4.752 feet, and the errors in the three cases expressed in feet will be as follows: (c.) - (3) (y) + of 8 ea = – “I So ea = — 'o6 I +- Ca 65 •o26 65 - – •o93 6, = — •o3O – If we had taken a triangle whose sides are 120, 440, and 360 miles, the errors would have been evidently the above multiplied by 23 or 32, giving (2) (3) (y) ea = + 2. I76 ea = — 4.8oo ea = - O-992 e, - + o-832 e = — 2.976 cº = — o'960 From these considerations it is clear that Legendre's Theorem may be applied without appreciable error to spheroidal triangles of much larger size than it is ever necessary to compute. §. IV. Latitudes, Longitudes, and Azimuths. 22. Let x be the latitude of the given point A.; s, z, the distance and azimuth of a point B, whose latitude and longitude are required, together with the meridional bearing of the given point A. Let H be the point of intersection of the vertical at A with the axis of revolution, andlet A H = v, B H = r, A H B = 6; then if a be the difference of longitude, q, the inclination of r to the plane of the equator, the three lines H. A., H B, HP, (P being the north pole of the earth,) will form a spherical triangle of which the sides are 90° — », 90° — p, 0; the angle included by the first and second is w, that by the first and third 2, that by the second and third is nearly but not quite equal to the azimuth o' of A at B. * . PRINCIPLES OF CALCULATION. 247 By equation (18) we have, neglecting Pº, which is quite admissible, 22 cos" X cos” c. (#) $) S l * =####, s . M e” log; + . He (29) log 6 ſy © S \ 2 COS” A cos” cc ( ...) º which determines 6 with accuracy sufficient for any purpose; indeed, the second term is so small that for a distance of a degree along the meridian it only corresponds to a quantity less than six tenths of an inch, therefore for ordinary distances s = v0. Now the two sides 6 and 90° – 2, with the included angle & will give by spherical trigonometry p and o, and we may find 7' the latitude of B thus: join B with the centre of the spheroid and let x, be the geocentric latitude of B, then tan A, rsin b - ve” sin A tan ºp r sin (p Q? v sin A y * --- * = ==º-ºr-mºº –-s tan x = i, tan ºp (1 “Fsin #) (30) This is the only direct expression for A', and the ratio of v to r may be assumed equal to unity, unless great accuracy is required, when from (16) which is a minute quantity, and quickly estimated. Having thus obtained A’ and w, the value of c.' is expressed by equation (15), viz.: . X' + A c.' + Cº. SIIl 2. CU COt r) = -- tan : sº X' - 2, 2. COS 2. 23. Tor actual calculation, however, the following method is preferable: Let & + & be the third angle of the spherical triangle just considered, then if x = 90° – A, we have by spherical trigonometry * f ºr — ^ tan + (2 + 4 + wy =### }cotº a sin + (x – 6 * unº (2 + 3–2 =####cot, a | (31) sin # (2 + , – c.) sin + (c.' + 3 + 2) tan + 6 2 tan + (j - A) = We may determine the quantity & in the following manner: Let K be the intersection of 248 PRINCIPAL TRIANGULATION, the normal of B with the axis of revolution, then from the spherical triangle determined by the lines B.A, B H, B K, sin c." T sin ABH T HA sin BAH , - " in tº I + , cot c. T v sin p. Now neglecting quantities of the order el 6°, sin w = sin P.; therefore from equation (16) e2 92 . I - € * = } a cos’. A sin 2 & (32) This quantity & is so small as not to amount to a tenth of a second even in a distance of a hundred miles. It remains now to find the difference of latitudes x' – A, which depends upon the Distance of Parallels. 24. Trom equation (29) it follows that the distance of parallels of A and B is equal to v (? – ?) { I — m (4) — x)} . The quantity @ — » is obtained from the third equation of (31); writing it in the form tan 4 (? – ?) = k tan 40 and substituting for the tangents their equivalent series, we find § - ?, 7. 62 — h" 6. — h” tºº. 6) = H(t+ +G *) + = (-k) (, 3*) The term in 64 will be generally insensible, and therefore we may put 4–2 = 40 (1 + £6 – 9) and since s = v % I — m (§ – ?)” } we shall have, by replacing the value of k, and putting S for the distance of the parallels of A and B, _ , sin # (2' + 3 − 2) 6* ..., c.' – c. =#####(, ; #co. ==) (33) This equation is also equivalent to the following:— _ a sin 4 (2' – c.) , 6” as a c.' – c. s=s:#; 1 + H cos’ → 2)] 3 tº ſ (34) = I —º- cos’ x + I – c’ 25. The difference of latitudes may be obtained by dividing the meridian distance by the radius of curvature of the meridian for the mean of the extreme latitudes. To prove PRINCIPLES OF CALCULATION. 249 this, let a distances, be taken along the meridian from a point whose latitude is a to a point whose latitude is x -ī- a, then ds \ & d’s c.” dźs cº S, - (#) ... + (;) I -2.2° + (#) I.2-3.2% + - - - and ifs' be the length of the meridian curve measured in the opposite direction to a point whose latitude is A – ; c., dsx c. d’s c.” dés c.3 ’ — tº-º-º: sº - +-º-º-º: *-ºn-º-º-º-º-º: sº sº-is sº-º-º-º: S’ - (#) 2. + (...) I , 2.2° (...) 1.33:2, " ſº , /ds I /dºs * • * * *=(;) = + , #) a + . . . But d d S 3.5 ...) = g; (...) = 3 e”g cos 2 x + . . . neglecting the higher powers of e”; therefore if s be the length of an arc of meridian whose amplitude is 2, g the radius of curvature for a the mean of the terminal latitudes, s = g c + g (#) ecos 2 x (35) S c. \3 Cº - - - (: e” cos 2 X g 2. This correction is generally extremely small, vanishing altogether at the latitude of 45°. In an arc of n degrees whose middle latitude is 60°, it amounts only to nº x o46 feet, and it is therefore seldom necessary to use the term in e”. 26. The following set of equations, therefore, contains the whole solution of the problem of geodetic latitudes and longitudes when great accuracy is required:— tan + (c.’ g cos 4 (2 – 6) cot ‘ N { # (c. + = + 9 =::= } 2. I f ... / _ sin # (x - 0) co, & tan + (c. - * + 9 =##F#, cot . '- =#######( # corº'-2) A. * ~ * sinjº Taiº 1 + a cos # (2' – c.) (36) 6 #( I cº 02 2 **) = – I + = COS* A COS" dº ºy 6 I — e” _ 1 c 6: 2 x sin o 2, * : = , = cos’ in 2- J * By extending the value of this quantity, so as to include terms of the order e 93, it becomes ------- 2 AH2 I 62 #. cos” # (A' + x) sin (2' — 2) % = + 4. due to Mr. O'Farrell of this office. I - I i 25o . PRINCIPAL TRLANGULATION. The equation s =v.6 may generally be taken without correction. The small quantity & in seconds may be obtained from the following table, by multiplying the quantity corre- sponding to the given latitude and azimuth by the square of the number of degrees in 0. | Values of I 62 e” 5 ºr cos” A sin 2 & LATITUDE X AZIMUTH a. 2° 889 4° 86° 80 82° I2° 78° I6° 74° 20° 70° 25°|65° 30° 60°35° 55°|40° 50°45° 45° O ſ/ £/ Af f / f/ f/ f / // Af f/ Aſ 49 o-oo:3 o-ooo o.org o.org o.o.24 o.o.29 o.o.35 o'o69 o'o43 o°o45 o.o.45. 5o o-oo:3 o-ood o.o.12 o.org o.o.23 o.o.28 o.o.33 o.o.38 o.o.4I o'o63 o'o44 5I o-oo:3 o.o.o.6 o.o.12 o.o.17 o.o.22 o.o.27 o.o.32 o.o.36 o.o.39 o'o4I o.o.42 52 o-oo:3 o-ood o.or I o.org o.o.21 o.o.26 o.o.31 o.o.35 o.o.38 o.o.39 o.o.49 53 o-oo:3 o.o.o.5 o.or I o.oió o.ozo o.o.25 o.o.29 |o-o:33 o.o.36 o.o.38 o.o.38 54 o-oo:3 o.oo; o.oro o.org o.org o.o.23 o.o.28 o.o.32 o.o.34 o.o.36 o.o.36 55 o-oo:2 o-oo:5 o.oro o'ora o.org | O'oz2 o.o.27 o'ogo o.o.33 o'o64 o'o65 56 o'ooz o.o.o.5 o.o.o.9 o'or 3 o.o.17 | O'oz I o.o.25 o.o.29 o.o.3.I o.o.32 o.o.33 57 o-oo:2 o.o.o.4 o-oog o.org o.or 7 o'ozo o.o.24 o.o.27 o.o.29 o.o.31 o.o.31 58 o-ooz o.o.o.4 o-oo& o.orz o.org o.org o.o.23 o.o.26 o.o.28 o.o.29 o.o.30 59 o-oo:2 . o.o.o.4 o.o.o.8 o.o.11 o.o.15 o.o.18 o.o.2I o.o.24 o.o.26 o.o.28 o.o.28 6o o-ooz o.o.o.4 o.o.o.7 o.o.11 o.o.14 o.o.17 o'ozo o'oz3 o.o.25 o.o.26 o.o.26 6I O OO2. o-oo:3 o-oo? O OIO O-OI3 o'oro o-ol.9 o.o.2I o'o.23 o.o.24 o.o.25 In illustrating the working of these formulae, we shall take the side A C of the spheroidal triangle worked in Art. (7.), and assuming the length of the side, namely II 37025.201 feet (214 miles); the latitude of A 52° o'; and the azimuth of C 59° 26' 22".8116; from these data determine the latitude and longitude of C and the bearing of A at C. - We have then given a = 59° 26' 22".8116 x = 52° o' log s = 6.05577Oogo7 to find x' a' w. If we express 0 in seconds, then log É) = log S iſ +cco.862 (Axcosy- Any approximate knowledge of A A, the difference of latitude, is sufficient for this calculation; in the present instance Ax = 1° 30', the work then stands thus:— * The logarithms of (v sin 1")-1 and (; sin")-- are tabulated in the “ Account of the Measurement of the Lough Foyle Base, by Lieut.-Col. Yolland, R.E. " the semi-axes of the spheroid being 20923713 and 2085.38.10 fect. ºf PRINCIPLES OF CALCULATION. 251 Const. . . 4.6868 log s = 6.0557700907 sin’ A x .. 6.8359 (v sin I")" .. 7.9928850557 cos' A • - 9-5787 . . . . . 1262 . log I262 = 3. IoI3 : 4.0486552726 6 = 3° 6' 25".A967 % - 0) = 1; 26.4%.2517 cos ... 9.9795472525 sin - 9:476852558o #(x + 6) = 20 33 12.7484 Sec. • , o.o.28564326 I cos • o°454,590,7919 # & = 29 43 II-4058 cot . . o.24347888 Io cot -- o'24.347888.Io tan • o-2515904596 tan • * o-1749222.309 # (2 + £4. a)= 60° 44' 19":3689 Tab. 8 = 'og5 a' = 116° 58' 38”.4016 4 (a' + g—w) = 56° 14' 19":3687 % = 336 w = 4° 30' o”.oooz ;(2' + & – c.) = 2š 46 * #9630 sin . , 9.6823956659 Const. .. 3-9297.529 ;(x' + 4 + 2) = 88 12 30.7746 cos . . o.oOo.21231.96 6° . , 8.0973Ioš s • , 6.05577Oogo7 cos' 4 (2' – c.). - 9.88557.14 o-oooo&17777 e dº ſº tº 5°9126348 (g sin I”)** 7.993.933856I 3.73239371oo A' – X = 1° 29' 59".9994 •'. A’ = 53° 29' 59".9994 27. In the case of a long line running very nearly in the meridian, such as from Dunnose to Arbury, the simplest method is to add a small correction to the actual length to reduce it to the meridian distance; for when c. is small, if & be the projection of 0 on the meridian plane of A, 6 — # = tan” in 20 = } Also putting — a = } – A – 6, we have -- in 4 = in 6 + i): cos : in G + 0–3) = in 6 + 6– ) ( — , an $) 2 = 4 (1 + an 0 tan (a + 0) therefore, S being the distance of the parallels - c. sin 6 cos x . (37) S = s — 2 v tan”- tº it ºr 2 cos (A + 6) *r the longitude and azimuth & will then follow from the relations Č0 - sin 6 sin & T T cos (A + 6 — a sin . (A’ + x) cos # (A’ – A) (38) I8o° – o – c.' = a, II 2 252 PRINCIPAL TRLANGULATION. 28. When the distances does not exceed 40 or 50 miles, the following method is used. Take a point P, on the meridian of A, so that the angle B P. A shall be a right angle, and let x, be the latitude of P, ; take also on the same meridian another point P having the same latitudex with B. Let A. P. = q, B.P. = p, and let r be the radius of mean curvature for the triangle A BP, ; then \ :... ? S11) :- º -º-º: " _ P. s” — pº sin a = − = , ( + #) SIII - 7" tan 1. s” – d’ COS & = 7 = } ( – #) tant J f" s” s” . p = s Sun & ( – #, cos’ a); q = scos & ( + → sim” a) 6 7 - 3r And if a be the difference of longitude of A and B, we have º 2 º sin w = + ( – ;) = a ( –. ty' coS X' 6 v" 6 s sin & 2. s” sin” c. --- ſº º to − 27—7 ( * -º $ + Sec” A’ (c.) v' COS X' 67." 6 r? It is easily shown that the difference of latitude of P and P, is S” . A. - X’ = — sin” c. tan A1. 2 1.2 if therefore g be the radius of curvature of the meridian for the middle point between A and P, S s” S” - X' – X = - — sin” — — sin” ; cosa ( I + gºn a) = sm' a tan», (8) From equation (Io), if v be the convergence of meridians, tan + = sin #(x + x) tall to 2 cos (A' - A) 2 ; *— = sin #(A’ + x) (1 + w” Fº) w cos (A’ – A) \" IQ ... x' + 2. ( S” s” sin” c. dº y = Sl *—º-ººrsm- > *g, * * I sm–ms ºn sº-º-º-º- - a sin—a + 8 r2 24 r* ) (y) Now, M being the modulus of the common system of logarithms, put Ms.” * 2 A P 6F = f; fsinº & = g ; g secºx' = h PRINCIPLES OF CALCULATION. 253 then log (A, - A) = log; + 29 N A’ – A – _ ºf sin a tan», - ar' in " (39) log • = log(#F)—f + h | of COS X’ SIn I . .., x' + A\ , 3 f – 7 logy - log (asin **)+4+ . 29. The following is an example of the working of this formula:— Given the latitude of A, and the distance and azimuth of B, A = 52°42' 51".617 log s = 5.3700394 & = 35°57' 27". I.47 to find the latitude and longitude, x', a of B and the back azimuth & of A; the work stands thus:— log s 5'37Oo394 I.2.185 log S • 5°37'oo394 o:37122 cos & 9.9081913 log s”. . o. 7401 sin c. . . 9.7687753 s' sin” & “o.27763 (g sin I")' . .7. 9938649 sec A' . . o. 22.28849 tan X, •o. 12658 2g 62 log f : . I-9586 (v'sin I")". 7.9928o23 sin” c. ... 1.5376 – f -- h –3 5".963. o°77543 3.272 IoI8 ºmº A. - A = o' 31" II". I21 log g. . I-4962 3-3545oi6 . . . . w = o' 37' 42".o.47 - 5'963 sec *X' .4458 sin # (A’ + X) 9.9021965 x’ — A = o° 31' 5", 158 log h . . I-9420 + (3.f- 9) 6o 3.2567401 . . . . y = o' 3o' 5"943 The logarithm I 2185 may be taken constant for all latitudes; the logarithm o. 37122 is the logarithm of (2 r" sin I")-": it varies slowly with the latitude, but may be taken as constant for all latitudes when great accuracy is not required. 254 PRINCIPAL TRIANGULATION. & § V. Combination of Observations made at different Stations. 30. It is essential that, in every triangulation from which accurate results are required, the number of bearings observed should considerably exceed the number that is absolutely necessary for the fixation of all the points, and every observed bearing over and above that number must be considered as adding weight to the determinations of the relative positions and distances of the stations, and to the general results that may be deduced. If the observations were free from error, then any supernumerary bearings would be quite unnecessary, as all the points being once determined, the distance of any two, or the angle subtended by any two at a third point, could be calculated. But when the observations are increased so as to admit of a result being obtained by using different sets of observed quantities, then each different method of calculation will afford a different value of the quantity sought. The values thus obtained will exhibit differences which are functions of the errors of observation, and the magnitude of which will afford a general estimate of the accuracy, or rather inaccuracy, of the triangulation. And inasmuch as every result that can be arrived at by more than one series of observed quantities will be affected in a greater or less degree by the same discrepancies, the question becomes, in general, how to render the triangulation consistent with itself, or, to find that consistent triangulation which shall most nearly represent or be represented by all the observations; the question thus turns upon greatest probability, and is solved by the method of least squares, a result of the theory of probabilities. 31. In by far the greater portion of the extensive triangulations that have been effected in connection with the determination of the figure of the earth, no general method has been followed in dispersing the discrepancies, so that the results are within certain limits arbitrary. It has, however, in almost every instance been customary to make the sum of the three observed angles of a triangle equal to 180°, or rather, if the triangle be very large, to calculate the spherical excess and then to alter the observed angles until their sum shall be equal 180' + the “spherical excess.” In some cases these alterations or corrections to the three angles of each triangle have been made according to the relative degrees of dependence—in the opinion of the observer—to be placed upon the observed values of the angles, and in others this arbitrary apportionment has been avoided, and the residual error of each triangle divided evenly among the angles. In the earlier calculations of the triangulation for the Indian arc by Colonel Lambton, the error of each triangle was so divided that each angle received a correction proportioned to its magnitude, a method that cannot be supported on any principle. In more modern calculations, the errors of each triangle have generally been divided more correctly into parts inversely proportional to the calculated weights of the angles. But the adjustment of each triangle in itself is not the solution of the problem, as there are other conditions to be fulfilled which present a practical difficulty not so easily | PRINCIPLES OF CALCULATION. 255 overcome as the adjustment of triangles considered individually. Besides the necessity that the sum of the angles of every triangle should make up a known quantity, it is as necessary that the sum of the observed angles* round the horizon at any point should together make up 360°, and also that the length of any side may be the same by whatever route it may be calculated. 32. The complete solution of the problem, to determine the most probable corrections to the observed bearings or angles of a network of triangulation, which appears to be due to Bessel, is an application of the “method of least squares” invented by Gauss. From the extremely laborious nature of the calculations, very few applications of the theory to actual triangulations have been yet made; the principal instances will be found in Bessel's account of his measurement of an Arc in Prussia, and in the calculation of the Arc in Lapland by Rosenberger, in No. 12 I and I22 of the Astronomische Nachrichten. Theory of most probable Corrections. 33. The following results of the theory of probabilities are those most applicable to the calculation of geodetical results:— (A.) If a series of direct and independent observations be made under similar circum- stances of a quantity r, then the weight of the result is equal to the number of observations, divided by twice the mean of the squares of the differences of the individual observations from the mean or average of all the observations; thus, suppose m, m, m, . . . . m., to be the observed values of r, and m their mean, then the weight of this determination of v, is 3D = # n” — --" (m – m,) *-i- (m – m,)?-F, - - - (m-ma).” T 29. where p is the mean square of the errors. The corresponding probable error is p=64 (;) = 4; (3) so that the weight is inversely as the square of the probable error. The nature of the ‘probable error” may be defined as being such that it is an even chance that the truth will lie between the limits m + p and m — p, or that the chances of the error exceeding or falling short of p without respect to sign, are equal. (B.) The probable error of a quantity which is a function of several observed elements, is equal to the square root of the sum of the squares of the probable errors that would arise from each of the observed elements taken separately. Thus if u be a function of * That is, supposing the angles to be independently observed, which is not the case in the Ordnance Survey. 256 PRINCIPAL TRIANGULATION. the observed quantities w, v, * . . . . of which the probable errors are e, e, e, . . . then the probable errors that would result in u from each of the v's taken separately would be du 6 du du € ==mº º-ºº: 6. * i. dir, dr, da’, ‘’ ºr t and the probable error of u, tº . du” , , du” . , , du” . , $ If w = a-, + ar, + ar, . . . . then we should have e = (e.” + e,” + c,” + . . . .)* and if w be the weight of the determination of w it will follow that # = 1 + i + i + . . TU) to: 102 103 (C.) If a 3 y . . . be the observed values of the quantities A B C . . . which are connected by certain necessary relations, then the most probable values of A B C . . are those which render the quantity U = w, (A –ay + to, (B – 3) + to, (C- ?) -- º º an absolute minimum; w, w, w, . . . . being the weights of a 37 . . . . respectively. From (B) we may draw immediately the following conclusions:—The weight of an angle which is the sum or difference of two observed angles is the reciprocal of the sum of the reciprocals of the weights of the observed angles. If two base lines be measured under similar circumstances and with the same apparatus, the probable errors of the measurement will be as the square roots of the lengths, and the weights will be inversely as the lengths. As an example of the application of this principle, suppose it required to find the probable errors in the sides a 0 of a triangle as calculated from the measured base c and the observed angles 4 and B, and let Y & 3 be the respective probable errors of the three last quantities; then E C – sin A sin (A + B) da — b da a cos G dA T sin C dB TTsin C # = : and therefore the probable error of a is equal to * - 0. 2 of Y + sin” C. -- sin” C ( 2. b° 2* , a 3’ cos’ gy ".f !i PRINCIPLES OF CALCULATION. 257. consequently if we put x for the ratio of the probable error of c to c, the probable errors of a and b will be ea = (a x) + (a b cosec C) + (a 3 cot cº)" 65 = ((? x)” + (a 3 cosec C)” + (2 b cot cy) the errors therefore increase rapidly as the angle C approaches zero or 27. Again; let it be required to determine the probable errors of w and y as obtained from the equations i a a + b y + m = o a'a -- by + m' = o a'a. -- b'y + n” = o m m' m” ... being the results of independent observations. The most probable values of a and y are - JC E (ab) (bm) — (bº) (am). 7/ = (ab) (am) — (a) (bm) ūjº)={ai} : * ~ Tºâ)=(i); which, making (a”) (bº) — (a) = Q, may be put in the form * = , (n(a)" – () a + m (a)V-()') + . . . . .) 3y = & m{(ab) a - (a”) w) + m' {(ab) a' — (a”) a'} + . . J Now, assuming the probable errors of the observed quantities m to have an average value cº, the probable errors of w and y are obtained by summing the squares of the coefficients of m, thus we get (ab)*N – # e. = ; (a) (bº)" – (ab)* (P) = ('in (@) º (5) From (C) we may derive immediately the following well-known principle :-Suppose one series of observations of a quantity a give the value m with a weight w, while others give the values m' m” . . . with the weights w' w” . . . . , then the most probable value of a is found by multiplying each value by its weight, and dividing the sum of these quantities by the sum of the weights; for the quantity to be made a minimum is * 2 u = w (z — m) + w” (a — in')" + w” (a — mº) + ... . . # =w& – m) + w" (a — m') + w” (a — m'') + [.. º. . = o w'm' + win + w”m" + . . . . w -- w” + to" ----. . . . ſº * * -- 258 .PRINCIPAL TRIANGULATION. If observations made upon two quantities w and 3), between which there existed the necessary relation aw -- by = e, gave the values m 'm' . . . for a, and m, m,' . . . . for y, with the respective weights w w . . . and w, w, . . . . , then we should have 2 u = to (a — m) + w(x - m') + . . . . 4 w; (y – m.)” + w,' (y – m,') + . . ... O = (* @-m) + w(x-m)+ tº J de + (e.g-m)+ wº-mº) + . . . J dy but from the necessary connection of a and y we have ada' = — bay, and therefore, using brackets to denote summation, o = br (w) — ay (w,) + a (w.m.) – b (w m) which, together with the equation of condition between w and y, will serve to determine those quantities. 34. The principle (C) is of great importance, and enables us to obtain that particular system of corrections to the observed angles in a triangulation (out of an infinite number that will satisfy all the required geometrical conditions) which has the greatest probability. For instance, suppose A, B, C, to be the true angles of a triangle, and that the mean of the observations of the angle A gives a value a with a weight we and let 3, Y be the observed values of B, C, their weights being w, w, ; then if s be the error in the sum of angles of the triangle, the equation of condition is A — a + B — 3 + C – Y = and the most probable values that can be given for 4, B, C, result from the condition that to, (A – a)' + v. (B – 3)' + wi (C —y)* shall be a minimum, A, B, C, being the variables. Differentiating these equations, we have - sº- w, (A – c.) dA + iv, (B - 3) dB + w, (C– y) dO = o dA + dB + d = Co from which by eliminating do' there results (e. (A - a) — w, (C-7) dA + (w, (B – 3) – o, (C-7) dB = o the differentials d4, dB, being indeterminate, their coefficients in this equation are neces- sarily zero; we have therefore for the determination of A, B, C, these three equations:— 4 – 2 + B – 3 + C — y = e w; (4 – c.) — w, (C - y) = o w, (B – 6) – w, (C- y) = 0. PRINCIPLES OF CALCULATION, 259 which give the following values to, w, w, so that to rectify the error of any triangle taken without any further connection, this error must be divided into three parts proportional to the reciprocals of the weights of the angles. - 35. Or again, suppose it be required to fix a point P in connection with a triangula- tion already completed, and so calculated that its results will admit of no further modification. Let Q, R, S, be three points of this triangulation, and suppose the angles observed for the con- nection to be PQR, QPR, QPS, RPS, PSR, each angle being observed independently. Let &, 3, p., y, 3 be the observed values of the angles with the weights w, w, w, w, w, the true or most probable values being A = 2 + v., B = 3 + 4, B + C = [.. + ar, C=y+ 474, * D = 3 + 4's, *. w- Now we know the angle QRS, and therefore the sum of the angles A, B, C, D ; this gives the equation. - a', 4 r, + +, + æs = f ' ' ' ' ' (I) where f is known from the angle QRS. It is also evident that ...” a', -i- a, - a, = p – 3 — y = g . . . . . (2) The triangles QRP and RSP will give two means of calculating the line RP, and these two values must be equal; therefore * r sin A. sin D QR sin B T RS sin C - sin A Sin C = RS = i, ** sin B sin D T QR where h is known, since RS, RQ, are given. Substituting for A, B, C, D, their assumed values, Ç * - sin (2 + æ,) sin (y -- a.) sin (3 + æ,) sin (3 + æs) = h . * - K k 2 26o PRINCIPAL TRLANGULATION. Now sin (a + r.), supposing r, to be a very small quantity, is nearly equal to sin a. (1 + ar, cot &); if we substitute this and similar expressions for the other sines in the above equation, we shall have, since the squares and products of the quantities w are - neglected, º I + r. cot c. -- a, cot y - ar, cot 3 — a's cot 3 = h sin à sing Sl Il dº Slil 'y or, to abbreviate, ar, — br, + cr; – ca. =.k (3) These three equations are necessary relations between the quantities r, and there are no other geometric conditions to be fulfilled. Then to obtain the most probable values of r, a..... they must be such as to render a minimum the quantity w, v,” + ...... w, v,”; hence w, v, dr, + w; r.'dr, + w; as drº-Fw, w,'da, + w; as dr, - o (4) Now were the quantities dai, da, .... all independent, this equation would simply resolve itself into a, - o, a, = o, &c., but by differentiating the equations (I) (2) (3), we get - dr, + dr, + dr, -i- da's = o 2. dir, – dr, + da: , – o adr, – bar, + cdr, - edits = o and, by transforming, * (a + e) dr, – (5 + c) dr, + (e + °) dºs = o (a + C) dr, – () — e) dº, + (2 + e) da; = o — (a – c) dr, + (5 + c) dº, + (2 + 6) dºs = o thus the differentials dr, dro dº, can be eliminated from equation (4), which will then take the form P dar; + Q da, -o and these differentials being arbitrary, we have P = o, Q = o ; or, substituting their values, w, (c + e) r, - w; (a + e) a, -u, (a + e) w; + w; (a – c) as = o w, (c + c) r, -i- w (b. 4 c) r, + wa (b — e) a; - w; (b + c) as = o These two equations, taken with the equations of condition, tr are-ba, + cz - cr: = } +, + ar, -- a-, + as = f a'a - a, + æ, - 9 are sufficient to determine the five unknown corrections. 36. We proceed now to consider the question more generally. The equations of condition of a triangulation are those which exist between the supernumerary observed quantities and their calculated values. For after there are just sufficient observations to fix PRINCIPLES OF CALCULATION. 261 all the points, then any angle that may be subsequently observed can be compared with its calculated value. If a triangulation consist of n + 2 points, two of which determine the base line, or the magnitude and azimuthal position of the network, then the remaining n points will require 2 n observed angles for their perfect fixation, so that if m be the actual number of observed angles then m – 2 m will be the number of equations of condition. The manner of obtaining the equations is as follows:—Suppose a number of points A B C. already fixed, and that a new point P is observed from and observes recipro- cally m of these points, then there will be formed m — I triangles, PAB, PBC .... in each of which the sum of the observed angles must equal 180°,+ the spherical excess; this gives at once m—I equations of condition, which are generally termed “angle equations.” The m–2 distances will each afford an equation of the form PC PB PA PB PA DC * * not, however, necessarily limited to three factors ; equations of this form are called “side equations." Should P observe and be observed from only two pöints, then there will be but one equation of condition, an angle equation. When m is not less than 2, every other bearing not reciprocal, whether from P to the fixed points or from the fixed points to P, will give a side equation. Should m = 1, and P observe besides n points, there will be no angle equation, but n–I side equations; if m = o, and r points observe P, there will be thus formed r–2 side equations; and if m = o, and P observes r" points, r'—3 side equations must result, for it requires three observations from P to fix itself. When independent angles are the observed quantities, then another species of equation must enter arising from this consideration, that at every point where all the angles round the horizon have been observed the sum of these angles must be equal to four right angles. 37. Finally, if M be the total number of observed bearings, N the number of observing points, then there will be M-N angles for fixing N-2 points, which require only 2 N–4 angles, so that the number of equations of condition is M-3 N-H 4. If there be also P points at which there are no observations, it is easy to see that, since two observations fix such a point, the number of equations of condition will be M – 3 N – 2 P + 4 38. To these equations should be added those that may arise from the existence of more than one measured line in the triangulation, for if there be n bases there will exist n—1 side equations, in order that there may be no discrepancies between the different measurements and the calculated lengths. 39. The form of the equations of condition is simple. If a, r....a... be the corrections to the observed bearings, then since the angle equations arise from making the sums and Af 262 . PRINCIPAL TRIANGULATION. differences of a number of observed bearings with their corrections attached equal to a certain quantity, their form must be - o = a + ar, if a., + C I & C and in the side equations, if for the ratios of different sides we substitute the corresponding ratios of sines, the equation takes the form sin (A + æ) sin (B + r.) . . . . sin (C + æs) sin (D + r.) . . . . E I but since w, w, ...are very small quantities we may neglect their squares and higher powers, so that -- sin (A + æ) = sin A + ar, cos A = sin A (1 + r. cot A) and similarly for the other sines; substituting this and the corresponding values in the abóve equation, it becomes _ sin C sin D . . . T sin A sin B . . . a, cot A + z, cot B — r, cot C — a cot D + . . . . - I so that all equations of condition are of the form o = a + a, aſ, -i- a, wa F. daº's ºr . . . . 40. The problem then is this:—Given n equations, o = a + air, + ar, -- as"; t “ºn”m o = b + bºr, + bir, 4 º’s + “ ”n o = c + czar -- Caºa + C32.3 + ... ...] (1) o = q + q, r, -i- ſlava + 73's F ... ſlºw, between m, (m = n), unknown quantities, to *., “ºn, which are the corrections to the observed bearings, to determine these quantities so that they shall satisfy the n equations, and make the quantity - a minimum. The corrections thus determined must evidently give a consistent triangulation, . and also that one which is most probable or requires the least total amount of alteration of the observations, having respect to the different weights or probable errors of each mean bearing. Now in order that w may be a minimum, we must have du = o, or o = 10,4', 'da' -- war, dr, + ...... + war, dr" g ºr- (2) but by differentiating the equations (1) we have the following:— O E a.dr. -- a.da, + agda, + ... -- andºn *. o = b, dr, + bada, + badr, + ... + bºden * o = c.dr. -- c.dr. -- c,dr, + ... + c,dan (3) tº º ſº tº º ſº º ſº tº º g º e º ſº e º 'º º 'º C C C & © . . . . . ſº tº tº $ tº ſº tº º ſº ſº t o = q.dr. -- q,ar, -i- ſlida, 4 ... + Qadr.m PRINCIPLES OF CALCULATION. 263. which establish n relations between the m differentials; we may therefore determine n of them, in terms of the remaining m — n, and thus the number of differentials in (2) is reduced by substitution from m to m — n, which are perfectly arbitrary; and therefore making their coefficients respectively equal to zero, there will result m — n equations between the quantities r, which, together with the n equations of condition, will suffice to determine these corrections. But the method practically adopted is that of independent multipliers, which is as follows:—Multiply the equations (3) by indeterminate quantities 2, 2, . . . . xa, and adding their sum to the equation (2) multiplied by – 1, we have the following system of equations:— º . . . . . * * gº o = (- wºrk -- Ala, + A.b. 4- Age. -- ... Anqi) dr, + (– war, + xia, + x,b, + Age, 4- ... x,7,) dr, + (– wars -- Ala, + x,b, + Age, + ... A.T.) dº, ) (4) + (- wºn 4 Ala., + x,b, + x,c, + ... Aq.) dº, Now as there are n arbitrary quantities x, we may assume n of these coefficients of the differentials equal to zero; the quantities x being thus determined, and then substituted in the remaining coefficients, the expression will take the form o = P dic -i- Q dw 1 + ... containing m — n differentials; and these being independent, it follows that P = o, Q = o, &c. . . . which amounts to putting at once each of the coefficients of the m differentials in (4) separately equal to zero; therefore we have the following m equations:- - * * * * 2012, - A1a; + *J. + A3C, -- ... ?"(l. - tº,”, “ Ara, + A.b. 4- Agca + ... Anqa 1932, - A1a; + x,b, + Age, -- ... Alſº, - (5) © tº s º tº º º ſº tº e º 'º º 'º - C C º 'º º g º º º º e º 'º º e º 'º tomºm- *Ian + ^sºn + *3°m + {} º ſº. ^nſin Now substitute 4, w, . . . a, as derived from these equations in the n equations of condition; and we obtain the following set, - o = a + x, (†) + x, (#) + x, (#). tº 2. (# S •= b + x, (†) + x, (†) + . (#): . * . . . (...) • = c + x, (; +* (*) +x, (3) + . . . . .(3)) (6) •-a-, (3) + ()+...(?) . . . . . . £). From these n equations, the n quantities a must be eliminated, and their numerical values obtained. Finally, by the substitution of their values in (5), the numerical values of 4, w, . . . . win will result. 264 PRINCIPAL TRIANGULATION. 41. The different steps of the process are then as follows:– * + → * * sº Tirst, the obtaining of the geometrical cquations of condition supplied by the connexion of the triangulation. * * * . -- Second, the substitution in these equations, of the observed bearings, each with its unknown correction appended. In taking the logarithm of a side equation such as sin (A + æ) sin (B+ r.)... — I sin (C + r.) sin (D + r.)... T if the quantities a are to be expressed in seconds, then log sin (A + r.) = log sin A + M sin I"cot A'z Third, the equations of condition being written out in their algebraic form, and unknown multipliers assumed, the equations (5) are to be formed. - -- Fourth, from these equations the corrections must be obtained in terms of the multi- pliers, and substituted in the equations of condition. - Fifth, the n equations of condition being in terms of the n multipliers, these equations must be numerically solved and the actual values of the multipliers obtained. Sixth, the substitution of the values of the multipliers in the equations (5), whereby the values of the corrections are immediately obtained. - - - Seventh, the verification of the work by the substitution of the corrections in the equations of condition, and also by the working out of the whole triangulation. The work may also be examined in the following manner —Supposing we w, w, . . . to be the corrections to the bearings round a point, whose weights are we w, w, . . . respectively, then it is clear that a system of corrections w; + 3, 4, -ī- *, *, + 2 . . . . would have satisfied the requirements of the figure quite as well as ** *, *, . . . . Now in order that w,(r, + 2)” + to, (r, + 2)” + 10, (a, + 2) + ... should be a minimum, we must have z (w, + w; + wº 4 ...) + ivºr, + war, + tº 323 ... = O but as the above quantity will not, after 4, &, w, . . . are calculated, admit of further diminution consistent with the figure, & must be = 0, and therefore. wit, -i- 1022, -- 10343 + ... = o or the sum of corrections, to all the bearings round any point, each multiplied by the weight of the bearing, must = O. § VI. * * * * * & P g Meridian Arcs. ' ' ' ' ' ' ' ' ' ' " 42. If s be the length of an arc of the meridian contained between the latitudes x, and x, and if 2 x = x. + 2\,, p = x, — », then by equation (33) º = * – e’ (#) CCS 2A g PRINCIPLES OF CALCULATION. 265 Where the value of g is tº 3. I (I — e” sin” x)? g a (I — e”) If we suppose a and e to receive small increments 3 a and 8 e, then * becomes g S 3 a tº * = .8 2 g +fºr+gº • — e” . I - 3 ºr ‘ Sin” X 2 S 9 - - 9 (1 – e’) (1 – e' sin” x) If therefore we consider a, e, as approximate elements of the elliptic arc, and a + 3 a, e’ + 3 e”, to be the true, the value of p will be *=;-e (:) cosax + fu + gu putting 6 e' = v and 6 a = a u. If also A, X, be the observed latitudes, x, -i- w, x, -1-a, the true or most probable latitudes, then these last quantities must be substituted in the above equation. In so doing we may neglect quantities of the order et a, and therefore * - r =#–4–e (#) cos 2 x + ft 4 gº (I) g 2. in which s is the measured length of the arc, g the radius of curvature calculated with the approximate elements for the mean of the observed terminal latitudes, and p the observed amplitude. 43. If besides the extreme latitudes of the arc there are also given -the observed latitudes of several intermediate points, together with the corresponding measured lengths, , then there will exist the following set of equations, in which w, is the correction to the latitude of the southern station of the arc:— ar, - a, + h, + f, u + 9,v a, - c, -- ha + f, w 4- 9.0 ar, - a, + h; +f, u + 9,9 tº e º O C & © tº e º ſº tº Now in order to obtain those values of u and v which most nearly represent the obser- vations made at the different points in the arc, or which require the smallest amount of alteration of the observations, the quantity w; + æ,’ + a',' -- . . . . must be a minimum ; that is, U = ** + (*, + h; +f u + 9, v) + (a, + h, +f u + 9, v) + . . . . L l 266 PRINCIPAL TRIANGULATION. must be a minimum by the variation of v, u, v : therefore if n be the number of observed latitudes in the arc, na, + (h) + (f) u + (g) v = o (f) +, + (fl.) + (f) u + (f) v = o (g) ar, + (gh) + (f7) u + (g”) v = o by making the differential coefficients of U with respect to w, u, and v respectively – o. If in the last two of these equations we substitute the value of a, as derived from the first, we get these two equations:— - {º-dº - ſº- ºr ; , , , )-(º- 7. The quantities w and v thus obtained, determine the elliptic elements which best accord with the observed and measured amplitudes in the arc. If the terminal latitudes only, be observed, these two equations will become identical, and u and v consequently indeterminate, though connected by a necessary relation; that is, if any arbitrary value be assigned to w, a necessary value of v must follow, and vice versa. In combining a number of arcs of meridian in order to determine that spheroid which is most nearly represented by all the observations, the sum of the squares of all the alterations of the latitudes must be made the least possible ; that is, U = a,” + (x, -- h; +J, u + 9, v) + (r. 4- h, + f u + 9, v) + . . . . . + æ,” + (r,’ + h,’ +f," u + g,’ v) + (r.' + h,' +f.' u + g, v) + . . . . . -- ar,” + * i. º tº tº º iº i. tº ſº * ſº must be a minimum ; u, v, w, w,", r" . . . . being the independent variables. Making the differential coefficients of U with respect to these quantities respectively = o, we get n r, + (h) + (f) u + (g) v = o **, + (): (ſ) + (g) → -o and finally, by substituting the values of w, v,' . . . . obtained from these equations in the differential coefficients of U with respect to u and v, sºvº- (ſy } + = {go-ºº: v + X. {wo-ºº-e słgo-ºº: w -- > {o} – 92 }, + = {g*-*}=e (2) 44. The following is the method of development given by Bessel in the Astro- nomische Nachrichten, No. 333. If g be the radius of curvature of the meridian, s the length of the arc increasing with the latitude, - d's _ _ _ _a (I – e’) P. = g = (1 – c' sin ºx); i PRINCIPLES OF CALCULATION. 267 Now putting _ a - b º a — 4 * 72 = e ſº = - a + b * = a-Hy g = a (I — m) (1 — n°) (1 + 2 m cos 2 x + n)-; which may be put in the form g = a (I — n) (1 – nº) (1 + m2) —; (1 + nz-)-; By the application of the binomial theorem, the following general result obtains:– (1 + m2)”(1 + m2-)p = 1 + (pm)' + (20::= 0 *)' +- (20+}} –2) *)' +- - - - - I p” (p — I) p” (p — I)” (p-2) + (2 + ) (p +***** + # = n + . . . . . . . . ) • LY (P (P - 1), a P (P - 1) (P-2), . . . . . . . . . . . . + ( 2. +.) ( H= n + I 2.3 n+ + ) 3 + IY (p (p − 1) (p − 2) p' (p — 1) (p − 2) (p −3) tº º +- (s + ..) ( I-2-3 7-3 + I-2-3-4 m3 + ) of which the law is sufficiently obvious. In the present instance p = — #; therefore if we put 3°5', a N - 3 "…a × - \T224 º 1 + () ºr (ějºr No. = 3 n + 33.3 g + {} 2. 2-4. 2. Na' = 33 nº + 3:57.3, + . 2°4. 2-4-6 2 No.” = 3-5-7 713 -H 2-4-6 we shall have g = a (1 — n) (1 – nº) N (l — a .2 cos 2 x + x', 2 cos 4 x – c.", 2 cos 6 x + . . . .) If now s be the length of a meridian arc terminated by the latitudes x, x, - *A, s=/. gºd A and therefore, putting 2 x = x, + 2\,, p = x, — », a (I – n) (I — m”) N = a - º 2. + s = aſ (5–2 a sing cos 2 x + a sin a coax-j-" in 3% coso a 4. tº tº 8 .) The problem requires that the observed latitudes A, x, . . . . should be brought to accord With the measured distances by the application of small corrections ar, a , . . . . such that * + w; + . . . . shall be a minimum, the variable quantities being the elements of the figure of the earth, or a and n. Those values of a and n which make this function sº L l 2 268 PRINCIPAL TRLANGULATION. a.” -- a-, + . . . a minimum, determine the most probable figure of the earth, as far as depends on the arcs under consideration. Putting, therefore, x, -i- a, x, + ar, as the true latitudes in the above equation, we have S. f * tº 2. tº = @ – 2 a sin ºf cos 2 x + & in a cos4x -iz" in 3% co, 6x4 © tº º 0. • + p. (r, - ar.) pe = I – 2 & cos q, cos 2 x Instead of making a the unknown linear dimension, we may make the length of a mean degree of the meridian the required quantity: if we call this g, then 180 g = ºr a I S ºr tº Q?. - T. E - I — - 2 os 2 x – c.' sin 2 d cos 4 × * * * * 2 “I #(; ‘p + 2 & sin ºp cos ‘p cos 4 x + ) If nowg, and 2, be approximate values of g and 2, we may put I I + = + (1 + wy, & = &I (I + v 3 = , ( (1 + v) w and v being two small quantities to be determined. By means of the values of No. 2' . . . . in terms of m, we derive the following:— 72 = 2 & + I cº 3 9 a' = 5 c.” + .5 c. * 6 54 Cºr When therefore &, becomes cº, + cz, v, c.,’ becomes &,' + Tº “, v I ‘. cz' = &,’ + v (;a; + #4) 3 27 Therefore the expression for v, - a, becomes I 7ſ S º 5 i. * - r =; {#, – b + 2 & 1 sin ºp COS 2 X. – 4 a. in a coax} (3) I ºr S I 5 ſº +}{i}.} }{2-, sing cos 2 x 3 * in 24 coax}º in which we have omitted the terms in 2,”, as they are so small as to be insensible. The equation of condition thus formed corresponds with equation (I); the unknown quantities w v are not, however, the same in both equations. § VII. Logarithms. 45. Though logarithms to seven places of decimals are generally sufficient for ordinary calculations, yet when considerable accuracy is required for geodetical calculations, PRINCIPLES OF CALCULATION. 269 eight places of decimals must be used. It is not always or generally possible to have the last figure of the resulting logarithm after any lengthened calculations true. Errors of one and often of two units in the last place are very probable, and therefore there should be at least one Superfluous decimal. . In the absence of any printed tables to eight places, Vlacq's ten-place logarithms have been used. The method of interpolating by differences has been avoided as more trouble- some than that supplied by the usual series H H – K I / H – K \3 log ºr = 2M -º-º-º-º-º-º-º-º-º- tº º ſº tº °g K #4 (#) + } The second term within the bracket is always so small as not to be required; in those cases in which it might be required, other methods present themselves. If we make successively H=sin(A + iv), K= sin A, and H=tan (A + iv), K = tan A, and substitute these values in the above series, omitting the second term, we shall have in (A + æ) tan + æ l g sin(A + r. = 2 —- 93 -iù. 2 M ºn (A + , w) tan (A + æ)_ , M. sin a log #’= M sin (2A + æ) Also if we take N to represent any large number and n a very small number, * : * = &M T! log+R = 2x Gnº whence we have the following rules:— log sin (A + r) = log sin A + Ma: cot (A -- £) log tan (A + æ) = log tan A + 2Mr cosec (2A + r.) (c.) Mn log (N + n) = log N + N + 3 m This method is found much more manageable than that of differences when second differences are sensible. The logarithms of the functions of very small arcs are more easily calculated directly than obtained by interpolation. For this purpose the series ſº M ..., M \ (r F {`ſ Tº sº-ºs - * = 4 - log sin a = log a 3 * 180 ° log cos w = _ M acº — M 3:4 2. I 2 M 7M log tan r = log z + + 2* + – 8) - tº M . IIM . (r -: QºS *E* 2 # * * = ′ = } 4 log z = log sin r + a sin a + His sin” M I 3 M log z = log — tan- +3* tan, og at og tana: tan” a + 90 tall * 270. ..PRINCIPAL TRLANGULATION. are useful.” The remaining terms of these series are seldom required, but may be obtained from the general expressions sin r 2 an - 1 acaº 3. 72 I . . . 27. 2” - " (2.2m — 3?! log cos a = — M. X. ( 4) B 3C 72 2?! - I • 27. tall ºr 2”(2*- : I 273, logº* = + Ms "(***) 2?? - —t- º' 72 * I ... 2n n taking the successive values 1, 2, 3 . . . . and B representing the numbers of Bernoulli, B = % R = +, B. = +, B, - +, B, - # *The following Table gives the quantity to be applied to the last figures of logarithms to ten places, for the terms in acº, from 1% to 2°. O O , ſo ſo o o , C , o , o lo * | O lo o * | O Q ,'o * | O f : O iſ TERM. I | 6’ 4tºrs; 140, 42 || 44 146|| 48 isºrs: 54 56 I 58] 2 o | rºw M w. 2 4 || 6 || 7 • * * 17 is lies. 23 25 * * * 33 || 36 Tºr Max! 33 61 | 82 |106 |135 169 21. is, 28o 303 327 352 379 408 438 469 502 537 iſ, M & 31 58 |77|| 99 126 159 197 242 262 283 395 (329 354 38o 408 438 468 501 Tºr M. a." 24. 45 6o 78 99 |124 155 º 206 º: * 258 (278 299 321 344 368 1394 * M - Issies 4 & 3, 24 366 º 486 as 56, Sr. ss. º 758 813 |87o 930 5 | | S E C T I O N VII. REDUCTION OF THE TRIANG ULATION. THE results of a triangulation so well connected as that of the British Isles, extending from latitude 49°53' to 60° 50', and from longitude 1° 40' east to Io” 20' west, must have much weight in the determination of the general figure and dimensions of the earth, though the more immediate and precise result will be the knowledge of the nature and curvature of the surface within the limits of the triangulation. The general figure of the earth may be considered as already determined with much accuracy, the mean errors of Bessel's determination of the linear dimensions being one twenty thousandth part; and of the ellipticity, one sixty-fifth part. The magnitude of this error depends principally upon the existence of those small disturbances of the direction of gravity which may be expected at any point on the surface of the earth, and of which the mean value may be taken at about 2".6. The only method of eliminating the effect of this unavoidable source of error is the multiplication of the number of points having observed latitudes, the observations being of the best kind, and very numerous. The general figure of the earth, or more strictly speaking, that spheroidal surface which makes the sum of the squares of the apparent deflections a minimum for the whole of the astrono- mically determined points on the surface of the earth as far as connected by triangulation, being determined, the next point is to determine the variations of the surface or the osculating ellipsoid for as many parts of the surface as possible: and in order that this may be accomplished in each case with precision, it is necessary that the triangulation should in the first place be effected with the best instruments; in the second place, the connections of the various points with one another should be as numerous as possible—that is, the number of superfluous observations or of equations of condition should be abundant, as increasing the probability of the results; and thirdly, the triangulation should be calculated so that the results should be strictly the most probable, and unaffected by any arbitrary method. The first two of these conditions appear to be well fulfilled in the present triangu- lation, and the necessity for the fulfilment of the third is obvious. Acting upon these considerations, Lieut.-Colonel Yolland directed that the whole triangulation should be reduced according to the method of least squares. It will be evident from the explanation given in the preceding Section of the application of the results of the Theory of Probabilities to the determination of the proper system of corrections to be applied to the observed bearings of the various points in a triangulation, that the principal, and indeed only, obstacle to its being applied to any actual survey lies in the extremely voluminous nature of the calculations. 272 PRINCIPAL TRIANGULATION. There are in what may be called the principal triangulation 218 points, 1554 observed bearings, and therefore an equal number of corrections to be determined, and 920 cquations of condition: if, therefore, the whole were to be reduced in one mass, the solution of an equation of 920 unknown quantities would form part of the work. It is evident, therefore, that some method of approximation must be adopted; and this indeed is sufficient, provided that method be unobjectionable. Let o = a, + b, a -- c, ar, H & 43 + ' ' ' o = a, + b, a., + c, ar, -i- e, tº + ' ' ' o = a, + br a'a -F Cra, + i + era'a 4-2 ' ' ' be the equations of condition, then if the geometrical positions of the equations (i), (n), (r), as referred to the triangulation, be some hundred miles apart, with many intervening points, the equations containing a will not contain wº, nor will those containing as contain ap, nor will those containing a, contain w, The corrections that appear in the first equations of condition gradually disappear and are succeeded by others, which in their turn give way to others, as the equations proceed; which is merely in accordance with the obvious fact, that the position of a point is dependent upon all the observations made round it to a considerable distance: the influence, however, diminishes with the distance, and at a sufficient distance becomes almost imperceptible. It is then quite possible to obtain a satisfactory approxi- mation, as widely separated equations are in a manner independent; and the following is the method that has been actually carried out :—The triangulation was divided into a number of parts or figures, each affording,a not unmanageable number of equations of condition. One of these being corrected or computed independently of all the rest, the corrections so obtained were substituted (as far as they entered) in the equations of condition of the next figure, and the sum of the squares of the remaining corrections in that figure made a minimum. The corrections thus obtained for the second figure WCre substituted in the third, and so on. Four of the divisions of the triangulation are independent commence- ments, having no corrections from adjacent figures carried into them, but having the corrections determined in them carried out to the contiguous divisions.” By this means, however, the ratios of the measured bases have not entered into the equations of condition, no two bases falling into the same division of the triangulation; and in an extended triangu- * This method of approximation is not the best that might have been adopted, and is liable to some objections; but it is certain that the results so obtained, when the observations are not * * be very close to the truth: and without a further expenditure of labour, better results could not, by any method perhaps, be had. m |** REDUCTION OF THE TRLANGULATION. 273 lation in which the bases have been measured with equal care, the conditions of agreements between the bases should exist to prevent the accumulation of error; but the neglect of these conditions will bring out in the comparison of bases a good test of the accuracy of the theodolite work. Division of the Triangulation. Omitting in the first place the extremities of base lines and several sector points, which are connected to the general work by small and special triangulations, the remainder of the principal points were divided into 21 figures, which are indicated in Plate XVIII., and are as follows:— FIGURE I. (Plate IV.) N. E. Lough FoxLE BASE. S. E. LOUGH Foyie BASE. MoUNT SANDY. DRUNG PoſNT. CUNDTHAM. S. SNAGHT. IXNOCKLAYD. TROSTAN. SAWEL. DIVIS. WICAR's CAIRN. S. DONARD. CUILCAGH. FIGURE 2 (Plate IV.) S. SNAGHT. CUILCAGII. S. DoNAnD. S. LEAGUE. REEPER. NEPHIN. BENCORR. KNocKANAFFRIN. CROGHAN. JKIPPURE. BAURTREGAUM. FIGURE 3. (Plate IV.) BAURTREGAUM. . keeper. JKNocKANAFFRIN. RNOCKMEALDown. ICIPPURE. GALTYMoRE. TAUR. * * - IGNOCKNASKAGH. DooDIEVE. CAIIERBARNAGH. HUNGRY HILL. CARRIGFADDA. FIGURE 4. (Plate W.) JKNocKLAYD. TRosTAN. JDIPIs. S. DONARD. HowTH. AIPPURE, MERRICK. S. BERULE. CRIFFEL. . ScA FELL. BLACKCOMB. SNOWDON. GREAT WHERNSIDE. PENDLE HILL. WHITTLE HILL. MoWCOPT. AxEDGE. Holmſ E Moss. INGLEBOROUGH. &=m-— + A FIGURE 5. (Plate W.) GREAT WHERNSIDE. ASc4 FELL. CRIFFEL. HARTFELL. MERRIck. WISP. Cross FELL. WATER CRAG. DUNRICII. SAYRs Law. CHEvioT. BLACKIIEDDON. #. CoLLIER LAw. WORDESLOW. OTTON. HEAD. EASINGTON, M m +- . . .” PRINCIPAL"TRIANGULATION. i.); } # FIGURE 6. (Plate VI) . . . . . . . . . - ToULA. FAIR ISLE. . . - BRASSA.- ... RONAS. YELL. FETLAR. SAxAVORD. BALTA. º - º: * * FIGURE 7. (Plate.VI.) J - =s* * * * * * * * * * * * * * * BEN CLIBRIG. FASHVEN. * : * BEN HUTIG. SCARABIN. BEN CIIEILT. DUNNET HEAD. WART HILL. S. RoNALDSHAY. DEERNESS. STRONSAY. FITTY HILL. FAIR ISLE. FoulA. N. RoNALDSIIAY. START LIGHTHOUSE. .* * * * * * * * * * * * * * * - - - - * *-*-īāº ºr ºx-- * * * * * * * * * # * i-, - ºf * * * *... * * = . . tº-- ~~~ * * * r * * FIGURE 8. (Plate VII) * FASIIPEN. . . * * BEN HuTIG. JBEN CLIBRIG. CNOC-GIIIUBHAIS, NortTII RONA. " * * * *CLEIslıAM. TU REA. MONACII. STORR. SCOURNALAPICH. BEN MoRE, S. U. MAMSUIL. BEN NEvis. JURA. IBEN HEYNISII. * : ** * * * * * * * * * ~~. BEN -MoRE, MULL..... * * * * * * * * * ºr a w BEN TARTEvil. FIGURE 9. (Plate VII.) ScARABIN. . BEN CLIBRIG. SAYns LAW. ISEN LOMOND. . BEN CHEILT. Scourt.NALAPICII. “ BEN FIUTIG. . . . BEN Nevis. . . . JURA. MAMSUIL. . . . BEN MoRE, MULL. IBEN WYVIS. IBEN MACDUI. . . . . Cority11ABBIE. ICNOCK. CowIIYTHE. MoRMONTH. IBEN LAWERS. GLASHMEAL. MoUNT BATTOCK, º FIGURE Io. (Plate VII.) MoUNT BATTocK. Coſtnyi Abbie. MoRMonTII. JKNock. JBLUE HILL. JBEN MACDUI. IDUDWICK. > LITTLE STIRLING. FIGURE II. (Plate VIII) MoUNT BATTOCK. GLASHMEAL. . . . . . JBEN MACDUI. JBEN LAWERS. ... , BEN .NEPIs. . . . . ... ..., ...BEN MoRE, MULL. JUI.A. JBEN TARTEPIL. - S. SNAGHT. A NocKLAYD. TROSTAN. . . . . JDIPIs. S. DoNARD. S. BERULE. . . r: MERRIck. CitifFEL. FIARTFELL. DUNRich. GOAT FELL. LUMSDEN. BEN CLEUGH. &. * .:. : .* *. ; 3.º§ . f s t i-} ,s :º. - ; * f; i p # ! : REDUCTION OF THE"TRLANGULATION. 275 FIGURE 12. (Plate IX.) Wolf Rock. ... . . . . PENINNIS. . . . . . . . . . . - º ST. MARTIN’s. BEACON HILL, TREscow. FIGURE 14. (Plate X.) .** - , --, - * | “Cradle. . . . . . . . . PRECELLY. “ LUNDr ISLAND. . . . .” - - - - - : PARACOMBE. DUNKERY. MENDIP. i PILLESDON. . HIGH WILHAYs. RYDER's HILL. : BARRow HILL. MAKER. y . * * * * * * EROWN WILLY. TREvose. HENSBARRow. DEADMAN. t - * FIGURE 13. (Plate X.) JHENSBARRomº. Trevose. DEADMAN. ST. AGNES. , ... ... KARNBONELLIS. . . . . . KARNMINNIs. . . . . ; RARN GALVER. GoonLIILLY. PERTINNY. - ST. AGNES LIGHTHouse. TELEGRAPH ToweR. IBEACON HILL. WESTBURY. INKPEN. DEAN HILL. STORE IIILL. WINGREEN. MILR HILL. LIPCOT DOWN. FIGURE 15. (Plate XI.) * * *- :- ... . .” < * : * * * * ... s.a. r.-- * * * * * * * * * * **, * * * * * * * MILK HIEL. Upcot. Doryn. INKPEN. Beacon HILL. DEAN HILL. WINGREEN. WESTRURY. MENDIP. PILLESD0N. , Bannoy HIEL. PIIGI1 PWILHAYs. Jºyden's HILL. BLACKDOWN. . ... ... SWYRE BARROW... . . . . . . ...DUNNOSE. . . . . . . . ... CORRINGDON. HoRTON's GAzebo. BUTSER. FIGURE 16. (Plate XI.) CRADLE. MENDIP. Upcot. Down. MILK HILL. INKPEN. BUTSER. WIIITEHORSE. DUNNose. BROADWAY TOWER. TEITII HILL. MALVERN. BEACHY HEAD. CrowdOROUGII. . DITCHLING. WROTIAM. DUNSTABLE. ARBURY. y EPPING. BERKHAMPSTEAD. CHINGFord. RAIRLIGHT. ST. PAUL’s. SEVERNDROoG. FIGURE 17. (Plate XII.) KIPPURE. KNocKANAFERIN. PRECELLY. SNorydon. CRADLE. MoiycoPT. # 4xEDGE. . MALPERN. ARBURY. --- . Croghan. BROADWAY Toiyen. JKEEPER.' . . . . . . . WHITTLE Hızz. Hoºſe Moss. BALLYCREEN. * LoNgāious T. BARDON. CYRN-Y-BRAIN. t , TARA. . . . . . CADER IDRIS. ForTH. , . . . . . . . . . PLYNLIMMON. MoUNT LEINSTER. # ; * + ... * - ; F : * : §. • *... --- ºr “ , ” M m 2 276 PRINCIPAL TRIANGULATION., FIGURE 18. (Plate XIII) JEPPING. SEVERNDRoog. WRoTTIAM. LEITH HILL. BEACHY HEAD. FAIRLIGHT. PADDLESWORTH. , St. PAUL’s. GAD’s HILL. NORWOOD. DANBURY. ST. PETER's. ERITTENFIELD. WALtoN ToweR. EIGURE 19. (Plate XIII.) DUNSTABLE. BERKHAMPSTEAD. PPPING. * JDANBURY. THARFIELD. WALTON. | || TIIAXTED. StokE. NAUGHTON. OTLEY. MICRFIELD. LAWSHALL. BALSHAM. FLY MINSTER. SWAFFHAM. S. LopſiAM. BRANDON. FIGURE 20. (Plate XIV.) WALTON. OTLEY. MickFIELD. S. LoPHAM. BRANDON. Siyar FHAM. ORFord CASTLE. LAWSHALL. LAXFIELD. BUNWELL. HINGHAM. SouTIIworld. TOFTS. Norty ICH. BACONSTIIoRPE. GoRLESTON. + HAPPISBURGII. FIGURE 21. (Plate XIV.) JBotton HEAD. GREAT WHERNSIDE. Holiſe Moss. AXEDGE. BARDON. ARBURY. DUNSTABLE. Tiſairfield. JBALSIIAM. JELY MINSTER. ASWAFFILAM. BAconstitorpe. AcKLAM World. York MINSTER. GARFORTH CLIFF. BACK TOR. CLIFToM. CROWLE. LINCOLN MINSTER. BosTON. WALPole, ST. PETER's. DOCKING. EASTon. BUCKMINSTER. TILTON. NASEBY. KEYSoe. LYNN. HANSLOPE. It will be observed that with the exception of Figures 1, 6, 7, 12, 14, each figure has some names in italics; the points so printed in each case have been fixed in a previous figure, and the remaining points are those which are fixed in the figure in question. Thus, for instance, in Figure II the three points, Goat Fell, Ben Lomond, Ben Cleugh, are fixed dependently upon twenty other points which have been fixed in previous figures—namely, 1, 4, 5, 8, and 9. Figures I, 6, 7, 12, and 14 are independent. * 3. f it REDUCTION OF THE TRLANGULATION. 277 The following Table shows the mutual relations of the different figures, the number of points fixed in each, the number of bearings for the fixation of these points, and the number of equations of condition. Number of Points. Figures Dependent upon Number of Bearings. Number of Equations. Figures * Non- Observing. observing. I $ºmº . I3 Hºmº 74 39 2. I 8 º 4.O I6 3 2. 6 2. 52 3o 4. Is 2. I3 I IOO 59 5 4. I3 * -º Io9 64. 6 sº 8 Hºmº 37 17 7 º II 2. 82 45 8 7 I3 I 9I 5o 9 7, 8 9: tº º 87 6o IO 9 3 # == 2 I I2 II I, 4, 5, 8, 9 3 tº--º 90 77 I 2 sº I5 tºmº 8I 4O I3 I 2. IO 2. 88 54 I4. ſºmº 8 ºmºmº 45 25 I5 I2; I4. 5 I 77 56 I6 I2, I8; I4. I5 I IO3 56 17 2, 4, I2, 16 6 3 75 47 I8 I6 7 tºº 52 3 I I9 16, 18 I 2. wº 76 4O 2O I9 IO *º-ººs 69 39 2 I 4, 5, 16, 17, 19, 20 I4. 3 III 63 ToTALs mºmº 2O2. I6 I,554 92.0 Here if we put M = the number of observed bearings, N = the number of observing points, P = the number of non-observing points, 3 P = 606 2. Q == 32 3 P + 2 Q = 638 M + 4 = 1558 M– 3 P – 2 Q + 4 = 920 = the number of equations of condition. The circumstances which determined in each particular figure the boundary points and lines Were in general, that each division of the work should contain as many points and bearings as possible; and in the selection of the points forming the boundary line, the guiding Principle was, that they should all be points well fixed by observations to and from them in every direction. 278 PRINCIPAL TRIANGULATION. Method of Calculation exemplified. We proceed now to give in detail the calculation of the corrections in Figure 1. The first step is the obtaining of the Geometrical Equations of Condition, which we shall deduce successively. The points A and B are the extremities of the base line. The point C is determined by the bearings from A and B, and the observed angle at C gives the equation of condition - o = A + B + C – 180° – s; The point E is fixed by bearings from A and C, and the observed angle CEA gives the equation o = A + C + E – 180° — e. But the point E also observes and is observed from B: these two bearings furnish two equations of condition, for we have by the fixation of the point E the means of calculating the angles CEB and CBE. The ratio of the lines CE, CB expresses the ratio of the sines of CBE and CEB, and the ratio of the lines AE, AB expresses the ratio of the sines of AEB and ABE, which determine symmetrically the bearings of E at B, and of B at E. But a more simple equation suggests itself, for the angles of the newly-formed triangles CEB, ABE must fulfil the condition that their sum in each case = 180°-H e. We cannot, how- ever, use both these equations, as one of them is not independent of the other; but one of them o = B + C + E – 180° - e, together with the equation CB CE CA - - - I GE CA CB - will serve to determine the new bearings. We next take the point D. It is fixed by bearings from A and E.; and the angle ADE, being observed, gives the equation of condition o = A + D + E – 180° – s, But D also observes, and is observed from B. The two new angles thus formed give two equations of condition: one we may take as o = A + B + D – 180° - sº For the other we may take DA DB DE = 1 DB DE DA T This equation involves the sines of the angles DBA and DBE, which are very nearly right angles; and this is a little objectionable for the reason that the co-efficient of the unknown REDUCTION OF THE TRIANGULATION. 279 correction to either of these angles will be small. Instead, therefore, of this equation, We shall take the equation AB AC AE AD which contains the ratio of the sines of ADB, ABD. Take next the point F : this point is fixed by the bearings from A and E, and the observed angle at F gives the condition o = A + E + F — 180° - 66 But F also observes and is observed from B and D ; this gives four equations of condition, two of which are * o = A + B + F – 180° — s, O = A + D + F – 180° — es and the other two AB # – I ; : - I A F AD AF AF AE A Next take the point G: it is fixed by bearings from E and F, and the observed angle at G gives the equation • - E + F + 6-º'-'. The reciprocal observation of B at G and G at B gives these two equations 3– r o = B + F + G – 180°– e. and the side equation FB FG FE FG. FE FB But there is also a bearing to G observed at D, which affords the equation GD GEGF = 1 GE GF GD Taking now the point H, it may be considered fixed by the bearings from F and G, and the observed angle at H gives the equation - o = P + G + H – 180° — sº, 28o. PRINCIPAL TRIANGULATION. The reciprocal bearings observed at H and E furnish two equations of condition; these are o = D + G + H – 180° — sº, GE GF GH — — — = I GF G.H. G.E But H is also observed from D, therefore there is another equation of condition— namely, GE GH GD = I GH GD GE Taking next the point K, and supposing it fixed by the bearings from G and H, the observed angle at K gives the equation of condition o = G + H + K – 180° — sº, But K also observes and is observed from F: these bearings afford two more equations of condition, which are, o = G + F + IY — 180° — er; GH GF GK = , GF GK GH Take next the point L, and, supposing it first fixed by the observations from G and K, the observed angle at L gives o = G + K. -- L – 180° – s; But L observes and is observed from H and F, forming four new bearings, which must give as many cquations of condition ; they are o = G + H + L – 180° — sº, o = F + G + L – 180° — sº, GK GF GL GF GL GK = 4 GK GL GH GL GH GK I The point N may be first fixed by the bearings from L and G, and the observed angle at N will give the equation of condition - o = G + L + N – 180° — sis ; # t.r-~.: º2: REDUCTION OF THE TRIANGULATION. 28 I But N also observes and is reciprocally observed by K, hence two additional equations; these are o = G + K -- N – 180° — sis GL GN G K tº ºmºsº ºmºmº ºmsº I GN GK GL T Take next the point M, and let it first be fixed by the bearings from G and N; the the angle observed at M gives the equation - o = G -- M + N – 180° — s,s But M also observes and is reciprocally observed by L; hence the two equations, o = G + L + M. — 180° — ear GN GM GL_1 GM GL GN T Lastly, the point O being considered first fixed by observations from F and G, the observed angle at O gives o = IP + G + O. — 180° — ea. But O also observes and is observed from M and N ; hence there must from the four new bearings arise the following four equations of condition:- o = G + N + O – 180° — eas o = G + M + O – 180° — eat GM GN GO GN GO GM GIF GRC GN G0 = 1 *== mº, GK GN GO GF I The 39 equations thus deduced, being equal to the number of Superfluous bearings, are all the necessary geometrical relations of the figure—or more strictly speaking, they contain all the necessary relations; for many of them might be altered, and others substituted in their places, which would equally well contain the necessary relations. Each of the side equations, or those of the form AB AC AD. . . . AC AD AE might have been written in the form sin ACB sin ADC sin AIED [. sin ABC sin ACD sin ADE in which form they are actually used in the calculation. IN n 282 +. , PRINCIPAL TRIANGULATION, When the observed angles are substituted in these equations of condition, they should, but that they are all affected by errors, make all these equations identically true. As it is, however, none of them will be exactly satisfied, and the problem is, to apply to the observed bearings a system of small corrections that will, when the corrected angles are substituted in the equations of condition, render them identically true, and will also be the most probable system of corrections. For it is evident that the number of equations being less than the number of bearings or corrections, an indefinite number of systems of corrections might be obtained to fulfil the equations of condition, but that system which is required must make the function w it? -- w'a' + w” ar” + . . . the least possible, a w'a" . . . being the corrections to be determined, w w w” . the weights of the bearings to which they are to be attached. Spherical Evcess. In the calculation of the side equations, it is usual to subtract from each angle one- third of the spherical excess of the triangle to which it belongs, in accordance with Legendre's Theorem. The spherical excess is calculated from the formula _ a b sin 0. * = ...in IT Where a, b are two sides of the triangle, C the angle included by those sides, and r the radius of curvature of a vertical section of the surface in azimuth 45° for the mean latitude of the triangle.* l# . sm ---—- * In a former Section r was taken a mean proportional between the principal radii of curvature; the difference is insensible in the calculation of spherical excess, for the ratio of these two radii is g g / . where g g’ are the principal radii of curvature ; also e : . É.- : — & cosº a g Consequently the ratio of the radii is 1 + 4 el cos x which can only affect the 7th figure of the logarithm. - \-| . -- ſ- -.i|-g: $ .s : i REDUCTION OF THE TRLANGULATION. 283 The slowly varying quantity log (2 r" sin I”)-; computed with the elements of the figure of the earth given by the Astronomer Royal in the Encyclopædia Metropolitana, viz.: Semiaxis-major = 20923713 feet. Semiaxis-minor = 20.8538 Io feet. is shown in the following table:— Latitude. t! Latitude. 1. Latitude. t! 49 O •3717188 53 o •37I32I6 57 o • 3709399 IO . .3717ozo LO '37 I3053 IO '3709244. 2O •37I6853 2O •37I 2891 2O •37ogo90 3o .3716685 3o •37I2729 3o •37o8936 4O •3716518 4O •37I2567 4O •3708783 5o 371635I 5o '37 I2405 5o 370863o 5o o '3716184 54 o "3712244 58 o •3708477 IO •3716or 8 1O •37I2O83 IO '3708325 2O '3715851 2O •37II922 2O •3708174 3o •37I5685 3O •37II'762 30. 3708023 4O '37I5519 4O •37II602 4O •370.7872 50 '37I5353 - 5o '37 II.442 5o 370.772 I 5I O '37I5187 55 o ' ' ' '37 II 283 || 59 o '37o'7572 IO •37I5022 Io 37III 24 IO •3707422 2O 37.14856 20 37 Io965 2O || 3707273 3o •371469.I 3o 37 Io807 3o •37O7I25 40 •37I4526 40 ' | 37Io949 4O •3706977 5o •37I4362 5o •37IO492 5o •3706829 52 O •37I4I97 56 o 37Io934 6o o .3706682 IO '3714033 IO •37IoI77 IO •3706536 2O •3713869 20 37 Iooz I 2O •3706390 3o •37 I3705 3o 3709865 3o •3706244 4O •37 IS542 4o 3709709 4o .3706099 5o 3713379 5o 3709,554 5o || 3705955 53 o 3713216 57 o 3709399 || 61 o 37058 II log s = (absin C) + u – Io The spherical excesses of the triangles are thus found to be A/ Af . . . .ſ/ 5, -o-3942 s = 2.6370 sº- 5'9265 sa=o'5037 so-2-3667 sig= 7-586.4 ss=o. Io95 sri = 7. I598 sig= 14.8086 sa=o-4857 sia-4:4664 g sao F 5'5590 ss=o.3804 sis = 2.2464 * * 52 r = 8.or 57 £6= I'oz24 sit-7-2I29 sa,- 8.6094 5,-o.8oor sig=7.5oG9 sas–21.6768 ss=o.5oro sió=9-2973 sai-I2-3897 The following also enter into the side equations — (DEG) . . sas = I" 26oo (DFG) . , e, , = I". 34.13 (DHG) • , e, , = 5", 6931 N n 2 284 PRINCIPAL TRIANGULATION. Formation of the Algebraic Equations of Condition. We must now append an unknown correction to each of the observed bearings, and then substitute them in the equations of condition. Tor these unknown corrections, the notation (I), (2), (3), (4) . . . . . . (n) is adopted as convenient: that is, the bearings being written out consecutively, the n” bearing has the quantity + (n) attached to it. The following Table contains the observed bearings for all the points in this figure:— NAMEs of STATIONs. Bearing Reciprocal of ſº Weight. IFrom To O Z & J. Slieve Snaght 129 31 56-89 + (1) o-o8o Drung Point . . . 143 38 42-61 + (2 o-2O6 SouTII END OF BASE • { | Cundtham I54 26 43.58+ (3 o. I 58 Mount Sandy I97 9 34-2O+ (4 o.338 North end of base I97 9 35. I2 + (5 o-226 T! Sawel . . . . 8 55 54.08+ (6) 3.4355 South end of base J7 I2 28.36+ § I • 2 II ºw \* Drung Point . . 90 49 46.56-- (8) O-292 NORTII EMD or DASE.- Slieve Snaght IoI 37 42.67 + (9 o,886 Cundtham • Io'7 49 47.66+(Io I O23 L| Mount Sandy . . I97 I2 24.41+(II) O. I4I Mount Sandy 256 53 42-oo--(12 O-251 DRUNG POINT’ - º North end of base 27O 39 53. II +(I3 o-285 South cnd of base 323 31 41-394-(14 o:314. ſ| Slieve Snaght 8 46,734 (1 5 I-7I.4. - . Sandy .# s: ::::::::: o°359 * * * gº tº º Knocklayd & C 272 28.4I +(17 I-694 CUMUTII.ſ.lf HILL il North end of base § * 4.17+(18 o-og I South end of base 334 20 :::::::::: o: 291 L. Sawel . . . . 352 II 23:23-F (2O I-695 ſ Sawcl . . * 9 39 17:31 +(21) o.638 North end of base 17 13 II-94-H (22) o'o64 | South end of base 17 13 15.38--(23) O-206 MIow.y.z" SANDI" . : Drung Point . 77 4 22-13+(24) o.218 Cundtham 9I I3 I-16--(25) o: I 9 Slieve Snaght 93 46 32.44+(26 o:383 º ICnocklayd 272 37 40:18+(27), o-371 * i * ! } '# * # ; REDUCTION OF THE TRIANGULATION. NAMEs of STATIONs. Reciprocal of Bearing. Weight. From To O M W/ ſ' Cuileagh . tº dº C. I5 42 47. I7+(28 2.9Coş ICnocklayd • . . . 272 43 29-64-H (29 I.o861 Mount Sandy • . . . 273 26 45.74--(3o o. 2808 Cundtham . • . . . 275 48 ::::::::: O-4IO 5 SLIETE SyagirT • * { | North end of base . . . 281 1843-61 +(32 o-3671 Trostan • . • - || 282 5 *:::::::: I-82.57 Divis . . . . . . 307 7 I5-og-H ;: | 5:4849 South end of base . . . .309 I5 51.55+(35 I-7072 | Sawel . . . . . . . .335 39 5o-o8+(36) o:3139 ſ Cuileagh . Ç 36 17 4o.47+(37 4 IQI9 Slieve Snaght º I55 54. 24.72 + (38 O'3935 North end of base . 188 51 27.97 £3. o. Ig72 Mount Sandy . . . . I89 34 6.97+(4o O' Iy 44 SA IV.EL e • * • { | Knocklayd . . . . . 232 36 #: o:63o4. | Trostan . • . . . 245 42 3-63+(42 o:3952 Divis . . . . . . . 289 o 24.91 +(43 o:5746 | Slieve Donard . . . . .314 -2 12-off--(44 2.409 I Vicar's Cairn . . . . | 333 33 36.69+(45 4'9953 ſ Sawel . tº º 0. 53 I5 36.63+(46 o:4652 Mount Sandy . . . 93 II I2-o9+(47 o. I752 I(MoCALAYD . . . . . Slieve Snaght . . . 93 36 47-49+(48 o-2178 Trostan . . . . . 334 43 48-o/-H (49 O-3475 Divis . . . . . . . .346 I3 22.81 + (50 o-4856 ſ Sawel tº 0 & 0 & C 66 25 24-98-1-(51 2.6068 Slieve Snaght . . . . Io9 3 32-60+(52 3-4087 TROSTAy • 3 || ICnocklayd . . . . . I54 48 31.92 + (53 O-2530 Divis . . . . . . . .349 37 46-12 + (54 O-5222 Slieve Donard . . . 35o 58 27-o8+(55) 2 * 2 I-44. Vicar's Cairn . . . . 47 21 I6.71 + (56 o:27.75 Sawel . . . . Io9 5o 24.48-1-(57 C-5482 DYI. IS • * * * * Slieve Snaght . . . . I28 II 45-91 + (58 o:2427 Inocklayd . . . . 166 24 47-61 + (59) o:5O23 Trostan • • • | 169 44 31.59-1-(6o O-95og Slieve Donard . . . 352 27 5.77 + (61 o:73ol. gº iſ . . . 82 41 54.37-1-(62 I5'5I9 I * Cy ("f Sawcl . . . . I II.64-H (6. * - ºr VICAIR'S CAIIEN ‘il Divis . . . . .# º: 58-79 ić º: Slieve Donard • 286 20 Io. I5+(65) 2. I358 ſ| Cuileagh . . . . 9I 50 Io-oš + (66 O'24.32 | | Vicar's Cairn . . . Ioé 53 :::::: 2.6985 Szrey E. Doy ARD . . . . Sawel . * † 134 56 41.86+ (68 o. 1815 Trostan . . Ö 171 9 49.62+(69 o. 2167 l Divis tº I72 31 46.07 --(70 o. 2886 Slieve Snaght . . 195 19 23-89-1-(71) 1.3281 | CUILC4G II . , Sawel . tº º 2 I 5 39 ; :º) O'4924. Vicar's Cairn . . 261 42 41.93 + (73 o:54:55 L| Slieve Donard 27o 18 14.77-1-(74) o.82.47 -----sº 286 . . . PRINCIPAL TRIANGULATION. In the substitution of these bearings in the equations of condition, we shall take first the angle equations in the order in which they have been deduced, and after them the side equations in the order in which they have been deduced. The substitution will then be as follows:— - - - - - - - - I. A = 33 36 53.51 - (2) + (5) I} = 73 37 18.20 — (7) + (8) C = 52 51 48.28 – (13) + (14) I79 59 58-99 180 + s = 18o o o-3942 - 1.4042 sº o––14042–(2)+(5)-(7)+(8)–(13)+(14) III. f B = 105 23 3%85 — (8) + (II) E = 59 51 Io.19 – (22) + (24) C = 13 46 II. II – (12) + (13) I79 59 59. I5 18o + s = 18O O o'Io95 - O'9595 o-—o.9595–(8)+(II)-(12)+(13)–(22)+(24) V. D = 46 35 48.62 — (18) + (19) A = 42 42 51.54 – (3) + (5) B = 90 37 19:30 — (7) + (Io) I79 59 59:46 180 + s = 18o o o-3804 – or 92.04 II. A = 53 36 539 – (2) + (4) E = 59 5r 6.75 – (23) + (24) C = 66 37 59:39 – (12) + (14) I79 59 57.73 18o + s = 180 o o'5037 — 2.7737 cº-º-º-º-º-Go-Gº-Go IV. s : * D = 63 ºf 23.87 – (16) + (19) A = 42 42 50-62 – (3) + (4) P = 73 59 45-78 – (23) + (25) I79 59 59.27 180 + i = 180 o , o,4857 — I-2157 of -1.2157–(3)+(4)–(16)+(19)–(23)+(25) VI. 49 5-8I – (30) + (35) 37 37.31 — (1) + (4) 33 17-off — (23) + (26) F = 35 E = 76 I8o 180 + s = 180 O o. 18 o 1 oz.24 — o'8424 o-—o.92O4–(3)-1-(5)–(7)+(Io)–(I 8)+(9) o:= -0.8424–(1)+(4)–(23)+(26)–(30)+(35) VII. O Af £f F = 27 57 7.94 – (32) + (35) A = 67 37 38.23 — (1) + (5) B = 84 25 I4.31 – (7) + (9) I8o O o-48 180 + s = 180 o o'80of — o'32OI w vii.I. : 27 20.87 – (31) + (35) 54 46-69 — (1) + (3) 37 53-94 - (19) + (15) F = 33 A = 24 D = I2 I * I8o * 18o + c = 18o o I-50 o o'5olo + o-9999 o=—o.3261-(1)+(5)-(7)+(9)-(32)+(35) o- +9.9999-(1)+(3)+(15)–(19)–(31)+(35) :* | # l REDUCTION OF THE TRIANGULATION. 287 IX. O J Af Q = 33 39 42.25 – (38) + (40) F = 62 13 4.34 – (30) + (36) P = 84 7 15:13 – (21) + (26) I8o o 1,72 180 + i = 18o o 2.6370 — o'917o o--o'917o-(21)+(26)–(30)+(36)–(38)+(40) XI. G = 76 43 3&42 –(38) + (41) F = 62 56 20-44 – (29) + (36) H = 4o 21 Io.86 – (46) + (48) I8o o I-72 18o + e = 18o O 7. I 598 – 5.4398 o=-5.4398-(29)+(36)–(38)+(41)–(46)+(48) XIII. O f & W G = 13 5 8.49 – (41) + (42) H = 78 31 48.56 – (49) + (46) K = 88 23 6.94 – (51) + (53) I8o o 3.99 I8o + s = 180 O 2.2461 + I-7439 o- + I-74.39–(41)+(42)+(46)–(49)–(51)+(53) XV. L = 59 .54 7. II – (57) + (60) G = 43 18 21-28 - (42) + (43) K = 76 47 38.86 – (54) + (51) I8o o 7.25 I80 + s = 180 o 7' 5069 — o.2569 95 -o-2569–(42)+(43)+(51)–(54)–(57)+(60) C. XVII. L = 18 2í a£43 — (57) + (58) G = 133 6 o'19 – (38) + (43) F = 28 32 34.99 — (34) + (36) I79 59 56.61 18o + s = 18O o 5'9265 ſº-º-º- – 9:31.65 °= ~9:3#65-(34)+(36)–(38)+(43)–(57)+(58) X. G = 32 57 3.25 – (38) + (39) F = 54 21 6.47 – (32) + (36) B = 92 41 48.59 – (6) + (9) I79 59 58.31 180 + s = 18o o 2.3667 – 4:0567 o-–4,0567–(6)+(9)–(32)+(36)–(38)+(39) XII. G = 43 & 48.17 –(4) + (41) E = 97 I 37.13 – (27) + (21) H = 39 55 35.46.- (46) + (47) 18o o o,76 180 + s = 180 o 4.4664 — 3-7064 o- -3.7c64+(21)–(27)–(40)+(41)–(46)+(47) XIV. O & f/ G = 89 47 38.91 – (38) + (42) F = 53 34 19-33 - (33) + (36) K= 36 38 7.62 – (51) + (52) 18o o 5.86 180 + s = 18o o 7.2129 – I-3529 or= -1,3529–(33)+(36)–(38)+(42)–(51)+(52) XVI. L = 55 34 23:13–(57) + (59) G = 56 23 29.77 – (41) + (43) H = 67 2 13.82 — (50) + (46) I8o O 6.72 180 + e = 180 o 9.2973 – 2-5773 - o- -2.5773–(41)+(43)+(46)–(50)–(57)+(59) XVIII. N = 3; 35 4:21 –(68) + (70) G = 25 I 47.15 – (43) + (44) L = 117 23 18.71 — (61) + (57) I8o o Io-o'7 180 + s = 18o o 7.5864. + 2.4836 o= +2.4836–(43)+(44)+(57)–(6%)- (68)+(70) 288 PRINCIPAL TRIANGULATION. XIX. N = 33 13 746 –(68) + (69) G = 68 20 8.43 – (42) + (44) R = 75 26 57.90 – (55) + (51) I8o o I.4°og 180 + e = 18o o 14.8086 — o'7186 o––o.7.186–(42)+(44)+(51)–(55)–(68)+(69) XXI. G = 44 33 II.78 – (43) + (45) L = 62 39 7.77 – (56) + (57) M = 72 57 47.15 – (63) + (64) 18o o 6.70 180 + s = 180 O 8-ol. 57 – I 3 I57 o-–1.3157–(43)+(45)–(56)+(57)–(63)+(64) XXIII. O f Af O = 54 38 22.53 – (72) + (74) G = 82 15 28:4I – (44) + (37) N = 43 6 31.81 — (66) + (68) 18o o 22.75 180 + s = 18o o 21.6768 + I of 32 o- + 1.0732-1-(37)–(44)–(66)+(68)-(72)+(74) XX. C f 7, G = 19 31 24.63 – (44) + (45) N = 28 3 39-41 – (67) + (68) M= I32 24 58.51 – (63) + (65) I8o O 2-55 18o + s = 180 o 5:5590 – 3:oogo O = –3:0090-(44)+(45)–(63)+(65)–(67)+(68) XXII. O f f/ O = 20 20 28.35 – (71) + (72) F = 4o 2 57.09 – (36) + (28) G = I 19 36 44.25 – (37) + (38) I8o 9-69 18o + s = 180 o 8.6094 + 1-oSoó o- + I'oSoó--(28)–(36)–(37)+(38)–(71)+(72) XXIV. O = 46 2 49-69 – (72) + (73) G = 62 44 3.78 – (45) + (37) M = 71 13 17.27 – (62) + (63) I8o o Io. 74 I8o + s = 18o O I2.3897 – I-6497 9- - I-6497+(37)–(45)–(62)+(63)–(72)+(73) In these equations the co-efficients of the unknown quantities (1), (2), (3) . . . are all units, positive or negative; in the side equations each has a co-efficient to be calculated, on this principle: if A be any given angle, and w a very small unknown angle whose square may be neglected, log sin (A + z) = log (sin A + a cos A) = log sin A + M & cot A Where M is the modulus of the common system of logarithms. If a be expressed in seconds, not in arc, then Where p = M sin I". The quantity p. cot A a has therefore to be added to log sin A log sin (A + z) = log sin A + p cot A & 2 and as it is convenient to take out from the logarithmic tables those figures which are to .#1 | REDUCTION OF THE TRIANGULATION. 289 be added to the last decimals of 7-figure logarithms, we must add 7 to the logarithm of pº, so that log p = log M sin 7” = I 3233592 The calculation of the side equations will be as follows:— XXV. in CBB in CAE in CBA-, sin CBE sin CEA sin CAB T CEB = 55 5í 1619–62365-(22)+(24) CBE = 106 23 37.85–69363– (8)+(II) CAE = 53 3o 51-59–o. 1679– (2) + (4) CEA = 59 5 I 6.75—o. 1679–(23)+(24) CBA = 73 37 18.20–o. 1314— (7)+ (8) CAB = 53 3o 52.51—o. 1314— (2)+ (5) 9.936 8846 263+12-2284 (24)–(22)} 9.982 or 16 636+ 6.1878 (8)–(11)} 9-905 2.588 175+ 15:57 19ſ (4)– (2)} 9.936 8802 589-1-12.22894(24)–(23)} 9-982 oog I 154+ 6, 1882% (8)— (7)} 9-905 2603 of 9-1-15.5717 ( (5)– (2)} 9.824 I525 592 9.824 I522 294 2 2.94. + 3 298 ^ = + 3.298 – o-oooz (2) + 15:5719 (4) — 15:5717 (5) – 6.1882 (7) + o-ooo4(8) + 6.1878 (11) - I2:2284 (22) + 12.2289 (23) – o-ooo.5 (24). XXVI. sin ACB sin AEC sin ADE sin ABD = I sin ABC sin ACE sin AED sin ADB T ACB = 53 5: 48.28–6(314–(3)+(4) ABC = 73 3% 1820–é1314– (7)+(8) ABC = 59 51 6.75—o. 1679–(23)+(24) ACE = 66 37 59.39–o. 1679–(12)+(14) ADE = 63 17 22.87—o. 1619—(16)+(19) AED = 73 59 45-78–o. 1619–(23)+(25) ABD = 90 37 I9.30—o. 1268– (7)+(Io) ADB = 46 39 48.62—o. 1268–(18)+(19) 9-901 5662 958+15.94514(14)–(13)} 9.936 8802 589-1-12.2289((24)–(23)} 995o 99.25 396-- Io:5944((19)–(16)} 9.999 9744 o89+ o-2286% (7)–(Io)} 9789 4135 og2 I8 92.4 + I6 Io& 9,982 oog I 154-H 6, 1882; (8)– (7)} 9.962 8351 240+ 9.097oſ(14)–(I2)} 9.982 83.29 529-- 6.0391 ((25)–(23)} 9.861 7347 ool + 19.8668((19)–(18)} 9-789 4II8 924 ** * *ioš + 6.4168 (7) – 6, 1882 (8) – o 2286 (10) + 9-0970 (12) — 15.9451 (13)+ 6,8481 (14) - Io:5944 (16) + 19.8668 (18) — 9.2724 (19) — 6, 1898 (23) + 12:2289 (24) – 6:0391 (25). 290 PRINCIPAL TRIANGULATION. sin AFB sin ADF sin ABD ſº sin ABF sin AFD sin. ADB 7" O / Z/ A/ AFB = 27 57 7.94-o'2667–(32)+(35) ADF = 121 37 53-94-o' 1670–(19)+(15) ABD = 90 37 19:30–o-I268— (7)+(Io) 9-670 9262 of 1 +39.6790{(35)–(32)} 9.93o I529 I71 + 12.96.92 ((19)–(15)} 9.999 9744 obo + o-2286 (7)—)Io)} 9-601 off35 31 I 46 I55 — Io 844 & f f / ABF = 84 25 14.31—o.2667— (7)+ (9) AFD = 33 27 20.87—o. 1670–(31)+(35) ADB = 46 39 48.62–o. 1268–(18)+(19) 9.997 93.75 820+ 2.0568% (9)- (7)} 9,741 3823 334+31,8644((35)–(31)} 9,861 7347 ool + 19.8668(19)-(18)} 9-60I oš46 I55 o = — Io,844 + 2.2854(7) – 2.0568 (9) — o'2286 (Io) – 12:9692(15) + 19.8668 (18)—6.8976 (19) + 31.8644 (31) — 39.6790 (32) + 7.8146 (35). sin AFD sin AEF sin ADE sin ADF sin AFE sin AED ~ * AFD = 33 27' 20:87–04670–(31)+(35) AEF = 76 33 17.06–o.3408-(23)+(26) ADE = 63 17 22.87—o. 1619-(16)+(19) 9,741 3823 334+31,8644((35)–(31)} 9.987 93.07 466+ 5.0337((26)–(23)} 9.95o 9925 396-- Io:59444(19)–(16)} 9.68o 3056 196 13 787 + 42 409 O / f/ f / ALF = 121 37 53.94–6.1670–(19)+(15) AFE = 35 49 5-81—o-34o8–(30)+(35) AED = 73 59 45-78—o. 1619–(23)+(25) 9-930 1529 171 + 12.96.92 ((19)-(15)} 9,767 3155 ob7+ 29.1742 ((35)–(30)} 9.982 8329 529-- 6:03914(25)–(23); 9.68o 3013 787 o = + 42.409 + 12.96.92 (15) - Io:5944(16) – 2.3748 (19) + 1-ooj4(23) – 6.0391 (25) + 5.0337 (26) + 29.1742 (30) – 31.8644(31) + 2.6902 (35). pº REDUCTION OF THE TRIANGULATION. 29 I sin FGB sin FEG sin FBE sin FBG sin FGE sin FEB T' Q £ f/ £/ + FGB = 32 57 3.25—o.7889–(38)+(39) FPG = 84 7 15:13—o.8790—(21)+(26) "BB = 95 34 41.74—o-o;41— (9)--(11) 9:735 5326 oz.4+32-4833 ((39)–(38)} 9.997 7094 753 + 2.16824(26)-(21)} 9-997 93.84 645+ 2.0564ſ (9)-(II)} 9-73 I I 805 422 46 792 – 41 37o O & &/ #/ FBG = 92 41 48.59–0.7889— (6)-- (9) FGE = 33 39 42-25-o.8790–(38)+(40) FEB = 76 33 20.5o-o-o/41 —(22)+(26) 9.999 5188 215-H o'99.17% (6)– (9)} 9743 7333 453+31-6169(40)–(38)} 9.987 9326 I24+ 5.0333{(26)–(22)} 9.731 1846 792 o = - 41-370 - O'991.7 (6) + 3.0481 (9) — 2.0564 (11) – 2.1682 (21)+ 5,0333 (22) — 2.8651 (26) - o'8664 (38) + 32-4833 (39) — 31-6169 (40). sin GED sin GFE sin GDF sin GDE sin GEF sin GFD ~ * GºD = 8; 33 43.85–64200-(21)+(25) GFE = 62 I3 4.34—o.8790–(30)+(36) GDF = Io9 47 23.5o-o-4471-(2O)+(15) 9°995 2733 o42 + 3-1234((25)–(21)} 9.946 808o 174+ 11.0929((36)–(30)} 9,987 2983 848+ 5-16765((20)-(15)} 9-929 3797 of 4 813 188 – 16 124 GDE = 8: 7 53.31-cºco-(16)+(20) GEF = 84 7 15:13–o.8790–(21)+(26) GFD = 59 51 19-40–o.4471–(31)+(36) 9.994 7764 574-- 3:285354(20)-(16); 9.997 7094 753 + 2.1682 ((26)–(21)} 9.936 8953 861 + 12.2272 {(36)–(31)} 9-929 3813 188 **T***4- 5:16765 (15) + 3.28535 (16)+1.8823 (20) – o 0552 (21)+3:1234 (25) – 2:1682 (26) ~ II og29 (30) + 12.2272 (31) — I. 1343 (36). 292 PRINCIPAL TRIANGULATION. XXXI. sin GFE sin GHF sin GEH sin GEF sin GFH sin GHE ** O / A / A/ x O & // & / GFE = 62 13 4.34–0.8790–(30)+(36) GEF = 84 7 15:13–6.8790—(21)+(26) GHF = 4o 21 Io.86–2.3866–(46)+(48) GFH = 62 56 20-44–2.3866–(29)+(36) GEH = 97 I 37.13–14888–(27)+(21) GHE = 39 55 35.46–1.4888–(46)+(47) 9.946 808o 174+ 11.0929((36)–(30)} 9.997 7094 753 + 2. 1682 ((26)–(21)} 9-8II 2306 465+24,78158(48)–(46)} 9.949 6424 594-H Io-7567 ((36)–(29)} 9.996 7259 368+ 2.5952 ((27)-(21)} 9.807 3990 862+25:1584(47)–(46)) 9.754. 7646 oo7 9.754. 75Io 209 5Io 209 + 135 798 o- + 135.798—o.4270 (21)– 2:1682 (26) + 2.5952 (27) + 10-7567 (29)—11.0929 (30)+o.3362 (36) +o-3769 (46)–25-1584 (47) +24.7815 (48). XXXII. sin GHE sin GDH sin GED º sin GEH sin GHD sin GDE T * O / 4/ f O y z ř f f GHE = 39 55 35.46–1,4888–(46)+(47) GEH = 97 I 37.13 — 1.4888 —(27)+(21) —(15)+(17)} GDH = 8o 1 54.82—1.8977–(17)+(20) GHD = 39 36 53.4546–1.89778–(29)+(31)} -(46)+(48)} GED = 81 33 43.85–0.4200-(21)+(25) GDE = 81 7 53.31 –o.4200 —(16)+(20) 9.807 3990 862-1-25-1584 (47)–(46)} 9.996 7259 368+ ° 2'5952 ((27)–(21)} (17)–(15)} 9.993 3933 153+ 3-7007((20)-(17)} 9-804 5595 902 +25°4384 (31)–(29)} - {(48)–(46)) 9.995 2733 oz-F 3-1234((25)-(21)} 9.994 7764 574+ 3.28535((20)—(16)] 9.796 off.57 o'S7 9-796 of 19 844 19 844 + 37 213 o- +37.213+25.4384G15) +3.38535 (16)–29,1391 (17)+ o-41535(20)—o.5282 (21)+ 3-1234(25) – 2:5952 (27)+25°4384 (29)-25'4384(31)+o:28oo (46)+25-1584 (47)—25.4384(48). REDUCTION OF THE TRLANGULATION. 293 XXXIII, sin GFH sin GKF sin GHK I sin GHF sin GFK sin GKH T GFH=6; 56 2644–33866–(29)+(36) GHF=43 21 1686–3.3866–(46)+(48) GKF =36 38 7.62–2.4043–(51)+(52) GFK=53 34 1933–2.4043–(33)+(36) GHK=78 31 48.56–0.7487–(49)+(46) GKH =88 23 6.94—o.7487–(51)+(53) 9.949 6424 594-H Io-7567}(36)–(29); 9-8II 2306 465+24,781.5% (48)–(46); 9,775 7648 632 + 28-3149; (52)–(51)} 9-905 5784 924+ 15:5395{(36)–(33): 9.991 2388 284-- 4:2723;(46)–(49); 9.999 8274 627+ o-5936}(53)—(51); 9-716 6461 5 Io 9.716 6366 or 6 366 or 6 + 95 494 o = +95.494-10-7567 (29)+ 15:5395 (33)–4,7828 (36)+29,0538 (46)—24,7815 (48)—4,2723 (49) –27-7213 (51)+ 28-3149 (52)—o:5936 (53) XXXIV. sin GFK sin GLF sin GRL I sin GKF sin GFL sin GLK T . A & J/ - O / / / Z/ GFK=3; 34 1933–34043–(33)+(36) GKF=36 38 7.62–2-4O43–(51)+(52) GLF = 18 21 21-43-I-9755–(57)+(58) GFL=28 32 34.99–I-97.55–(34)+(36) GKL=76 47 38.86–2.5023–C54)+(51) GLK=59 54 7. II–2.5023-(57)+(60) 9-905 5784 924+ 15:5395 (36)–(33)} 9.775 7648 632 + 28-3149 (52)–(51)} 9.498 1869 857+63-4591 (58)—(57)} 9.679 2557 496+38-7103}(36)–(34); 9,988 3594 756+ 4.9410}(51)–(54); 9.937 og77 489-1-12.2046}(60)–(57); 9°392. I249 537 9-392 II.83 617 * * 183 617 + 65 920 * . ° = +65'920-15:5395 (33)+38-7103(34)–23-1708 (36)+33-2559 (51)–28-3149 (52)–49419 (54) -51-2545 (57)+ 63-4591 (58)-12-2046 (60) 2.94. PRINCIPAL TRLANGULATION. .DXXXV. sin GLK sin GHL sin GICH sin GRL sin GLHI sin GHRT * GLK=5554 #11–3.5023-(57)+(60) GRL=764; 38.86–35923–(3)+(3*) GHL=67 2 13.82—3.0991-(50)+(46) GLH=56 34 23:13–3.0991-(57)+(59) GICH=88 23 6.94—o.7487–(51)+(53) GHK=78 31 48.56–0.7487–(49)+(46) 9-937 og77 489-H 12.2046 (60)–(57); 9,988 3594 756-H 494Lo;(51)–(54); 9:964 I428 Io2+ 8.92.165}(46)–(50); 9.921 4684 762 + 13,898o;(59)–(57); 9.999 8274 627+ o-5936 (53)—(51); 9.991 2388 284+ 4,2723 (46)–(49); 9-901 of,8o 218 9-901 off07 802 67 802 + 12 416 o = + 12.416+4.64935 (46)+4.2723 (49)–892.165 (50)-5-5346 (51)+0.5936 (53)+4.9410 (54) + 1.6934 (57)—13.898o (59)+12-2046 (60) XXXVI. sin GNL sin GIKN sin GLK º sin GLN sin GNK sin GKL T I GNL=3; 3; 421–3.5288–(68)+(70) GLN=11; 23 1871–35288–(61)+(57) GKN = 75 26 57.90–4,9362–(55)+(51) GNK= 36 13 7.76–4,9362–(68)+(69) GLIC=59 54 7.11-2.5023-(57)+(60) GKL= 76 47 38.86–2.5023–C54)+(51) 9,785 2736 788-|- 27.35674(70)–(68); 9.948 3704 779-F Io:9083! (61)–(57); 9.985 8395 551 + 5.4656 (51)–(55); 9.771 4782 857+ 28.749.9% (69)–(68)} 9,937 ooz7 489+12-20464(60)-(57); 9,988 3594 756+ 49419 (51)–(54); 9,708 2109 828 9.708 2082 392 o82 392 + 27 436 o = + 27,436+o:5246 (51)+4.941o (54)-54656 (55)-1-2963 (57)+12-2046 (60)-10-9083 (61) + 1.3932 (68)—28,7499 (69)+27.3567 (70) f§: ; ; : º t ! : | * . - REDUCTION OF THE TRLANGULATION. 295 XXXVII. sin GMN sin GLM sin GNL * sin GNM sin GMI, sin GLN = I O f // Z/ GMN = I32 24 58-51-I-8530–(63)+(65) GLM = 62 29 7.77–2.6719–(56)+(57) GNL = 37 35 4:21–2.5288–(68)+(70) 9,868 2152 767 -- 19.2366 ((63)–(65)} 9.947 8687 283 + Io.9678((57)–(56); 9.785 2736 788+27.3567((7o)–(68); 9.601 3576 838 491 539 + 85 299 GNM = 28. § 33.41–18530–(67)+(68) GML = 72 57 47.15–2-6719–(63)+(64) GLN = II.7 23 18.71–2.5288–(61)+(57) 9-672 4697 or 4+39.4985((68)–(67); 9-98o 5089 746+ 6.4523{(64)–(63)} 9.948 3704 779-i-Io-9083{(61)–(57); 9-60I 3491 539 o = +85299-ro'9678 (56)+21,8761 (57)—10.9083 (61)+25.6889 (63)–6,4523 (64)— 19:2366 (65) +39.4985 (67)–66,8552 (68)+27.3567 (70) XXXVIII. sin GNM sin GON sin GMO sin GMN sin GNO sin GOM E I GNM = 28 3. 39%.1-#8530–(67)+(68) GON = 54 38 22.53—7.2256–(72)+(74) GOM = 71 13 17.27–4,1299–(62)+(63) 9-672 4697 or 4+ 39.4985 ((68)–(67)} 9-911 428o 201 + 14.9424 {(74)–(72)} 9-976 2414 945+ 7.15945{(63)–(62)} 9:56,o 1392 I60 57 859 + 34 30I GMN = 133 24 5831–18530–(63)+(65) GNO = 43 6 31.81–7.2256–(66)+(68) GOM = 46 2 49.69—4:1299–(72)+(73) 9.868 2152 767- 19-2366{(63)–(65)} 9,834 65oo 599-H 22.4947((68)–(66)} 9.857 2704 493 + 20-300I {(73)–(72)} 9:56,o I357 859 °= +34'301-7-15945(62)-12-07725(63)+ 19.2366(65)+22.4947(66)—39.4985(67)+17°oo38 (68) +5.3577 (72)-20-3oor (73)+ 14.9424 (74). 296. PRINCIPAL TRIANGULATION. GKF = GNK = GON = GFO = sin GIKF sin GNK sin GON sin GFO sin GFK sin GKN sin GNO sin GOF T * º 36 38 7.62–3.4043–(51)+(52) 36 13 7.76–4,9362–(68)+(69) 54 38 22:53—7.2256-(72)+(74) 4o 2 57.09–2.8698–(36)+(28) 9.775 7648 632 + 28-31498 (52)–(51)} 9.771 4782 857+ 28.74994(69)–(68)} 9-91 I 428o 20I + 14.9424 (74)–(72)} 9-808 5042 860+25.0496 (28)–(36)} 9.267 I754 55o 442 obg + 312 461 GFIX GKN GNO GOF - O Aſ A/ & / 53 34 1933–2.4043–(33)+(36) 75 26 57.90–4,9362–(55)+(51) 43 6 31.81–7.2256–(66)+(68) 20 20 28:35–2.8698–(71)+(72) 9-905 5784 924+ 15:5395{(36)–(33)} 9,985 8395 551 + 5.4656((51)–(55)} 9,834 65oo 599-1-22.4947 ((68)-(66); 9.541 of 61 or 5+56.7964 (72)-(7I)} 9-267 I442 obg o= +312.461 +25.0496 (28)+15:5395 (33)-405891 (36)-337805(5)+28.3149(32)+5.4656 (55) +22.4947(66)–51-2446(68)+28.7499(69)+ 56.7964(71)–71-7388 (72)+ 14.9424 (74) The 39 geometrical equations of condition, when expressed algebraically, are then as follows:— II. II I. IV. VI. VII. VIII. IX. XI. XII. XIII. XIV. XV. XVI. Equations 4. º — 1.4042 – (2) + (5) – (7) + (8) — (13) + (14) – 2,7737 – (2) + (4) — (12) + (14) - (23) + (24) – o'9595 – (8) + (II) - (12) + (13) — (22) + (24) — 1.2157 – (3) + (4) - (16) + (19) — (23) + (25) – o 92.04 - (3) + (5) – (7) + (Io) – (18) + (19) — o-8424 - (1) + (4) — (23) + (26) — (30) + (35) – o'320I – (1) + (5) – (7) + (9) — (32) + (35) + o-9999 - (1) + (3) + (15) — (19) — (31) + (35) o:917o - (21) + (26) – (30) + (36) — (38) + (40) — 4.0567 - (6) + (9) — (32) + (36) — (38) + (39) – 5.4398 - (29) + (36) – (38) + (41) — (46) + (48) — 3.7064 + (21) — (27) — (40) + (41) — (46) + (47) + 1.7439 – (41) + (42) + (46) — (49) + (51) + (53) — 1.3529 – (33) + (36) – (38) + (42) — (51) + (52) – o 2569 – (42) + (43) + (51) - (54) - (57) + (60) – 2,5773 – (41) + (43) + (46) - (50) — (57) + (59) I!EDUCTION OF THE TRIANGULATION. 297 2XVII. XVIII. lXIX. YXXI. XXII. 2XXIII. YXIV. YXXV. : . 9°3165- (34) + (36) – (38) + (43) – (57) + (58) + 2'4836- (43) + (44) + (57) – (61) – (68) + (7o) - Oº7I86- (42) + (44) + (51) – (55) – (68) + (69) - 3*oo9o- (44) + (45) - (63) + (65) – (67) + (68) - I-3157- (43) + (45) - (56) + (57) – (63) + (64) + I-o8o6+ (28) - (36) – (37) + (38) – (71) + (72) + I-o732 + (37) - (44) - (66) + (68) – (72) + (74) - I-6497 + (37) - (45) - (62) + (63) – (72) + (73) + 3-298o-o-ooo15 (2)+15:5719 (4) - 15.57175 (5) – 6.1882 (7) + o-ooo4577 (8) +6-1878 (II)-12-2284 (22)+12-2289 (23)—o-ooo5 (24) + 16-1o8o+6-4168 (7) - 6·1882 (8) – o.2286 (1o) + 9-o97o (12) — 15.9451 (13) +6·8481 (14) - Io*5944 (16) + 19.8668 (18) - 9-2724 (19)—6.1898 (23) +I2-2289 (24) - 6-o391 (25) - Io·844o+2-2854 (7) - 2-o568 (9) – o·2286 (1o) – 12-9692 (15) + 19.8668 (18) -6-897o (19)+31-8644 (31)-39-679o (32)+7.8146 (35) + 43°4o9o+I2-9692 (15) - Io-5944 (16) - 2-3748 (19) + 1.oo54 (23)-6-o391 (25) +5-o337 (26)+29-1742 (3o)-31-8644 (31)+2-69o2 (35) - 4I-37oo-o-9917 (6) + 3-o481 (9) - 2-0564 (11) - 2-1682 (21) + 5-o333 (22) -2-8651 (26)-o-8664 (38)+32-4833 (39)-31-6169 (4o) - 16· I24o-5-16765 (15) + 3•28535 (I6) + I-8823 (2o) - o-9552 (21) + 3-1234 (25) -2-I682 (26)-II-o929 (3o)+I2-2272 (31)-I-I 343 (36) + I 35-798o-o-427o (2I)- 2-I682 (26) + 2-5952 (27) + Io-7567 (29) - II-0929 (3o) +o-3362 (36)+o-3769 (46)-25·I 584 (47)+ 24-7815 (48) + 37-213o+ 25-4384(15) +3•28535 (16)-29-I 39I (I7)+o-41535 (2o)-o*5282 (21) + 3-I234 (25)-2-5952 (27) + 25•4384 (29) - 25•4384 (31) + o•28oo (46) + 25· I584 (47)-25-4384 (48) 95•494o-1o-7567 (29)+ 15-5395(33) - 4-7828 (36) + 29-o538 (46)- 24°7815 (48) -4-2723 (49)-27-7213 (51)+ 28-3I49 (52)-o*5936 (53) 65-92oo-I5-5395 (33)+38-71o3 (34)-23•17o8 (36)+33•2559(5I)-28·3149(52) -4-94Io (54)-51-2545 (57)+63·459I (58)-I2-2o46 (6o) 12•416o+4-64935 (46) + 4•2723(49) - 8-92I65 (5o) - 5-5346 (51) +o*5936 (53) +4-941o (54)+I-6934 (57)-I3-898o (59)+I2-2o46 (6o) - 27-436o+o-5246 (51) + 4-94Io (54) - 5•4656 (55) - I-2963 (57) + I2•2o46 (6o) - Io-9o83 (61)+ I-3932 (68)-28-7499 (69)-F 27-3567 (7o) - 85-299o-Io· 9678 (56)+2I-8761 (57)- Io*9o83 (61)+ 25•6889(63)-6.4523 (64) -19-2366 (65)+39-4985 (67)-66.8552 (68)-+27-3567 (7o) - 34-3o1o-7-15945(62)-12-o7725(63)+ 19-2366(65)+ 22-4947 (66)-39-4988 (67) + I7-oo38 (68)+ 5-3577 (72)-2o-3ooI (73) + I4•9424 (74) • +312-461o+25-o496 (28)+15-5395 (33)-4o-5891 (36)-33-78o5 (51)+28-3149 (52) + 5-4656 (55)+22-4947 (66)-51.2446 (68)+28-7499 (69)+56-7964(7*) -7I •7388 (72)+I4•9424 (74) XXVI. XXVII. 2XXVIII. YXXIX. XXX. YXXXI. XXXII. XXXIII. 2XXXIV. XXXV. YXXXVI. XXXVII. XXXVIII. YXXXIX. -H -+ IP p 298 PRINCIPAL TRIANGULATION. These equations correspond to the equations of condition (I) o = a + a, r, -- a, c, -- a, a, + . . . o = b + b, w, + b, c, -i- b, a, + . . . o = c + c, r, + c, ar, -- c, as + . . . O = q + qi ar, + q, w, -- 7, as + . . . . at page 262, and we have now to form the next set of equations; namely equations (5) page 263 to, ºr = a, A. -- bi A, 4- c. As + . * • Q: An wa wa = a, A1 + b, A., + c, As + . . • ?: An to; a`3 -: as ºr + b. *, + c, A, -- . . • ?: An wn am = an A. -- bin X, + Cm *3 + ' ' ' ' qm An x, x, x, . . . being a new system of unknown quantities. These quantities are generally designated by the Roman numerals I, II, III, IV, V, ' ' ' ' The method of formation of this second set of equations is obvious, the symbols w, w, w, . . . w, corresponding with the symbols (1), (2), (3) . . . (m). They are as follow:— Equations B. s: (1) = — VI — VII — VIII sº (2) = — I — II — O.OOO2 XXV sia (3) = – IV — v + vin - is (4) = + II + IV + VI + 15:5719 XXV o°338 sia (5) = + 1 + v + vir – 15:57.7 xxy -- (6) = — X – o 99.17 XXIX 3.4355 +H: (7) = — I — V – VII - 6°1882 XXV + 6.4168 xxvi + 2.285.4 xxvii + I — III + O.OOO4 XXV – 6.1882 XXVI + VII + X – 2:oj68 XXVII + 3.0481 xxix -j- (10) = + v - o'2286 XXVI – o 2286 xxvii -- -j- (11) = + III + 6-1878 XXV – 2.0564 xxix o° 141 à (12) = – II – III + 9-0970 xxvi sº (13) = - I + III – 15.9451 xxvi + (14) = + I + II + 6.8481 xxvi + VIII - I2.9692. XXVII + 12.9692. XXVIII — 5:16765 XXX + 25.4394 xxxii # (16) = — IV - Io:5944 XXVI – Io. 5944 XXVIII + 3.28535 XXX + 3.28535 XXXII i.:.-3. . REDUCTION OF THE TRIANGULATION. 299 ;:;; (17) = ΣΙ (18) = :;(19) = Σi; (2o) = Σi; (2 I) = ;;;; (24) = =; (25) = Eis; (26) = =:; (27) = ;:; (28) = ;:;; (29) = ;ia (3o) = ;:;:, (31) = ;;;, (32) = ;:;;:; (33) = ;:;;;(34) = ;*#;, (35) = ;j;, (36) = ;;;, (37) = ;;, (38) = ;;;, (39) = =;;, (4o) = :;:;:; (41) = E. (42) =  (43) = ΣΕ (44) = Σ, (45) = £, (46) = Σῆ (47) = 355 (48) = ΣΕ (49) = Σὰ (5o) = Å (51) = FÈ, (52) = &#£ (53) =  (54) = -+ -- -+ -+- 29* 139I XXXII V + I9-8668 xxvI + I 9.8668 xxvII IV -+- V — VIII — 9. 2724 XXVI — 6.897o XXVII — 2.3748 XXVIII I. 8823 xxx + o.4I535 XXXII IX + XII — 2. I682 XXIX — o. 9552 XXX — o. 427o XXXI — o. 5282 XXXII III — I2. 2284 XXV -+- 5•o333 XXIX II — IV — VI + 12.2289 XXV — 6. I898 XXVI + I •oo54 XXVIII II + III — o-ooo5 XXV -+- I 2.2289 XXVI IV — 6-o39I XXVI — 6-o39I XXVIII + 3. 1234 XXX + 3. I234 XXXII VI + IX -+- 5-o337 XXVIII — 2.865 I XXIX — 2. I682 xxx — 2. I 682 XXX1 XII + 2•5952 XXXI — 2•5952 XXXII XXII -+- 25-o496 XXXIX XI + Io·7567 XXXI + 25-4384 xxxII — Io·7567 XXXIII — VI — Ix + 29. 1742 XXVIII — I I.o929 XXX — II.o929 XXXI -+- -+ -+ VIII + 3*8644 XXVII — 31.8644 XXVIII + 12.2272 XXX — 25-4384 XXXII VII — x — 39.679o xxvII XIV + I5*5395 XXXIII — I5-5395 XXXIV + I 5.5395 XXXIX XVII + 38.7 Io3 xxxIv VI + VII + VIII + 7.8146 XXVII + 2.69o2 XXVIII IX + X + XI -+- XIV -+- XVII — XXII — I. I343 XXX + o. 3362 XXXI — 4.7828 xxxIII — 23• I7o8 XXXIV — 4o. 589 I XXXIX XXII -+- XXIII -}- XXIV IX — X — XI — XIV — XVII + xxII — o«8664 xxIx X -+- 32•4833 XXIX i. IX — XII — 3I •6I69 xxIx XI -+- XII - XIII — XVI XIII -+- XIV — XV — XIX XV -+- XVI -+ XVII — XVIII — XXI XVIII -i- XIX - XX — XXIII XX -+- XXI — XXIV XI — XII + XIII + o.3769 XXXI + o. 28oo XXXII + 29•ο538xxXIII + 4.64935 XXXV -+- XVI XII — 25. I584 XXXI + 25. I584 XXXII XI + 24-78I5 XXXI — 25-4384 XXXII — 24.781 5 XXXIII XIII — 4. 2723 XXXIII + 4•2723 XXXv XVI — 8. 92165 xxxv XIII — XIV -+- XV -+- XIX — 27. 7213 XXXIII + 33•2559 XXXIV — 5-5346 XXXV + o. 5246 XXXVI — 33-78o5 XXXIX XIV + 28-3I49 XXXIII — 28.3149 XXXIV + 28.3149 xxxIx XIII — o. 5936 xxxIII + o. 5936 xxxv T *V — 4*94Io xxxIv + 4.94Io xxxv + 4•94Io XXXVI IP p 2 3oo IPRINCIPAL TRLANGULATION. ¤7, (55) = ΣΗ; (56) = ££, (57) = =#, (58) = ;:;, (59) = sia, (6o) = ;;:; (61) = IĘ (62) = ;#;, (63) = ;;;. (64) = £is (65) = =;;, (66) = £;; (67) = ;;;;; (68) = si;;; (69) = 3=i; (7o) = ;5; (71) = (72) = 3-5: (73) = ;;;;;, (74) = . o* 4934 — xIx — 5-4656 XXXVI + 5-4656 XXXIX — XXI — Io-9678 XXXVII xv — XVI — XVII + XXI — 51.2545 xxxIv + 1.6934 xxxv — 1.2963 xxxvI + 2 I-876I xxxvII -}- XVIII x XVII + 63-459 I XXXIv -. XVI — I3-898o xxxv XV — I2. 2o46 xxxIv -+- 12. 2o46 XXXV + I 2-2o46 xxxvI XVIII — Io.9o83 XXXVI — Io.9o83 XXXVII — XXIV — 7. I 5945 XXXVIII — xx + xxiv + 25-6889 XXXVII — I2-o7725 XXXVIII — XXI + XXI — 6.4523 XXXVII + xx — 19. 2366 XXXVII + I 9.2366 XXXVIII — XXIII + 22-4947 XXXVIII + 22-4947 XXXIX — XX + 39-4985 XXXVII — 39-4985 XXXVIII — xvIII — XIX + xx + XXIII + 1-3932 XXXVI — 66.8552 xxxvII + 17. oo38 xxxvIII — 5 I •2446 XXXIX + XIX — 28. 7499 XXXVI + 28. 7499 xXXIX + xvIII + 27-3567 XXXVI + 27. 3567 xxxvII — XXII + 56. 7964 xxxIx + XXII — XXIII — XXIv + 5.3577 xxxvIII — 71-7388 xxxIx + XXIV — 2o-3ooI xxxvIII + XXIII + I4-9424 xxxvIII + I.4.9424 XXXIX : IFrom these equations we immediately derive the values of (I), (2), (3)... in terms of I, II, III • • • • I. *- * : -* Eqvatioms G. o.o8oc vI — o.o8oo vII — o-o8oo VIII o. 2o6o I — o. 2o6o II - o-oooo3o9 XXV o. 1 58o Iv — o. I 58o v + o. I58o VIII o-338o II + o-338o IV + o.338o VI + 5. 2633o2 xxv T* o. 226o I + o. 226o V + o. 226o VII — 3*5I92I 5 XXV 3.4355 x — 3-4o695o XXIX *.* I*aiio i - *3rio V — I-2I Io vII — 7.493936 xxv + 7.77o745 xxvi 4. 2.76;619 XXVII o-292o I — o. 292o III + o.oooI 33648 xxv — I.8o6961 xxvI o-886o VII + o.886o x — 1.822325 xxvII + 2.7oo616 xxrx I. o23o V — o. 2338578 XXVI — o. 2338578 XXVII o. I4Io III + o. 872475 XXV — o. 2899533 XXIX o.25 Io II — o. 25Io III + 2-283347 XXVI o. 285o I + o. 285o III — 4.544353 XXVI REDUCTION OF TIIE TRIANGULATION. 3oi -H i o-3I4o I + o-3I4o II + 2. I 5o3o3 xxvI i*7i4o VIII — 22.2293o6 XXVII + 22.2293o6 xxVIII — 8.857355 xxx + 43-6oI42 XXXII o-359o IV — 3.8o34oo xxvI — 3•8o34oo XXVIII + I. I7944o XXX + I. I7944o XXXII 49-36I636 xxxII o-o9Io V + I.8o7879 xxvI + 1.8o7879 xxvII o-29Io IV + o.29 Io v — o. 29Io VIII — 2.698269 XXVI — 2-oo72o2 XXVII — o.69Io668 XXVIII 3. I9o499 XXX -+- o.7o4I82 XXXII o-638o IX + o. 638o XII — I-3833oo XXIX — o.6o94I76 xxx — o. 272426 xxxI — o. 33699 I 6 XXXII o-o64o III — o-78262o4 XXV + o.322 I 293 XXIX o. 2o6o II — o. 2o6o IV — o-2o6o VI -+- 2*5I9I59 XXV — I•275o99 XXVI + o•2o7 II 24 XXVIII d. 218o II + o. 2I8o III — o.oooIo9 xxv + 2.6659o xxvI o- i93o IV — I. I65537 XXVI — I. I 6554o xxvIII + o.6o2817 XXX + o.6o2817 xxxII 0-3830 VI + o.383o Ix + I. 927896 XXVIII — I.o97333 xxIx — o.83o4I4 xxx — ο•83o4I4 XXXI - o-37 Io XII + o. 9628o56 XXXI — o. 9628o56 xxxII 2*9oo5 XXII + 72.65638 xxxIx I-o86I XI + II.68286 xxxI + 27-62865 XXXII — II.68286 XXXIII o-28o8 vI — o. 28o8 Ix + 8. I9212 I XXVIII — 3. II4876 xxx — 3. I I4876 XXXI o-4Io5 VIII + I 3-o8o33 XXVII — I3-o8o33 XXVIII + 5-oI 9283 XXX — Io.44247 XXXII o-367 I VII — o. 367 I x — I4-566I6 XXVII I-8257 XIV + 28.37o42 xxxIII — 28.37o42 XXXIV + 28.37o42 XXXIX 5-4849 XVII + 2I2-3223 XXXIV I •7o72 vI + I. 7o72 VII + I •7o72 VIII + I3-34Io9 XXVII + 4-5927 Io XXVIII o-3I39 IX -+- o-3I39 x -+- ο•3I39 XI + o. 3I39 XIV + o-3I39 XVII — ο•3I39 XXII — o-356o567 XXX + o. Io55332 XXXI — I •5oI32I XXXIII — 7.2733I3 XXXIV — I2-74o92 XXXIX 4. I9I9 XXII + 4. I9I9 XXIII + 4- I9I9 XXIV o-3935 IX — o. 3935 X. — ο•3935 XI — ο•3935 XIV — o. 3935 XVII + o-3935 XXII — ο•34o9283 XXIX o- I 972 X -+- 6. 4o57I3 XXIX o. I 944 IX — o. I 944 XII — 6. I4633o XXIX o•63o4 XI + o. 63o4 XII — o.63o4 XIII — o-63o4 XVI o•3952 XIII + o. 3952 XIV — ο•3952 XV — o. 3952 XIX o- 5746 XV + o. 5746 XVI + o. 5746 XVII — o. 5746 XVIII — o. 5746 XXI 2-4o9I XVIII + 2-4o9I XIX — 2-4o9I XX — 2-4o9I XXXIII 4*9953 XX -+- 4•9953 XXI — 4•9953 XXIV o-4652 XI — o.4652 XII + o.4652 XIII + o.4652 XVI + , o. 1753339 xxxi + o. I3o256 XXXII + I 3-51 583 XXXIII + 2. I62878 XXXV 9* 1752 XII — 4.4o7756 XXXI -+- 4-4o7756 XXXII °°**78 XI + 5.3974o9 XXXI — 5.54o485 XXXII — 5.3974o9 xxxIII °*3475 XIII — I -484613 XXXIII + 1.48461 3 xxxv 3o2 . PRINCIPAL TRLANGULATION. (5o) = — o. 4856 xvI — 4-332356 xxxV (51) = — 2.6o68 XIII — 2.6o68 XIV + 2-6o68 XV + 2.6o68 xIx — 72.26388 xxxIII + 86.69148 xxxIV - I4:42759 XXXV + I. 367527 xxxvI — 88.o59o2 xxxIx ; (52) = + 3-4o87 xIV + 96*5I7o4 XXXIII — 96.5I7o4 XXXIV + 96.517o4 XXXIX \ (53) = + o. 253o XIII — o. I5oI863 XXXIII + o. I5oI863 xxxv (54) = — o.5222 xv — 2:58oI89 xxxIV + 2.58o189 xxxv + 2.58o 189 xxxvI (55) = — 2.2I44 xIx — 12. Io3o6 xxxVI + 12. Io3o6 xxxIx i (56) = — o. 2775 XXI — 3-o43555 XXXVII i (57) = — o.5482 xv — o-5482 XVI — o.5482 XVII + o.5482 XVIII + o.5482 XXI — 28.o977 1 xxxrv j + o. 928322 XXXV — o.7Io6316 XXXVI + II. 99248 xxxvII (58) = + o. 2427 XVII + I 5.4oI 53 XXXIV (59) = + o.5o23 XVI — 6.98o96o XXXV (6o) = + o.95o9 xv — II.6o539 XXXIV + II.6o539 XXXV + II.6o539 XXXVI (61) = — o-73oI XVIII — 7.964I5 XXXVI — 7.964I5 XXXVII (62) = — I5-5191 XXIV — III. Io8I5 XXXVIII (63) = — 7.7595 XX — 7-7595 XXI + 7-7595 XXIV + I 99•333o XXXVII — 93*7I343 XXXVIII (64) = + o.4I75 XXI — 2.693856 XXXVII (65) = + 2. 1358 xx — 41-o8561 XXXVII + 4I·ο856I XXXVIII (66) = — o. 2432 XXIII + 5:47o7Io XXXVIII + 5-47o7 Io XXXIX (67) = — 2.6985 XX + Io6.5867 XXXVII — Io6.5867 XXXVIII (68) = — o. I8I5 XVIII — o. I8I5 xIx + o. 1815 XX + o. I8I5 xxIII + o. 252866 xxxvI— 12. 134218 XXXVII + 3-o86189 XXXVIII — 9.3oo894 xxxIx (69) = + o. 2I67 XIX — 6.23oIo3 XXXVI + 6.23oIo3 xxxIx (7o) = + o. 2886 XVIII + 7.89515 XXXVI + 7.895I5 xxxVII . (71) = — I. 3281 XXII + 75-43135 XXXIX (72)]= + o.4924 XXII — o.4924 XXIII — o-4924 XXIV + 2•638I3I XXXVIII — 35-324I8 XXXIX i (73) = + o. 5455 XXIV — II-o7372 XXXVIII i (74) = + o.8247 XXIII + 12.32297 XXXVIII + I2-32297 XXXIX i The next step is the substitution of the quantities (I), (2), (3) thus expressed, in the 39 equations of condition A., and the following is the result of the substitution :— Equatioms D. o = — I •4o42 + 2-534o I + o'52oo II — o.577o III + 1.437o v + 1.437o VII + 3-974886 xxv — 2.883o5o XXVI — 2:76761 9 xxvII o = — 2*7737 + o'52oo I + I 533o II + o.469o III + o.544o Iv + o.544o VI + 2-744o65 xxv + 3:8o7955 XXVI — o. 2o7II 24 xxvIII o = — o. 9595 — o'577o I + o.469o II + 1.25 Io III + I. 6548528 xxv — 2.354839 XXVI — ο•6I2o826 XXIX o = — I •2I 57 + O*544o II + I-545o IV + o.449o v + o.544o VI — o. 449o VIII -+- 2*744I43 XXV + I-2I4693 XXVI — 2-oo7262 XXVII + I. 73968I XXVIII — o. 5766226 xxx — ο•5766226 xxxII o = — o.92o4 + I:437o I + o.449o IV + 3-oooo v + 1:437o VII — o.449o VIII + 3.974721 xxv — I2*5Io751 XXVI — 6.816558 XXVII — o.69Io668 xxvIII . REDUCTION OF THE TRIANGULATION. 3o3 sc =* = — o'3424 + o.544o II + o.544o Iv + 2.995o VI + 1.7872 VII + 1.7872 VIII + o.6638 Ix - + 2*744I43 XXV + I. 275o99 XXVI + I 3-34Io9 XXVII — I •878627 XXVIII — I*o97333 XXIX -+- 2•284462 XXX + 2.284462 XXXI a - 0*33oI + I. 437o I + I.437o v + I. 7872 VI + 4.4773 VII + I. 7872 VIII + I. 2531 x + 3*974721 XXV — 7.77o745 XXVI + 23-3173I XXVII + 4-5927 Io XXVIII + 2. 7oo6I6 xxrx + 0*999o — o.449o Iv — o.449o v + I. 7872 VI + I. 7872 VII + 4.36o7 VIII + 2.698269 XXVI - I9-96I34 XXVII + 4o. 5934I3 XXVIII — I3-876638 XXX -+- 54-o4389 XXXII - o°9I7o + o. 6638 VI + 2-2o36 IX + o.7o74 X + o.7o74 XI — o-8324 XII + o.7o74 XIV + o·7o74 XVII — ο•7o74 XXII — 6.264225 XXVIII—5-51 9438 XXIX+2.537823 xxx + 2.662421 xxxI + o.33699I6 xxxII — I-5oI32I XXXIII — 7.2733 13 XXXIV — I2•74o92 XXXIX — 4-o567 + I •2531 VII + o.7o74 IX + 5-5932 x + o.7o74 XI + o.7o74 xIv + o.7o74 xvII — o-7o74 XXII + I 2-743835 XXVII + I 2.8542o7 XXIX — o.356o567 xxx + o. Io55332 XXXI — I •5oI 32I XXXIII — 7. 273313 XXXIV — I2-74o92 XXXIX — 54398 + o.7o74 IX + o.7o74 x + 3. Io69 xI + I. o956 XII — I »o956 XIII + o.7o74 XIV — I*o956 XVI + o.7o74 XVII — o.7o74 XXII + o. 34o9283 XXIX — o.356o567 xxx — 6.355252 XXXI — 33.29939I XXXII — 8.7317o XXXIII — 7.2733I3 xxxIv - 2. I62878 XXXV — 12.74o92 xxxIx — 3*7o64 — o:8324 Ix + I. o956 XI + 2.4742 XII— I-o956 XIII— I. o956 XVI + 4.763o33 XXIX — o-6o94I76 XXX. — 5-8I832I 5 XXXI + 4*9o33 I4 XXXII — I3-51 583 XXXIII — 2. I 62878 xxxv - + I*7439 — I •ο956 XI — I •ο956 XII + 4.698I XIII + 3•oo2o XIV — 3-oo2o xv + I. o956 XVI — 3-oo2o XIX + o. I753339 XXXI + o. I3o256 XXXII + 87. II4I4 XXXIII — 86.69I48 XXXIV + I5-256o4I XXXV — I. 367527 XXXVI + 88-o59o2 XXXIX — I-3529 + o.7o74 IX + o.7o74 x + o.7o74 XI + 3•oo2o XIII + 8. 9438 XIV — 3-oo2o xv + o·7o74 XVII — 3-oo2o XIX — o. 7o74 XXII + o•34o9283 XXIX — o. 356o567 xxx + o. Io55332 XXXI + I38.9o9I8 XXXIII — I62. I 1 I4I XXXIV -+- I4-42759 xxxv — I. 367527 XXXVI + I43-46472 XXXIX — ο•2569 — 3-oo2o XIII — 3-oo2o xIv + 5-5979 XV + I. I228 XVI + I. 1228 XVII — I. 1228 XVIII + 3-oo2o xIx — I. 1228 XXI—72. 26388 XXXIII + Io5-76399 xxxIV — 6.33o7I I XXXV + II. Io336 XXXVI — II. 99248 XXXVII — 88-o59o2 XXXIX - 2:5773 — I •ο956 XI — I -o956 XII + I>o956 XIII + I. I 228 xv + 3•2o63 XVI + I. I 228 XVII — I • I 228 XVIII— I. I228 XXI+o. I753339 XXXI-4-o. I3o256 XXXII+ I3<5I583 XXXIII + 28. o977 I XXXIV — I.4I4o48 XXXV + o.7Io63I6 XXXVI — II •99248 XXXVII — 9-3165 + o.7o74 IX + o.7o74 X + o.7o74 XI + o.7o74 XIV + I. I228 XV + I. I228 XVI + 7.5578 XVII — I. 1228 XVIII — I. 1228 XXI — o.7o74 XXII + o.34o9283 xxix — ο•356o567 XXX + o.Io55332 XXXI — I. 5oI 32I XXXIII — 176. o9637 XXXIV — o. 928322 XXxv + o·7Io6316 XXXVI — II-99248 XXXVII — I2-74o92 XXXIX + 2'4836 — I. I 228 xv — I. I 228 xvI — I. I 228 xvII + 4.732 I XVIII + 2:59o6 XIX — 2.59o6 xx + I. 1228 xxI — 2.59o6 xxIII — 28.o977 I XXXIV + o.928322 XX*V + I4.8958o2 xxxvI + 39.986oo xxxvII — 3-o86189 XXXVIII + 9-3oo894 ***** - °7i86 — 3-oo2o xIII — 3.ooao xrv 4- 3.oooo xv 4- 2.59o6 xvIII + 8:o237 *** - 2:59o6 XX—2.59o6 xxIII—72.26388 xxxIII +86.69I48 xxxIv—14:43759 XXXV + 6.987618 xxxvi + 12. 134218 xxxvm — 3.o86r89 xxxVIII + 84:63i08 ***** PRINCIPAL TRIANGULATION. O = O = — 3-oo9o — 2.59o6 xVIII — 2:59o6 XIX + 2o. I797 xx + 12.7548 XXI + 2.59o6 XXIII — 12.7548 XXIV + o. 252866 XXXVI — 359. 1395 XXXVII + 244-47 I 93 XXXVIII — 9-3oo894 xxxIx — I •3I57 — I. I 228 XV — I. I228 XVI — I. 1228 XVII + I. I 228 xvIII + 12.7548 xx + 14:5726 XXI — I 2-7548 XXIV — 28.o977I xxxIv + o. 928322 xxxv — o-7io63I6 XXXVI — I86-99o82 XXXVII + 93-7I343 xxxvIII + I.o8o6 — o-7o74 IX — o-7o74 x — o-7o74 XI — o-7o74 XIV — o.7o74 xvII + 9.62o3 xxII — 4.6843 XXIII-4:6843 XXIV-o-34o9283 XXIX+o-356o567 xxx—o.Io55332xxxI + I. 5oI32I XXXIII + 7.273313 XXXIV + 2-638I3I XXXVIII — 25.35823 xxxIx + I·ο732 — 2.59o6 XVIII — 2.59o6 XIX -+- 2.59o6 XX — 4.6843 XXII + 8.3428 xxIII + 4.6843 XXIV + o. 252866 XXXVI — I2. I34218 XXXVII + 7-3oo32 XXXVIII + 32.87555 XXXIX - — I •6497 — 12.7548 xx — 12.7548 XXI — 4.6843 XXII + 4:6843 XXIII + 33:5o37 XXIV + I 99.333o XXXVII + 3.68287 XXXVIII + 35-324I8 XXXIX + 3.298o + 3.974886 I + 2-744o65 II + I. 6548528 III + 2-744I43 IV + 3*97472 I V + 2. 744I43 vI+ 3. 9742I VII + 228.9o96I XXV — 63-68234 XXVI — I7-I2664 XXVII + 2. 532763 XXVIII — 5-7333o3 XXIX. + I6. Io8o — 2.883o5o I + 3*8o7955 II — 2-354839 III + I-2I4693 IV — I2-5Io75I V -+- I •275o99 VI-7-77o745 VII + 2-698269 VIII—63-68234 XXV + 317.8I 935 XXVI + 72-34Io6 XXVII + 52-45947 XXVIII — I6. I35952 xxx — 16. I 35952 XXXII — Io.844o — 2*767I9 I — 2-oo72o2 IV — 6.8I6558 v -+- I3-34Io9 VI + 23-31 731 VII — I9-96I34 VIII+ I2-743835 x- I7. I2664 XXV +72-34 Io6 XXVI + I447.2o82 xxvII — 664.437o XXVIII — 5-554628 XXIX -+- 274-8o96 xxx — 898.22o8 xxxII + 42-4o9o — o. 2o7II 24 II.+ I-73968I IV — o.69Io668 v — I.878627 VI + 4. 5927I vII + 4o-5934I3 VIII-6:264225 Ix-+2:532763 XXV + 52-45947 XXVI—664.437o xxvII + IoI5-3352 XXVIII — 5:5236I5 XXIX — 385-9996 XXX — 95-o541 I xxxI + 882-o848 XXXII — 4I-37oo — o-612o826 III — I*o97333 VI + 2.7oo616 vII — 5. 519438 Ix + 12.8542o7 x + o-34o9283 XI+4*763o33 XII + o.34o9283 XIV + o.34o9283 XVII—ο•34o9823 XXII — 5*7333o3 XXV — 5-554628 XXVII — 5-5236I 5 XXVIII + 422.6737 XXIX + 3-7oo548 xxx + 2.969888 XXXI + o.73o6593 XXXII — I6. 124o — o. 5766226 IV + 2.284462 VI — I3-876632 VIII + 2.537823 IX — o.356o567 x — o-356o567XI-o-6o94176 XII—o.356o567 xIv—o.356o567 XVII + o.356o567 XXII — I6. I35952 XXVI + 274-8o96 xxvII — 385-9996 XXVIII + 3*7co548 XXIX + I56-2463o xxx + 36-4939I xxxI — 345-5948 xxxII + I •7o2948 XXXIII + 8:25oII9 xxxIV + I4.452o2 xxxrx + I35-798o + 2-284462 VI + 2.662421 Ix -j- o•Io55332 X — 6.355252 XI — 5-8I832I 5 XII + 0'J753339 XIII + o.Io55332 XIV + o. 1753339 XVI + o. Io55332 xvII — o* io55332 XXII — 95-o54I I xxvIII + 2.969888 XXIX -+- 36.4939I xxx + 4o9-387o XXXI -+- 46-694o XXXII — 254-8355 XXXIII — 2-4-45288 XXXIV + o.8I5I89 xxxv — 4-283497 xxxIx + 37•2I3o — o-5766226 IV + 54•o4389 VIII + o. 33699I6 Ix — 33:29939 I XI + 4.9o3314 XII -+ o• I3o256o XIII -+- o• I3o256 XVI —— I6. I35952 XXVI — 898.22o8 XXVII + 882-o848 XXVIII + o.73o6593 xxIx — 345-5948 XXX + 46.694o XXXI + 3776-5692 XXXII — 156. Io743 XXXIII + o.6o56o6 xxxv ; $ i ; * ? j $ .i . REDUCTION OF THE TRLANGULATION. 3o5 o = + 95-494o o = + 65-92oo o = + I 2-4I6o o = + 27-436o o = + 85.299o o = + 34-3oIo o = + 3 I2-461o I-5oI32I Ix — I. 5oI32I x — 8.7317o XI — I3-51 583 XII + 87. j I4I4 XIII I38-9o9I8 XIV — 72.26388 xv + I3<5I583 XVI — I. 5oI32I xvII—72.26388 XIX I-5oI32I xxII + I •7o2948 XXX — 254.8355 XXXI — I56. Io743 XXXII 5842.7o53 XXXIII — 5542. I468 XXXIV + 456.35964 xxxv — 37-9o963 XXXVI 5675-78o3 XXXIX 7.273313 IX — 7.2733 13 x — 7. 2733I3 XI — 86.69I48 XIII — I62. II I4I XIV Io5.76399 xv + 28.o977 1 XVI— 176.o937 XVII—28.o977I XVIII + 86-69I48 XIX 28.o977 I XXI + 7. 273313 XXII + 8.25oII 9 xxx — 2.445288 XXXI 5542. 1468 XXXIII + 17oI6.2I69 XXXIV — 681.77 I6 XXXV — 72:4869 XXXVI 6I4-6684 XXXVII — 58o6. 9977 XXXIX z. I62878 XI — 2. I62878 XII + I 5-256o4I XIII + I4-42759 XIV — 6.33o7 II XV I.4I4o48 XVI—ο•928322 XVII + o. 928322 XVIII— I4.42759 XIX + o. 928322 XXI o•815I89 XXXI + o.6o56o6 XXXII + 456.35964 XXXIII — 681.7716 xxxIv 387. 972 I XXXV + I45-6I6I8 XXXVI + 2o-3o8o6 XXXVII + 487.37 I3 xxxIx I. 367527 XIII— I. 367527 XIV + II. Io336 xv + o.7 Io6316 XVI + o.7Io6316 XVII I4-8958o2 XVIII+6-987618 XIX + o. 252866 xx—o.7 Io63I6XXI+o. 252866 XXIII 37:9o963 XXXIII — 72.4869 xxxIv + 145-6I6I8 XXXV + 7o4*5o542 XXXVI 27o4o95 XXXVII + 4. 299679 XXXVIII — 3o4-4I 928 XXXIX II*99248 XV— I I-99248 XVI— II. 99248 XVII + 39.986oo XVIII + 12. 134218 XIX — 359. I395 XX — I86.99o82 XXI — I2. I342I8 XXIII + I 99:333o XXIV — 6I4-6684 XXXIV + 2o-3o8o6 XXXV + 27o.4o95 XXXVI + II 548.2I65 XXXVII — 7614-o86o XXXVIII + 621.813I XXXIX — 3-o86I89 XVIII—3-o86I89 XIX -+- 244-47 I93 Xx+93-7 1343 XXI+2-638I3I XXII + 7.3oo32 XXIII + 3.68287 XXIV + 4. 299679 XXXVI — 7614-o86o XXXVII + 7526-2424 XXXVIII — 4o•2Io64 XXXIX — I2-74o92 IX — I2-74o92 x — I2-74o92 XI + 88-o59o2 XIII + I43-46472 XIV — 88-o59o2 xv— I2-74o92 XVII + 9•3oo894 XVIII—84.63Io83 XIX-9-3oo894 XX — 25-35823 XXII + 32.87555 XXIII + 35-324I8 XXIV + 14:452o2 XXX — 4.283497 XXXI + 5675-78o3 xXXIII — 58o6.9977 XXXIV + 487-37I3 xxxV — 3o4.4I928 XXXVI + 621.8131 XXXVII — 4o. 2Io64 xxxVIII + I6332. 9962 XXXIX. -+ from these 39 equations, which correspond to equations (6) page 263, the valües of the 39 unknown quantities I, II, III . . . . xxxIx have to be extricated. Their logarithmic values are found to be as follows* Log I = 9.9I96637 + ILog VIII = o. 2o8I743 + Log xv = o.o979o64 — II = o. III7I 52 -+- IX = 8.8848523 — xvI = o. 3 I I8859 + III = 9.8I97849 + x = 9•69o5475 -+- xvII = 9.72o2759 + IV = o. o8996o5 + XI = 9.92 I 38o8 + xvIII = 9-6Io4961 + V = 8. 5525879 + XII = 9•5o9275o + XIX = 9:44-43796 + VI = 9• 55o24I4 — XIII = 9.882o947 - XX = o. 1o43927 + VII = 9.8652624 — XIv = 9.866888I + XXI = 9.44I2I22 — *-*-* . * ij* i-* The sign placed after the logarithm indicates the sign of the correspónding natural number; thus, vIII is a positive quantity, Ix a negative quantity. Q q. 306 PRINCIPAL TRIANGULATION. Log XXII = 9.2646586 + Log XXVIII = 8.9635387 – Log xxxiv = 8.1902448 — s XXIII = 9.792,553I - XXIX = 8.90.41661 + XXXV = 8.7135943 + xxIV = 9.9164167 + . XXX = 9.2665455 + XXXVI = 8-5559922 – . xxv = 8.8178796 – XXXI = 9.593.2397 — xxxvi I = 8.6481505 — ! xxvi = 8-8435415 - XXXII = 7.9263.407 -- XXXVIII = 8.9397225 — | xxv.11 = 8.3985923 – XXXIII = 8.8042253 – XXXIX = 7-97.974.5o — By the substitution of these quantities in the equations C. we obtain finally the required corrections (I), (2), (3) . . . Their values are:— sº, i § # } $ § : (1) = — o'o.421 (26) = — o-2585 (51) = + o-8335 (2) = — o'4376 (27) = — o'5054 (52) = – 3.0660 (3) = + o-o552 (28) = — or 16oo (53) = - or 1755 (4) = + o-3869 (29) = – 4:5079 (54) = + o-'7348 (5) = + o-2616 (30) = + o-oi 35 (55) = — o'2962 (6) = — 1.9580 (31) = + 1-oš13 (56) = + o-2120 (7) = — o'28o3 (32) = + o-4539 (57) = — o'6775 (8) = + o-1759 (33) = − 2.9824 (58) = — or III2 (9) = + o-o47o (34) = – 6.1707 (59) = + o-6690 (10) = + o-oš87 (35) = + o- 1429 (60) = — o-8289 (11) = + o-ol.25 (36) = + o-9528 (61) = + o-3430 (12) = — o-6496 (37) = + o-o871 (62) = — 3.1312 (13) = + o-2683 (38) = — o'9424 (63) = – 2.0329 (14) = + o-517 I (39) = + o-6 IoA. (64) = + o-oo.45 (15) = + o-oi 25 (40) = — o'5706 (65) = + o-'9675 (16) = + o-4012 (41) = — o-o825 (66) = — o'3776 (17) = — o-4166 (42) = + o-3748 (67) = + 1. Io.18 i (18) = — or 1746 (43) = + o-6845 (68) = + o-3445 (19) = + o-2004 (44) = + o-o833 (69) = + o-2250 - (20) = + o-5953 (45) = + o-8522 (70) = — o'5175 i (21) = + o-I355 (46) = — o'756o (71) = – o 9642 (22) = + o-o:35o (47) = + 1.8215 (72) = + o-o973 (23) = + o-5424 (48) = − 1.6367 (73) = + 1 .4139 (24) = + o-2400 (49) = + o-4362 (74) = − 1.7017 ,(25) = + o-5423 (5o) = — I.2198 The application of these corrections to the observed bearings will give those which must be considered the most probable bearings, and with these the triangulation may be worked out in the usual manner. The process is precisely the same for each of the figures. The geometrical and corre- sponding algebraical equations of condition are given in the following pages. GEOMETRICAL E QUATIONS OF CONDITION. FIGURE 2, Angle Equations. - I. : o = 0' + N’ + B — 180° — s, VII. o = 0 + D + E – 180° — s, II. o = O’-- N'-- A — 180° — e. VIII. o = 0 + E + H – 180° — ss III. o = O'+ 4 + B – 180° — e, IX. o = 0 + H + T – 180° – e. Iv. o = O'+ B + C – 180° — s, x, o = 0 + O' + T – 180° — sis v. o = 0' + A + C – 180° — e. XI, o = 0' + 1 + K – 180° — sº, VI. o = 0 + B + D – 180° – e. XII. o = O'+ K -- F — 180° - e,, Side Equations. xm. 9...94.9'B. O'B . O’C. O'4. • O'A. O’B 07W = i XIV. 576 57.1 OT = I 00' . OB CD. CE. CH . CI XV. Of CD ' GE GH OF 60 = 1 O'N'. O'B . O’C. O'I. O’K. O'F' . O'G' XVI. O’F 57G Öºf '57: O'Fu' 576, OTW = + FIGURE 3. Angle Equations. I. o = E + F + C'— 180° – e. VII. o = G + C' -- K - 180° — s, II. o = F + C'+ D'— 180° — e, VIII. o = R + H + G – 180° — es III. o = K + E + F – 180° – e, Ix, o = D'+ H + G + C'— 360° — s, IV. o = K + E' + C – 180° – s, x, o = R + I + H – 180° — sis V. o = G + 0 + F – 180° — e. XI. o = E' + K -- L – 180° — sº, VI, o = G + C* + E/- 180° - e.g XII. o = L + K -- I — 180° — sº, Side Equations. * GE GE, ETF = 1 XVII. G.75, 67F 576, ºf = 1 xv. º. 4'0'. B'ſ sym, ſº 19. Iſº E.G. E.R. EF = I iſoft MG iſ; - ? xy. 9"I: . O’G . O'B' MF . MO'. MK i O'G G/E/ 67Rf E I XIX. MC" MIX MF E I xvi. º. 6Y. GO! ME'. IIIC. MIC GK GO, GF = 1 XX. Tö, III: TE = 1 Q q 2 PRINCIPAL TRIANGULATION. XXII. YXIII. II. III. IV. V. VI. VII. VIII. IX. XI. XII. XIII, XIV. IX. X X. XXXI. XXXVI. XXXVII. MH MG . MO'. MD' MG MC MD’ MIT MK . MH . MG . MF MH' MIK IG, . IIC . IH gººm-º: fº = 1 RI KL RE’ RG -—- " - * = o = H'-- L’-- D — I80° o = K’-- L’ + D — 180° o = N7 -- K’-- D — 180° o = A + L’-- D – 180° = A + N’ + D — 180° A + N’ + B' – 180° IV’ + A + C – 180° N7 -- B' + C – I'8o° B' -- W -- N7 – 180° + D + E — 180° + 0 + F – 180° + D + F — 180° + E + F – 180° + A + M. — 180° XXIX, O = - : == H'K' . HºO H'L'. H'G' E I XXVI. = I xxvii. XXVIII. JOH --- - I XXIX. RI XXX FIGURE 4. , Angle Equations. - 8, XV. – e. XVI. — s, XVII. – s, XVIII. – s; IXIX. – 56 XX. — s, XXI. - 88 XXII. — so XXIII. - Ero XXIV. - err - XXV. - era. YXVI. – els XXVII. - era XXVIII. = U + T + R — 180° Side Equations. 75 TTE, 7& FK, L'H' L'I) L'N' L'G' - =-º-º-, - ==== * *mºmºmº ſº. I LZD TV, 7,767 LTF = W4 - N'B' . N'O' . N'G' . N'K' . N’D DKXXIV. = { XXXII. XXXIII. N’B/ g * === * - * → * , *memºmº. $ººm. I * = * * = * ºmsº flºº E 2 Q L/N7 L/D L'A. R7A K' D K’I, i. ºmº º +=== tº W07 WG WF, WD WT = * XXXVIII, o = A + D + M – 180° — o = A + E + M. — 180° — o = A + F + Aſ — 180° — s o = P + M + F — I 8o° — o = R + C + M – 180° — o = R + C + F – 180° — o = R + M + P – 180° – o = Q -- P + F – 180° — o = Q -- R + F – 180° — o = R + S + Q – 180° — o = R + P + S – 180° — o = T + 0 + R — 180° — o = T' + R + S – 180° — o = T' + R + P – 180° — 528 . GEOMETRICAL EQUATIONs of CoNDITION. 309 XLI. XLII. XLIII. XLIV. XLV. XLVI. XLVII. LVI. LVII. II. III. IV, VI. VII. VIII. IX. XI. XII. XIII. XIV. XV. XVI. XVII. XVIII. 4D . A F : AN, I}ſ IF IP A F AW, If = i XLVIII. IF FE If = } 4lſ. AF AC FC FR FM FA. AF Tö ' If = i xirs. FE Fif FA FC; 4.E. A.D . Allſ RF RMſ. RP Al) ANſ ME = 1 L. Rºlf RP EF = 1 FA FE , FM IC . IM . II: FE FF F1 = 1 LI. Tºf TR Fă = i FO FI FAſ RP RF RQ FT FI FG = + LII. FF Tº EP = } Ilſ IF IA IQ IP IF — * —- " - E I LIII. --, * → * - = I IF IA IM IP IF IQ FC FP FM FA PR PS PQ FB Fir FZI FG = *Y. Es Fö FF = ry R.T. R0. R.F. RQ. RS RC RF RQ RS RT T RS RP RT O TR TU RP R7 RS = LVIII. TÉ Tij 75 = + IR IC . IT SU SR . ST_ TG 77, 75 = tº 5 S7, SE - 1 FIGURE 5. - Angle Equations. = K -- F + Q — 180° — s, XIX. o = Z + X + J – = R + F + E — 180° — e, xx. o = Z + J + W — = 1 + F + D – 180° — , XXI. o = X + J + Y – = V + D + IY — 180° – e, XXII. o = X + Z + Y - = V + E + K – 180° – s; xxIII, o = K + Q + H — = V + F + IY — 180° — sº xxiv. o = Q -- F + H – = B -- V -- IC – 180° — s, xxv. o = H + X + L – = B -- E + IY — 180° — es xxvi. o = J + K -- L – = J + V + B – 180° — s, xxvii. o = N + H + L — = J + V + F — 180° — sis xxvii.I. o = N + L + J – = J + V + K – 180° — sº, xxIX. o = G + Q + H — = W -- V -- E — 180° — sº, xxx. o = G + Q -- K — = W -- B + V – 180° — sº, XXXI. o = G + L + H — = W -- V -- K - 180° – e, xxxLI. o = G + L + N – = W -- W -- J – 180° — sº, xxxiII. o = 0 + N + J – = X + TV + V – 180° — sis xxxiv. o = 0 + N + L - = X + W -- B – 180° — sº, xxxv. o = 0 + N + H – = X + W -- J – 180° — sis xxxvi, o = 0 + N + G – 180° I80° 180° I80° 180° I80° I80° I80° 180° I80° I80° I80° 180° I8o° I8o° I8o° I8o° 18o° - Eao 521 522 3 Io PRINCIPAL TRLANGULATION. XXXVII. XXXVIII. XXXIX. XL. XLI. XLII. XLIII. XLIV, XLV. IXLVI. XLVII. XLVIII, XLIX. I. II. III. IV. FE . FK . AB = , Tº FD FE T FE . FK . F2 . FR . FM II. FQ FR FM FE T IK . IQ , IF 70 IF IR = ED EV EF E7 EF E5 = 1 FV FK . FD FK FD FW BE BK BV Tºjº E7 EE 7-E VI) VB TVD VB VE BF . BE BK T; ER EF = * KV . KF KJ. RF ºf Rºy BK. BTV BJ By Bf BK TVB VE VW VE VW WB VJ. V.K. VIV i. •=-- * = - 7& 7W 77 WB WY. W.J. WV WJ WB J. W. JB JX JB JX J W o = A + B + C – 180° o = B -- E + C – 180° o = 0 + B + D — 180° o = 0 + E + D – 180° o = 0 + E + F — 180° XL o = G + H + D — 180° — sº, Side Equations, LI. I LII. LIII. I, IV. LV. LVIII. LIX. LX. LXI. LXII. LXIII. LXIV. |FIGURE 6. 55 Angle Equations. VI. VII. VIII. IX. X. JV . JB . JX JB JX JV - * * * - E tº gººmsºmº * - tº-g *-* * *- * = * o = 0 + D + F — 180° o = 0 + E + B – 180° o = F + E + H – 180° o = E + D + H – 180° o = G + H + F – 180° GEOMETRICAL EQUATIONS OF CONDITION. 3 II Side Equations. xm. £4. FB. BC – xv. 34. £2 . . . . . EB Eó E1 = 1 * EO EF EH T XIII CB. CD . CE XVI PH. B.D. EF CD OF • OF → * ED EF EH T xiv. º. 32. F2 – 1 xym. HP. Hg. #' = 1 EC ED EF T HG HF HD T FIGURE 7. Angle Equations. I. o = 0 + G + D – 180° - e, XII. o = I + E + K – 180° — sº, II. o = 0 + D + E – 180° — s, XIII. o = I + K + H – 180° – e,, III. o = 0 + G + E – 180° — s, XIV. o = I + E + G – 180° — e. Iv. o = G + G + F – 180° — e. xv. o = I + E + C – 180° — e.g v. o = H + 0 + F – 180° – , , XVI. o = I + E + D – 180° – e.g VI. o = H + 0 + G – 180° — e. xvi.I. o = K + I + L – 180° - e, VII. o = H + D + G – 180° – s, xvi.II. o = R + L + P – 180° — sis VIII. o = K + 0 + F – 180° — es xix. o = P + K + 0 + G — 360° — so IX. o = K + H + F – 180° – s, xx. o = L + P + MI — 180° — 8, X. o = R + D + 0 – 180° – els xxI. o = K + P + Aſ — 180° — e. XI. o = R + E + C – 180° — sº, xxII. o = P + 4 + M. — 180° — e,, XXIII. o = P + B + A – 180° – sas Side Equations. xxiv. 32.9% .32 = xxxiii. # #. # = GE GD Gó = } * EI EH EG. T XXV CF. CH . CG XIV EC . EI. Płł , * GH Gä EF = xxxiv. EF EH Ed = X CG CD . CH XXV KD. K.I. （E = 1 XVI. EB GH GG = + XXXV. KF FE FD = XXVII EC EG - EH --- XXXVI II: . Itſ. Pºſ = , Ed EH EG = * ***** LI LH LK T XXVIII KH. K. Kø , xxxvii KG . KP. K.L. Kſ , KF KO RH T * KP KL RI RG T XXIX CK. CD. OH I XXXVIII CG . CP . 9% CD CH OK. T * * CP OR CG T xxx. £2.É. £2 = , . Pllſ. PL RE ICD KO xxxix. Hiſ EE FK = + XXXI, £. KG. K. OK . OP OM ICC KF KO * 55 ° 5if Ök = xxxii. #. £1. Kg OP OR OA 3 I2 PRINCIPAL TRIANGULATION. XLII OP . 04 . 04 – 1 - ExLIV MN MP. MA OA OM OP • TE T.I.' TW = } xiii. º. # #= xiv. PM . P4. BP * NP NMI NK II IB IW = } FIGURE 8. Angle Equations. ,t:--*º. I. o = F + E' + A* – 180° – s, XV. O = P + M + N – 180° II. o = F + E' + H – 180° — s, XVI. o = Q + N + M – 180° III. o = E' + II + C – 180° – , XVII, o = Q -- N + P – 180° IV. o = K + H + F – 180° – s, XVIII. o = Q -- N + 0 – 180° V. o = K + H + MI — 180° – s; XIX. o = S + N + Q — 180° VI. o = M + H + Cº. — 180° — es xx. o = S + M + Q — 180° VII, o = K + M + L – 180° — s, XXI. o = R + Q + S – 180° VIII, o = M + H + L – 180° — es XXII. o = R + Q + N – 180° Ix. o = C' + 0 + H – 180° — so XXIII. o = R + Q + M. — 180° x. o = 0 + IY + H – 180° - ele XXIV. o = T + Q -- N – 180° xI. o = R + 0 + P – 180° — sº, XXV. o = T' + Q + R — 180° XII, o = K -- M + P – 180° - e, , XXVI. O = T + Q -- S – 180° XIII. o = R + 0 + N – 180° - e, , XXVII. o = U + S + T – 180° XIV. o = R + P + N – 180° — sº, XXVIII, o = U + S + R — 180° Side Equations. XXIX E'I' . I'4'. E'0'. B'H XXX. HK HO HC HE X ** {} F'A' WO JE/H B}/F = } X VIII. HO’ TTC, HE, TR = xxx. # , 45.4% = , xxxix. £1 . ſº . K9 . Aſ A/G A'E' A/F T KP KO KH KM T xxxi. #: . （ .. 43 = , ICE . Iº9 . ſº H.E. H.G. H.F. T ** 76 FW #5 = xxxii. # , º, . * = - ICM . KP . IºM = r xxxii. ºf FE FH = 1 XII. FE #y Hiſ = xxiii. # £ # = QM.. QN , QP xxxiii. Hiſ HF HE = i xiii. 37 ºf Qi — FK FH . Flſ QP QN Q0 XXXIV. FET FM PK E I XLIII. QN * QO’ * , QF E I xxy. 4. . 4: . Hºlſ. HC. MS MN. . MQ xxxY. HH Hiſ Hö, HE = i xiiv Ty iſ TS = &xvi. #4 # # = , xry, RM. RQ . RS xxxvi. FH Fif FE = RQ RS TV = 1 FK FL FH RM RQ RN • - " - = I XLVI. -- * —t. - xxxvii. FE F# F# RQ RW TIf = | GEOMETRICAL EQUATIONS OF CONDITION. 313 º RQ JRMſ RP = I XLIX. QN QT QS = 1 . QR QN Qi R U RS RT XLVIII. Zºº. * ~ * - - -—e * --— ” e-- - QN QT QR = 1 I. T.S 77, Tir = 1 FIGURE 9. Amgle Equations. I. o = W + P + Q – 180° — s, xvi. o = D + 0 + B'— 180° – si6 II. o = W -- O -- Q — 180° — e, xvi.I. o = D + W -- C'— 180° — sº, III. o = W -- O -- 07 – 180° — e, XVIII. o = D + TV + X – 180° — sis IV. o = TV + A*-i- D’— 180° - e, XIX. o = D + W-- Q — 180° — sº, v. o = TV + Cº. + D’— 180° — e. xx. o = D + W -- P – 180° — eas vſ. o = V + Q + P – 180° — ed XXI. o = D + TV -- 0 – 180° — sat VII. o = V + Q + R — 180° – s, XXII. o = 0 + X + V – 180° – sa, VIII, o = V + Q + T — 180° — es XXIII. o = 0 + X + D – 180° – sas IX. o = X + Q + V – 180° — , XXIV. o = B -- X + D – 180° - 6, X, o = X + P + V — 180° — sis xxv. o = B + 0 + D – 180° - eas XI, o = X + 0 + Q — 180° — sº, XXVI. o = A + D + B — 180° – sas XII. o = X + TV + Q – 180° — sº, XXVII. o = A + D + D’ – 180° — ear XIII, o = X + W -- C – 180° — sº, xxvii.I. o = B -- Y -- 4 – 180° – sas XIV. o = X + TV + D’ – 180° — sº, XXIX. o = D + B + Y + B' — 360° - #29 XV. o = D + TV + D'— 180° — sis xxx. o = Z + D + D’ – 180° — ess XXXI. o = Z + D + B + Y — 360° – s; , Side Equations. ... ... 20. QP . QW xxxii. QF OTſ Q0 = 1 * * * 00. . OW tº OQ. . ON. tº OK. O.H. = I xxxiii. 57 00 ON OK OH 00: ........ D'C'. D'4". D'W IXXXIV. D'A' D’W. D'O' = I YXXV tº O'H' C/E/ O'A' O'D' C/ IV C’O * =mº xxxvi. #4, #7, # a 97.99. . 2. xxxvi, FW FF F = 1 xi. 90 Ox OTW = QT' .. QR QV ... XY . X0, . XC' *Wii. 5; 57 57 = 1 XLI. x0 Xà XW = 1 ..., XQ XP XV WD IVC . IVX ... Q0 . QP QX CD' CB’. Cºx xxxix. EP QY JJ = 1 XLIII. G.F Gºx JD = 3I4. º: PRINCIPAL TRIANGULATION. . . WX , TVQ . WD BX BD BC XLIV. Tº WD TVX = III. HD itſ fix = 1. TVx , IVP TVD D.A DB DX DD’ XLV. Tºp WD TVX = 1 I,III. IF Dx 55 DT = 1 TVX TVO TVD B’D B'D' B/A XLVI. Wö TV5’ Tº = i *Y. FD, FT Fij = 1 C/X C/O C/D YB YA VD XLVII. Ed GT5 CTX = 1 *W. F. 75 ' If = 1 YD/ XO/ XD DY DB . DX DIW XLVIII, X5 Xī VE7 = 1 IVI. DE DX DIW D F = 1 C/D/ C/Bſ C/D yTV º YD’ º VD XLIX, CTF, Eij Oſij = i LVII. Fij, VD yTV = 1 XC XV XP XI) YD . Y.B. YD L. X7 XE XD xú = * LVIII. T.I., 75 75 = 1 WX VC VP I)' Y D'Z D'D LI. VC: º WP {º 7x = 1 LIX. I)'Z DVD D7 = l g IX. TT), EZ Fij = i FIGURE Io. Amgle Equations. 1. o = F + 0 + E'— 180° — s, IV, o = H + F + E- 180° — s, II. o = F + A*-i- E' – 180° — s, V. o = H + B'+ E' — 180° – s; III. o = F + B' + E'— 180° — s, VI. O = B' + F + G – 180° – s; VII. o = H + F + G – 180° — s, Side Equations. B'E' . B'E' ...B.A. . . . . FD’. FC FE' with FF ET FE = i X, FG, FE FD = i IX. EF E757 IVF = 1 XI. ET; ETH EF = I XII. FH FE, FE, FG = 1 FIGURE II. Amgle Equations. I. o = 0' + Q’-- H’— 180° — s, VI. o = G'+ Q' + V’– 180° — sº II, o = O'+ R' + H/– 180° — s, VII. o. = V’-- G'+ E”- 1860 — 57. III, o = 0' + G'+ Q’ – 180° — s, VIII. o = W’-- V’-- E/– 180° — sº Iy o = 0' + G'+ R'— 180° — e, IX. o = N + K'+ E”- 180° — s, v. o = H'-- G'+ Q' — 180° – s; X. o = I24- E + C'4 B-360°– s. t GEOMETRICAL EQUATIONS OF CONDITION. 315 XI. o = P + IY’-- B'— 1869 – sº, xxiv. o = B + N’-- E'— 180° - 5, XII. O = A + V’-- TV- 1869 — 512 xxv. o = B -- E + D’ – 180° – sas XIII. o = 4 + V.4. R/- 180° – 3, xxvi. o = B -- N'-- L'— 180° - 6,6 XIV. o = A + V’-- Q'— 180° — sº, xxvii. o = 0 + N'-i K’— 180° — s, XV. o = A + G'+ Q'— 180° – s; XXVIII. o = 0 + N’-- L’— 180° — eas XVI, o = 4 + G'+ F – 180° — sig xxix. o = 0 + N’-- V’— 180° — e.g XVII. o = A + G'+ E/- 180° — sº, xxx. o = 0 + N’+ A – 180° — ess XVIII. or = A + V’-- X’– 180° — sis xxxi, o = 0 + N’-- B – 180° — es: XIX, o = A + V’-- N7– 180° – so xxxii. o = 0 + E' + D'— 180° — sº, XX. O = B -- A + F — 180° — sao XXXIII. o = 0 + E' + B – 180° – sas XXI. O = B + A + G’ — I 8o° — Far XXXIV. o = Cſ + E' + A* – 180° — *34 XXII. o = B -- A + Q’ – 180° – sa, XXXV. o = 0 + E’ + C – 180° — sis XXIII. o = B -- A + N’– 180° – sas XXXVI. o = 0 + B'+ K’– 180° — e.g Side Equations. xxxvi. 4%. º.º. Q'R' Q'O'. Q'G'. Q'V' *** * * * º O'R/ O'H' O'Q' E I XXXIX, Q70, Q'G' Q'V' Q'R' = I Q'H' Q'G' Q'O' Q’ V, Q'R' Q'G' XXXVIII, 77 ° 7, 7,775, = &L. Zºº, 777 FT% = Q'G' Q'O' QH = + xi ºf Jä 077 = 1 xii. FS Fö, Fä FW = i xim Gºſſ'. Gº" . Gº .97.99 — , tº G'F. G. E. G. V. G'Q' G'H' sº …, "Y'. J."g". £º , YLIII. F.G. F. E. F. W. T xviv. º. WY. W. Yº!’. W.2. º. º – * Vºy, V, IV, VT, 79. WG: V/L), WN7 - xix. W. Wºlſ. YY. W.Y. º. WF, WF, W7 WE, WR = 1 ... PG' . B'D' . E4: . PI3. EN’. B'W' XLVI. JE/D’ JE/A. f JE/I(? E/N7 E/ y, E'G' ſºmº ...... C.D . CA’. CIC’ gym. Cº. 94.94.9% XLVII. E. ER, GF = XIVIII. G.I, GF GF GE = 1 sus, KI. Jººlſ. KY. º. £4. É * Fip FW, jã K.I, KB, iºT = } L. GTR, 57F C7F = Q'R' QA Q'V' T ... R'V' . R'T". R.A. In 4% .4% .4% = , it iſ ET #77 = 1 AG. A. V’ AQ' T r G’A. º G'Q' tº G/H7 wº G/F/ º G/E/ LIV. G'Q' G/Hz G! F/ G'E' G'A = I R r 2 316 PRINCIPAL TRIANGULATION. AN, A V’. 4B' ... AF" . AB . AG' º LV. TV, AE, IW, = I LXII. AJ3 i. AGF t; MF, : I A. F. AG’ AF' º G/Dr G B G'F' i LVI. I.G, ME, TF = 1 LXIII. 7F GF 675 = } Trº A. V. N. V.Y. iſs JBD” BG' BE/ LVII. 7W, 7x, VI = } * Hä, E, # = 1 O'R' O'T' O'A ... BG’ BE BN, B IVIII. Ö77 OZi 675 = 1 LXV. BE, RW E.I # E I in Hº ; ; , ºft- Exvi. # # # = , º “ UT” Uz V, U*A BE/ BN7 BK/ is, W4. W.T. . WY’ Exvii. #'ſ. . * : * = . “ ſy/Ty W. W. W. A. • * JBA BN' BV’ LXI 4G" . 4B . 49 LXVIII. N'L' . N'B . N’K. Wilſ' == AB AQ' ALG' * N’B N/I(? Nº Mſ. Nº L/ N/O. N. R. N. M. N'L' LXIX N'K' . N'M' . N'Y' . N' V’. N'C I * Nºlſ, N.Y. N. V. N.C. N. R. T LXXI NA. . Nº V. N.C. LXXIV. D’B . E.C. . EID" I “ Nr 17, N/C N/A E/C} E/D' E/B T CN/ CB OA E/D/ EVA’ E/C} . LXXIII CB . CN' . CE - LXXVI 0'E' . 04' . 0'0 -dºh-ººh-l... -- tº CN7 CE’ CB “’ “ CºA, C/C} C/E/ E I i ** * * CA’ CB’ CK7 CE/ : FIGURE 12. : Angle Equations. 1. o = A + E + B – 180° – e. XIII. o = F + H + E – 180° — sº, II. o = A + D + B – 180° — s, XIV. o = K+ M + H – 180° — sº, III. o = A + D + E – 180° — s, xv. o = F + K + N – 180° — sis Iv. o = F + 4 + E – 180° — s, xvi. o = F + H + N – 180° — sig v. o = F + K -- E — 180° – s; xvi.I. o = F + G + H – 180° — sº, vſ. o = F + IY + A — 180° — so xvi.II. o = G + N + H – 180° — sis VII. o = A + D + K – 180° — e. XIX. o = 0 + K + M – 180° – sº VIII. o = B -i- D + C – 180° – 58 XX. o = 0 + H + Mſ – 180° — sis Ix. o = D + 0 + I — I 8o° — so XXI. o = 0 + N + K – 180° – s, x, o = D + 0 + L – 180° - 616 XXII. o = 0 + N + K + MI — 360° - e,, xI. o = D + JC + L – I80° - 61, XXIII. o = 0 + 1ſ + K+ L – 360° — sº, xII. o = F + H + IY – 180° - 6. XXIV. o = N + P + Q – 180° —s, GEOMETRICAL EQUATIONS OF CONDITION. 317. Side Equations. XXV 4D . 4B . AB - - * KXXIII FH . FN FK AE AB AD ~ * xxxiii. Fy F# Fir xxvi. º. ºf . F4 – , , …, MEſ. MIK. WIW FK FA FE = 1 xxxiv. F. FN FFF - xxvii. Pº. PK. P4 – xxxv. Hº. #'ſ. # = DK D.I DE * * *Y. Hy HF Hø – JDK. D.A DB DC MTH MIK IO XXVIII. - - - - - - - - - = XXVI. * – “ — = * D.I if ‘jº 5% = + * III, II, III: I)I, DK. DC JTW R H KO KXIX. — " — " — = XXXVII. * --- * – - ** BR Bā E = i "* ## Kö ºr = i Pl: . FH. F.E. xxxviii. 42.4%. Mº. MP *** F# FE FK = MN MK IIL iſ, T xxxi. # , ºft.* = . II . NK. NO DIK DE DII T xxxix. W. Wö WE = i XXXII Kiſ. KH. KE. KD KL * AP . WQ. M.M. Nº RH K E RD Ki, ºf ~ * * Nº Wii WR NF = FIGURE 13. Angle Equations. I. O = A^+ D'+ K – 180° — e. XIII. o = M + D’-- K – 180° II, O = A^+ D'+ F – 180° — e, XIV. O = 0 + M + L – 180° III. o = A^+ F + K – 180° — s, XV. o = 0 + MI -- K – 180° IV. o = G + F + K – 180° — s, XVI. o = M + R + 0 – 18o° V. o = G + IY + D’ – 180° – s; XVII. o = R + 0 + L – 180° VI. o = G + E' + D’ – 180° — sº XVIII. o = S + 0 + L – 180° VII. o = E”-- F + D’ – 180° — s, xIX. o = S + 0 + Mſ – 180° VIII. O = L + A*-i- I — 180° — ss * XX. o = S + 0 + R — 180° IX. O = D'+ E”-- H – 180° — so XXI. o = 0 + It + P – 180° X, o = H -- E + G + K -- L – 540° – sie XXII. o = 0 + S + P – 180° XI. o = MI + II + L – 180° — sti XXIII. o = P + L + MI — 180° XII. o = M + H + D’ – 180° — era XXIV. o = P + M + R — 180° XXV. o = B' + A* + K – 180° — sº, Side Equations. YXVI A/F º A/D’ º A'R. = I XXIX 4'L. * 4'K 4'F Q 4'D' A'D' A'K A/F T A/R A/F A'D' A'L XXVII FG . FIC . FD' XXX KL . KA' . ICF ICG FK F5 Fă = i KA' KF KG II, wº E’F ED' E.G. GE' GD’ GH XXVIII. - - - - - - - - * —- - * —- " - E. JE/D/ E’G JE/F = 1 XXXI. GD’ GH GEſ I 318 PRINCIPAL TRLANGULATION. XXXIII, XXXIV. XXXV. XXXVI. XXXVII. IXXXVIII, XXXIX. XLI. XLII. XLIII, II. III. IV. V. VI. XIV. XV ºf RF RE GM . GII . Gº. , * GFI GL GM T XLIV. HL . HD . Hiſ smsº HD, Hiſ HE - * XLV. GD º GK tº Glſ I XLVI GK GM G L T MII, JIR MO iſk j70 iſ, * * XLVII. MI, i. JIH tº JIN" ſº MO # = jſłł MW MO TD = * Olſ † : OL * . OR _ XLIX Oſ, OR Of T * *...* NO NM NR XLVIII. Wºlf WT. WO = L. Olſ ſº OS º OL gº I LI OS OL OJI T OR ſº OS tº Olſ := I LII. OS OJI Olć NS NO NR —- * • ——- - - III, NO NR NS I LIII RO . I'P . I'M LIV RP Tºf RO T * ſº IFIGURE 14. Angle Equations. o = F + H + IY — 180° —, s, VII. o = E + H + F — 180° — s, VIII. o = D + K + F – 180° – s, IX. o = D + K + H – 180° — s, X. o = D + E + F – 180° – s; - XI. o = 0 + F + E — 180° – s; XII. GE . GE' . GF . GK GL GE' GF GR 67 GH = + JRO . RP . RL FF FE Kö = OS . OP, . OR OF OF • OS = PL . PO. , PK PO PR PE QS QP . QR QP QR QS PR PQ . PL FQ PL PR T PR . PQ . Pllſ Fø Fiſ FR - 4'D'. 4'I 4'B' TÉ TÉ TD = A/D' A'B' A/F A7R, A7F 175, * E/F . EG - E/B' E7G EIF EF = + D'E' . D'C'. D'H' D76, D'H DTE, F FD' FB' FE FF FE Fij = 1 o = C + F + D – 180° — s, o = 0 + H + D. — 180° — es o = B + H + D — 180° — o = B -- D + F — 180° — sie o = B + I( -- D — 180° — sº, o = B + D + 4 — 180° — sta XIII. o = D + C + A – 180° — sis * * Side Equations. KF' . ICE . ICH J&E RH II.' T ICE . ID . J.T E I XVII, ICF RD KH XVI. Prº " : " - = I RD I H KF ICC . ICD . ICF RD #F F6 = + GEOMETRICAL EQUATIONS OF CONDITION. 3I9 XVIII DF . D0 . DH * * * BF. B.B. Blſ DC; DH jF = 1 xxii. FE ºf TF = XIX DC DE DF YXIII B.E. BE . Bø DE DF DG = + xxiii. EF Ed : EE = xx, PH. D.B. . DK exiv. * : * : * = . DE DR DH = + ***''' BA BD BC T xxi. #'ſ. PB . PK xxv, * : * : * = 1 LB DIX DF. T *'' ED EC EA T FIGURE 15. 47gle Equations. I. o = A' + N’ + H' — 180° – s; xv. o = D + N’ + B — 180° — sis II. o = 4’ + N’ + K’ — 180° - e, XVI. o = D + L' + B – I 80° — sis III, o = A' + N’ + L’ – 180° – s, XVII. o = D + Mſ’ + B – 180° — sº, IV. O = A + H2 + N’ – 180° – *4 XVIII. o = D + N’ + C – 180° – sis v. o = A + H2 + L' – 180° — e. XIX, o = E + B + D – 180° - sis VI. o = A + H2 + M’ — 180° – s; xx. o = E + D + C – 180° - suo VII. o = B + N2 + 4 – 180° – s, xxI. o = E’ + A' + N’ — 180° - sai VIII, o = B -- M' + A – 180° — es XXII, o = E' + N’ + C – 180° — sa, IX, o = B -- L' + A – 180° — e, xxIII. o = E’ + N’ + D – 180° – sas X, o = B -- H' + A – 180° — sis xxIV. o = E' + E + 0 – 180° – sas XI. o = 0 + N’ + B – 180° — err xxv. o = B' + E' + E — I 80° – sas XII. o = 0 + MI’ + B — 180° — era xxvi, o = B' + E' + D – 180° – 5,6 XIII. o = C + L' + B — 180° — sis xxvii. o = 0' + B' + E — 180° – ean XIV. o = C + A + B – 180° — sº, XXVIII. o = D' + C' + E — 180° — eas Side Equations. - NIK, NA' | N'H' ........ Alſ’. 4I.' . 4B * Wä, FHF WF = 1 XXXVI. T. II, IP = + xxx. Wºº. . W4. N'L' XXXVII 4N. . 4I/. 4B I W.T. Wiſ WF = + **** AL, AB ANZ T xxxi. N'G' . A 4. . Mºſ' I XXXVIII BM" . B4 . BC I “ WAZ WH. W.G. T. ” “ B.A. BC; BMr T XXXII FG" . F.H. tº F/A/ = I XXXIX BL' i. B4 {. BC = I FEI F/A' FG, T B.A. BC BLZ T H/M/ H/N, H. A BN’ BMT BOY XXXIII. t º – XL. --- * * , --— = FW, H.T Hºf, * * ; * Hiſ Rö fly, JI’Aſ’ H/I,’ H/A NYC N7D N7 B XXXIV. -- " -- - - - w (T.T. --— " — " -- = H.E. HT #77 = 1 . Xiſ. WD WB WG = } XXXV 4L' AH/ AB BN’ BMſ’ BD AH, Aſ TE = 1 xiii. EP, Ef EW, * * 32O ſ PRINCIPAL TRIANGULATION. XLIII. XLIV. XLV. XLVI. XLVII. XLVIII. XLIX, III. XXXII. BN’. BL’. BD = Hiſ FD fººt * FC . FD - FB = , FD FB FC T FB . FC FM: tºmº FC FF, FFT * * FD . Flſ' FN. FF, FW FE = 1 FC , FE FB FF FF Fă = 1 FD FE FB FE FF F5 = } BC EE’. ED EE ED E6 → * = H’ + F + L – 180° = A' + H2 + L – 180° = U -- A' + L – 180° = U + L + G – 18o° = L + A' + G – 180° = L + U + K – 180° = L + G + IY — 180° = G + K -- H – 180° = H + 1 + I, + K — = H' + A + MI — 180° = H’ + L + M – 180° = I + I, + M. — 18o° = B + A + N – 180° = A. + 1ſ + N – 180° = lſ -- TV + N – 180° XXXI. H'F' . H'I, . H.A.' L. N/E/ * N/A" ſº Nº L/ º NYC; - 1 N/A/ Nº Lº NYC N/E’ T LI N'D' . N'4' . N'L' . N’D I tº JW7A/ M7L’ N” D N7 E/ º in. Bº .37% . BºD FE, FD FE * * E’B' E'A' E! Nº E/D LIII. T. T., " … " ...-- " -, - I E'A' E'N' E/D E. B' LIV” E"0" . B'B' , E'E EIF FE FG, F * E/Oſ. E. B. E. D LW. T.T. " Tº Tº, - I IX B E' D E/C/ LVI E’D' . E"C" , E'E jø FE Eij, F * FIGURE 16. Angle Equations. — 5, XVI, o = 1ſ + I + W — 180° — sis – sa XVII. o = M + 1 + R — 180° — 517 – s; XVIII. o = }ſ + R + TV – 180° — sis – s; XIX. o = M + 1 + S – 180° — sº, – s; XX. o = }1 + S + TV – 180° — sis – 86 XXI. o = M + T + TV – 180° – s, — s, XXII, o = Aſ + S + T — 180° — sº, – 58 XXIII. o = M + T + R — 180° – s, 360°– so XXIV. o = U + T + TV – 180° — s, - 8 to XXV. o = U + T + R — 180° – e. - six XXVI. o = MI + Q -- W — 180° — sis - era XXVII. o = P + N + TV – 180° – s, – sis XXVIII. o = P + Q -- TV – 180° – sas – s; , xxix. o = B -- N + 0 — 180° — 529 – sis xxx. o = M + N + 0 – 180° — sº, o = N + 0 + P – 180° – sar Side Equations. XXXIII LG" . L.H. . LI” . . jFF EF E67 = 1 4'N' . A 'E' . A 'Q'. 4'P' . A'L 4'H' H.J. H.A. HTF = } xxxiv. Tº LP . L4'. LG LA’ LG LP’ = I A'Q' A'P' A/L A'H' A'N' J.G. L.P. LA XXXVI. *T* * *-*-* * ------ - LF EF E3 = 1 - GEOMETRICAL EQUATIONS OF CONDITION. 32 I XLII. XLIII. XLIV. XLV. XLVI. XLVII. XLVIII. II. III. IV. VI. VII. VIII. IX. * *= WiF = + W0 WiF = 1 • = I I8o° I80° I80° I8o° I80° I8o° I8o° I8o° I8o° - #19 I8o° - 6ao * XXXVII. GK GL GH I GL GH GK LA' LG LH LI J. Mſ LEI’ ........ H'L H'M HA H'N' H'A' XXXIX. — ” • -- * —, " -- = I FI’M H’A H’N7 H/A' H’L xt, 4H. . 4M . 4M .4B Z[]7 TW II; AIT = * xvi. Mſſ... Mſſ. Mſ.M. . iſzt. . Mºſſ'. II. iſy iſy- 7.1 iſſp. 177 TT = * MII MTV MR T ** ify FF 75 MS MI MW QN QW QP jff jFW jS = + * @TF OF ON = + IIS . M.R . ][W_ NM NO NB . MR MTV MIS T * Wö WI, W.I MT . MS MW in Wilſ. WW . AP, MS MTV MT T * WW WF Wö R!'... RW , Rlſ im. Zºll. TV... "Y RJW RM RT T “ TIV TV TMſ lſ! . Mſ. MU , LIV VT . VR . Vlſ MTV MU MT T * TVR VM TrT RU RT, . RW RMI ry. Tº . TU . . 47 RT I? IV RM R U T * TU TV TR Lvi VW VS ** = . WS Vlſ Try T FIGURE 17. Angle Equations. o = B -- C' + D’ – 180° — s, xi o = G + E + H2 — o = D + 0 + B — 18o° — s, XII. o = G + H' + K’ — o = D + B + C – 180° – s; XIII. o = K + II' + IY’ — o = 0 + B + D’ – 180° — s, XIV. o = K -- H' + G — o = 0 + D’ + E' — 180° – s; xv. o = R + G + N’ — o = L’ + C + D’ – 180° — so xvi. o = JC + Q’ + N’ — o = L’ + 0 + E' — 180° — s, XVII. o = R + Q’ + P’ – o = L’ + C + D – 180° – ss XVIII. o = H + G + E' – o = G + M7+ N” — 180° — s, XIX. o = H + G + H' – o = G + MI’-- L' + Ey – 360°– sis xx, o = H + G + K’ - 322 12RINCIPAL TRIANGULATION. IXXI. IXXII. XXIII. XXIV. XXV. XXVI. XXVII. XXVIII. ' YXIX. XXXII. XXXIII. II. III. IV. VI. VII. CE’. CD/ CD CD' . CB 4I/. A0 Flſ' FL’ o = B + E' + D’— o = B + D'+ I’— o = B + E' + H/– o = A + B + I’— o = D + 4'-- D’— o = D + B + D’— o = D + A*-i- C – ... CD'. .. Side Equations. B9 Elſ' . IBB" XXXIV. II, D'E' ... PG D/B/ º XXXV. E. AO/ XXXVI FG. AB. T FE/ B'D' . BB I xxxvii M/L/ B'B B'A T si. M/E/ 4D XXXVIII PH'. 16 = 1 E/G . BC – I XXXIX H'K' BE, T H/G . BC" . BD = 1 xi. 9º BD” BC T Q'K 4.D. = I XLI N'lſ' A.C. N’G CD’. I XLII GK. OE, T GN/ CB . . CD' xiii. 5; Ö' OE = * GK7 O'L' JE/HT CD, - I XLIV. FH, tº AID * H/R/ — " - XLV. -— AL’ I H’ H. FE/ HF/ XLVI. — FM/ * HE, ..., HG' . HF" . HH' XLVII. HF" FIH’ ITG.; := I FIGURE 18. tº mº iſ smºmºmº * I8o° — I8o° — I8o° — I8o° — I8o° — 180° — I8o° — 51 52 53 54 55 56 57 Angle Equations. VIII. IX. X. YI. XII. XIII. XIV. xv. o = D + G + F — 180° Pl: . EP. EE, Elf, * * PE . Pilſ' , EM, EG T FE' FM' Fif, F6 = + lſ'L'. Ilſ'E' . . M'G M'L' M/G M/N/T M. Nº EG - Elſ' . B'L' E'H' Eºſ, E'L' E/D' T E/D/ . H'G . H'E' * H/E/ H/IX/ Q'K QP. E I Q'P' Q.N. T N7 K. NZQ. T N'Q' GN' Glſ. GE' GH’ Gif GE GH, GR = 1 GK. . GK ãf ÖH, * * E'H'. EG Fū EH = * . HºH . Hº , FI’G H’K’ HE . HH! – 1 HH7 HF" o = A^+ C + C – 180° – is o = B -- E + D’– 180° — s, = E + D + D'— 180° — sis E + D + C – 180° — sº, o = F + B + D – 180° — sº, o = F + B + E – 180° — e, o = A + F + B – 180° — s —sis GEOMETRICAL EQUATIONS OF CONDITION. 323 -- rºm - Side Equations. ~ * XVI. E'H' . E'G' . B'D' . E'B XXIV B'0 B'A' | B'C' E/G/ E/D/ E/B E/H/T I B'A' Fº B/C} – I xym. Błł' . BB' BD' BI' D’E D/B D D ſº 7 75 R, " : " -, - I XXV. -- " — " → = I BE' BD” BT, EFF, D’B DºD DE xym. "B . PI . FD’ CD/ CD CE * 77, P, " …. " - = I XXVI. - " - " — = F'I' F/D, FB CD CE CD/ XIX. £4 £2 . "I , XXVII AB . ED. EF F/B F/I/ FA T … -- * * *-* * * * * * ED EF EB T xx. º.º.º. -, ºut £4.4.22. He . * –, C.A. C.D. O'D T B1, BD, EE EF EA - xxi. Dº . P'A'. DºD . D’B xxix. £º .92.93. – DZT DVD DT, DE = GD GF GE T xxn, 92 : 94'. 90 exx. GB . GD . Gº" , i. C/A/ O/O C/D E I XXX. GD GF GB jº. xxiii. 94' .92.0D – exx, 64 . GB .9′ = 1 CD OD, GA = 1 xxxi. GE GF da = FIGURE 19. * Angle Equations. - - I. O = 0' +4' + A – 180° — s, XII. o = 0 + G + E' — 180° — era II. O = D'-i-A’ + B — 180° — s, xIII. o = F + G + E' — 180° – 5,3 III, o = 0 + B' + B + A — 360° —s, XIV. o = F + G + H – 180° - 614 IV. o = A + B + A* – 180° – s, xv. o = E + H + F — 180° — e.g V. o = 0 + D'+ E' – 180° – e. XVI. o = T + E + H – 180° - 616 VI, o = 0 + F + E' — 180° — sº XVII. o = L + D + A – 180° - sº VII. o = F + E + D’ – 180° – s, xvi.II. o = M + I + E — 180° – sis VIII. o = 0 + E + F — 180° — as xix. o = M + E + D + L – 360°-5.9 IX. o = 0 + E + B + D’ – 360°– s, xx. o = K + E + I — 180° – sas X. o = D + A + B — 180° — sis xxI. o = R -- M + I — 180° – ear XI. o = D + B + E — 180° — e. xxII. o = K + M + L – 180° — sa, XXIII. o = R + L + 4 – 180° — s, Side Equations. IXXIV B'C' B'A B'C' XXVII D'4'. D’B. D'C D'4' B'A B'A' T B/A/ D/B D'O D/E/ D'E' XXV. 4'0' * 4'4 i. 4’B. tºº 4'0' XXVIII EC 4. E/F ſº E"D' := I A/A AZB AZD, T AZD, E/F E. D. E/C T B'B B'A' BºA CE, CD/ CB CF XXVI. - - - - - - - - – * * * — “ — ” – “ — F I B.A. BT FF = * E, 35 ań &# = S s 2 324. PRINCIPAL TRIANGULATION. XXX CE. C.F. CB XXXIII FE'. FC. FG • OF CB CE FG Fà FE = 1 EF EB ED’ FC FE FH FG * * * * D. BE . B.D . BA’. BA ....... IF IE IH xxxii. EE HE, ET ET Fij = 1 *Y. H. # # = 1 xxxvi, PA. PB . P4. DL. . Dilſ DE DA DE Dr DE * * FI EH EF EB ED EMI XXXVII. — " — " — " — " — " — = EH EF EB ED EMI EI XXXVIII JCI. KWI. KE_ XXXIX MI., ME. MD . MD . MIK * Fif FE FF = 1 ME MD ML MK MI LK . J.M. L.D. L4 - * Liſ ED LI ER = 1 FIGURE 20. Angle Equations. I. o = A + F + E' — 180° — s, XII. o = D + 0 + B — 180° — sº, II. o = A + F + B – 180° – s, XIII. o = D + E + B – 180° — sº, III. o = F + G'+ B – 180° – e. XIV. o = I + E + F – 180° — sº, IV. o = G' + H/+ B – 180° – s, XV. o = I + E + B – 180° – s; V. o = E + H2 + B — 180° – s; XVI, o = I + E + D – 180° — sig VI. o = E + H/+ G’ — 180° — eg XVII. o = R + A*-i- F – 180° — sº, VII. o = E + H/+ B' – 180° — s, XVIII. O = K + I + F – 180° — sis VIII. o = F + H/-H E — 18o° — ss XIX. o = G + D + C – 180° — sº, Ix. o = F + H2 + B' — 180° — so XX. O = G + D + I — 180° – sas x. o = F + H/-ī- A'— 18o° — slo XXI. o = H + I + D — 180° — eat XI. o = 0 + A + B — 180° – s; , XXII. o = H + I + G – 180° — sa, XXIII. o = II + 1 + IY – 1869 – #23 Side Equations, sy %'. . ſº . "4 . FºE’. PD ...,,,,, 4’ſſ' .403'. 4'E YX. I'B I” A. F/E/ F/D’ F'G' * = } XXVIII. A 'B' A.’ E A 'H' = I ... G'F' GD . G'H' G'B … II"I" . II'E . H'B' ** 675 GH, ° ºf GF = 1 xxix. HPE IFF FFF = ..., H.B. H'G' . H'B xxx, Hº!’. Hº!". H'B' XXVI PI/G/ HZE EI*JB E I ſº H/F H/B/ II/A’ I H.G. H.C. H.R. H.E. , xxxi. "9" . "H" . FB' xxvii. Hø, F#, HE Hò, º F#, FF F6 = + GEOMETRICAL EQUATIONS OF CONDITION. 325 XXXIII. XXXVI. XXXVII. II. III. IV. VI. VII. IX. XI. XII. XIII. O O O O O O O VIII. O O O O O O XIV. O O XXXII. XXXIII. XXXIV. XXXV. xxxn, £4. Rſ. 36. PE. B.D. BC — , BR' BG' BE BD BC BA PD. EI. EB EI EB EH/ EF EI JEB Ej = i XXXIV, FE EHF EF EF * * xxxy. Aſ . A . FH". F4'. FK FE FHZ FA' FK FI R.E. KF KI IG. IH ID jº FF FE = + XXXVIII. TH 75 76 = + 20. DB. D.I. DG xxxix. 42. P. A. P. H. I).B DI DG DC TE : TF 77 °FH 75 = 1 FIGURE 21. Angle Equations. = G' + B + F – 180° – s, XVI. o = P + Q + S – 180° — sig = E + E' + G' + B — 360° – e. XVII, o = P + Q + B' – 180° — sº, = A + F + B – 180° – s; XVIII. o = 0 + S + K’ — 180° — sis = A + B + E – 180° — s, XIX. o = 0 + S + Q – 180° — sº, = D + E' + G’ + B — 360° — e. XX. o = 0 + S + P – 180° — eas = D + 4 + B — 180° — sº XXI. o = M + L' + K’ — 180° — eat = 0 + 4 + D – 180° – s, XXII. O = M + 0 + K’ — 180° — s, = 0 + 4 + E — 180° — ss XXIII. o = N + L'+ JC’ – 180° — sº, = B' + C + F – 180° — s, XXIV. o = N + 1ſ + K’ — 180° — s, = 0 + E + F — 180° — sis XXV. o = JC + MI + L’ – 180° — ess = E + F + C + E’ — 360°– s; , xxvi. o = I + lſ -- N – 180° — e.g = A^+ Q + B' – 180° — ar, xxvii. o = R + MI + 0 – 180° — s, = S + H2 + K’ – 180° — sº, xxvii.I. o = K + 0 + P+B'+ F-540°–s,s = S + H2 + D’ – 180° — sº, xxix. o = R + L + MI — 180° — e,, = S + D’ + A' + Q — 360° — sis XXXI. XXX. Side Equations. ºf Gº, T G. E. GB. G'ſ" G! A T G/E G/B GE ºf 675 = 1 XXXVI. XXXVII. XXXVIII. XXXIX. o = I. -- L + N – 180° — ess o = M' + L’ + N + L – 360° – 53: BD BA BG' EI HG E5 = } 4E .40 . 42.4B AC AID AIB AF CE". GG CE Cſó ÖI7+ 675, E/G/ E/E E/G E'G' 7; ' E75 E7G = ECW 326 PRINCIPAL TRLANGULATION. , EE . EG'. E4. EC. P.G. ... H.D. H'S H'D' XI. Hå, ET | EC EG EE, *Y. HS HTiz, * Hik, GE GO, GF D'A' D'Q D'S I)'A' YLI. ' -->. • — " - = I * *-* * *-* * = := - GO/ GF GE YLVI. D'Q D'S D'H' D'H' * GE GF . GO". GE' * SN7 SK/ SH? XIII, 6; Gö, GE GE * * * Sk, SH, SW = ... GB' . GI" . GO" * RD' RA’ RQ RS XLIII. GF GO/ GB/ E I YLVIII. RAZ Tø TS * RD’ E I XLIV. 4'B' wº 4'Q º 4'B' XLIX R4' RD' RQ * = A'() A'D' A'D' FD - E) FA = } , RH'. RS. ºp. * T.S RD, RH = * 94.9ft 9: , º, . QP. LI. QB' QP QS QD” QA’ : I in B.C. B.E. B. H. B.P. B/2 B'0' * FF FH EP E.G. B.T. T. F.I. In 80 . SK. SH'. SD!. SQ - SK SH' SD SQ SO I SP . S0 . S0 = 1 ry. Pił. P2. P2. PB ity, Sö 50 SF = I('L' K'L' ML/ MN *mºnºmº MN MK ML/ IVII: FW TR, j77 ſº - LVIII. -- " - . * — = MR III, TW = * tº dif OF OS OF OH OR = + HO HP HB' HF HI& T - NK NL . Wilſ L'I(7 L/M L'L L'K’ NL Wºr I IXIII. --- * r 7 T * ºr TF, - Tº LXII. R,ES ULTIN G. A L G E B R AIC AL EQUATIONS OF CONDITION. FiounE 2. Notation. (1) O'C 2) O'I (3) O'K O'B ) O'A (6) N'B (7) N'A (8) BD $ B C # BA # JB0' ,# BN7 # A C 14) A O' (15) AN7 # AB 17) CE $# CHI (19) CI 2 o) CO' (2 I) CA 22) # (23) CD (24) DE (25) DC (26) DB # JEH (28) EC # #? # JHE (31) HI # PHC (33) IH 34) IK (35) IO' KI (38) KF (395 KO (46) FK - Equations. I o = + o.oo6o + (4) — (6) — (11) + (12) II o = + 5.893o + (5) — ( 7 ) — (14) + (15) III o = + 7.7866 — (4) + ( 5 ) — (1o) + (11) — (14) + (16) *V o = - o.52II + ( 1 ) — (4) — ( 9 ) + (11) — (2o) + (22) . V o = - o.838I + ( I ) — ( 5 ) — (13) + (I4) — (2o) + (2I) VI o = + 7.1555 — (8) + (9) — (22) + (23) — (25) + (26) VII o = - 2.5o64 + (17) — (23) — (24) + (25) — (28) + (29) VIII. o = — 1.6834 — (17) + (18) — (27) + (28) + (3o) - (32) IX o = - 3.76o7 — (18) + (19) — (31) + (32) + (33) - (36) X o = + 1.81o4 - ( 1 ) + ( 2 ) — (19) + (2o) - (35) + (36) *I o = + 2.8791 — ( 2 ) + (3) — (34) + (35) + (37) - (39) XII o = + 1.6281 — ( 3 ) — (38) + (39) + (4o) s º o = + 423-696 — 4.4833 (6) + 19.4147 (7) — 32-3375 (Io) + 47.8757 (II) - 15-5382 (12) — 25.9o66 (I4) + 1o.5o81 (15) + 15-3985 (I6) - *IV o = + 245-639 + 7.9611 (9) — 32-3375 (1o) + 24-3764 (II) + 9-6672 (13) - 25-o657 (14) + 15-3985 (16) + 18-2567 (2o) - 3IºoIoI (2I) + I2-7534 (22) *V o = - 187.742 — 24-8522 (1) + 8.352o (2) + 16.5oo2 (4) + 36.9493 (8) -44-91o4 (9) *. + 7.9611 (11) + 17.1o1o (24)— 2o-22o8 (25)+ 3-1198 (26)+ 12-7692 (27) -56-o291 (28)+43-2599(29)+ 16-2913 (3o)-4-6934 (31)- 11 5979 (3*) XVI. + I4-94I5 (33) + 5.9998 (35) - 2oº9413 (36) ° = - 114-888 + 4.4833 (6) + 7.9611 (9) — 234993 (11) + 15-5382 (12) + 27 3973 (º9) - 4o 15o7 (2o)+ 12.7534 (22)+ 19-746o (34)-25-7458 (35) +5.9998 (36) + 3 31o4 (37) + 5-4228 (38) — 8.7332 (39) + 24-86o5 (4°) 328 PRINCIPAL TRIANGULATION. The logarithmic values of the multipliers are as follow : Log I = 9.987.0812 – Log VI = 9.9866076 — Log XII = 9.25Io890 – II = 9. 19246O4 + VII = 9.436 Io'77 -- XIII = 8.485II.44 – III = 7.6641943 – VIII = 9.52944.42 + XIV = 8.0311923 – IV = 9.8382516 — IX = 9.0333518 + XV = 7.8577.019 + v = 9.5983072 — X = 9.468o706 — XVI = 7.8316477 -- XI = 9.54I2O88 — FIGURE 3. Notation. f f º ! E: p C. G. C. K. § # 3 # 6, #: ; ; ; ; ; ; ; ; (15) E'K (16) E L (17) FK § FE” 19) EQ. (29) J.A. (2) J.D. (22) FM (23) FG (24) gº (25) GI (26) GK § GE (28) GF 29) GC 30) GA (31) GM (32) III (33) IIIC 34) IIG (35) HA § HAſ º #. $38, # % # 7" (40) #. § #% § % § # §§ #: § III (46) KI (47) LE (48) L (49) L Equations. I. o = - or 131I – (8) + (12) — (18) + (19) II. o = + 6-3997 - (4) + (8) — (19) + (21) III. o = - 1.1280 – (12) + (15) – (17) + (18) — (39) + (40) IV, o = — 4,6627 – (7) + (15) — (39) + (41) v. o = + 1.9887 – (6) + (8) — (19) + (23) – (28) + (29) VI. o = + 4,2596 – (6) + (14) — (27) + (29) VII. o = + 4,7523 – (6) + (7) – (26) + (29) - (41) + (44) viii. o = + 3:0055 – (24) + (26) - (33) + (34) - (44) + (45) Ix. o = – 8.3978 – (2) + (6) + (24) - (29) - (34) + (37) x, o = — o'9747 – (32) + (33) - (45) + (46) – (51) + (52) XI. o = + o-1682 – (15) + (16) - (38) + (39) — (47) + (48) XII. o = + 1.9619 + (38) - (46) - (48) + (49) — (56) + (51) XIII, o = + 31-621 + 17-1342 (4) + 434918 (12) – 24.4848 (18) + o-I525 (19)+24.3323 (21) XIV. o = + 123°35 + 59:2675(7) - 79.3501 (8) — 4,7567 (17) – 19.7281 (18) + 24,4848 (19) + io.7787 (39) - 5.6930 (40) — 5,0857 (41) XV. o = + 13:244 + 28.6329 (14) – 15:4709 (15) + 6.9748 (26) – o'7423 (27)—6.2325 (29) + 5°9857 (39) + 17-6937 (41) – 22.7794 (44) XVI. o = - 16:473 – 9-9482 (6) + 38.1oo9 (7) – 28.1527 (8) — 2.9490 (17) – 11.4822 (19) + 14:4313 (23) - 7.0620 (40) + 22.7794 (41) – 15,7174 (44) XVII, o = + 148,978 – 8:ooró (3) + 17.1342 (4) — o'4581 (6) - 1.4045 (9) – 12.8561 (19) + 24’3323 (21) - 11:4822 (23) – 3.0291 (28) + 15.7331 (29) – 12.7046 (31) XVIII. O = – 212-749 - 34.4545 (6) + 8.4121 (8) + 26.0424(9) + 21-1520 (19) — 92. I 172 (22) + 70-9652 (23) – 26.5953 (28) — 12.2459 (29) + 38,8412 (31) i 3. | ALGEBRAICAL EQUATIONS OF CONDITION. 329. XIX. XX. XXI. XXII. XXIII. XXIV. XXV. XXVI. XXVII. XXVIII. XXIX. XXX. - = = — 25-o87 — I 1.9829 (7) + 8.4121 (8) + 3.57o8 (9) — 3. 1665 (17) + 2 I. I52o (19) — 17*9855 (22) + 9. 1763 (4o) — 27. 2o28 (41) + I8-o265 (43) = — 89:482 — II-9829 (7) + 9.4285 (9) — 83.5292 (13) + 44-7o22 (15) — 26-3oI2(39) — 27*2o28 (41) + 53-5o4o (43) = — 961.998 + 43:3659 (2) — 53-23oI (3) + 34-4545 (6) — 92. I55I (9) — 9.2639 (24) + I2-2459 (29) — 2-982o (31) + 3o. 7283 (34) — 153-3575 (36) + I 22-6292 (37) = — 312.6o2 + 3. 1665 (17)—74. I3I 7 (22)+ 7o. 9652 (23) — 9.2639 (24)—26.5953 (28) + 35.8592 (31) + 3. 1235 (33) + 3o7283 (34) — 33.8518 (36) — 9-1763 (40) + 3 I-8469 (43) — 22.67o6 (45) = — 2o. 997 — 26.5235 (24) + 51.92 Io (25) — 25-3975 (26)—27.o9oo (32)+ I7-7993(33) + 9.29o7 (34) + o. 818 I (44) + I5-Io35 (45) — I5-92I6 (46) + 215-243 + 67-34I I (14) — 77-6o5o (I5)+ Io. 2639 (16)+4-4356 (24)—76.4o2I (26) + 7I·9665 (27) + I7-7993 (32) — 28-o599 (33) + Io. 26o6 (34) + 17.592 I (47) — 35-9789 (48) + I8-3868 (49) + 5-4243 (5o) — Io. 7276 (51) + 5-3o33 (52) + 96o464 + I 59-7293 (1) — 39.8o62 (5) — 35-4587 (Io) + 3 II-824 + 2o-53 I 5 (7)— 12.2161 (1o)+88.2o97 (II)—32-3917 (I5)+ 15-8832 (39) + 48-54I7 (41) — 64.4249 (42) - — 47*7o4 + 2o-53 I 5 (7) — I 5.5298 (8) — 5-ooI7 (Io) + 8.36I4(17) — 34•oo78 (19) + 25:6464 (2o) — 16.3558 (4o) + 48.54I7 (41) — 32. 1859 (42) = — 84-o27 + 8.3614 (17) — 45-3776 (2o) + 37-oI62 (23) + I 7. 7536 (26)— 5. Io25 (28) — I2-65 II (3o) — 16.3558 (4o) + 76.4861 (42) — 6o. I3o3 (44) = — 296.54o + 39. I985 (24)+ I7-7536 (26)—56.952 I (3o)+4*5596 (33)-85-9662 (34) + 8I-4o66 (35) + 46-5486 (42) — 6o. I3o3 (44) + I3-5817 (45) = + 87.8oo — I5-oI4o (2) + 43-69I4. (5) — 2o.53I5 (7) + 5o•96o3 (Io) — 4:5596 (33) + 4o-4485 (35) — 35-8889 (37) — 48-54I7 (41) + 62. I234 (42) — I3-5817 (45) The logarithmic values of the multipliers are as follow: Log I = o.59oI368 — Log XI = 9. I789756 — Log XXI = 8.2469789 + II = o. 2568569 — XII = 9.8732519 — XXII = 8.o343 I2o + III = 9.8976666 — XIII = 9. I734659 -+- XXIII = 7-o275o58 + Iv = o. 242887 I + xIv = 7.64758oo — XXIV = 7.787 5585 — V = 9.26948o5 + xv = 7-8o6o222 + XXV = 8. I839522 — VI = 9.627 I3oo — XVI = 9-o972o27 + xxvI = 7.62o66oo — VII = 9.96 II 52o — XVII = 9•ο94o7I2 — XXVII = 8.846o658 — VIII = 9.976I6oo — xVIII = 7.4939438 — XXVIII = 8.7Ioo859 — IX = o. Io9I774 — XIX = 7-8792245 -+- XXIX = 8. I 5134o7 + x = 9*9o86995 — xx = 7-o 16o55 — XXX = 8. 2339243 + T' t; ! 33O. PRINCIPAL TRIANGULATION. III. IV. VI. TVII. VIII. IX. : XII. XIII. XV. 2XVI. xvi.I. XVIII. XIX. XX. xxi. XXII. xxIII. XXIV. XXV. XXVI. XXVII. XXVIII. XXIX. FIGURE 4. Notation. HD (2) LI2 (3) L/4 (4) K'D NA (9) N'C (Io) N'W' (ii) B. V. yº N7 I6) DA 17) DN7 18) DL’ { } JDM § AB' { } A V7 AD (30) AE (31) AF § AM EM (37) EA (38) ED 39) FM FE (44) FQ (45) FI (46) FP MD (51) ME (52) MF (53) MI Cp7 § CN’ (59) CA (60) CF 65) QR º QP (67) QI PM (72) PF (73) PI (74) PQ RT (79) RU (80) RC (81) RM #3 º #; ; ; ; # SP (100) SQ 94) 95) Equations. —Io-6748 — (1) + ( 2) — (18) + (20) + 6.3417 -- (2) - (4) — (18) + (19) + 4,619.1 - (4) + (5) – (17) + (19) + 1-9983 – (8) + (12) — (24) + (26) — 4.8379 – (9) + (13) — (56) + (58) – I'320I – (ro) + (11) — (14) + (15) ; (12 (19 33) (40) (47 61) (68) (75) (82) (89) (96) JB'A § ſº -- AI FC IPR MP CM QF PS RF US TS + o-7171 – (8) + (9) + (26) — (34) - (58) + (59) – 2,0621 + (16) – (21) — (29) + (30) - (37) + (38) + 5-7016 – (31) + (34) — (40) + (41) - (59) + (60) — 2.2003 + (16) – (22) — (29) + (31) - (41) + (42) + 4:1603 – (30) + (31) - (35) + (37) - (41) + (43) + o-8399 – (32) + (34) – (48) + (49) - (59) + (61) — 1.3524 + (16) – (23) – (29) + (32) - (49) + (50) + 7.94.37 – (30) + (32) - (36) + (37) – (49) + (51) + 2.4265 – (31) + (32) - (39) + (41) — (49) + (52) + o-4656 + (39) - (46) - (52) + (54) — (71) + (72) + o-8404 + (48) - (55) - (61) + (63) — (86) + (81) - I-8471 + (40) - (47) – (60) + (63) — (80) + (82) + o-5895 - (54) + (55) + (71) — (77) — (81) + (84) + o-9234 - (44) + (46) – (66) + (68) — (72) + (74) + 1-6096 - (44) + (47) — (65) + (68) — (82) + (85) + 4'3269 + (65) — (69) — (85) + (86) — (98) + (1oo) + 1-8929 - (75) + (77) — (84) + (86) — (98) + (99) — 5:1172 - (63) + (64) — (78) + (80) — (92) + (93) – o 2006 + (78) — (86) – (93) + (96) — (97) + (98) + o-7338 - (76) + (77) + (78) — (84) — (93) + (94) – 8:2069 - (78) + (79) — (88) + (90) — (91) + (93) + 1-8441 – (2) + (3) — (16) + (18) — (27) + (29) + o-8679 – (5) + (8) — (16) + (17) — (26) + (29) N7 E JB'C' DH' AL' AC FA MC MIP CI PT I? I UT ST N'F J7 B' JDE A.K.’ EF FD MA CB’ CR JPC PR JRP TU SR ALGEBRAICAL EQUATIONs oF CONDITION. '33 I XXX. XXXI. ” XXXII. · XXXIII. XXXIV. IXXXV. · XXXVI. xxxvII. XXXVIII. · XXXIX. XI. XLI. YLII. xun. IXI,IV. xiv. xw. XLVII. XLVIII. YÇLIX. = - I3o*299 + 6.6857 (2)+ 7.24o6 (4) + 33-7636(18)—175•4396 (19) + 141-676o (2o) + 76· I77 + 5-38o4 (1) + 18.8489 (5) + 64·1o35 (17)- 97.8671 (18) + 33-7636 (2o) + I74-626 - 18.8489 (5) - 3•4697 (8) + 15-7134 (16) – 64·1o35 (17) . + 48·39oI (18) + 39-5491 (26) - 49-o576 (27) + 9-5o85 (29) + 47·86o + 8.o589 (2) + 17-7279 (3) - 4-333o (16) + 44-9391 (18) - 4o-6o6I (I9) - 74-625I (27) + 92-3309 (28) - I 7.7o58 (29) + 2I9-ooo + I-o353 (4) + 34-65o9 (I2) + 29-9784 (16) - 52-3315 (17) ' + 22-3531 (19) + I9-8o48 (24) - 18.433I (26) – I-3717 (29) O = - 26-721 - 34-65o9 (I2) + 3-6396 (I3) - I9-8o48 (24) + 27.9759 (26) - 8•17II (34).-F 24°5649 (56) - 67.6659 (58) + 43•1o1o (59) - I44·384 + I-6139 (8) -F I6.6727 (9) - 18.2866 (Io) + 3o-2138 (25) - 2o-74o9 (26) - 9°4729 (34) - 2I-36oo (57) + 34-9968 (58) – 13.6368 (59) + 221-o13 + 16-6727 (9) - 174-8898 (Io) - 59-3751 (11) + 14.7882 (13) + I24-9or6 (56) - I59-8984 (57) + 34.9968 (58) + 99· I58 - 62°383o (5) + 95-3834 (6) - 33-ooo4 (8) + 5-7351 (16) + 7:5998 (17) - 13-3349 (21) + 14·24o2 (26) + 35-97o4 (29) - 5o-2Io6 (3o) - 2I-548-9-5744 (16)-5-7351 (21) + 15·3095 (22)- Io-o855 (35) + 15-769o (37) - 5•6835 (38) - 8· I 199 (41) + 1o-7672 (42) – 2.6473 (43) - I24-7o6 + I6-9344(5) - 39-7o86(8) + 22-7742 (9) - 45-2879(16) + 29-9784(17) + I5·3o95 (22) + 17-4917 (4o) - 28·2589 (41) + 1o-7672 (42) + 43-IoIo (58) - 7o•2723 (59) + 27.17I3 (6o) + 527.853 + 16.9344 (5 ) - 2o7.8o92 (7) + I9o-8748 (8) - 45•2879 (16) + 29-9784 (17) + 15-3o95 (22) - 115· I43o (26) + II5· I43o (31) - Io*7672 (41) + Io•7672 (42) \> .• - I55-63o - 16-6412 (39) + 17.4917 (4o) - o-85o5 (AI) - II-2309 (48) + o•7569 (49) + Io•474o (52) – o•224o (59) + 27-17 13 (6o) - 26.9473 (61) + 57-239 - I6-oo23 (16) - 5-7351 (21) + 21-7374 (23) - I6-2994 (36) + 2I-9829 (37) - 5•6835 (38) – 9·1 59o (49) + II-7o3I (5o) - 2-5441 (51) + 367-323 + 32-7188 (30) – 132.859o (31) + Ioo-I4o2 (32) + 87°7I7I (35) – 97-8o26 (36) + 1o-o855 (37) – 1o-474o (49) - 32-oo9o (51) + 42-483o (52) – 38o-963 - 97-8691 (31) + 97.1531 (33) + o*716o (34) - 4·265I (4o) + 34-6238 (41) - 3o-3587 (45) – 27.1713 (59) + 84-4766 (6o) - 57°3053 (62) + 443·185 - 62-5293 (31) + 178.2645 (32) - II5-7352 (33) + 4°319o (39) + I7-7213 (4I) - 22-o4o3 (45) - 71-4367 (49) + 3-7229 (52) + 67-7138 (53) 262-7I4 - Ioo-8562 (31) + Ioo·I4o2 (32) + o·716o (34) + 33-2846 (4o) - 33-2846 (46) - Io-474o (49) + 15-3898 (52) - 4-9158 (54) - 27·1713 (59) + 27-1713 (6o) - 35-4147 (7o) + 79-7477 (71) - 44-333o (72) - 166-27I + 4-319o (39) + 67-5o42 (45) – 71-8232 (46) + 3-7229 (52) - 52-9236 (53) + 49-2oo7 (54) + 2o-4654 (71) - 35-oo91 (72) + 14°5437 (73) - II-258 - Ioo-8562 (31) + Ioo-I4o2 (32) + o•7I6o (34) - Io•474o (49) + 19-74o4 (52) - 9-2664 (55) - 27.1713 (59) + 51-9o68 (6o) - 24-7355 (63) - 2•4543 (8o) + Io4-4825 (81) – Io2.o282 (82) • + 53-o87 - I4-8242 (39) – 166.2857 (46) + 181. Io99 (47) + 9.2664 (52) + 112-371o (54) – 121.6374 (55) – 1ã773ð (71) + 28.2865 (72) - 11:5975 (77) T t a 332 PRINCIPAL TRIANGULATION. LI. LII. LIII. LIV. LV. LVI. LVII. LVIII. I,IX. o = – 288.424 – 4:3408 (48) + 35.8154 (53) – 31.4746 (55) + 53.6650 (61) – 115-6815 (62) + 62-oró5 (63) — 7.4236 (80) — 27.4776 (81) + 34,9012 (83) o = + 438-457 + .33:1464 (44) – 166.2857 (46) + 133-1393 (47) + 90.0994 (65) 88-2215 (66) – I-8779 (68) + 28.2805 (72) + 28.5049 (74) — 56.7854 (77) o = + 524.479 + I34,9228 (44) — 206-7460 (45) + 71-8232 (46) + 12.0494 (66) – 65-6230 (67) + 53.5736 (68) + 35-oo91 (72) — 58.3154 (73) + 23.3063 (74) o = + 158-662 + 88.2215 (65) – 60.8365 (66) – 27.3850 (69) — 64.0408 (84) + 49.5355 (85) + 14,5053 (86) – 47.4335 (98) + 83.3237 (99) – 35.8902 (Ioo) o = - 360.ogo + 14.0722 (40) + 33-1464 (44) - 47.2186 (47) + 24.7355 (60) – 78.2265 (63) + 53-4910 (64) – 45-1216 (65) - I-8779 (68) + 46.9995 (69) + 6.4337 (92) – 41.8863 (93) + 35-4526 (96) - 8:58oo (97) – 6:5306 (98) + 15. IIoô (Ioo) o = – 624,395 – 34,3576 (75) + 92.3015 (76) – 57.9439 (77) – 1846974 (93) + 220.15oo (94) — 35-4526 (96) + 8.58oo (97) + 38.8535 (98) - 47.4335 (99) o = + 226.915 – 37.1348 (62) + 62-oi65 (63) – 24.8817 (64) – 78.9687 (78) — 7.4236 (8o) + 86,3923 (83) – 3:4413 (92) + 155-5163 (93) – 152.075o (95) o = + 239.841 + 53-49 Io (63) – 53:491o (64) + 55.0429 (78) — 56.6985 (79) + 1.6556 (80) + 208.3694 (87) — 13.8783 (88) — 194,491 I (90) + 238-3808 (91) 238-3808 (92) g o = + 177-170 – 27.8166 (78) + 13.4157 (79) + 14,4009 (86) + 39.4210 (88) — 78-1964 (89) + 38.7754 (90) — 20.1362 (91) – 35-4526 (93) + 55.5888 (96) The logarithmic values of the multipliers are as follow : Log I II III IV V VI VII VIII IX XI XII DXIII XIV XV XVI XVII XVIII XIX -: 9.9386663 + Log DXXI = 9.9589597 + Log XLI = 8.2993604 º 'º = o-3787853 — XXII E 9.28o9485 + XLII = 8.66.40524 + = o. II.44088 + xxIII = 9.8453975 - XLIII = 8.5.129342 + = 9.7435278 – xxIV = 9.8077968 — XLIV = 7.696.5464 — = 9.2522873 – xxv = 8-99.27779 — XLV = 7.8363203 — -: o:5247987 + XXVI = 9.8048858 §ºmº XLVI = 8.0569.139 Hºmº = o.5528706 – xxvii = 8.8561226 + XLVII = 7.9882062 + = 9.8436849 – XXVIII = 9.6575788 + XLVIII = 7.3126416 — = 9.7674572 + XXIX = o'5587721 + XLIX = 7.98.43685 + = 8.3200632 + XXX = 8-014.46co + L = 6.9512656 + = o. 2555.262 - XXXI = 8.4969474 – LI = 8.3957.517 -- = 9.4065574 + XXXII = 8-9203735 — LII = 8.1389918 – = o.222I406 – XXXIII = 7.890o858 + LIII = 6.8526288 — = 8.3738.972 E ºf $ XXXIV = 8.92.16569 — LIV = 7.874I 256 + = 9.4759462 – XXXV = 8.6040323 + LV = 8.32497Io + = 9.6251369 – XXXVI = 8.9948o85 + LVI = 7.999.1345 + = 8.67 II349 – xxxvii = 8.1856824 – LVII = 7.9967856 – = o-ooo7198 + XxxviiI = 7.9752.209 – LVIII = 7.8508316 + = 9.2837939 + xxxix = 8.952.1893 + LIX = 8.9251873 — = o. 1358889 – XL = 8.47.00998 — -- ALGEBRAICAL EQUATIONS OF CONDITION. 333 VII. XIII. XIV. XV. XVI. IXVII. XVIII. XIX. XX. YXI. XXII. XXIII. XXIV. XXV. XXVI. XXVII. XXVIII. XXIX, D W FJZ QG VK BK JKJ HK Iypr LXV JB JN JZX LO NG OG (2) DB (3) DK (9) FB (Io) FJ (16) VK. {:}} JZD (23) VF (24) BE (30). KF (31) KE (37) KL (38) KG (44) HL 45) HN (51) WX 52) WZ § A ſy º A. P. (65) JV 66) J }}^ 72) JG 73) J.L. 79) PZ (8o) PJ § J. G. § NQ (93). GQ (94) GII (roo) OII (Ion) OL - I'o696 - (II) + (13) + (30) — (40) + o-5809 – (7) + (11) — (30) + (31) + I-5982 * - (3) + (II) g- (30) + (32) FIGURE 5. Notation. (11) (18) (25 (32 (39) § (53 (60) (67) § (81 (88) (95) (1 oz.) EW FK J//p/ By JKD REI IIO JVJ _X2, JX 2.J. JLHI NHT GK ON Equations. JE IV FPI VX. J3 Pſ" ATP" JKQ JTG: JWRC AJ JY 2 Jy JLK NL GJ, OJ – 4,7687 – (I ) + (3) + (17) — (22) — (32) + (33) – 4:4335 – (4) + (7) + (16) – (22) — (31) + (33) + 3.4296 – (8) + (11) — (22) + (23) – (30) + (33) + 1.4635 – (21) + (22) + (25) – (29) — (33) + (34) º : 2.8090 – (6) + (7) + (24) — (29) – (31) + (34) o.7453 – (20) + (21) — (25) + (28) — (64) + (65) o:2764 – (8) + (Io) – (20) + (23) — (63) + (65) I-6250 – (20) + (22) — (33) + (36) – (62) + (65) o.5595 – (4) + (5) + (16) – (18) — (49) + (50) 1.0919 – (18) + (21) — (25) + (26) + (50) — (55) 1.8643 – (18) + (22) — (33) + (35) + (50) — (54) + 1-5999 – (18) + (20) + (50) — (53) — (65) + (66) + 3.7658 – (18) + (19) + (50) — (51) – (57) + (58) + o-2042 – (26) + (27) — (51) + (55) — (56) + (58) + o-4907 – (51) + (53) + (58) — (61) — (66) + (67) + 2.8169 – (60) + (61) — (67) + (69) — (74) + (76) + 3.3622 – (52) + (53) — (66) + (69) — (74) + (75) + o-o328 – (59) + (61) — (67) + (68) + (78) — (80) — o-o221 – (59) + (60) — (76) + (77) + (78) — (79) – o'5or 7 – (13) + (14) — (39) + (40) + (43) — (48) – 4,2903 – (12) + (14) + (42) tº (48) - I-3934 – (37) + (39) — (43) + (44) — (81) + (82) + 4:5389 – (36) + (37) + (62) — (73) — (82) + (83) - o'2953 – (44) + (45) + (81) — (84) — (88) + (89) - I-3885 - (71) + (73) — (83) + (84) — (89) + (90) + +5123 - (4) + (15) – (47) + (48) — (93) + (94) . : : : 3 i 334 PRINCIPAL TRIANGULATION. XXX. IXXXI. XXXII. XXXIII. XXXIV. XXXV. 2x XXVI. XXXVII. XXXVIII. XXXIX. XL. XLI. IXLII. XLIII. XLIV. XLV. XLVI. XLVII. XLVIII. XLIX, L. LI. LII. LIII. LIV. LV. i 2.1516 – (13) + (15) - (38) + (40) — (93) + (95) o-o297 – (44) + (47) + (81) - (86) — (94) + (96) 2.3421 – (84) + (86) + (89) — (92) — (96) + (97) 1.1521 - (70) + (71) - (90) + (91) — (102) + (103) 1.5781 – (84) + (85) + (89) — (91) — (IoI) + (Ioz) o-6762 – (45) + (46) + (88) — (91) — (1oo) + (102) 3.0522 – (91) + (92) — (97) + (98) — (99) + (Ioz) 84.936 – 50-3070 (3) + 2 I-7576 (7) – o'8653 (30) + 17,3026 (31) I6.4373 (32) 251.917 -- 21,7576 (7) + 25.5147 (13) – 18-1796 (30) + 17.3026 (31) o:8770 (40) 51.879 + 11.3254 (11) + 11.6777 (13) + 9.6987 (30) + 51.2182 (40) 60-9169 (41) 65.337 + 20-1358 (1) + 58-5535 (8) – 68.4859 (16) + 17.0643 (17) 51.4216 (23) 7.037 + 8.9 Io9 (1) – 50-3070 (3) + 6.3395 (17) + 35-8446 (22) – 42-1841 (23) 14.2236 (30) – 16.4373 (32) + 2.2137 (33) * 134.866 – 33-61oo (4) + 44,8879 (6)– 11.2779 (7) – 3.9942 (16)–38. 1266 (21) 42-1208 (22) – 21.4385 (31) + Io?:590o (33) – 86.1515 (34) 231-oo7 + 93-3791 (1)– II3’5149 (2) — 36.2905 (4)--33.61oo (6)–29.2666 (17) 29.2666 (21) + 8.2192 (24) – 8.2192 (25) 4.676 + 17.2700 (6) – 11.2779 (7) – 47.1615 (9) + 17-9259 (II) — 1.8686 (30) 2I-4385 (31) + 23-3071 (34) 198.069 – 9.5631 (8) + 38.5668 (Io)-29'oo37 (II)- 12.6021 (20)--48.4467 (22) 35-8446 (23) – 61.2925 (62) + 68.7298 (63) — 7.4283 (65) 222,819 + 32.9993 (20) - 75-12oi (21) + 42-1208 (22) + 107.590o (33) 133-3496 (34) + 25-7596 (36) + 15:5787 (62) - 84.1681 (64) + 68-5894 (65) 201,799 + 159-6947 (4)-193'3047 (5)+33*61oo (6)+8.2192 (24)—33:2448 (25) 25.0256 (26) – 794389 (49) + 67-4023 (50) + 12.0366 (55) - 428.380 + 82-7026 (33) - io9'1618 (35) + 17.4592 (36) + 22.5786 (50) 11.3308 (53) — II.2478 (54) + 7.4283 (62) – 88.4120 (65) + 80.9837 (66) 47,612 + 15-7046 (18) — 19:5385 (20)-3-8339 (21)+25.0256 (25)–24.9083 (26) o. 1173 (28) + 34-1724 (64) - 80.9837 (65) + 46,8113 (66) 7.552 + o-ri 73 (26) + 17.2924 (27) – 17.4097 (28) — 16:3228 (51) 29:4582 (53) – 13:1354 (55) + 14,2885 (56) – 1,5218 (58) — 12.7667 (61) 19:039 - 34.3433 (19) + 57.3426 (20) – 32.9993 (21) + 17,9163 (25) + 17:2934 (37) – 35,2087 (28) + 14.2885 (56) – 2.7160 (57) – 11.5725 (61) + 63.558 - 16:3228 (51) + 81.6791 (52) — 65.3563 (53) — 1.5218 (58) - 45-6573 (60) + 47.1791 (61) – 15:1994 (74) + 19.1882 (75) – 3.9888 (76) + 85-230 - Io. 1834 (59) + 45.6573 (60) — 35-4739 (61) - 12.6799 (74) + 3.9888 (76) + 8.6911 (77) – 3.0543 (78) – 43.8174 (79) + 46.8717 (80) — 724.579 + 33-7Io9 (11) – 88.9464 (12) — 83.5088 (13) + 68.0318 (14) – 3:4232 (30) + Io5.8220 (39) — 102:3988 (40) * - 180-390 + 38-5668 (10) – 72.2777 (II) + 33.7109 (12) + 18.4466 (42) – 34,7009 (43) + 16-2543 (44) — 120.3432 (62) + 68-7208 (63) + 51,6224 (73) + Io:2552 (81) – 8.4059 (82) — 1.8493 (83) {} + i - r: ALGEBRAICAL EQUATIONS OF CONDITION. 335 LVI. LVII. LVIII. LIX. LXI. LXII. LXIII. LXIV. o = + 234'327 + 10.8243 (36) – 21.2596 (37) + 10-4353 (39) + 16-2543 (43) - 57.8789 (44) + 35.6246 (45) + 51.6224 (62) + 43.8608 (71) – 95.4832 (73) + 33°4197 (88) — 40.8293 (89) + 7.4096 (90) ° = + 146-218 + 83.5088 (13) — 83.5088 (14) + 10,4353 (37) – 112.8341 (39) + Ioz:3988 (40) + 26.org3 (45) — 26.org3 (48) + o-5674 (81) + Io.2552 (82) - Io. 8226 (84) + 90.2019 (87) — 123.6216 (88) + 33.4.197 (89) o = - 283.660 + 31,6854(44)—35.6246(45)+3.9392 (47)—33-4197 (88)+37-3551 (89) - 3.9354 (92) + 33-4122 (94) — 69-0306 (96) + 35.6184 (97) o = - 55.719 + 35.0374 (43) — 16-2543 (44) – 18.7831 (47) — Io.2552 (81) + 29.4884 (82) — 19-2332 (86) + 67.817o (94) — 146-5643 (95) + 78.747.3 (96) o = + 671-869 + 83.5o88 (13) — 87-8649 (14) + 4,3561 (15) + 35-o207 (38) – 137.4195 (39) + Ioz:3988 (40) + 4o. 1795 (93) — Io?.9965 (94) + 67.817o (95) o = + 177.586 + Io.8243 (36) – 43-7215 (37) + 32.8972 (38) + 51.6224 (62) + 96.2750 (72) - 147-8974 (73) + 44-6749 (83) – 44,6749 (86) + 78.747.3 (95) — 78.747.3 (96) o = + 4*155 - 3.9392 (44) + 92.2212 (46) – 88.2820 (47) – 8.3452 (81) - 65.2049 (85) + 73.5501 (86) – 16.8532 (99) + 26-2765 (Ioo) – 9.4233 (IoI) o = - 96.851 – 18-4206 (45) + 92.2212 (46) – 73.8o06 (47) – 8.3472 (88) - 43.9367 (91) + 51.3839 (92) – 25-6532 (99) +26-2765 (Ioo) – o 6233 (Ioz) o = - 346.404 + 188.5746 (70) — 232.4354 (71) + 43.8608 (73) + 2.3081 (83) - 37°450I (84) + 35-1420 (85) + 51.0461 (IoI) — 160-3904 (Ioz) + Io9.3443 (103) The logarithmic values of the multipliers are as follow : II III IV V VI. VII VIII IX X XI YII YIII XV XVI XVII YVIII XIX Log I = o'5293965 + Log XXII = o-3916240 + Log XLIV = 8.1403302 — = O'3975379 + XXIII = o'573II95 – XLV = 9.6208954 + = o'7958668 + XXIV = o-8155366 + XLVI = 8. Io. 4492 - - o-7921918 + XXV = o:51684.57 + XLVII := 7-1647008 tºº = o'3036.479 + XXVI = 9.9144I7o + XLVIII = 6.9762179 – = o.6884.514 – XXVII = 9.269306I + XLIX = 9.248.1761 – = 9.975I943 - XXVIII = o'5913.993 + L = 9.07678.49 + = o-oo.43347 -- XXIX = 9.9462862 + LI = 9. I691290 – = o-6717515 — xXX = o-4163.191 – LII = 8.8525309 – = o-6715208 — XXXI = o-6672II2 + LIII = 9.0753716 – = O'5242174 + XXXII = 9.9960731 – LIV = 9.2335784 – = o. I932298 – XXXIII = o-'7658271 + LV = 9.447750I - = o'3503383 – XXXIV = o'70II.470 + LVI = 8.88666.2 I – = 9-6264556 + XXXV = 9.6687.342 + LVII = 8-03372O4 – = o'5704234 + xXXVI = o'o.256.032 – LVIII = 8.1593.081 + = o’ I 5657oo — XXXVII = 9.8460294 + LIX = 8.8585oor – = 9.5989.273 + XXXVIII = 9.8753184 – LX = 8.9322040 – = 9-ooo.4I48 — XXXIX = 8.455644I + LXI = 8.3961392 - = 9.5596608 + XL = 8.8153312 – LXII = 8.5850545 + = o-6387752 – XLI = 9.8320881 — LXIII = 7.8265083 + = O-I 81818.1 – XLII = 8.378.9766 + LxIV = 8.4594747 tº XLIII = 7.7388931 336 PRINCIPAL TRIANGULATION. EIGURE 6. Notatiom. AB • (2) AJE (3) AC (4) BE (5) BD 6) BC (7) BA $ $ CB $ CE (1 1) CD 8$ CH &? CF { 8 IDC (Î5) DB (16) DE 17) D II (18) DG 19) DF £} IEB 2 IY EHT 27,Y EIF (23) JED $ JEC (25) FC (26) FD (27 29) FG (3o) GF 3 1) GD (32) GH (33) IIF (34) HC' 35) HD 36) IIE (37) HIG JEquations. . I. o = + 3*5387 — ( I ) + (3) — (6) + (7) — (8) + (9) i. II. o = + 2. I97o — (4) + (6) — (9) + (Io) + (2o) — (24) I. III o = — o<35oo — (5) + (6) — (9) + (II) — (I4) + (I5) IV. o = — o-o953 — (Io) + (II) — (I4) + (16) — (23) + (24) v. o = — 2-9738 — (Io) + (13) — (22) + (24) — (25) + (27) - . vI. o = — o.7oI 9 — (II) + (13) + (14) — (19) — (25) + (26) ; VII. o = — 3-7769 — (Io) + (12) — (21) + (24) — (34) + (36) 3s i. VIII. o = + o.6564 — (21) + (22) — (27) + (28) — (33) + (36) Ix. o = — 7.2969 — (16) + (17) — (21) + (23) — (35) + (36) x. o = — 2.89Io — (28) + (29) — (3o) + (32) + (33) — (37) XI. o = + 3.4623 — (17) + (18) — (31) + (32) + (35) — (37) XII. O = —• 48. o99 + 42. I448 (I) — Io2•51o5 (2) -H 6ο•3657 (3) -+ 28.469 I (4) — I6•6282 (6) — II-84o9 (7) — 18.9 I4I (8) — 9.6582 (9) + 28:5723 (Io) xIII. o = — 17.897 — 16.6282 (4) + 24:8198 (5) — 8. I9I6 (6) — I5-5474 (14) + I 7.2o2I (15) — 1.6547 (16) — Io. 7552 (2o) — 7-286o (23) + I8-o412 (24) xIv. o = + 83.338 + 19.419o (Io) — 48.2364 (II) + 28:8174 (13) — I.6547 (14) — 34.9142 (16) + 36. 5689 (19) + 12-o992 (25) — 68:38o3 (26) + 56.281 I (27) xv. o = £ 59.415 — 3.3787 (1o) + 32:196* (i3) — 28:8174 (13) — 12-o992 (25) + 4.5617 (27) + 7.5375 (28) — 23.o799 (33) + 29:8961 (34) — 6.8162 (36) xvI. o = + 321.247 — 25-7495(16) — Io-8i94 (17) + 36.5689 (19)—68.38o3 (26)+6o.8428 (27) •*. + 7.5375 (28) — 23:o799 (33) + 5I-9724 (35) — 28.8925 (36) xVII. o = — 124-859 + 62. i656 (17) — 94:7478 (18) + 32.5822 (19)— 15. 7576 (26)— 74-97o6 (28) + 90-7282 (29) — 29:52o6 (3o) + I4-59o7 (31) + 14.9299 (32) The logarithmic values of the multipliers are as follow : Log I = o-o3o5I4I — Log VII = 8.8373977 + Log XIII = 8. 54833o5 + . II = 9•94I4277 — VIII = 9-55o77I9 -+- XIV = 8-39I8345 — i. III = 9•oI69674 -+- IX = 9.49o9562 — XV = 8. I23476o — £. Iv = o. 572oI 27 — X = 9.9I79Io6 + XVI = 8·9o44266 — : V = o•54729I9 -+- XI = 9•5362399 — XVII = 6. I283993 + VI = o.499 I39 I — . XII = 7.8354559 + ■» ALGEBRAICAL EQUATIONS OF CONDITION. 337 JEC HG JKD RTL IK MK PB AN BA FIGURE 7. Notation. IY CF 2. T § 3 ; ; ; # 3 # & # & #. (#5) Gº (16) GI (175 GH (18) GE (19) GD (26) GC $22) 29 (23) D.R. (24) DII (25) DI (26) DE (27) ED (29) 3G (36) EK (31) EI (3%) IIC (33) HD (34) IIC (36) HE (37) HK (38) HL (39) HI (43) KE (Aij KII § Kg §§ † (45) # 4% º (47) ſºy (48) ºf (50) KI (51) IE (52) ID (53) IC (54) III (55) IG (57) IL (58) LI (59) J.K. (60) LP (61) LM (62) ML (64) MP (65) MO (66) MN (67) M.A. (68) PIC (69) PG (71) PA ; PO (73) PN § PM (75) PL (76) AM (78) AO (79) AP (80) AB (81) BN (82) BO (83) BP Equations, I. o = - 17545 - (2) + (8) — (19) + (20) — (21) + (22) II. o = - o'7343 – (18) + (19) — (22) + (26) — (27) + (29) III. o = + o-4095 - (2) + (7) — (18) + (20) — (28) + (29) IV. o = + 4,9734 - (1) + (2) — (11) + (12) + (13) — (20) V. o = + o- 17 II – (1) + (5) — (10) + (12) — (34) + (36) VI. O = + I-5737 – (2) + (5) – (17) + (20) — (34) + (35) VII. o = + 3.88oo — (17) + (19) — (22) + (24) — (33) + (35) VIII. O = – o-6179 — (1) + (4) — (9) + (12) — (43) + (44) IX. o = – 3.3731 – (9) + (Io) — (36) + (37) – (41) + (44) X. o = + o-9324 – (4) + (8) — (21) + (23) - (42) + (43) XI. o = + 3.1264 — (4) + (7) — (28) + (30) – (40) + (43) XII. o = — o-3108 – (30) + (31) + (40) — (50) — (51) + (56) XIII. o = + 3.4130 — (37) + (39) + (41) — (50) — (54) + (56) XIV. o = + 3:5314 – (16) + (18) — (29) + (31) — (51) + (55) xv. o = + 7.6777 – (6) + (7) — (28) + (31) — (51) + (53) XVI, o = + 4,8698 – (25) + (26) — (27) + (31) - (51) + (52) XVII. o = — 2.7555 – (49) + (50) — (56) + (57) - (58) + (59) XVIII. o = — o-3474 – (45) + (49) — (59) + (60) + (68) — (75) XIX. o = + o-8732 – (2) + (4) — (14) + (20) — (43) + (45) - (68) + (69) XX, o = — o'7505 – (60) + (61) — (62) + (64) — (74) + (75) XXI. o = — 3.3194 — (45) + (48) — (63) + (64) + (68) — (74) XXII. o = + 3.6755 – (64) + (67) — (71) + (74) — (76) + (79) XXIII. o = — 2.2697 – (70) + (71) — (79) + (80) + (83) — (84) XXIV. o = + 34.415 + 4-1042 (2) + o-o571 (7) – 4:1613 (8), 4 33-1458 (21)–28.2034 (22) — 4.9424 (26) + Io-4970 (27) – 36.2319 (28) + 25.7349 (29) XXV. O = — 59-621 + 12-2004 (Io) – 18.5ooš (II) + 6.30ol (I2)--4,8239 (13)+o.7489 (17) - 5:5728 (20) + 5.7622 (34) – 40.6764 (35) + 34.9142 (36) * 9 = + 92.753 + of 4.89 (17)+20.0543 (19)—20.8o32 (20)-37.6207 (21)+33-1458 (22) + 4'4749 (24) – 27.5208 (33) + 68.1972 (34) – 40.6764 (35) XXVII. o = - 52-422 — O-O 57 I (2 )–37. I263 (5 )+37-1834 (7 )+33.2372 (17)-45'5493 (18) + 12:3121 (20) + 12,6532 (32) — 16.88o3 (34) + 4,2271 (35) U u 338 PRINCIPAL TRLANGULATION. XXVIII. XXIX. XXX. XXXIV. XXXV. XXXVI. XXXVII. XXXVIII. XXXIX. XL. XLI. XLII. XLIII. XLIV. XLV. — 2oI. I36 — 4:6427 ( I )+ Io8:7641 (4)— Io4. 1214 (5)—72-7759 (9)+78.4432 (Io) — 5-6673 (12) + I9-oI65 (34) — 4-o9o5 (36) — 14.926o (37) — 12o. 8o4 — i-3286 (21) — 3. I463 (23)+4.4749 (24) — 27.52o8 (33)+ 8.5o43 (34) + I9-oI65 (37) — 28-4756 (41) + 37.2358 (42) — 8.76o2 (43) * — 6:2o2 + 7-7881 (4) — 24. 2292 (7) + 16.441 I (8)— 3. I463 (21)—24.6575 (23) + 27.8o38 (26) — 2o.2258 (27) + 3*9o57 (28) + I6.32oI (3o) + I76:488 + 4:6427(1)— 18. 1977 (2)+ I3-555o (4)+37.o464 (9)—42.7137 (11) + 5-6673 (12) + 3 I. 7242 (13) — 39.6663 (I5) + 7.9421 (2o) + 8o-936 — 22-74oo (I5)+85. I 985 (I6)—62-4585 (17)+5-5314. (35)+7. I 595 (37) — 12.69o9 (39) — I3-7473 (54) + 2o. 8744 (55) — 7. 127I (56) + 24.747 + 27,8389 (16)—33.2372 (17)+ 5-3983 (18) — 6-8318 (32) — 4-2271 (35) + II-o589 (39) + 9.45oo (51) — 28. 1213 (54) + 18:6713 (55) — 82. 191 — 37. 1263 (5) + 41.9355 (6)—4.8o92 (7)+5:82I4(32)— 16:8803 (34) + I I.o589 (39) — Io-3I58 (51) + 38-437I (53) — 28. I2I3 (54) + I49•7o6 + 29.917o(23)—57.72o8(25)+27.8o38(26)—2o.2258(27)—26.8o2o(3o) + 47-o278 (31) — I. 355o (51) — o. 4618 (52) + I.8I68 (56) - 299.782 + 2I-438o (37)— Io3-2242(38)+8I-7862(39)—5. I56o(41)+3o-6632(49) 25.5o72 (5o) — 32-5693 (54) + o-o953 (56) + 32:474o (57) 252.453+87.o842 (14)— 172.2827(I5)+85-1985(I6)+2o. 8744(55)—2o-779I (56) o-o953 (57) + 17.541 5 (58) — 2I-9355 (59) + 4-394o (6o) — 7o. 26oo (68) 49:6645 (69) + 2o.5955 (75) 257.239 + 46.o857 (2)— 121.6o34(3)+75:5I77 (4)+71-27oI (14)-28-9345 (15) 42.3356 (2o) + 2I. 279o (68) — 2I. 279o (69) - 31.935 + Io.67o7 (45)—24.7897 (48)+ I4. II9o(49)+4-394o (59)- I7-7I66 (6o) 13.3226 (61) — o. 9964 (62) — Io-o834 (63) + II·ο798 (64) 181.931 + 39.2217 (45) — 137-3I2o (47) + 98-o9o3 (48) — 25-o26o (63) — 5.4395 (64)+ 3o.4655 (66) — 8-9854 (68) + 36.o668 (73) — 27.o814 (74) + 269.689 + Io.5I5I (7o)—51:4287(71)-+4o. 9136(73)+82-91o3 (77)—77-7681 (79) — 5. I422 (8o) — 95-576o (81) + 6o-6485 (83) +. 34:9275 (84) - — 157.664 + 5-4395 (64)—6I*9665(66)+56.527o(67)+51.4287 (71)—78.51oI (73) + 27.o814 (74) + I 36-3295 (76) — 214-o976 (77) + 77.7681 (79) — 55-8o3 + 53-97I3(45) — II5-oI26(46)+61.o413(48)— 18.8367(63)—8. 7616(64) + 27-5983 (65) — 18:6553 (68) + 32.6999 (72) — 14.o446 (74) — 6:682 — 34*o430 (64) — 4-o615(65) + 18. io45 (67)+ 12-o933 (71)—28.o876(72) + I5*9943 (74) — ioo435 (76) — 37-4o61 (78) + 47.4496 (79) — 56:796 — 13:699o (7o) + 24-o538(71)— Io. 3548(72)— 13.5o2I (78)+o.5241 (79) + i3*978o (8o) + 3:4614 (82) + Io.6774 (83) — 14. 1388 (84) . The logarithmic values of the multipliers are as follow: Log I = o.6886588 — Log VII = o-oo29665 — Log XIII = o. I6oI638 — II = o•2222725 — vIII = o. 52I82oI + XIV = 9.2698267 — ' III = o-8859485 -+- Ix = o.49o58o6 — XV = o. 5o7o954 — Iv = 9.8524366 — x = o. 37I4597 + XVI = o. 3996o5o — v = o. 3953496 — xI = o.42822 II + XVII = o.639o89o + VI = o. 5667 297 — XII = o.6933756 + XVIII = o.43 III 53 + ALGEBRAICAL EQUATIONS OF CONDITION. 339. Log XIX = 9.0972469 — Log XXVIII = 7.7234285 + Log XXXVII = 7.4796287 - XX = o'o658242 + XXIX = 8.95987.40 + XXXVIII = 6.9322992 - XXI = 9.6121636 – XXX = 8.9665120 + xxxix = 7.5478818 – XXII = o'I457979 — XXXI = 8-0221754 + XL = 6.9774635 + XXIII = o'3465679 — XXXII = 7.93.19356 — XLI = 7.6008689 — XXIV = 9.3295629 — XXXIII = 7.6570.157 -- XLII = 7.6172851 + XXV = 8. I454820 + XXXIV = 8.6962o.25 + XLIII = 8.4265598 + XXVI = 9. 1074823 — XXXV = 8.0279.055 + XLIV = 8.6292516 — XXVII = 9. 1854.048 — XXXVI = 7.91.25576 + XLV = 9.3017605 + FIGURE 8. Notation. º 1) US 2) UR 3) UT TU TS (6) TW (7) TR § TQ § I? Uſ & RS & RN & RMſ § I? Q § J.T. 15) SA (16) S.M. (17) SQ (18) SR % ST 6. SU (21) QT ; QE (23) QS (24) QN § QM (26) QP 27) Q0 § ź. 29) PS § PM (31) PK (3%) PO (33) PQ (34) OP (35) QA (36) OK 3. OH (38) OC § O Q § NK (41) NM § NO (43) NP 44) NG! (45) NR (46) N.T (47) NS (48) MS % MN 50) MK (51) MH (32) MF § ML (54) MC (55) MP (56) MQ § MR (58) LM (59) LK (60) LH (61) LF (62) KN (63) KG (64) KH (65) KF (66) KE" (67) KL (68) KO (69) KP (70) KM (71) HK § FIG. § HF (74) HE' (75) HC (76) HO (77) HL (78) HM (79) CO (86) CM § C’II § E' K § EH (84) £1. § EG (86) AF § A'G § FH (89) FG (90) FA’ (91) FE Equations. I. o = – 6.3841 – (84) + (86) — (90) + (91) II. o = + 6.3356 – (73) + (74) — (83) + (84) + (88) — (91) III, o = + 1.4.183 – (74) + (75) — (81) + (83) IV. o = + 4.8551 – (64) + (66) + (71) — (74) — (82) + (83) V. o = + 3-1818 – (50) + (51) — (64) + (70) + (71) — (78) VI. o = — 2.7757 – (51) + (54) — (75) + (78) — (80) + (81) VII. o = — o'ol 56 – (50) + (53) — (58) + (59) — (67) + (70) VIII. o = – 3.8351 – (51) + (53) — (58) + (60) — (77) + (78) IX. o = — I-3457 — (37) + (38) — (75) + (76) — (79) + (81) x, o = — 5:2424 - (36) + (37) – (64) + (68) + (71) – (76) XI. o = – 3:5667 — (31) + (32) — (34) + (36) – (68) + (69) XII, o = + 4,2114 – (30) + (31) — (50) + (55) — (69) + (70) XIII. o = — o-Io?6 – (35) + (36) – (40) + (42) + (62) — (68) *TV. o = + o-9718 – (29) + (31) — (40) + (43) + (62) — (69) *V o = + o-9711 – (29) + (30) – (41) + (43) + (49) — (55) * * = + 1.9638 – (24) + (25) — (41) + (44) + (49) — (56) *W* 9 = + 2.1715 – (24) + (26) + (29) — (33) — (43) + (44) XVIII, , o = * sº. - TJ u :2 . # *44 – (24) + (27) + (35)–(39) — (a) + (4) 34O PRINCIPAL TRIANGULATION. lXIX. 2XX. JOXI. XXII. IXXIII. lXXIV. IXXV. IXXVI. XXVII. XXVIII. 2XXIX, YXX. DXXXI. XXXII. XXXIII. XXXIV. }XXXV. xXXVI. DXXXVII. IXXXVIII. XXXIX. XL！ XLII. XLIII. DXI,IV. O :>: – 4-3345 - (15) + (17) - (23) + (24) - (44) + (47) – 2-3785 - (16) + (17) - (23) + (25) + (48) – (56) + o·2735 - (Io) + (I3) - (17) + (18) – (22) + (23) - 3-7o85 - (II) + (I3) - (22) + (24) – (44) + (45) + o-9382 - (I2) + (I3) - (22) + (25) – (56) + (57) - o·4239 - (6) + (8) - (21) + (24) – (44) + (46) + o*9412 - (7) + (8) - (13) + (14) – (21) + (22) - o-6181 - (5) + (8) - (17) + (19) – (21) + (23) + 4-6412 – ( I ) -F (3) - (4) + (5) - (19) + (2o) - o·7339 – ( 1 ) + ( 2 ) – (9) + (Io) - (18) + (2o) — Io67-45o + 465-4882 (73) – 516-938o (74) + 51-4498 (75) + 2.1-56o6 (81) + 256.543o (86) - 21-1o27 (88) + 58-5673 (9o) - 37-4646 (91) – 351-669 – 46.2719 (84) – 1o3-7o48 (85) + Io5•6o5o (86) + I7-6o3I (87) + 83-86o5 (89) - I42-4278 (9o) + 58-5673 (91) + 1 17.o29 - o-7943 (72) + 13-2o34 (73) - 12•4o91 (74) - o*9o48 (83) + 23•1o1o (84) - 22• 1962 (85)- o-o832 (88) -- 2 1 · 1859 (89)-21 · Io27 (91) 1 1 53.888 + 195· I558 (63) - 2o4.8161 (64) + 9-66o3 (66) + Io5•4196 (7I) 13o-9236 (72) + 25°5o4o (74) + 65-6416 (82) - 79-o185 (83) + 13-3769 (85) + 285-824 - 86-7917 (64) + 132-7318 (65) + 45-94o1 (66) + 82-o482 (71) - 82-o482 (73) - 79-oI85 (82) + 1o2.1195 (83) — 23•1o1o (84) – 2I-Io27 (88) + 2I-1o27 (91) + ' 62-979 + 9-2984 (5o) - 3o-5948 (51) + 2I •2964 (52) + 5o-6836 (64) - 5I-8226 (65) + I-I39o (7o) - 27.99oI (71) + 22-6832 (73) + 5·3069 (78) - 64o-637 - 34· I 758 (5o) + 48·3181 (51) - I4-I423 (54) - 53°3815 (64) + 45-94oI (66) + 7-44I4 (7o) - 2I-3596 (8o) + 42-92o2 (81) + 79-o185 (82) — 88. I4o2 (83) + 59-677 - 26-572o (5o) + 34·1758 (51) - 7-6o38 (53) — 8-o675 (58) + 27-o957 (59) - 19-o282 (6o) - I5-5793 (7I) - 1o-51 5o (77) + 26-o943 (78) — I 36.9o9 + 5-7o12 (59) + I3:54o4 (6o) - 19-2416 (61) - 5o-6836 (64) + 7o.9582 (65) — 2o·2746 (67) + 27-99oI (71) - 31-86o3 (73) + 3-87o2 (77) – 717.2o3 – 48.5849 (36) + 63°3I46 (37) - 14-7297 (38) - 45-IoI7 (64) + 45-94o1 (66) – o·8384 (68) - 5·3958 (79) + 26-9564 (81) + 79-oï85 (82) - 88.14o2 (83) - 44.447 - 75·1583 (3o) + 81-7779 (31) - 6-6196 (32) + 4-7699 (34) + 43-815o (36) – 48-5849 (37) - 66.9666 (5o) + 34·1758 (51) + 32-79o8 (55) -- I 7•948o (71) – 8.1463 (76) + 26-o943 (78) - 47-oIo - 27. 1218 (29) + 33-7414 (31) - 6.6196 (32) + 4-7699 (34) + 27:5878 (35) – 32.3577 (36) – 1.8584 (4o) + 1o-3287 (42)- 8-47o3 (43) - 89· I24 + 27·1218 (29) – 75-1583 (3o) + 48-o365 (31) + II-o985 (4o) -H 48·88o - 2-7642 (29)+11-9877 (3o)-9-2235 (33)+ 23· I725 (41)+54-o939(43) 3o-9214 (44) + 7.8978 (49) - 42-6529 (55) + 34-755I (56) I22-o32 + 2-7642 (29)+39·8441 (32)-42-6o83 (33)-48-6486 (34)+o-4365(35) + 48·2I2I (39) + 44-1761 (42) - 54'o939 (43) + 9-9178 (44) – 82-232 + 3o*3236 (I5) - 47-62Io (16) + 17.2974 (17) + 9-5929 (23) - 41 ·oo35 (24) + 31-4Io6 (25) + 26-3437 (41) - 23•1725 (44) - 3•1712 (47) ALGEBRAICAL EQUATIONS OF CONDITION. 34 I XLV. XLVI. XLVII. XLVIII. XLIX, L. O = : + + 196795 – 6.4951 (15) – 527217 (17) + 59.2168 (18) + 57.3804 (22) 72-3734 (23) + 14,9930 (24) + 36.4019 (44) - 79.0842 (45) + 42.6823 (47) 37.887 - 11.9320 (22) — 14,9930 (24) + 3.0610 (25) + 6-7170 (41) 36-4019 (44) + 29.6849 (45) + 6.4606 (49) + 27.3238 (56) – 33.7844 (57) 2I-74o + 13.2407 (22) – 3-0610 (25) — Io-1797 (26) – 30-1878 (28) 2.9960 (30) + 27, 1918 (33) + Io-3190 (55) – 27.3238 (56) + 17-oo.48 (57) 43-IIo – 12.8515 (6)+33.6551 (7)—20.8o36 (8)—I-9931 (II)+ 15.9507 (13) I3-9576 (14)-13-3637 (44)+36.4619 (45)–23-0382 (46) 19.349 + 6-o816 (5) – 12.8515 (6) + 6.7699 (8) + I-7045 (15) – II.3169 (17) 9.6124 (19)+8-9978 (44)—23.0382 (46)+ 14.0.464 (47) 43.770 + 26.2 Io9 (I) - 55-71.43 (2) + 29-5035 (3)-14.5864 (4)–23.5oo3 (5) + 38.0867 (7)+12.9062 (18)—22.0387 (19)+9-1325 (20) The logarithmic values of the multipliers are as follow: Log I = o'4283263 – II = 9.29.07821 + III = 9-364797I + IV = 9. 1288847 – V = 0.6918108 — VI = 9.8123425 — VII = o'5130646 + VIII = 9.7523412 + IX = o-o8o3963 + X = O-2924153 + XI = o'3597.306 + XII = O'O4I4945 – XIII = 9.9617855 — XIV = o'4727129 + XV = o-4883180 + XVI = 0. OI 2 O - 9.988or 29 XVII = 8. 2 ſº - 8.7966825 § A W (2) C. W. 8) D'Z (9) D’Y (15) WO 16) WA’ § O W. § OD (29) PK § Q W. §§ 3 P (37) XO (43) XB 44) XC (5o) D W §§ DC” (57) DB (#8) PB' §: 2 D’ § ZB' 71) W T (7%) wº (78) CX 79) CD (85). BA (86) xy . Log XVIII = 9.5706921 – XIX = o'635850I + xx = or 1484740 – XXI = O.3449634 + XXII = 9.5836747 -- XXIII = o-og791.25 — XXIV = o'3270.535 — XXV = 9.5382508 + XXVI = 9-629.9985 + XXVII = o-59332O6 — XXVIII = o-4159666 -- XXIX = 7.7727637 -- XXX = 8.3243628 + XXXI = 8.964II.5o — XXXII = 7.3732306 + xxxiII = 7-9726905 + xxxiv = 8.6064233 – Log XXXV = 8.52.96897 -i-. XXXVI = 8.8213057 — XXXVII = 8.029IoAI — 8.3178675 — 8.6176608 – 8.0537098 — FIGURE 9. Notation. Cº D (4) CX (5) D'Á D'D (11) B'Y (12) B'D IVC (18) WD" (19) WY OX (25) PIV (26) PD QD § QX (33) QV YW (39) XC (40) XD' DC (46) DX (47) DQ DD’ (53) DB' (54) DZ YZ (Čo) PA (61) PB AB (67) AD (68) A Y VQ (74) VP WX CB (81) BC (82) B.A. XXXVIII - XXXIX = XL = XLI XLII = XLIII = IXLIV = XLV XLVI = XLVII = IXLVIII = = 9. IoSo847 -- 9.0457163 – 8.532790I + 8.6082 I28 + = 8.60II666 — 8.3134690 -- 7.7165618 +. 8-6793.920 — XLIX = 9.35638Io + L = 8.6128918 + # ($ WQ I4 IVD § PX 28 Ž. § _XB (42 DP (49) JDP' (56) Z}^ (63) AD’ (7o J7C (77 PD (84 342 PRINCIPAL TRIANGULATION, ' II. III. IV. VI, vI I. VIII. XIII. 2XXVIII. XXIX. IXXX. XXXI. DXXXII. 2XXXIII. DXXXIV. xXXV. lXXXVI. JØXXVII. xXXVIII. XXXIX. XL. IXILI. Equations. — o·8266 - (I3) + (14) - (25) + (3o) – 2•2188 - (I3) + (15) - (22) + (3o) - o•2931 - (2) - (I5) + (17) + (22) + o·8944 + ( I ) - (6) - (16) + (18) + 2•9716 + ( 2 ) – (6) - (17) -F (18) + o·886o - (29) + (33) - (73) + (74) + 2-7166 - (33) – (72) + (73) + (86) + o·8381 - (33) – (7I) + (73) + (87) + o*68o1 - (32) + (33) - (34) + (35) - (73) + (75) - o·67oo - (27) + (29) - (34) + (36) - (74) + (75) + I-86o4 - (24) + (32) - (35) + (37) + o·8Io9 + (13) - (2I) - (3o) + (32) - (35) + (38) + oº9o78 + ( 2 ) - (4) - (17) + (21) - (38) + (39) + I-47o9 - (5) + (6) - (18) + (21) - (38) + (4o) - o·8129 + (6) - (Io) - (18) + (2o) - (5o) + (52) + o·63o1 + (3) - (I2) - (5I) + (53) - + 3-3889 + (2) - (3) - (17) + (2o) – (5o) + (51) - o-1595 - (2o) + (2I) - (38) + (42) – (46) + (5o) - o*6965 + (13) - (2o) - (3o) + (31) – (47) + (5o) - I•551o + (14) - (2o) - (25) + (26) - (48) + (5o) - 3•9183 + (15) - (2o) - (22) + (23) - (49) + (5o) – I-6297 + (34) - (44) - (75) + (76) - (77) + (78) + I-18o7 - (42) + (44) - (45) + (46) - (78) + (79) - o•5549 - (42) + (43) + (46) - (57) - (82) + (83) + I-o435 + (45) - (57) - (79) + (8o) - (81) + (83) - o.o792 – (56) + (57) - (66) + (67) - (83) + (85) + 1.7336 – (7) + (Io) - (52) + (56) - (67) + (69) - 1.86o1 – (6o) + (61) - (66) + (68) - (84) + (85) + 3•686o – (II) + (12) - (53) + (57) + (58) – (61) – (83) + (84) + 2•9o14 – (8) + (Io) - (52) + (54) - (63) + (64) + 2·166o - (54) + (57) + (59) - (61) - (62) + (63) – (83) + (84) + 86.514 -8-549I (I3)+53•I363 (I4)-44°5872 (15)+22-7623 (22)-22-I428 (25) + 256-266 + 92-o67I (2) +44°5872 (I3) —9.5767 (15) -35-oIo5 (17)+66.8183 (30) - 37·816 - I2-964o (1) - 2-8o37 (2) – 23.855o (16) + 3o.462o (17)-6.6o7o (18) - I72°284 + I9-II 58 (6)- 35-oIo5(15)+ 4-5485 (17)-F 3o-462o (18)-F 64•26i8 (22) - I7'o9I -Io·II33(29)- 1o-5926 (33)-I7.2894(72)+28•1519(73)-Io-8625(74) - 125'794 +1o-8263 (71)-28-1519 (72)+17-3256(73)-42-2273 (86)+45-2854(87) + 12-88o + I5-3195 (27)-23-7731 (29)-22-o89o (32)+ 16.992o(33)+o-34I1 (73) - Io*6576 (74) + 1o-3165 (75) o = - I4*424 - 9°4295(24) + 8-4536(27)-6-3o36 (35)+ 29-5363 (36)– 23.2327 (37) o = + 178-688 + 59-8198(13)-44:5872 (15)-I5-2326 (21)+22-7623 (22)+9.4295 (24) -- 16. 1613 (35) + 23•2327 (37) - 7-o714 (38) o = - 4o-862 - 38'9962 (2) + I4-9845 (4)-3-9423 (15)+ 18.71o4 (17)– 14-768i (21) — 7•1o45 (22) + 6-9I88 (24) ALGEBRAICAL EQUATIONS OF CONDITION. 343, XLII. O = XLIII. XLIV. XLVI. XLVII. XLVIII. XLIX. LI. LII. LIII. LIV. LV. LVI. LVII. LVIII. LIX. LX. o – -== : : - 161'422 – 41.7999 (2) + 38.9962 (4) — 23.0286 (5)--42.1444 (6)–33.2480 (38) + 57.8209 (39) — 24.5729 (40) - 30-933 + 5°9339 (4) + o-o/42 (5) + 5°9887 (39) — 56.0701 (40) + 50.0814 (41) + Io:289 + 5.4954 (30)—20.5422 (31) + 15.0468 (32)+7.0714 (35)–10,2402 (38) + 3'I688 (42) + 7.0508 (46) – 15.8063 (47) + 8.7555 (50) - 36.424 + 9,4959 (25) – 17.8680 (26)+8.3721 (27)+29-0317 (36)–32-2005 (38) + 3-1688 (42) + 7.0508 (46) – 40.4259 (48) + 33.3751 (50) + 84.091 + 9.9777 (22) – 17-0822 (23) + 7.1045 (24) + 37.5971 (37) – 40.7659(38) + 3-1688 (42) + 7.0508 (46) – 50-6242 (49) + 43-5734 (50) + 72-940 - 8.0455 (23) + o-1857 (24)+18.1370 (37)—29.6018 (39)+II.4648 (42) – 4:1515 (46) – 16:3027 (49) + 20-4542 (51) – 224-196 + 67'1238 (3) — 59:1329 (4) + 74.2389 (5) – 74.3131 (Io) – 9.6961 (46) – 4:1515 (51) + I3-8476 (52) - -- 31-349 + 6-oA63 (Io)+ I'or 36 (12) + 15.0924 (51)–51-6544 (52)+36.562o (53) 45.838 + 62,4419 (26)–86.2150 (27)+23.7731 (29)+33.7036 (45)–55,5277 (46) 21.8241 (48) + Io.6576 (74) — 55,9238 (75) + 45-2662 (76) + I-8529 (77) 19.0228 (78) + 17.1699 (79) - - 4.937 + 23-7731 (27)–44,7953 (28)+21.0222 (29)—13-1459 (34)+5.5172 (36) 7.6287 (44)–12.9289 (74)+12.9289 (76)—1.8529 (77)+1.8529 (78) 33-268 + 12'o632 (42)-39.992.1 (43)+27.9289 (44)–22.2020 (45)+5.4549 (46) I6'7471 (57) – Io. 6667 (78) — 9.3467 (79) + 2.0.org4 (80) - - 262-090 + 74.3131 (5)--24.8557 (7) – 99.1688 (Io)+24.3513 (40)-36.4145 (42) + 12-off32 (43) + 27.5623 (66) – 40. Io92 (67) + 12.5439 (69) + 21:5503 (82) — 32.7681 (83) + II.2.178 (85) + 38:297-4.4481 (7) — II-3564(Io) + 154,5060 (52) — 161-04Io (53) + 6.5350 (56) +8.6918 (67) – 143°3958 (69) + 134,7040 (70) + 35.030 – 53:or70 (55)+47-5499 (56)+5.4671 (57)–13-7141 (66)+59.3097 (67) — 45-5956 (68) – 36.2134 (83) + 70.2019 (84) – 33.9885 (85) — 180.073 + 77.9572 (19)—119-1508 (20)-1-41-1936 (21)+3-1688 (38)-15:2320 (42) + 12.0632 (43) + 16-orgo (50) — 36.8709 (55) + 20,8579 (57) + 21:5503 (82) — 78.6216 (83) + 57.0713 (84) --- + 118.648 + 4 or 31 (6)+ 50-9774 (9)-54-9905 (Io) + 16-9746 (18)-78-9188 (19) + 61.9442 (20) - 7.0371 (50) — 13.8652 (52) + 20,9023 (55) — 165.330 – 52.2601 (9)--54-9905 (Io)+57,8949 (II)-64,7737 (12)+13.8652 (52) + 18-3845 (53) + 4.5.193 (55) ºx + 34,104 – 9:4498 (8) + 4.815o (9) + 4,6348 (Io) – 6.3098 (52) + 15:5402 (54) – 9-2304 (55) – 3:4958 (62)-2-6219 (63)+ 6-II77 (64) - – 50.400 – o 3648 (8)-11-3564(Io)+154,5060 (52)–174.9744(53)+20,4684 (54). – 7:16Io (63) — IoI-8058 (64) + 108.9668 (65) 344 PRINCIPAL TRIANGULATION. The logarithmic values of the multipliers are as follow: Log I = o'9429I33 + Log XXI = o'892626o + Log XLI = 9,7416345 + II = 1.302045o - XXII = 9.9126585 — XLII = 9.4200602 – III = I.315390I - XXIII = o-2166834 — XLIII = 8.437.5524 – IV = 7.88324II — XXIV = 9-9026820 + XLIV = 8.6603569 — v = 9.8965607 -- XXV = O. 2349931 – XLV = 8.858.2670 + VI = 9.6691.458 + XXVI = 9.4912OI5 — XLVI = 9.403238o — VII = O.303959I – XXVII = 9. 1438.476 — XLVII = 8.792.1528 + VIII = o'384I409 — XXVIII = 9.2045400 – XLVIII = 9.5123951 — IX = o-6632037 – XXIX = 9.6552.32 I + XLIX = 9.8066049 + X = o:25I4039 + XXX = 9.790 I434 – L = 8.0624617 tºº XI = 9-80827.55 + XXXI = 9.9644769 – LI = 7.5163747 -- XII = o'7031322 – XXXII = 9.2006.317 – LII = 8.3073570 + XIII = I-2403970 + XXXIII = 8.48547.58 LIII = 8.3522,597 -- XIV = 1.221 1784 – xxxiv = 7.8070612 + LIV = 8.3896863 + XV = I-43 II4O4 + XXXV = 9.5333186 + LV = 8.3813678 — xv.1 = o'797.1839 – XXXVI = 9. I271456 + LVI = 8.440.7863 + xvi.I = 1.431917o – XXXVII = 7.9.197421 + LVII = 8.3422667 + xvi.II = o'3322505 - XXXVIII = 7.8694,077 – LVIII = 8.7023642 + XIX = 9, 1765198 — XXXIX = 9. 1187768 — LIX = 8.5239753 + xx = 9.63.58077 – XL = 9.0232.369 – LX = 8.4356676 + TIGURE Io. Notation. º º, 'F CF A/F (6) B'F B' H º #. § # § # § FC § FA’ § FB' & J.G. (15) HE (16) HB (17) HF 18) HG (19) GH (20) GF (21) GB Equations. 1 o = — 1.9732 + (1) - (4) - (Io) + (II) II o = — o' 1137 + (1) - (5) - (Io) + (12) III o = — 4.7979 + (1) - (6) - (Io) + (13) Ivo = + 4,1475 - (1) + (2) - (9) + (10) — (15) + (17) vo = – 2:308o + (2) — (7) — (15) + (16) vi o = — o.2322 + (6) - (8) — (13) + (14) — (20) + (21) vii o = + 1.4964 + (9) — (14) — (17) + (18) — (19) + (20) VIII o = + 178,619 – 148,8676 (1) + 47.8071 (5) + 26.8616 (Io) + 7.9700 (12) - 34,8316 (13) Ix o = + 171.349 – 148,8676 (1) + 81.0836 (4) + 26.8616 (Io) – 2.9689 (II) - 23.8927 (13) x o = + 9.372 + 17, 1856 (I) – 75-7595 (3) + 35.88or (4) xi o = + 30-256 – 36.41 13 (6) + 45-1760 (7) – 35-768o (9) + 8-9064 (Io) + 26.8616 (13) — 1.2565 (15) - II.5963 (16) + 12.8528 (17) xir o = + 114,060 – 188:2737 (1) + 39.4061 (2) - 61-1368 (6) + 24,7255 (8) — 12.8528 (15) — 57.2041 (17) + 70.0569 (18) + 16-6399 (19) – 27. Iodo (20) + 10,4661 (21) ALGEBRAICAL EQUATIONS OF CONDITION. The logarithmic values of the multipliers are as follow: Log I = 8.545oo20 + Log V = 9.961.6757 -- Log II = o'624984I — VI = 9.94.13961 + III = o'5226363 + VII = 9.8026935 — IV = o'2564729 – VIII = 8.4493316 – FIGURE 11. -- Notation. . O'H' O'G' Q'H' - ( ) Q'G' * (5) QB - 6 § R'G' § R’A § TA § A’A (12) V'G' § (15) PB ; PE" 17) WC 18) N'A (19) N'B ...} (22) L'E : J. C. §: R’B (25) K'C (26) K'E' (27 § FC. 3o) I'B' (31) AU (32) AT" (33) AR" (34) 36) AG' (37) AF' (38) AB (39) 4E (40) 40 (41) (43) 4ſ. (44) 4'ſ. (45) HQ (46) H.R. (47) HQ. º (52) ºf $5;} @ 9 (52) gº (53) G4 (54) GW (55 § D'C (58) D'B (59) BA (66) Bq (61) BG' (62) 64) B.E. (65) BC (66) BL (67) BN" (68) CV (69) 71) CD (72) CE (73) CA' (74) CC (75) CB (76) 78) CN' (79) E V (86) EA (81) EB (82) ER (83) 85) A'C (86) A.K.’ § C.C (88) B'C', (89) B'I' (90) Equations. I. o = — 3.7889 – (I) + (3) + (45) — (47) II. o = — 2.3402 — (I) + (7) + (45) — (46) III. o = — 4,7466 – (2) + (4) — (49) + (51) IV. o = – 7.5260 – (2) + (8) — (48) + (51) v. o = — 1.6697 - (3) + (4) + (47) — (49) VI. o = + 2.2707 – (4) + (12) + (49) — (54) VII. o =. – o 3159 – (12) + (16) + (54) — (79) VIII. o = — 2.3205 – (16) + (20) + (79) — (84) IX. o = — 1.0618 – (20) + (26) — (82) + (84) X. o = — or 5765 – (26) + (28) + (82) — (90) XI. o = + o-2944 – (28) + (30) – (89) + (90) XII, o = – 6.2161 — (Io) + (13) + (32) — (43) XIII. o = — o'8422 — (9) + (13) + (33) — (43) XIV. o = — o-6529 – (6) + (13) + (34) – (43) xv. o = + o-8115 – (4) + (6) — (34) + (36) + (49) - (53) XVI. o = — o-2317 – (36) + (37) + (53) — (56) XVII. o = + 2.8952 – (36) – (39) + (53) — (8o) XVIII. o = – 3:4764 + (11) — (13) — (42) + (43) xix. o = - 1.1644 – (13) + (18) — (41) + (43) XX, o = + 4.3220 — (37) + (38) — (55) + (56) – (59) + (62) xxi. 9 = + 3:5748 – (36) + (38) — (52) + (53) — (59) + (61) XXII: o = + 7.2494 — (5) + (6) — (34) + (38) — (59) + (60) IX = X E XI = QA J77. A N7 E” JK'C' A Q' - AN’ G/IR/ FB BF CA CK' JE/C BK 8.3590965 + 8.3705973 - 7.331836I + XII = 8.1731029 — R" H’ prºv N'C A'B' A O' AX7 G' Q' I’A RD' CB CL’ FN7 X x 346. PRINCIPAL TRIANGULATION. XXIII. XXIV. xxv. XXVI. XXVII. XXVIII. XXIX. XXX. XXXI. IXXXII. XXXIII. XXXIV. XXXV. XXXVI. XXXVII, XXXVIII. YXXIX. XL. XLI. XLII, IXLIII. XLIV. XLV. XLVII, XLVIII. XLIX, LI. LII. – 6.1 170 – (18) + (19) - (38) + (41) + (59) — (67). + 1.7139 – (19) + (20) - (64) + (67) + (81) — (84) – o 2186 + (58) — (63) + (64) — (81) + 3-3798 – (19) + (22) — (66) + (67) — o'o.256 – (21) + (25) — (76) + (78) + 1.5oo7 – (21) + (23) – (77) + (78) — 1.1339 – (17) + (21) + (68) — (78) — or 5902 – (18) + (21) — (40) + (41) + (69) — (78) + 3-0432 — (19) + (21) — (65) + (67) + (70) — (78) + o-5341 + (57) — (71) + (72) — (83) – 3:3487 – (64) + (65) — (70) + (72) + (81) - (83) + o-9520 – (72) + (73) — (83) — (85) + 2.4789 – (72) + (74) + (83) — (87) + o-'7263 – (25) + (28) — (75) + (76) + (88) — (90) — 39.268 + 5.4670 (3)-Io:5117 (7)—1.3799 (45) — 13.2726 (46) – 14-6525 (47) – 93-744 + 18.0535 (1) - 20-0643 (2)+14,6525 (45)-5-oz40 (47)+6,4281 (49) – 28.3275 (51) - * + 214,431 + 20,0643 (2) + 25.2446 (12) — 40-3708 (49) + 28-3275 (51) + 12-o433 (54) g – 283,414 – 35.2440 (8) + 25.2446 (12) — 239.4933 (48) + 227.45oo (49) + 12.0433 (54) -- - . - . . . . + 2.08.252 + 19.5631 (2) - 2.7427 (4) + 43-6886 (49) — 153.1148 (50) + Io9'4262 (51) * + 6-oš3 + 53.3125 (3) - 57.0478 (4)- 40-7074 (12)+15,4628 (16)–9.6285 (47) + 16-3990 (79) - - m - + 58,713 + 80.4248 (12) - Ioff.3938 (14) + 25.9690 (16) – 18.4182 (54) + 4,4449 (79) - * - + 22.503 + 3-7353 (4) - o'6253 (20) + 12.0433 (49) — 17.9987 (54) — 55-8222 (79) + 39.4232 (84) - + 126-022 + 12'o617 (16) + 1.4871 (26) + 39.4232 (79) + 37.3966 (82) — 76.8198 (84) - - – 150.357 + 15:4628 (12) - 27.5245 (16) – 9:3455 (20) -- 1.4871 (26) + 5.9554 (54) – 42-1716 (82) + 56.9619 (86) i ºr - - +1224.885 + 36:4029 (26) + 306,5869 (27) – 342.9898 (28) + 6.1932 (82) — 420.6563 (86) + 342.9898 (90) - * * * : - 198377 F 36-4029 (26) – 99.8323 (27) + 63.4294 (28) --- 6.1932 (82) + 3.7795 (90) - ' , , - - 89.269 +9°9708 (20)--1-0373 (30)—34,2294 (82)+37.3966 (84)—31.1347 (86) + 84.2319 (89) — 78.2163 (90) . - - - * - + 301-189 + 66.0709 (27) – 63,4294 (28) - 74,3538 (29) + 66.5306 (30) * ..º.º. (90) l . – 340-518 – 30.1218 (10) + 14.8115 (13) - 63-07Io (32 6o-c + 2.0718 (43) - - º *7io (3) + 60.9992 (33) – 56,476 - 8.4076 (9) + 189374 (73) – 132-3470 (33) + 133.6053 (34) imº I .2583 (43) . º* ALGEBRAICAL EQUATIONS OF CONDITION. 347 LIII, LIV. IV. LWI. LVII. LVIII. LIX. LXII, LXIII. LXIV, LXVI. LXVII. LXVIII. LXIX. LXX. LXXI. IXXII. IxxIII. LXXIV. LXXV. O :- O - OOOO.o :-====::=-: . o = = + + + + + + 4. +. : 31'550 + 23.8899 (4) — 50-3138 (6) – 146.1049 (12) + 127-1675 (13) 7-6569 (49) + 114,451.1 (53) – 122-1080 (54) - 124°360 + 53.3125 (3)-77-2024 (4) + 23.8899 (6) +8.2542 (34)–8.7331 (36) o'4789 (39) – 9.6285 (47) + 41-5403 (80) 81-995 + 26-6051 (13) — 20.6851 (16) – 43.2377 (18) + 14.4733 (20) 44-728o (79) + 29-0426 (80) + 15-6854 (84) 98.855 — 22-9.262 (53) + 45-7226 (56) – 25.60Io (80) 457-670 – 76-2467 (II) + 28.7644 (18) + 26.8599 (41) – 94.3695 (42) 67.5096 (43) -- 93-256 – 12-1474 (9) - 5-oš6o (Io) – 20.2588 (32) + 4o. 1988 (33) I9.94.00 (35) -- - is - 164,571 + 33:3764 (ro) + 3 ozoö (13) + 148.6583 (31) — 135-olzó (32) 13-6457 (43) - 14.845 + 1-8940 (Io) + 19.8063 (13) – 27.8251 (32) – 38.2975 (43) 66.1226 (44) 205:654 + 23.8899 (4)–108.1228 (5)--84.2329 (6)--7-6569 (49)+ 16-4962 (52) 24. I531 (53) + 66-6717 (59) — 91.1524 (60) + 24-4807 (61) II.4.293 – 16,4962 (52) + 29.3458 (53) + 22.3507 (55) – 59.2887 (56) 20. Iozo (59) — 24.4807 (61) + 4,3787 (62) 16.183 – 64472 (55) + 169957 (58) + 27,9276 (61) – 27:3867 (62) o'5409 (63) * * Ioff.861 – 67.4498 (52) + 41.0588 (58) – 44,5715 (81) 279-746 + 28.8707 (18)—88.6853 (19)+59.8146 (20)--o'9631 (36)–7.5991 (38) 6.6360 (41) – III.4459 (52) + 16-4962 (53) — 59.9957 (81) + 14:5615 (84) 346.091 – 57.6216 (19) + 59.8146 (20) + 63-7353 (24) — 53-7174 (26) 12.6139 (81) — I-9476 (82) + 14:5615 (84) 108.721 + 30.1110 (13) — 37.4683 (15) – 28-8707 (18) + 22:1543 (19) 14.5505 (38) – 6.6360 (41) – 7-91.45 (43) 162-oA4 – 34,5062 (19) + o-3389 (22) + 44'5241 (24) - IoS-3177 (66) Ioš-3177 (67) 28.069 + 9.9079 (23) + 5.3751 (25) + 19.9345 (76) - 88-8925 (77) 68.958o (78) 124,242 + 20,8045 (17) + 5.3751 (25) + 28-9265 (68) + 19.9345 (76) 48.86 Io (78) * * * - 83-891 + 5°920o (13) + 20,8045 (17) – 19.6645 (40) + 46.5244 (41) 26,8599 (43) + 28.9265 (68) - 7.3973 (69) – 21.5292 (78) 131.676 – II.Oo37 (18) + 42.6061 (19) – 31.5994 (21) – 44-o454 (38) 63-7099 (40) – 19.6645 (41) + 11.7302 (59) – 30-8674 (65)+ 19.1372 (67) 190.952 – 42.6061 (19) + 173.8684 (20) — 131.2623 (21) – 13:3915 (64) 32.5287 (65) — 19-1372 (67) – 8.4685 (81) – 84,5370 (83) + 93-oo:55 (84) 142.80.5 + IoS-1237 (57) – 24-0631 (58) — I6-9529 (63) + 30-3444 (64) 13.3915 (65) — 15.0927 (70) + 91-7121 (71) –76.6194 (72) 88.162 + IoS-1237 (57) + 91-7121 (71) — II 8:42.05 (72) + 26.7084 (73) + 42-Ioa:3 (8.5) xx = 348 * PRINCIPAL TRLANGULATION. Lxxvi. o = + 23-320 + 16-2036 (72) — 83.4013 (73) + 67.1977 (74) — o-o869 (83) – 22-1762 (85) LXXVII. o = - 146.964 + Io9'2693 (25) - II6-o/57 (26) + 12.8064 (28) — 70.5122 (82) + 80.4119 (83) – 45-6179 (85) – 34,9047 (88) + 25.8911 (90) The logarithmic values of the multipliers are as follow: |# Log I = o'4O49316 + Log XXVII = o-o/86685 — Log IIII = 7.977O694 – II = o-I23oo85 — XXVIII = o' 1292990 — LIV = 9.50382.24 + III = o'7751602 – XXIX = 9.6347616 + LV = 8.9827.049 – IV = o-or 75138 + XXX = O'514454I + LVI = 8.5158238 + V = o'9169162 + XXXI = o'4857572 + LVII = 8.7782869 – VI = O'9854319 — XXXII = o-3307567 – LVIII = 8.3986277 – VII = o'594.1234 + XXXIII = o-8838135 + LIX = 8.392.2868 — VIII = o-3620531 + XXXIV = 9.98oo827 -- LX = 8.4648323 – IX = O'64742O5 + XXXV = o-228864o — LXI = 7.7636915 – X = I.o.664646 + XXXVI = 9.74527 I2 — LXII = 9-og.992.48 + XI = o-8815449 + XXXVII = 8.6789671 + LXIII = 8-9979099 + xII = o'4780612 – XXXVIII = 8.7526ozo – LXIV = 9.5268.476 — XIII = 9.533.4272 + XXXIX = 9.55oz.138 — LXV = 9.242.1950 + XIV = 9.7412979 + XL = 7-85199 II + LXVI = 8.6896373 — xv = 9.83ol.9II – XLI = 7.7049428 + LXVII = 9.6365472 + xv.1 = o'2486421 – XLII = 9.354.8562 – LXVIII = 8.6536908 + XVII = o'3949979 - XLIII = 8.4316460 + LXIX = 8.2379522 + xvi.II = 9.8336oi6 — xI.IV = 9.2.486009 — LXX = 9.5IOS440 – XIX = 1.0236208 + XLV = 8-6272466 — LXXI = 9.4006849 + XX = O-320597I + XLVI = 9.5963568 + LXXII = 9.0855183 + xx = 9.8532763 + xLVII = 8.6144258 + LXXIII = 8.3155085 + XXII = 9.8235858 — XLVIII = 9. I275357 -- LXXIV = 9-O44 II.24 – XXIII = 9.7175043 + XLIX = 9. Io97383 + LXXV = 9. IoIo576 + XXIV = o.634,5447 - L = 8.6651646 – LXXVI = 8.5529661 + xxv = o-'7420813 + LI = 8.961.9154 + LXXVII = 8.2204089 + xxvi = o'6439164 - LII = 8-0261834 – TIGURE 12. Notation. * * IY BD (2) BE - g § # 3 # & # 3 #3 & # & # & # 15) F.H. § Ż. (17) EH (18; £F (19) EA (23) EB § JED 22) DK. (23) DH (24) DE § D.A. (26) DB (27) DC (28) DL 29) 9ſ. (32) º (31) CD (3.j CB" (33) LQ (34) LR (35) LD 36) LC {} JKO (38) KN (39) KII (40) KF (41) KA § RE 43) KD 44) £2 (45) KL (46 kyſ (47) MO (48) MN (49) ºr (56) MX (51) M.A. (52) MQ QN (54) QP (55) QM. (56) QL § P0 (58) PM (59) PK § PQ § AIO § JIN" § % § { } { } {# º ż (; ; ; ; ; ; N 2. 3) 4 * Q NO § 3. § 6; $ $# § § G3) 76) (77) ALGEBRAICAL EQUATIONS OF CONDITION. 349 I. II, III. IV. W. VI. VII. VIII, IX. X. XI. XII. YIII, XIV. XV. XVI, XVII. YVIII. XIX. XX. XXI. YXII. XXIII. XXIV. XXV. XXVI. XXVII. XXVIII. XXIX, XXX. XXXI. XXXII. O E Pgwations. ~ 2:39.5I – (2) + (3) — (5) + (7) — (19) + (20) + o-oo74 — (1) + (3) — (5) + (6) — (25) + (26) - or 2203 – (6) + (7) — (19) + (21) — (24) + (25) + I-7918 – (7 ) + (9) — (12) + (13) — (18) + (19) – 2.9055 — (13) + (14) — (16) + (18) — (40) + (42) + o- 1559 – (8) + (9) — (12) + (14) — (40) + (41) – o-91.76 – (6) + (8) — (22) + (25) — (41) + (43) + o-12o.9 -- (1) — (4) — (26) + (27) — (31) + (32) + 1-9227 + (22) – (27) — (30) + (31) — (43) + (44) — o-2522 – (27) + (28) — (29) + (31) — (35) + (36) + o-5640 + (22) — (28) — (34) + (35) — (43) + (45) — 5-3237 – (14) + (15) — (39) + (40) — (64) + (66) — 1.7055 – (13) + (15) – (17) + (18) — (64) + (65) + 3-7027 + (39) — (46) — (49) + (50) — (66) + (67) + o-7918 + (Io) — (14) — (38) + (40) — (72) + (74) + 5'7245 + (Io) — (15) — (62) + (64) — (72) + (73) + 7.83O3 + (II) — (15) — (63) + (64) — (68) + (60) + 2.7628 – (62) + (63) — (69) + (70) — (71) + (73) + 1-o890 + (37) — (46) — (47) + (50) — (79) + (80) – 6.6946 – (47) + (49) + (61) — (67) — (78) + (80) – 4:5944 – (37) + (38) — (74) + (76) – (77) + (79) — 2.8493 + (38) — (46) + (50) — (52) — (53) + (55) — (74) + (81) — o-6668 – (33) + (34) — (45) + (46) - (50) + (52) — (55) + (56) – 4:4765 – (53) + (54) + (58) — (60) — (75) + (81) + 20,290 + 7-6602 (1) – 12:4659 (2) + 4.8057 (3) + 27:0097 (19) – 9-1647 (20) – 17.8450 (21) + 22.8259 (24) — 33.6137 (25) + Io-7878 (26) + 1.315 + 33.5344 (7) – 71.6484 (8) + 38.1140 (9) + 43369 (16) – 19:3414 (18) + 15:0045 (19) + 40-5079 (40) — 57.2132 (41) + 16-7053 (42) + 168.503 + 120.6336 (6)–170.7849 (7)+50-1513 (8)+2:52.13 (16)+17.8450 (19) — 20.3663 (21) + 17.8978 (41) – 63,7826 (42) + 45.8848 (43) — 81.862 – 27:5133 (1) + 7.6602 (3) + 19.8531 (4) + 19.5514(5) – 69-7027 (6) + 50-1513 (8)+45.3601 (30)—53.6350 (31)+8.2749 (32)+ 17.8978 (41) – 53.8688 (43) + 35.97Io (44) + 39.841 +11:4089 (29)—45.3601 (30)+33.9512 (31) +20 4001 (34)–25.3972 (35) + 4.9971 (36) + 19-oo:55 (43) — 35-97 Io (44) + 16.9655 (45) – III-986 + 43369 (16)–174493 (17)+13-1124(18)+Io.6348 (39)—27.3401 (40) + 16.7053 (42) + 19.0282 (64) – 22.7336 (65) + 3.7054 (66) — 406,622 – 2.5213 (16) – III.2679 (17) + 113.7892 (21) – 4o-oč64 (22) + 165-9896 (23) – 125:9232 (24) – 20:4024 (39) + 63.7826 (42) – 43-3802 (43) + 272-770 – 37.0602 (16)+39'5815 (17)-2-5213 (21)–12.4635 (22)+9.8616 (24) + 2.6019 (28) — 20-4001 (34) + 20-400I (35) – 79.0931 (45) + 79.0931 (46) + 14,1217 (49) – 93-7734 (56) + 79.6517 (5) + 27.7259 (65) – 73.6.15% (*) + 45.8897 (67) 35o PRINCIPAL TRIANGULATION. XXVII = 8.2oo2517 — • * xxxIII. o = + I63. I8I-3:9556 (38)+ Io-6348 (39)—6.6792 (4o)—26.8o39 (62)+23.o985 (64) + 3*7o54 (66)-25-3861 (72)+4I-466o (73)— 16.o799 (74) xxxrv. o = — 145:92o-64-9881 (38)-3:4II7 (39)+68-3998 (46)+4o.8835 (48)+21.5364 (49) — 62.4I99 (5o)+ 12:3885 (62)+45-8897 (66)— 58.278a (67) xxxv. o = — 268. I2o-* io6:o244(io)—45:5978(II)—60.4266(15)— 11.6663(68)+24.2o82(69) — 12.5419 (7o)—6.3813 (71)+4I-466o (72)—35-o847 (73) .- XXXVI. o = — 79-942 — 7.324o (37) — 34I I 7 (39) + Io. 7357 (46) — 3.2511 (61)+45.8897 (66) — 42-6386 (67)+2I. 2888 (78)—7I-II 2 I (79)+49.8233 (8o) xxxVII. o = — I. I73+ 13:8963 (61)—23:49I6 (62)+9-5953 (66)+43-7269 (73)— 33. 1353 (74) — Io. 5916 (76)+ 17-oo83 (77)—39. 2835 (78)+22.2752 (79) . xxxVIII. o = + 26.365 + 64.988 I (38) + 84. Io48 (45) — I49-o929 (46) — I Io. I8o9 (48) + I4I-5I3o (5o) — I 29-9698 (51) + 98.6377 (52) + 63-56o2 (53) — 123. I973 (55) + 59-637 I (56) » XXXIX. o = + o.27o-- 97. I 73o (37)—97. I 73o (38)—55-3449 (57)+74.2o92 (58)— I8-8643 (59) + 23-6289 (74) — 28.8578 (75) + 5-2289 (76) — I 7-oo83 (77) + I 7-oo83 (79) XL. o = — 27.426 + 2-5682 (38) — 2-5682 (46) — o. 5423 (48) — 4-3549 (5o) + 4-8972 (52) — I27-673o (53) + I43:4722 (54) — I5-7992 (55) + 58-4513 (58) + I8-8643 (59) — 77.3156 (6o) — 23-6289 (74) + 23-6289 (75) * The logarithmic values of the multipliers are as follow : Log I = o. 2248932 -+- Log XIV = o.739o3o2 + Log XXVIII = 8.4348489 + II = 8. 968868o — xv = o. 3849 II 4 — XXIX = 8.54o8I73 + III = o.62 I 5364. — xvI = o. 328229 I + XXX = 8.83961 96 + Iv = 9.56I87I2 —- XVII = o. 37I 56I2 — XXXI = 8-o678869 + v = 9.6224763 — XVIII = 9*9o5693o — XXXII = 8.6175o89 + VI = 9.9239776 + XIX = o. 3922I7I — XXXIII = 8.6965oo3 + VII = 9.7742o29 + XX = o-6385232 + XXXIV = 8.8o72679 + YIII = 9.73 I978o *-* XXI = 9-86I7436 -+ XXXV = 8.83242o3 + IX = 9•9275444 — XXII = o*35oo43o -+- XXXVI = 5. I5o3729 — x = 9.582 Io22 -+- xxIII = 9.5855898 + xxxvII = 8.6767 298 — XI = 9-7385247 -+- XXIV = 9-9624oo3 + xxxvIII = 8. 2983o58 + xII = o. 772 II 37 + XXV = 9-o53oI43 — XXXIX = 8. I7I3874 -i- xIII = 9.222I2 I3 — XXVI = 7. I573356 + XL = 7-9I644I7 — , ] ALGEBRAICAL EQUATIONS OF CONDITION. 351 . FIGURE 13. (1) D'H' § D'G (3) D'M § D'K (5) D'F (6) EH (7) EG, Jºſ' (9) A'F (ſo) A K (ii) A'L (12) HN (13) HM (14) HL § H.G. (16) HD. (17) HE (18) GK 19) GF 20) GD' § GE' 22) FG (23) FK § FA' 25) FD' % FE/ 27) KM (28) KL 29) KO (30) KA' (31) KB' 32) KF (33) KD' §§ J& G. § LM ; LQ (37) LR (38) LS LO (40) LP LA' } LK LD" (44) LG 45) LH 46) MN (47) MQ (48) MR (49) MS 50) MO (51) MP § ML 53) AIK (54) MD' (55) MG (56) MH 57) RQ (58) RP (59) IPS (60) R0 (61) If L 62) RM § RN SR (65) SQ (66) SP (67) SO (68) SL 69) SM 7o OR (72) OS § OP 74) OK § OL (76) OM § ON ( (78) PQ PK (8o) PL 81) PM 82) PO 83) PS (84) PR (85) B'G § B'Q (87) B'R (88) CH' ) ( Equations. - I'9343 - (4) + (Io) — (30) + (33) + 4:9821 - (5) + (9) — (24) + (25) – 7:0598 - (9) + (Io) — (23) + (24) — (30) + (32) + 6-904I – (18) + (19) — (22) + (23) — (32) + (34) + 2.9969 - (2) + (4) — (18) + (20) — (33) + (34) – 3-2119 + (2) — (7) — (20) + (21) + o-'7633 + (5) – (8) — (25) + (26) + o-4588 – (Io) + (II) – (28) + (30) — (41) + (42) — 1.9885 + (I) — (6) — (16) + (17) - * * + 2.0244 - (6) + (7) – (14) + (17) + (18) — (21)+(28)–(34)–(42)+ (45) – 3-0395 - (13) + (14) + (35) — (45) — (52) + (56) º + o-8635 - (I) + (3) — (13) + (16) — (54) + (56) — I-6807 - (3) + (4) + (27) — (33) — (53) + (54) + 4:7459 – (35) + (39) — (50) + (52) — (75) + (76) XIV XV. + 5.5356 – (27) + (29) — (50) + (53) — (74) + (76) IXVI. — 5.330I – (48) + (50) — (60) + (62) + (7I) – (76) IXVII. — 7.78II – (37) + (39) — (60) + (61) + (71) – (75) XVIII – 2,6250 – (38) + (39) — (67) + (68) + (72) — (75) XIX. — 5.0651 – (49) + (50) — (67) — (69) + (72) — (76) XX. + o-3756 – (59) + (60) + (64) — (67) — (71) + (72) xxi. + 7.0660 – (58) + (60) — (71) + (73) — (82) + (84) XXII + 9.4772 – (66) + (67) — (72) + (73) — (82) + (83) XXIII. + 3.9404 – (35) + (40) - (51) + (52) — (8o) + (81) XXIV. + 2. 1228 – (48) + (51) — (58) + (62) — (81) + (84) xxv. — 3.4642 + (Io) — (30) + (31) — (87) IXXVI + 48.039 + 6.5930 (4) — 8-8931 (5) + 29.7044(23) – 10:1845 (24) — 19:5199 (35) + 16-6427 (30) – 61-IIoA (32) + 44.4677 (33) - XXVII. o = + 95.259 + 55-7925 (2) – 218-2243 (4) + I62.4318 (5) + o-Ioog (18)— 18°4440 (19) + 18-3431 (20) + 156,8638 (32) — 189.9146 (33) + 33-0508 (34) - . . * xxviii. 9 = + 90.473 – 13.8485(2) + 47.388 (5) +4.3687 (19) – 37,4585 (zo) + 33-0898 (*) + 5°3031 (22) + 30-6102 (25) – 35.9133 (26) 352 PRINCIPAL TRIANGULATION. XXIX. 2XXX. XXXI. 2XXXII. XXXIII. XXXIV. XXXV. 2XXXVI. 2XXXVII. 2XXXVIII. XXXIX. XL. XLI. 2XI,II. 2XI,III. 2XLIV. XLV. 2XILVI. 2XLVII. XI,VIII. xLIx. O .-= + 463-519 - 8.8931 (5) + 6-2784 (II) + 29-7o44(23)- Io-1845(24)- 19-5199(25) + 65-o388 (28) - 3-9284 (3o) - 61 •I Io4 (32) + 16.63o2 (41) – 73•4728 (42) + 56.8426 (43) + 12II-817 + 71-9244 (9) - 69I-o395 (Io) + 619-1 151 (II) – o-1oo9 (18) + o-Ioo9 (19) + I3-27o9 (22) + 16-4335 (23)- 29-7o44 (24) + 158-5989 (28) - 158-5989 (34) + 73°47a8 (41) - 275-222I (42) + 2o1-7493 (44) + 235-339 + 64-o824(1) - 5o*2339 (2) - 4o-o147 (6) + 38.545o (7) - 1o-4369(15) + 19-I855 (16) - 8.7486 (17) - - 62-o51 - 4o-o147 (6) + 83•4598 (7) - 43·4451 (8) - 15•6295(14) + 24-3781 (15) — 8.7486 (17) + 18-574o (22) -- 13•27o9 (23) - 5·3o3I (26) + 31-724o (28) - 33-o5o8 (32) + 1-3268 (34) - 43-15o4 (42) + 84°5374 (44) - 4I-387o (45) – 91-531 — 9-7866(13) + 15•6295(14) - 5-8429(15) + 9-2o67(35) - 5o:5937 (44) + 41-387o (45) – 14-9694 (52) + 56-1167 (55) - 4I-I473 (56) + 215-523 + 39-2393(1) - 39-2393(3) + 32-9617(14) - 32-9617 (16)+ I-2311 (35) + 53-o422 (43) - 54·2733 (45) + 3-o762 (52) - 25-9526 (54) + 22·8764 (56) – 126.55o + 15· I254 (27) - 3I ·724o (28) + 16.5986 (34) - 9-2o67 (35) + 43-15o4 (42) - 33-9437 (44) + I4-9694 (52) - 3o-1 239 (53) + 15-1545 (55) — I73-874 - Io-9789 (27) - 55-6I7I (28) - 44-6382 (29) + 4-o539 (35) + 2oº7Io5 (39) - 24-7644 (42) - I83*oo77 (74) + 2oo.6476 (75) – 17.6399 (76) - 438-o43 + 67-5249 (12) - 169°5768 (I3) + Io2-o519 (14) – 21-9416 (35) + 2oº7Io5 (39) + 1-23 1 1 (45) - II*2458 (46) - 11 •599o (5o) + 22.8448 (56) + 2oo.6476 (75) – 237.52o8 (76) + 36-8732 (77) – 123·443 — 2o.71o5 (35) + 257°335o (37) - 236.6245 (39) - 21o-4532 (48) + 193.6823 (5o) + 16.77o9 (52) - 4-6o32 (6o) + 28-374o (61) - 23-77o8 (62) + 21o.553 + 6.4799 (46) - 33-7504 (48) + 27-27o5 (5o) + 12-1622 (6o) - 63.o936 (62) + 5o-9314 (63) - 7:3623 (71) + 48.4722 (76) – 41.1o99 (77) - 912.923 + 2o-71o5 (35) - 447°°5°9 (38) + 426-9424 (39) + 351.5191 (49) — 334.7482 (5o) – 16-77o9 (52) + 6°9854 (67) - 37-6689 (68) – 3o.6835 (69) — 15o.432 + 21o-4532 (48) - 35*:5*9* (49) + 141-o659 (5o) + 56.1897 (59) — 79.96o5 (6o) + 23-77o8 (62) - 36°6129 (64) + 67.2964 (67) – 3o-6835 (69) + 35.973 + 3-5122 (59) - 12·1622 (60) + 8-65oo(63) – 2.1378(64) + 15-1296(67) – 12.9918 (7o) + 7:3623 (71) - II-4956 (72) + 4·1333 (77) + 684.435 + 39°48ºº (48) - 21o-4532 (5o) + 17o-9732 (51) – 7-3o93 (71) - 12-1554 (73) + 19°4647 (76) + 2-0536 (81) – 6.4442 (82) + 4-3906 (84) + 437°447 + 7º:5432 (37) - 257-335o (39) + 186.7918 (4o) – 11.8472 (71) – 12-1554 (73) + 24-oo26 (75) + oºoo99 (8o) - 6.4442 (82) + 6.4343 (84) + 86°160 - 19°6222 (58) + 56.1897 (59) – 36.5675 (6o) – 36.6129 (64) + 7-7836 (66) + 28·8293 (67) – 5.8843 (82) + 12.3285 (83) – 6.4442 (84) + ï339°º5º + 687-68o2 (39) – 7o7.9681 (4o) + 2o.2879 (42) + 746.1758 (73) - 684·1290(74) - 62-o468(75) + 548.76o6 (79) + 195•4357(8o)- 744-1963(82) - Io*33° - II*I342 (57) – 2-5757 (58) + 13-9o99 (59) - 31-1624 (64) + 25°o673 (65) + 6-o951 (66) – 17-3o25 (78) – 25-5347 (83) + 42.8372 (84) + 34-979 - 199°3356 (36) + 186.7918 (37) + 12-5438 (4o) + I1.1758 (57) - 13:5393 (58) + 2-3635 (61) – o-28o4 (78) - 13·4711 (8o) + 13.7515 (84) - 26:546 - 174·2768 (47) + 17o-9732 (48) + 3-3o36 (51) + 1 1.1758 (57) - 11-7o85 (58) + o*5327 (62) - 2-5751 (78) – 11-1764 (81) + 13.7515 (84) ALGEBRAICAL EQUATIONS OF CONDITION. 353 I. LI. LII. LIII. LIV. O O The logarithmic values of the multipliers are as follow : Log I = o-3357402 + II = o-668o 586 — III = o-'9028661 — IV = 9.757.1802 — v = o'5552083 – VI = o'3087398 + VII = o'8361258 — VIII = o.o.49.1172 + IX = O.6456229 + X = o'5568856 — XI = o. 1802842 + XII = o' IoS2335 — XIII = O'ol.25374 + XIV = o'4279482 + XV = 8.9395886 — XVI = 9.8742.5oz + XVII = o-2832146 + XVIII = o' 1413915 – (1) FK (2) FD (3) (8) HD (9) HE (Io) (15) KF § RH (17) § DPI 23) DK (24) 29) EH (30) CK (31) (36) CH § BH (38) (43) AE (44) AD (45) I. O = II. O = III. O = IV. O = W. O = Log XIX XX IXXI XXII XXIII XXIV XXV XXVI XXVII XXVIII XXIX XXX XXXI XXXII XXXIII XXXIV XXXV XXXVI FE PIC DA JEK CE BF AB : iº * o:3942867 + o:55 Io.484 - o°49 II 574 + o:24I 95.24 - O-6225395 — o.2623455 - o,7412896 -- 9.5784364 - 8-7449783 – 9.2606399 8-943O367 7.6568901 8.4468962 8.6932,485 + 7.58.13175 - 9.09.02871 — 9-oo.48053 + 8. I4oo947 -- +- iºm FIGURE 14. Notation. (4) I I FC ) HF } DC FD ) CD BK 26 33 4o Equations. Yy (5) 12) Log XXXVII IXXXVIII XXXIX XL XLI XLII IXLIII YLIV XLV XLVI XLVII XLVIII XLIX L LI LII LIII : 7.70I9375 + 7.7195917 -- 7-8504249 - 7.8368841 + 6.61979 Io + 8.6629859 — 8.2237804 – 8-ool 3494 + 8.777.7939 – 7.4686291 - = 8.4151247 - 6.6266218 – 7. I903675 + 8,828920o + 9-oo.49788 + 8.5614607 – 7.8838826 – LIV = 9.85585II - PB JHB JDE JEC CA BD (6) (13) (20) (27) (34) (41) – 4,9488 + (1) — (6) — (7) + (11) — (15) + (16) - o-8530 + (3) — (6) — (9) + (II) — (28) + (29) + 2.98.16 — (1) + (2) — (13) + (15) — (21) + (23) ~ 2:6356 – (7) + (8) — (13) + (16) – (22) + (23) + o-2722 - (2) + (3) — (19) + (21) + (25) — (28) FH JKD JDB JEB CB BA AIK JKB DF JEF CF AC – 112,664 + 6-5930 (4) + 39.7285 (30)—84-1962 (31) + 44.4677 (33)-45.7964(87) + 542-459 – 8.8931 (5) – 39.6297 (9) + 19.5199 (24)— 19:5199 (25) + 80.8336(86) - 81,473 – 27.4199 (7) + 154634 (8) – 4:3687 (19) + 4,3687 (21) – 5:3031 (22) + 5:3031 (26) + 71.3477 (85) – 45.2226 (86) + 33-544 – 29.8555 (6) + 15.6761 (16) – 15.6761 (17) + IIo:4537 (88) + 244,094 – 20.5791 (5) + 8.8215 (8) + 26-3305 (86) 354. PRINCIPAL TRIANGULATION. VI. VII. vIII. IX. X. XI. XII. XIII. XIV. XV. XVI. XVII. XVIII. xix. XX. XXI. XXII. XXIII. XXIV. O = - o = - o = -+ O = — o = -i- o = — O = -+- o = -|- O = — O = — O = — O c — O = -+- O = — O = — • -i- O E — O E — O = -+ O = -+- -H o = -|- -+ 3:6662 — (3) + (4) — (26) + (28) + (31) — (35) 2. Ioo7 — (2) + (4) — (18) + (21) + (32) — (35) 2:34oI — (8) + (Io) — (18) + (22) + (32) — (36) 2.3464 — (8) + (12) — (2o) + (22) — (37) + (4o) o-3o93 — (2) + (5) — (2o) + (21) — (38) + (4o) o-o672 — (13) + (I4) — (2o) + (23) — (39) + (4o) o-98o2 — (17) + (2o) — (4o) + (41) + (44) — (45) o·7477 — (17) + (18) — (32) + (33) — (42) + (44) * _. 48-952 + 2o-364o (I) — II-3552 (3) — 9-oo88 (6) — I3-7879 (7) + 16.3964 (9) 2-6o85 (II) — 9.74oo (24) — 6.283o (28) + I6-o23o (29) •* I5-489 — 3. 1691 (1) + I4.5243 (2) — I I-3552 (3) + 3. 1382 (19) + 7-9 194 (21) I I. o576 (23) + I3-4241 (24) — 7. I4I I (25) — 6.283o (28) m&- 81.658 + 23.533 I (I) — r4.5243 (2) — 9-oo88 (6) — I7-962o (7) + 2o-57o5 (8) 2.6o85 (II) — 7.9I94 (21) + I8.3712 (22) — Io. 4518 (23) 95. 186 — 2o. 7284 (I) + 14:5243 (2) + 6.2o4I (4) + II. II7I (18) + 7-9I94 (21) I 9-o365 (23) + 5o. 6538 (3o) — 29:8373 (32) — 2o.8I65 (35) 52. I 18 + 3-7618 (2) — I7-o4oo (4) + 13-2782 (6) — 4. 2129 (8) + 3 I.8814 (1o) 27.6685 (II) — 1. 1 1 19 (32) — 3.5098 (35) + 4-6217 (36) 96 oo4 — 174.89 18 (2) + 191-9318 (3) — 17-o4oo (4) + 74.4236 (25) 44-74I3 (26) — 29.6823 (28) + 2o5-67I6 (31) — 2o2. I618 (32) — 3. 5o98 (35) 123-427 — 2o. 57o5 (7) + 26:9I88 (8) — 6.3483 (I2) — 14-7 138 (13) I6.394o (14) — 1.68o2 (16) — I3-263o (37) + 36-432 I (39) — 23. I69 I (4o) 9.395 — 14. 5243 (1) + 3-6595 (2) + Io-8648 (5) — I-7669 (13) + I6.394o (14) 14.627 1 (15) — 3o. 9666 (38) + 36:432 I (39) — 5:4655 (4o) 2o.983 — 8. o967 (3) + 2o 4834 (5) — I2-3867 (6) — 9-o252 (9) + 29-o319 (11) 2o.oo67 (12) — 15.875o (27) + 30:4394 (28) — 14:5644 (29) 11.953 + 8.o967 (3) + 9-2524 (4) — 17-349I (5) — 43-4oo9 (26) + 73-84o3 (27) 3o4394 (28) + 22. 1434 (31) — 33:4559 (34) + II-3125 (35) 28.815 — 31.5o37 (17) + 57*9946 (18) — 26.49o9 (2o) — 27.23o6 (32) 3.4649 (33) + 23:7657 (34) + 5:8788 (42) + 5-o7o7 (44) — 1o.9495 (45) 446.366 — 32.2252 (i7) + 59:9337 (18) — 27.7o85 (19) — 233.5183 (31) 2o5-6716 (32) + 27:8417 (33) — 49.81 I4(42) + 242-7768 (43) — 192-9654 (44) The logarithmic values of the multipliers are as follow : Log I = o.o8674I I + Log Ix = 9.679oo84 + Log XVIII = 8.645o689 + II, = o. I8o7674 -+- III = 9.56o92o6 -H Iv = 8.6847529 — v = o. 24879I8 -+- vI = o. 59482I6 + VII = o. I9I699I + VIII = o-4752867 — X = o. I 5oo379 — XI = o-o55283 I + XII = 8.7 I76344 — XIII = 9.9465396 — xIv = 8.6I626I7 + xv = 8.3932264 + XVI = 9-o646936 + xvII = 8. 769289 I + XIX. = 8. I 572618 — XX = 7• 5556467 — xxI = 8.534947 I + XXII = 8•23o5I 58 — XXIII — 8.693 I7o5 — XXIV = 8.6876129 — XXV = 7•9365944 — ALGEBRAICAL EQUATIONS OF CONDITION. 355 § § 22) 29) § (43 § (57 § II. III. IV. VI. VII. VIII. IX. XI. XII. XIII. XIV. XV, XVI. XVII. XVIII. XIX. XX. XXI. XXII. XXIII. XXIV. YXV. XXVI. XXVII. XXVIII. YXIX. YXX. XXXI. IXXXII. G.'A' JL' A’ M’B N7D AH' BL’ CF DE" E. D.' JED JE' D O E FIGURE I5. Notation. § £4 & # 3 #3 & # & 9) L'A Io) L'B (11) M'C 12) M'D (13 (16) N'E' §: N'A' (18) N'A' 19) N'B (20 § R'A' (24) AB (25) AC § 4N (27 (30) BD § BC (32) BE 33) BI” (34) (37) BH' (38) BA (39) CD (40) CE (41) (44) CL' (45) CM’ (46) CA (47) CB (48) § #} {:} # 3 # 33 # 3 (58) EC (59) EB' (60) EE (61) EF (62) (65) A'H' (66) A.K.’ (67) A'L' (68) A'N' (69) (72) E'E (73) L'E (74 CE (75) CID (76) Bquations. * 2.5810 + (3) — (17) — (65) + (68) o:3932 – (17) + (23) — (66) + (68) 2-65 Io + (8) — (17) — (67) + (68) 2:316o - (4) + (18) — (26) + (29) 2.7920 - (4) + (9) — (28) + (29) I'4589 - (4) + (14) — (27) + (29) o,4427 – (18) + (19) — (24) + (26) — (34) + (38) I-3457 – (14) + (15) – (24) + (27) — (35) + (38) 3.2584 – (9) + (Io) – (24) + (28) — (36) + (38) o:5341 - (4) + (5) – (24) + (29) – (37) + (38) 3.5566 – (19) + (21) — (31) + (34) — (42) + (47) o:8705 + (II) — (15) – (31) + (35) — (45) + (47) 4.1626 + (6)– (10) – (31) + (36) – (44) + (47) 3-7955 – (24) + (25) — (31) + (38) — (46) + (47) o,8394 – (19) + (22) — (30) + (34) — (51) + (56) 2.3226 + (7) — (Io) — (30) + (36) – (53) + (56) o:6990 + (12) — (15) – (30) + (35) – (54) + (56) o:2398 – (21) + (22) — (39) + (42) — (51) + (55) o. 1744 – (30) + (32) — (49) + (56) – (62) + (64) 2.8361 – (39) + (40) — (49) + (55) — (63) + (64) — 1.9838 – (16) + (17) — (68) + (69) + o-5434 + (16) – (21) — (41) + (42) — (69) + (70) + 3.3166 + (16) – (22) — (50) + (51) — (69) + (7I) – 2.5223 – (40) + (41) — (60) + (63) — (70) + (72) + o-'7754 – (59) + (60) — (72) + (76) — 2.2156 – (48) + (50) — (71) + (77) + 1.7682 – (58) + (59) + (74) — (76) + 1-oA79 – (57) + (58) + (73) — (74) . : : + 31.734 + 34,7236 (3) — I-701.2 (23) + 16.5873 (65)–17.8476 (66)+ 1-2 I'C M7F N7F AM’ BN’ CE" DB' I) C JEB E! N7 B'E L'I) M’A AL' JBMſ CN’ DE JDB JEC E. C. B'D # 603 (68) – 58.677 + 22:3687 (8)— 1.7012 (23) – 17.8476 (66) + 28-3341 (67)-roº (68) + 57.832 – 31.0871 (1) + 34.7236 (3) + II-9778 (8) + 16-58 — 4,6095 (68) . . + Io9'732 – III-2059 (1) + 61.2787 (2) + 88.1951 (3) 73 (65) – 11.9778 (67) Yy 2 356 PRINCIPAL TRIANGULATION. l)XXXIII. XXXIV. 2XXXV. xXXVI. xXXVII. XXXVIII. XXXIX. XL. XLI. XLII. YXI,III. XI,IV. xLV. XIÀVI. XIVII. XLVIII. IXIL IX. L• III. LII. LIII. I,IV. LV. LVI. O E :–: - 29-695+4-964o (14)-22-8544 (18)-I7-6513 (26)+22-o219 (27)-4-37o6 (29) - 21-728-7-72o4 (9)+4-964o (14)+ 22-o219 (27)—41-3147 (28)+ 19-2928 (29) - 49-o89 + 4o-o335 (4)-42-5693 (5) - 36-74o8 (9)+ 29-o2o4 (Io) + 16-9736 (36) -31-4921 (37) + 14°5185 (38) + 27-673 + 1 1-7283 (9)-29-o2o4 (1o)-Io-Io19 (14)+ 18.9o33 (15)+ 14-3544 (35) - 16.9736 (36) + 2-6192 (38) + 29-898 + 39-953o (9)-29-o2o4 (Io)-59-24o8 (18)+ 33-7324 (19)+4-4222 (34) - 16.9736 (36) + I 2°5514 (38) + 3•135 + 1o-6o87 (11)+ 18.9o33(14)-29-512o (15)+ I9-2764 (24)-24-4475 (25) +5-1711 (27) + 1o-65o3 (45) - 36-5053 (46) + 25-855o (47) + 135-639 + 19-1949 (6)+ 29-o2o4 (9)-48-2153 (Io)+ 25-5182 (24)-24-4475 (25) - 1-o7o7 (28) + 5-961 I (44) - 36-5o53 (46) + 3o:5442 (47) + 142-689-1o-6o87 (11)+2I-o1 16 (15)-44-4o92 (19)+ 2o-4291 (21)-4-8557 (42) - Io-65o3 (45) + 15-5o6o (47) – 27-o51 - 31-525o (3o)+ 34-8347 (31)-3-3o97 (34)-3-o5I 2 (39) + 7-9o69 (42) — 4.8557 (47) - 7-II 54 (51) + 7-22I7 (55) - o• Io63 (56) + 54-9o1 – 8-2425 (12)+ 18-6454 (15)- 37-8896 (19)+ 13-9o95 (22)+o-Io63 (51) – 14-6243 (54) + 14°518o (56) - + 48·364 - 15-9446 (7)+ I 2-7893 (Io)- 2oº95o7 (19)+ 13-9o95 (22)+o-Io63 (51) - 9•2o58 (53) + 9-o995 (56) - 67-399 - 39-8413 (3o) + 44-6o93 (31)- 4-768o (33)-9-8661 (39)+ 8.44oo (43) + I-4261 (47) - 9-2324 (52) + 17-o337 (55) - 7-8oI3 (56) — 58-556-56-3929 (II)+54-o8o6 (13) + 2-31 23 (15) + 44-6o93 (31)-83-7o27 (33) + 39-o934 (35) + 48·2819 (43) - 49-7o8o (45) + I-426I (47) + 4o3-235-77-973o(12)+ IIo*9468(I3)+4o-2962(2o)-29-o575(22)-57.7187 (51) + 139-416o(52) - 81 ·6973 (54) - 23•6o3 + 44-6o93(31) - 52-4669 (32) + 7-8576 (33) + I-5758 (4o)-3-oo19 (43) + 1.4261 (47) + 6-4421 (61) - 37.8317 (62) + 31-3896 (63) – 58.288 + 39-8413(3o) - 52-4669(32) + 12-6256(33) – I-o7I7 (49)-6-7296(52) + 7.8o13 (56) + 13•2o12 (61) - 37·8317 (62) + 24-63o5 (64) + 573•179 - 37-387o (39) + 165°5312 (4o) - 128·1442 (41) - 185-5757 (49) + 156-6582 (5o) + 28-9I 75 (55) - 75°2742 (7o) + 11 2.1791 (71) - 36-9o49 (72) + 9o-o94+31-4157 (6) + 22-3687 (8)+ 12-3889 (41)-5o-6985 (42) + 38-3o96 (44) + 28-3341 (67) - 34-4392 (68) - 46.8789 (69) + 25.61o5 (7o) ¢ - 49°214 + 38:598o(7) + 22-3687(8) + 9.7212 (5o) – 58.5492 (51) + 48.828o(53) + 28-3341 (67) - 34-4392 (68) - 42.7532 (69) + 21-4848 (71) + 117°284+43°785o (48)-Io4-9318(49)+61.1468(5o)-46-5335(59)-32-o79o(6o) + 78-6I25 (64) — 34• Io43 (71) + 23-1229 (72) : + 235°239-18-9651 (16)+ 1 1.4521 (17)+ 7.513o (22)+61-1468 (48)-7o-868o (5o) + 9-7212 (51) + 6-1o51 (68) + 93.5124 (77) + 255:567 + 2o-9242 (58) – 32.o79o (59) + 11-1548 (6o) + 98.6375 (74) — I 32-3168 (76) - 7:536 - 21 · I423 (48) + 21.1423 (5o) + IoI-7188 (75) - 133-5169 (77) + II 2-843 + 9-637o (57) – 2o-9242 (58) + 11 •2872 (6o) + 82-5722 (73) - 98.6375 (74) ALGEBRAICAL EQUATIONS OF CONDITION. The logarithmic values of the multipliers are as follow: Log I II III IV V VI VII VIII IX X. XI XII XIII XIV KV s I XVII XVIII XIX III. IV. VI. VII. PG JP L GP LK JKG # MN ( | NO o'790O4oo — o,6848780 + o-o?877.25 — I-4I59362 + I-28.401.32 – o:9317037 – I. I.2936.76 + O-405592 I O'9833578 9.8097320 o:9976422 8-9932290 + o:5908574 – o:37.29639 – I-270I 573 + o:3162786 — o°417ol 29 — O'4o I3442 – o:2918009 — – P. K. IPAſ GJſ I, II A HI IS I? W. MI TMſ WN ) WS ) MV ) QM NB } OB : : . 3.0694 – (7) + (8) — (26) + (27) 4-6972 - (5) + (8) + (19) — (26) 8-6161 – (3) + (5) — (19) + (20) 6.9Loo - (1) + (3) + (15) – (18) — (20) + (21) I'1984 - (4) + (5) + (14) — (18) — (19) + (21) = + o-6412 - (2) + (3) — (20) + (22) + (28) — (31) * - 5:51.76 – (17) + (18) — (21) + (22) + (29) — (31) Log XX = 9.8315825 + Log XXXIX = XXI = 9.2205369 + XL = XXII = o-o558Io2 + XLI = XXIII = o-o/84902 + XLII = XXIV = 9.3693788 — IXLIII = XXV = 9. 1714078 — XLIV = XXVI = 9.9214317 – XLV = XXVII = 9.4640362 + XLVI = XXVIII = 9.6731183 + XLVII = XXIX = 9.56.444 II – XLVIII = XXX = 9-3905og3 + XLIX = XXXI = 8.4030635 + L = XXXII = 7-4033591 – LI = XXXIII = 9.5961.369 – LII E XXXIV = 9-0637900 + IIII = XXXV = 8.3819704 — LIV = XXXVI = 9.0888938 — LV = XXXVII = 9.527698o + I,VI = XXXVIII = 9-548.1392 + FIGURE 16. Notation. P.J. (4) A'G (5) A'L (6) G'L AM (11) AN (12) BN (13) BO G. K. (18) GL (19) LA' § J. P. J.I. § JEMI (26) LII’ (27) LF J&L (32) LIK (33) IIG (34) III IR (39) IW (40) IM (41) RMſ If T (46) RV § ST (48) SM SIV (53) UV (54) UM (55) UI: TIZ (60) TR (61) TU (62) TS IPAſ (67) WW (68) WT (69) WF WP (74) MA (75) MH' (76) ML MS (81) MT (82) MW (83) MO QW (88) QP (89) PO (90) PN JVA (95) NM (96) NPV (97) NQ ON (102) OM (103) OP Equations. 9' 5415I4I - 9-7I454.25 + o-ozá6147 — 8.3776649 — 9-7766917 — 9-7I792.55 + 8.6288226 — 8.4II4867 + 7,8654356 + 8.29870.47 — 8. I864935 — 8-6655906 — 9. 1639869 — 8-428O849 -i- 8.898.2671 — 8.6673619 — 8.7373943 - 8-5603551 - I'L GA' J. G. RP” IL JRI Uſy Tºy WR MI MO PQ NP 358 PRINCIPAL TRIANGULATION. VIII. IX. X. YXI. . . DXII. DXIII. XIV. XV. lXVI. XVII. XVIII. XIX. YXX. XXI. YXII. lXXIII. XXIV. IXXV. XXVI. XXVII. XXVIII. IXXIX. IXXX. IXXXI. XXXII. XXXIII. XXXIV. 2XXXV. XXXVI. XXXVII. XXXVIII. 2XXXIX. YI. XLI. := : -H -+ -+ o*3758 - (16) + (17) - (29) + (3o) – (32) + (33) 4-6322 - (22) + (24) - (30) + (3I) + (32) – (34) – (35) + (36) o*5638 - (9) + (Io) - (74) + (75) 2:5o37 - (8) + (9) - (25) + (26) – (75) + (76) - 1-65o2 - (24) + (25) + (35) - (4o) – (76) + (77) -H -!- -+ -+ + : ; -H w_w : : *~___ 3•1353 - (II) + (12) - (93) + (94) 3-o856 - (1o) + (II) + (74) - (85) – (94) + (95) I-Io86 - (65) + (66) - (82) + (85) – (95) + (96) 3•6593 - (39) + (4o) - (67) + (69) - (77) + (82) o·2575 - (38) + (4o) - (41) + (42) – (77) + (78) 2-86o5 + (41) – (44) – (66) + (7o) - (78) + (82) o·8o43 - (37) + (4o) – (48) + (51) - (77) + (8o) 3•7892 + (48) - (52) – (66) + (72) – (8o) + (82) o-o79I + (58) - (63) - (66) + (68) – (81) + (82) o-5438 - (47) + (48) - (58) + (62) – (8o) + (81) 2.7721 + (41) - (45) - (58) + (6o) – (78) + (81) I.6997 - (56) + (57) - (6I) + (63) - (68) + (71) 1.8928 - (43) + (45) + (55) - (57) – (6o) + (61) . o.6992 - (64) + (66) - (82) + (83) – (86) + (87) I-Io87 + (65) - (73) - (9o) + (92) – (96) + (98) 2-5577 + (64) - (73) - (87) + (88) - (91) + (92) 2-89I9 - (12) + (I3) + (93) - (99) - (Ioo) + (IoI) 2-o934 - (84) + (85) - (95) + (99) - (IoI) + (1o2) o-8624 - (89) + (9o) - (98) + (99) - (IoI) + (1o3) 29-386 - 6I-oo81 (5) + Io*5815 (7) - 5•2ooI (19) — I-o99o (26) + 6-2991 (27) 124-I93 + 57. 1619 (6) - 33-7352 (7) - 13-9279 (8) I 1 I-429 + 22-6348(3) + 1 ·9o38 (8) - 21-765I (19) + 16.565o (20) + 5-2oo1 (26) 57-519 - 26.4182 (I) + 49-o53o (3) + 16-9247 (4) - 15.1795 (5) + 17-243o (14) 9.8838 (15) - 27·1268 (18) 15-7o9 – 26-4182 (1) + 42-41o6(2) - I5-9924(3) + 9.8838(15) - 32-1189(17) 22-2351 (18) - 5-9438 (28) + 14-8637 (29) - 8.9199 (31) 6o-469 + II-3o9o (16) - II ·3o9o (18) - 3o-o818 (21) + 53°3635 (22) 23-2817 (23) + 37-7995 (29) - 22-9358 (3o) – 14.8637 (3I) + 65-o596 (32) 65•o596 (33) 277°957 + 16-9247 (4) - 77-9328(5) + Io-2o47 (8) - I2-Io85(9) + 17-243o(14) 24-5349 (16) - 4I-7779 (18) + I 1-3o9o (21) – 19-7o99 (23) + 8.4oo9 (24) 23°9618 (35) + 18-2o46 (36) + 5-7572 (4o) + 86-3o55 (75) - Io2-1626 (76) I5-857I (77) ” • 255-699 + 61-oo81 (5) — 4-226o (1o) + 5-2oo1 (19) + 2o-o599 (25) 25-26oo (26) + 23-4327 (74) – 1o9-7382 (75) + 86-3o55 (76) • 23·415 + 28·2373 (9) + 2o-o946 (12) - 21-899o (74) + 23-4327 (75) I-5337 (85) + 36-3995 (93) - 53-6225 (94) + 17-223o (95) 69-123 - 12-1o85 (8) - 16.1288 (9) – 25-713o (Io) + 29-939o (II) 16-287o (24) - 30-3469 (25) + 2o-o599 (26) + 5-7572 (35) + 3o.2933 (39) 36-o5o5 (40) + 2.4-6464 (65) - 34-o888 (66) + 9-4424 (69) + 17.223o (94) 28.5676 (95) + II-3446 (96) ¿* ALGEBRAICAL EQUATIONS OF CONDITION. 359 XLII. O = XLIII. O = XI,IV. O = XILV. O = XILVI. O = XLVII. O = XLVIII. O = XLIX. O = LI. O = LII. O = LIII. O = LIV. O = LV. O = I,VI. O = + 65:767 — 12.8oI 7 (38) + 3o. 2933 (39) — 17.4916 (4o) + 17.86o8 (41) + 3-ooI8 (42) — 2o.8626 (44) — 5. 1855 (66) + 9.4424 (69) — 4-2569 (7o) - 2:569 — II. 9875 (37) + 3o. 2933 (39) — I8-3o58 (4o) + 24-2278 (48) — 3-3o3I (51) — 2o. 9247 (52) — Io. 9285 (66) + 9.4424 (69) + I. 4861 (72) — io5-246 — 2o.8626 (4I) + 2o.8626 (44) + 26.64o9 (48) — 5-7I62 (5o) — 2o. 9247 (52) — 5-743o (66) + 4. 2569 (7o) + I. 4861 (72) -+- I-35o6 (78) — I-35o6 (8o) - + 67-oI5 — 54.4884 (47) + 33-5637 (48) + 2o. 9247 (52) — 3o. I458 (58) + 31.4698 (62) — I-324o (63) + II ·ο938 (66) — 9.6o77 (68) — I. 4861 (72) — 4.458 + 9. 9425 (58) — 62. 9o67 (6o) + 52. 9642 (63) + 4-2569 (66) — 9o.49I8(68) + 86. 2349 (7o) + 25-4I72 (78) — 39. 5297 (81) -+- I4. II 25 (82) - — 17.469 — II-3456 (54) — I4. IoI5 (56) + 25-447 I (57) + 12. 964I (58) — 14.2881 (61) + I-324o (63) — 5-6867 (66) + 9.6o77 (68) — 3.92 Io (71). — 86.845 + Ioo-7245 (41) — Ioo-7245 (43) — 88.2373 (54) + I46.9642 (55) — 58-7269 (57) — I87-6722 (6o) + I34-7o8o (61) + 52. 9642 (63) + 4. 2569 (66) — 9o-49 18 (68) + 86. 2349 (7o) — I4. II 25 (78) + I4. II 25 (82) + o. 576 + I5-3323 (64)— 24.6464 (65) + 9.3I4I (66)— Io.68I8 (83) + Io. 6818 (85) — I-o653 (86) + I.o653 (87) — 3.7936 (95) — I I-3446 (96) + I 5. I 382 (97) — I46-o77 — I Io.6o33 (64) + 88. I7o5 (65) + 22.4328 (73) + 39-3772 (9o) — 7 I •6652 (91) + 32. 288o (92) + 7 I. 7ooI (96) — 92. I 922 (97) + 2o.492 I (98) — 77-o55 + 29-939o (Io) — 24.8394 (II) — Ioo-8645 (12) + 8o. 7699 (13) — I. 5337 (74) + Io7-8566 (84) — Io6.3229 (85) + 23-o536 (Ioo) — II6.4577 (IoI) + 93-4o4I (Io2) + 86.329—38.5213 (65)+24.6464 (66)+ I3-8749 (73)+4-549o (82)— Io7-8566 (84) + Io3-3o76 (85) + 3I-454I (89) — 43-oo9I (9o) + II. 555o (92) + Io2.68 Io (IoI) — 93-4o4I (Io2) — 9. 2769 (Io3) + 346.oI 5+ o. 5666 (58)—86-o4o3 (59)+85-4737 (63)—9-6o77 (66)+249-362 I (67) — 239.7544 (68) — 72. 7641 (79) + II 2. I542 (81) — 39-39oI (82) — 189-796—61.57 15 (41)—65-5663 (45)+ 127. I378 (46)—6.6636 (58)+29-37o3 (59) — 22-7o67 (6o) — 98.8738 (78) + 172.2o45 (79) — 73-33o7 (81). … + I 18.968 + Io9-9578 (43) — 163-68o5 (45) + 53-7227 (46) — 26.26o9 (53) — 58. 7269 (55) + 84-9878 (57) + I2. II27 (59) — II-8436 (6o) — o. 269I (61) + 735-3o8 + 222-3683 (48) — 2o5-o657 (49) — I7-3o26 (52) — I3-o796 (66) + 42. I8I I (67) — 29. IoI 5 (72) — 336.6793 (79) + 358-3716 (8o) — 2 I •6923 (82) The logarithmic values of the multipliers are as follow : Log I = 9.3256339 + Log vII = o.36o8894 + Log xIII = o-7352728 + II = o.6845849 + VIII = o.639o8o2 — XIV = o-4o2o549 + III = I-oz46388 + IX = o.o47689o — XV = o. I722565 + IV = 9.658I463 — X = o-6o83462 + - XVI = o-4884429 -• V = 9•9336864 — - XI = o.69I7649 + XVII = o.44o479I — VI = o°33998o2 + . . . xII = o.5259586 +. . xvIII = o. 2o99442 + 36o PRINCIPAL TRLANGULATION. Log XIX = o'79.13370 + Log XXXII = 8.5634Io7 + xx = o'7944788 + XXXIII = 7.993.4.192 + xxI = 9.876.098o — XXXIV = 9.oz.46809 — XXII E o:24O6153 tºmº XXXV = 8-Oo30519 * : xxIII = o'546.4470 - XXXVI = 8.3944275 — xxIV = o'7173478 + XXXVII = 8.833.9360 — xxv = 9.4038878 + XXXVIII = 8.8292242 + xxvi = 8.4O93937 -- XXXIX = 8-916O489 + xxvi I = o'4476657 -- XL = 8.75II.509 + xxviiI = o'71462.12 — XLI = 8.5832O32 + XXIX = 9.725I423 + XLII = 9.4819.076 + XXX = 9.7505042 – XLIII = 9.67.09376 – XXXI = O'o645I24 + XLIV = 9.6597939 + FIGURE 17. Notation. § 3; ; # & #3 & # & # (§ D.C.' § DA § DB § DC (19) D.L.' § §. º £2. (24 gº. (25 º (26) BD % #}}, {32) #}}. §§ B.E., $33) # 33 #. 36) L'C § I.D. (38) LE (39) # $42 #. § M’E' ; M.G (45) Yg 3% ºf $47, †. (53) GF (51) GE (5%) G.E. (53) ºſ (54) Gł. § ; ; # 8% KY. ; KG (61) KK' 64; II.E. (65) IIII (66) III (67) JJG (68) KG § IPG (7%) IIII (73) III: 74) G'II § FIT Equations. 1. o = + 2.3877 — (1) + (6) - (28) + (30) II. o = + 1.5569 – (6) + (8) - (15) + (17) — (26) + (28) III. o = – 8.1617 – (17) + (18) — (20) + (22) + (26) — (33) Iv. o = — o'oz87 + (1) - (3) - (22) + (23) — (30) + (33) v. o = + 9-71.67 + (3) — (Io) – (23) + (24) VI. o = + 5:5764 - (2) + (3) — (23) + (25) — (36) + (37) VII, o = — 4.8792 - (9) + (Io) – (24) + (25) — (36) + (38) VIII. o = + o-2026 – (18) + (19) + (20) — (25) — (34) + (36) IX. o = - 1.6392 - (44) + (45) + (49) — (57) X. o = + 1.4024 + (9) — (12) — (38) + (44) — (49) + (52) XI. o = + I-4227 + (12) — (52) + (55) — (71) XII. o = + 5°4146 - (54) + (55) + (68) — (71) XIII, o = - 4:2153 - (61) + (62) + (70) — (73) xiv. o = - 7.0631 - (55) + (56) – (60) + (62) + (71) – (73) xv. o = + 3:31.34 - (45) + (46) — (56) + (57) — (59) + (60) Log XLV XLVII XI,VIII § IX F. § J.' D XLVI -: XLIX L LI LII LIII LIV LV LVI C’13 CD M’F Q'K GII’ KH' JKH 8.5405967 + 8.7553162 – 8.6517256 — 8.331216o + 9.4645718 + 8.745.125I + 8-3o40449 + 8, 1746653 + 7,8961683 – 9-97 I7976 — 8.37792I6 -- 7.8079933 – C’A JEE CA BC L'A M’E GM’ GK JKQ' J&K. ALGEBRAICAL EQUATIONS OF CONDITION. 361 xVI. IXVII. XVIII. XIX. XX. 2XXII. XXIII. XXIV. lXXV. XXVI. 2XXVII. XXVIII. YXIX. XXX. XXXI. YXXII. XXXIII. JCXXIV. 2XXXV. 2XXXVI. xxxv I. lxXXVIII. XXXIX. E : :>: â T + 2-4934 - (46) + (48) + (59) - (63) + 3•4954 - (47) + (48) + (58) - (63) + 2• I383 - (II) + (12) – (52) + (53) + (64) - (67) + 6.665o – (53) + (55) – (65) + (67) - (7I) + (72): + o·I 715 — (53) + (54) – (66) + (67) - (68) + (69) - + 353.977 – 81.o997 (1) + 117-1668 (6) + 13-7259 (28) - I14-o522 (29) + Ioo•3263 (3o) — 747.o61 + 21o-6435 (1) + 95-8186 (29) - 2Io-4861 (3o) + II4-6675 (31) + 48.659 -+ 69-4454 (1)-94-5o83 (5)-18o-7518 (6)+ 183·4765 (7)+95-7861 (27) – 1 18.8276 (28) + 92•4869 (29) - 69°4454 (3o) *~. – 52•4o1 - 3•1614 (1) - 2I-3233 (4) + 25-2849 (5) + 1o*5337 (27)-18•5338 (29) · + 8.ooo1 (3o) *. 71.696 + 18o-7518 (6)-215-3438 (7)+34°592o (8)+8-3434 (15)-38.62o7 (16) 3o.2773 (17) + 38-3264 (26) – 157-154o (27) + 1 18.8276 (28) 135o-582+ 17-5884(1)+92-4o97 (3)+36-5403 (22)+83-6396(23)-12o-1799(24) I Io*3172 (3o) + 232-5314 (31) - 122-2142 (33) + 3II · I44-I 2o-9827 (1) + 92•4o97 (3)— 157-6o19 (6)+26.9769 (8)-4-9379 (15) - 61-7554 (17) + 66-6933 (18) – 16.9297 (2o) – 66.7o99 (22) + 83•6396 (23) + 43°248-14-o254 (16)+3o-2773 (17)-16.2519 (18)-18-9531 (2o)+ 22-3658 (2I) - 3•4127 (22) + 38-3264 (26) - 27-3464 (27) - Io-98oo (33) - 15-719--36-4925 (2) - 32-o293 (3) - 15·3723 (9)+71-4379 (Io)-9o-9876 (36) + 98.8469 (37) - 7-8593 (38) - 315-o6o-+92•4097 (1)+36.4925 (2)-128-9o22 (3)+66.6933 (17)-7o-6952 (18) + 4-oo19 (19) + 3I-6oo4 (26) - 4I-3849 (3o) + 9-7845 (33) + 52-9391 (34) — I 51.786o (36) + 98.8469 (37) - 1254·334 - 92•4o97 (1) - 36.4925 (2) + I28-9o22 (3) + 26o-3625 (22) 26o-3625 (25) + 41-3849 (3o) + 3o9-3628 (32)- 35o-7477 (33) + 98.8469 (36) 98.8469 (37) 1626.991 - 34-9296 (16) + 16.2519 (18) + 18.6777 (19) + 18.953I (2o) – 34.8662 (21) + 15-9131 (25) – 117-678o (34) + 22o-7584 (35) - Io3ºo8o4 (36) + 399-o63 + 27-2897 (9) + Io5-2o39 (12) - I32-4936 (I3) + 38-6732 (38) - 63-8167 (4o) - I26.7512 (41) + 215·3279 (43) - Io5-2o39 (44)+ Io5-2o39 (49) - Io5•2o39 (52) + 3o6.215+ 28.4679 (9)+95-Io81 (12)-I23-576o(14)+82-646o(38)-97-8229 (39) - 239-o389 (42) + 32o-5728 (43) - 95-1o81 (44) + 95-Io81 (49) - 95-Io81 (52) + 674-o12 + 69-636o (12) - 69-636o (I4) - 2o6-o9I6 (42) + 32o-5728 (43) - II4•4812 (44) + 94-74Io (49) + 52-8528 (51) - I47-5938 (52) + 58o·243 + 78-6498 (12) - 78-6498 (13) - 94-1838 (41) + 215-3279 (43) - I21 · I44I (44) + 96-427o (49) + 3o-9732 (5o) - I27-4oo2 (52) - 282-655 + 26.6146 (38) - 59-4819 (43) + 41-1578 (44) + 7·1393 (45) - 49-8894 (49) + 33•1343 (52) + I6.755I (57) - 73-192+18-9288 (2)+13·4115 (37)-21-7o2o (38)-34·2949 (43)+23-3458 (44) - 8-o235 (49) + 8-9347 (52) - o-9II 2 (55) + 2I-53o3 (71) -+ ，_w_！ *_w！ = + 681.838 + 22-4513 (12)- o-9112 (32) – 297-19o7 (54) + 298.1o19 (55) + 63•2619 (68) - Z z 362 PRINCIPAL TRIANGULATION. XL. o = — Io8.640+30.5880 (46)–27-oS16 (47)—32.9671 (58)+15:3980 (59)+ 17.5691 (63) XLI. o = - 124.044+13:5475 (44)—o:6019 (48)+16.7551 (49)+10:05.17 (56)—26.8068 (57) — 46.2081 (59) + 30-8IoI (60) + 15:398o (63) - + XLII. o = + 396-681–22:4513 (12)+64'5036 (43)–78-0511 (44)—10.4092 (45)+3.2699 (46) + 41-1578 (49) - 41-1578 (52) + 30-8101 (59) – 41.2277 (60) + 10,4176 (62) – 26.92.16 (71) + 5.3913 (73) * * XLIII. o = - 87,452 – 9-5087 (60) + 19.9263 (61)-Io,4176 (62)—63.7454 (68)+o,4835 (70) + 87.6473 (71) — 5:3913 (73) - - - XLIV, o = - 471-6924-32.9743 (52)–32-0631 (53)-o:9112 (55)–71.4693 (64)+61.8643 (65) + 9-6050 (67) + 21.5303 (71) – 153.3506 (72) XIV. o = – 534,581 – 12:5582 (53) + 297-1907 (54) – 284.6325 (55) – 161.3413 (65) + 163,4534 (66) – 2.1121 (67) – 63.2619 (68) - 37.1746 (69) XLVI. o = + 298.277 – 75.4616 (11) – 149.9509 (72) + 65.8909 (75) XLVII. o = + 33-891 – 11.7082 (72) + 28.7347 (74) – 14.3470 (75) The logarithmic values of the multipliers are as follow: Log I = o'7ooI492 + Log XVII = o-2378173 + Log XXXIII = 7.9870.447 — II = 9-9057507 – XVIII = o. 16792.05 - XXXIV = 8.0596783 — III = 8.9590I99 — XIX = o. 1889868 – xXXV = 8.1944O4I + IV = I-296.1872 — xx = 8.4455Io8 + XXXVI = 7.7868391 + W = I-2402. Io9 — xxI = 8.8330II3 + XXXVII = 9.5493557 -- VI = 9.6507133 + XXII = 9.230947o + XXXVIII = 7.9435623. — VII = o-82III64 — xxIII = 8.3120561 – XXXIX = 9.39424oo + VIII = 8.8466519 — xxIV = 7.7648878 + XL = 9.2091238 + IX = o' II.3461o — xxv = 7.5461266 — XLI = 9.4905609 + . X = o'489.1544 – xxvi = 8.5621584 – XLII = 9.3080893 + XI = 9.8353075 — xxVII = 9.0376488 + XLIII = 9.9093460 — XII = 1.8623616 — xxviiI = 8.2080272 – . XLIV = 7.8564933 – - XIII = o-8o35058 - XXIX = 9. I52O939 – XLV = 7.4793262 + XIV = o-5816320 + XXX = 9.07 Ioos 1 + XLVI = 8.0836415 — XV = o'5939799 — - XXXI = 8.2070257 — - XLVII = 7.9248o22 — xv.1 = o-2916685 + XXXII = 7.8366746 + FIGURE 18. Notation. (1) A'D § A’C 3) C'C D'D (5) D'C (6) D'E (7) D'B (8) EB 9) IPB § I’B § I’A § AI’ §: AF 14) AB (15) A.G. I6) AF 17) BI' 18) BH' 19) BF 2O) BE' 21) BD' § RD 23) BE ; JBG 25) BF 26) B.A. § CC, 28) CB' 29) CA' 3o) CD 31) CE 32) ED' (33) EC 34) ED 35) EG 36) EF § EB 38) DC 8. DD’ 40) DC. 41) DA' § .D.G. . . 43) DF 44) DE 45) DB (46) FA 47) FB - (48) FE 49) FD (50) FG 51) GD 52) GF 4 ALGEBRAICAL EQUATIONS OF CONDITION. 363 II. III. XXII. YXIII. XXIV. IXXV. XXVI. XXVII. XXVIII. XXIX. XXX. O - = - : -: : = : * : + ! : JEquations. 2.8722 – (7) + (8) — (20) + (21) o:6059 – (7) + (10) — (17) + (21) 2.2503 – (8) + (9) — (18) + (20) 2-6353 – (Io) + (II) — (12) + (14) + (17) — (26) 3. I593 - (1) + (4) — (39) + (41) I-9694 – (4) + (7) — (21) + (22) + (39) — (45) 2.0604 — (1) + ( 2) — (29) + (30) – (38) + (41) 1.8252 – (2) + (3) — (27) + (29) I-4803 – (6) + (7) – (21) + (23) + (32) — (37) 2.5461 - (4) + (6) - (32) + (34) + (39) — (44) I.o.512 – (30) + (31) — (33) + (34) + (38) — (44) 5-5268 – (22) + (25) - (43) + (45) — (47) + (49) 4. II 69 – (23) + (25) — (36) + (37) — (47) + (48) o:2976 – (14) + (16) – (25) + (26) — (46) + (47) 8:5792 – (42) + (43) — (49) + (50) + (51) – (52) 5-596 – 28.7221 (7) + 3-7491 (9) + 17.8248 (18) — 76.2202 (20) + 58.3954 (21) 233-224 + 48-6108 (7) – 88.9.196 (8) — 58. 1163 (9) + 46-90.Io (Io) 20:745 + o-oG69 (7) + 3-3376 (Io) + 18.7311 (17) – 46.5300 (19) + 27.7989 (21) 2I-666 + 3:3376 (Io) + 8.7475 (II) – 35-5933 (12) + 70-9164 (13) — 35-3231 (14) I8-73 II (17) – 4o-oš99 (19) + 21.3288 (26) 244 or 8 + 4,4811 (1) – 8.8085 (4) — 39-9016 (39) + 69.4362 (40) – 29.5346 (41) 137,761 + 4,4895 (1) + 71.4678 (8) + 58.3954(20) – 73.5oE.7 (21) + 15-1063 (22) 33.81.96 (39) + Io:5875 (41) + 23.2321 (45) 169.432 + 4,4811 (1) + 20.5244 (2) – 23-6729 (27) + 23-3305 (29) + o-3424 (30) 25-6645 (38) + 55-1991 (40) – 29.5346 (41) → I79-194 + 14-0512 (1) – 67-ol-36 (2) — 45-8222 (4) + 35.2837 (5) + 97.3671 (38) Io9'o677 (39) + 5.7006 (41) 189-895-6.7325(2) + 84.3241 (3)—288.8981 (27) + 315-9476 (28)-27-0495 (29) 63.950 + 8-1408 (21) – 15-1063 (22) + 6.9655 (23) — Io-4322 (32) + 4,6343 (34) 5-7979 (37) + 7.1577 (39) + 16-o/44 (44) – 23:2321 (45) 76.050 + 45-8222 (4) — 90.7836(5) + 44.961.4(6) + 74,3379 (32) - 85.6404(33) II .3025 (34) – 127-2083 (38) + 103-0677 (39) + 24-1406 (44) 269,977 + 67.3836 (22) — 76-5746 (23) + 9-1910 (25) + 38.9499 (43) I53.0616 (44) + II.4.1117 (45) + 34,7915 (47) - 77°5774 (48) + 42.7859 (49) I4.023 + 31.570I (6) – 51.4588 (7) – 53:3034 (Io) + 34.2676 (II) + II.4774(12) 8-1275 (14) – 3.3499 (16) + 5.7979 (32) + 2.8086 (36) – 8.6065 (37) 34,2463 (46) – 69-0378 (47) + 34,7915 (48) * 65.61.5 + 12-162o (34) – 21-7944 (35) + 9-6324 (36) + 12.861 I (42) 16:3782 (43) + 3:51.71 (44) + 6.4480 (48) — 19:7925 (49) + 13:3445 (50) 50.887 -- 24.55oo (22) – 47.oo98 (24) + 22.4598 (25) + 16-7350 (42) 16:3782 (43) — o-3568 (45) — 5.3ior (47) – 19.7925 (49) + 25-1026 (50) * 34.701 + 7.1557 (14) – 47.0731 (15) + 39.9174 (16) + 23:3892 (24) **4598 (25) – o 9294 (26) – 21.6055 (46) + 5.3101 (47) + 16-2954 (5°) Z z 2 364 PRINCIPAL TRLANGULATION. The logarithmic values of the multipliers are as follow: Log I II III IV V. VI VII VIII IX. I II. III. IV. VI. VII. VIII. IX. X. IXII. XIII. XIV. IXV, : C’A D'C' AIK JBD CG JPII PIF JEMſ DM MK IHT i = : – o,8157Io3 + 9-1267212 – o.3289483 + 9.884.5124 + o.8oi6538 + 9.8885949 – o:7593692 – o,732.3468 — o:29Oo360 + o°491755I + D'C AD J3 E 30) CE. § B' B 37) FG. 44) III, (51) EI § JDE MIL (72) KA + Log XI = o'402.1730 — XII = 9-8579.187 — XIII = 9-3607321 + XIV = 9.7667154 — XV = 9.724.1568 + xv.1 = 8.7966108 — xvi.I = 8.2738882 + xvi.II = 8.3464482 – XIX = 7.8230366 + X A'A JE/F AB ) BC FC FE” FIIſ JEFI JDB MI JKL XX F XXI = FIGURE 19. Notation. (II) (18) § Equations. + 2.8486 — (1) + (3) + (13) – (18) 3.2191 – (4) + (5) + (19) - (25) A'B Jº’ G. AA' IBD' FD’ G. C. JTG JSF J.A ME JKM { 8-9900697 – 7.959909.I - 75) D’B AB' JBA' CD’ FB GF JºB ) EC LM IE JKI Log XXII XXIII YXIV YXV IXXVI XXVII XXVIII YXIX XXX. = 7.491.5465 + . 8.897.2770 + 8.2777369 + 8-9900848 – 8-384.1822 + 7.689 IIoo — 8.334996.9 8.6074617 -- 7-7253,128 + + xxx1 = 8.ol 88482 (6) D'E A C/ JB B' ; CE 34) FE GIT JED DA 62) LK (69) IK o:3284 — (1) + (2) + (13) — (17) — (20) + (21) o:6592 - (3) + (4) - (17) + (18) — (19) + (21) 2.6535 - (8) + (9) + (26) – (30) of iro4 - (9) + (Io) – (28) + (30) + (31) — (38) I-8525 – (7) + (Io) + (32) — (38) - 4:3456 - (27) + (28) — (31) + (34) — (53) + (54) - 1:0715 - (5) + (8) — (23) + (25) — (26) + (27) + (47) – (54) + o-0.45% - (16) + (17) — (21) + (22) + (55) — (59) + o-3109 - (22) + (23) — (47) + (48) — (58) + (59) + 2:0204 - (9) + (11) – (29) + (30) + (39) — (42) - 1:2054 - (ro) + (11) — (37) + (38) + (40) — (42) + 6-1639 - (36) + (37) — (40) + (41) + (43) — (46) + o-o364 - (34) + (36) – (43) + (44) — (52) + (53) RTE I)"F AL JBA CF FI GE' JEK JDL LD IM ALGEBRAICAL EQUATIONS OF CONDITION. 365 IXVI. IXVII. IXVIII. 2XIX. XX. JWXI. XXII. XXIII. XXIV. XXV. DXXVI. DXXVII, xXVIII. XXIX. XXX. JOEXXI. XXXII. XXXIII. XXXIV. XXXV. YXXVI. XXXVII. . ; *= :>: :>: : *~_w -w-w_… -|- -+ -+ ww-w_！ -+ +- -H . 4-o5Io - (44) + (45) – (51) + (52) + (68) - (7I) 4-5o65 - (I4) + (16) – (55) + (56) + (6o) - (63) 4-6427 - (5o) + (51) – (66) -- (67) - (68) -F (7o) I-42oo – (48) + (5o) – (56) + (58) - (61) + (63) + (65) - (67) o·3535 - (49) + (51) - (68) + (69) - (75) + (76) o·1835 + (64) – (66) - (69) + (7o) - (74) + (75) 2.8148 – (61) + (62) - (64) + (65) - (73) + (74) 4-51 Io - (14) + (15) + (6o) - (62) - (72) + (73) 175-55o + 18.1582 (1) + 15-3327 (3) - 53-7646 (I2) + 16.5975 (13) 37.1671 (18) 69.422 + 19-24o2 (1) + 1 I-5887 (5) + 3•228I (13) + 16.618o (18) - I7-1656 (19) + 4-9513 (21) + I2-2I43 (25) 21.278 – 15-3327 (3) - 3-57o4(4) + 36-o923(12) + I-o748 (17) - 37.167I (18) 4o-8844 (19) - 58.8554 (2o) + 17-97Io (21) 123.826 + 12-6781 (4) + 18.66o9 (5) - 18.66o9(8) + 2oº8212 (9) + I2-2143 (19) 28-5519 (24) - 4o-7662 (25) + 3-3456 (26) - 3-3456 (3o) I7-343 - 24-9215 (7) + 29-3532 (8) - 3-3456 (26) - 3•1492 (28) + 6.4948 (3o) I2-2953 (31) - 6:554o (32) - 5-7413 (38) 6oI-437 - 66-7537 (5) + 75-816I (7) - 38-4156(8) - 73-526o (9) + 52-7o48 (Io) 85-7o7I (24) + 85-7o7I (25) - 29-674I (31) - 75-8161 (32) + 93•1949 (33) I2-2953 (38) 262.888 + 75-8161 (5) – 75-8161 (7) + 3o-6548 (23) + 45-1613 (24) 75-8161 (25) + 18-33o8 (31) + 75-8161 (32) - 93•1949 (33) - o-952o (34) 3-o974 (47) + 27-6579 (53) - 3o-7553 (54) 13-3899 (17) 474-ooI - 22-61o1 (5) + 83-o367 (6) - 6o-4266 (7) - 3•4558 (23) + 3•4558 (25) 3-866o (32) + 84-56o3 (33) - 8o-6943 (34) - 6I · 2783 (47) + 6I-2783 (53) 98-62o + 2o-5563(3) - 33•2344 (4) - 61-4228(5) + 49-8341 (6) + 22-4158 (16) 35-8o57 (17) + 13-3899 (18) - 27.224o (23) + 27-224o (25) - 29-57o8 (47) 29-57o8 (48) + 9-o43o (55) - o-2o37 (58) - 8·8393 (59) .…• 282-914 + 52-7o48 (9) – 85-5o42 (Io) + 32-7994 (II) + 35· IoI8 (28) 31-9526 (29) - 3•1492 (3o) - 51-4221 (39) + 48-7136 (4o) + 2-7o85 (42) 84-84o + 17-5868 (27) - 49-5394 (28) + 31-9526 (29) + 5I-422I (39) 62-2616 (4o) + Io·8395 (4I) - 33•2372 (43) + 32-o766 (44) + I-I6o6 (46) 3I-1522 (52) - 58.8IoI (53) + 27-6579 (54) - 2I-614 + 5-886I (34) - 32-5624 (35) + 26.6763 (36) - 9-o7o9 (43) 3-7o28 (44) + I2-7737 (45) + 18· I378 (5I) - 23-35oI (52) + 5-2123 (53) Ioo-I45 + 28-6o3o (I4) - 5I-oI88 (16) + 22-41 58 (17) + 7.6485 (21) 22-9494 (22) + I5-3oo9 (23) + 29-57o8 (47) - 71-1o65 (48) + 41-5357 (5o) 5o-941o (56) - 93°3817 (57) + 42-4407 (58) + 32-3281 (6o) + 35-3192 (61) 67-6473 (63) 267-989 + 15-3oo9 (22) - 15-3oo9 (23) + 84°56o3 (33) – 75-7679 (34) 8-7924 (36) + 32-o766 (43) - 35-7794 (44) + 3-7o28 (45) - 61-2783 (47) 42-44o7 (48) - 42-4407 (5o) + 61-2783 (53) + 54-o387 (57) - 53-835o (58) o*2o37 (59) + 3o-9499 (66) – 3o-9499 (67) – 6-o675 (68) - 7·1242 (7º) I3•1917 (71) - 366 PRINCIPAL TRLANGULATION. YXXVIII. O = + 84.283 – 83.3234 (49) + IoI-7779 (50) — 18.4545 (51) – 76.5788 (64) — 19-9588 (66) + 96.5376 (67) – 13-2687 (68) + 30.3724 (69) — 17.1037 (70) xxxix. o = – 194.224 – o'905o (48) - 26:9574 (50) + 27.8624 (51) + 35.0832 (56) — 46.6812 (57) + II:598o (58) + 39.0841 (61) — 23.4623 (62) – 15-6218 (63) – 7:1242 (68) – 17 Io37 (69) + 24.2279 (70) + 4,3045 (73) — 1.5537 (74) — 2.7508 (75) * a XL. o = + 45,915 + 28.3694 (14) - 56.9724 (15) + 28.6030 (16) – 7-8995 (55) – 78.1247 (56) + 86.0242 (57) – 50.94Io (61) + 50.94Io (63) — 28.4130 (64) + 28.4130 (65) — 23.4075 (72) + 19. Io90 (73) + 4:3045 (74) The logarithmic values of the multipliers are as follow : Log I = o-372.4948 — Log XIV = 9-4429038 + Log XXVIII = 8.655oo29 – II = o'4O6945o + xv = o-27.28804 + XXIX = 7.42521.I4 - III = 9.8081068 + XVI = o-3358o04 + xxx = 8.2008387 + IV = o'2792.521 + XVII = o-2912955 + XXXI = 7.6064244 + V = o'3158.436 + XVIII = o-2884929 + XXXII = 7.9424673 - v1 = o-6715666 + XIX = o' 1764783 + XXXIII = 8.6396017 -- VII = o'o689693 – XX = 9.84862.44 – XXXIV = 7.9293535 — VIII = o'6617245 + XXI = o' 147996o - XXXV = 7.8089573 — TX = o-58o3O44 + XXII = 9.6123788 - XXXVI = 8.227.3099 — X = O-3527 I49 + XXIII = 9.5316819 + XXXVII = 7.8067849 + XI = o-4752.469 + xxIV = 8.9438312 – XXXVIII = 7.5162246 – XII = 9.79 IoI52 – xxv = 8.5986.290 – XXXIX = 8.936.1567 + XIII = 9.5oo7925 + XXVI = 8-3535254 ; : * * XL = 6-7471709 + xxvii = 6.3889178 — FIGURE 20. Notation. IY E’A 2) CF 3) B'F' (4) BE 5) FB 6) FA (7) GE § G' B } H'F & H'E (11) H'B & A'R. § A'F' . § AE’ (15) AF' : AB (17) AC 18) BF' (19) BG' (20) BH' (21) BE (22) BI 23) BD (24) BC 25) BA 26) EG (27) EH' § EB' § FA' (37) FK (38) FI (39) FE (40) FII (41) CA (42) CB (43) CD § CG § DB (46) DE (47) DI (48) DH {:}} JDG § DC (51) IE 52) IF (53) IK (54) III (55) IG 56) ID (57) IB § JKF (59) KA' (60) KH (61) KI {} GC (63) GD (64) GI (65) GII (66) Hr § HK (68) HG (69) HD * Equations. 1. o = + 2.3360 + (1) — (6) — (14) + (15) II. o = — 1.6022 – (5) + (6) — (15) + (16) + (18) — (25) III, o = — 3.6030 + (5) — (8) — (18) + (19) rv. o = + 4.3216 + (8) — (II) — (19) + (20) ALGEBRAICAL EQUATIONS OF CONDITION. 367 VI. VIII. IX. 2XI. IXII. JXIII. 2XIV. YXV. XVI. 2XVII. 2XVIII. 2XIX. XX. XXI. XXII. XXIII. XXIV. 2XXV. XXVI. XXVII. ” XXVIII. XXIX. IXXX. XXXI. YXXXII. YXXIII. XXXIV. IXXXV. lXXXVI. • O : : = E :~: + o·I829 - (Io) + (11) – (2o) + (21) + (27) – (34) + 3°3466 + (7 ) - (Io) – (26) + (27) - 4· I496 - (4) + (Io) – (27) + (28) + I-I57I - (9) + (Io) - (27) + (3o) - (39) + (4o) - I-o62I - ( 3) + (9) + (35) – (4o) - 4*44o7 + (9) - (13) + (36) – (4o) + 3•49o1 - (16) + (17) - (24) + (25) – (41) + (42) - 4-6oo5 - (23) + (24) - (42) + (43) + (45) - (5o) — o-o751 - (21) + (23) - (33) + (34) - (45) + (46) + o·256o -- (3o) + (32) - (38) + (39) - (5I) + (52) — I-32o9 - (2I) + (22) - (32) + (34) + (51) - (57) — o.3795 - (32) + (33) - (46) + (47) + (51) - (56) + 3.48oo – (12) + (13) - (36) + (37) - (58) + (59) + 3-8353 — (37) + (38) - (52) + (53) + (58) - (61) – 1-5761 - (43) + (44) - (49) + (5o) - (62) + (63) + o-3891 - (47) + (49) – (55) + (56) - (63) + (64) - 7-3847 - (47) + (48) - (54) + (56) + (66) - (69) - 8-3419 - (54) + (55) – (64) + (65) + (66) - (68) + 3•9513 - (53) + (54) – (6o) + (6I) - (66) + (67) + I-Io7 + 23·8794 (1) + 4*4659 (8) + 6-5o68 (14) - 25•4127 (I5) + 18-9o59(16) - 52-4989 (18) + 38-5322 (19) + I3-9667 (25) – 186.879 + 6-3o85(5) + 2I-3384 (1I) + 38-5322 (18)-54*6772 (19)+ I5-545o(2o) – 2o-416 - 47-9777 (7 ) + 3*o254 (8) + I5-545o (19) - 51-9639 (2o) + 36.4189 (2I) - 25•4o49 (26) + 2oº9oI7 (27) + 4-5o32 (34) •w + 38o-3o4+64-948o (4) +47-9777 (7)+ 25-4o49(26)-56·1484(27) + 3o-7435(28) - 2I-3o3 - Io-ooo2 (4) + 4-97oo (Io) + 3•6719 (27) - 2o-5459 (28) + 16.874o (29) - 189-853 + 24-476o (3) - 64-948o (4) + 32-2462 (27) - 3o-7435 (28) - I-5o27 (3o) + I4-9285 (35) + 22-6416 (39) - 37-57oI (4o) + 28-698-24-476o (3) + 33•2739(13)- I4-9285 (35) - 9°3537 (36) + 24•2822 (4o) + Io5-982 + 113-1141 (2) - 33-9192 (3) - 29-3336 (9) = - 45-999 - II-7621 (5) + 5•4536 (6) + I3-o9II (7) - I7-557o (8) + I8-9o59 (15) - 38-53o7 (16) + 19-6248 (17) + 26.6833 (26) + I4·8818 (33) - 4I•565I (34) + II-6338 (4I) - I6-3694 (42) + 4-7356 (43) - 3o-3233 (45) + I4-432o (46) + I5-89I3 (5o) - + 88•132 - 27-9426 (2I) + 35-7392 (22) - 7.7966 (23) - I4·432o (45) + 39-2756 (46) - 24-8436 (47) - 2I-5618 (51) - o-5o5o (56) + 22-o668 (57) - 3o-762 + 22-58II (9) - 29-4o67 (Io) + 6.8256 (II) + 36.4189 (2o) - 72-1581 (21) + 35-7392 (22) + I2-3277 (38) - 34-9693 (39) + 22.6416 (4o) - 48.8242 (51) + 26.7574 (52) + 22-o668 (57) + 2-233 - 54·1265 (9) + 22-5811 (1o) + 1 1-6o6o (12) – 44.8799 (13) - 1-5o27 (27) - 1-4oo3 (3o) + 2-9o3o (32) + 26.7574 (51) - 28-o2o4 (52) + I-263o (53) - 62-2413 (58) + 35-3o65 (59) + 26-9348 (61) + 19-o77 + 18.8o22 (3o) - 5o-I186 (31) + 31-3164 (32) + 24-3645 (37) --14-5148 (38) – 9.8497 (39) – 14-6153 (51) — 1·263o (52) + 15.8783 (53) 368 PRINCIPAL TRLANGULATION. XXXVII. O = XXXVIII. O = XXXIX. O = + 230-199 + 25.8376 (22) – 43.6823 (23) + 17.8447 (24) + 4,7356 (42) - 46.5595 (43) + 41-81.49 (44) + 41-9225 (55) – 62.9999 (56) + 21.0774 (57) + 22. 1324 (62) – 38-6747 (63) + 16.5423 (64) + 25-347 – 23-8573 (47) + 19.5781 (48) + 4.2791 (49) — 16:5423 (63) + 32-5621 (64) – 16-org8 (65) – 13.2532 (66) – 11.4556 (68) + 24.7088 (69) + 69-198 + 2.9930 (30) – 198971 (32) + 16.9941 (33) + 14:5148 (37) – 26.8425 (38) + 12:3277 (39) + 24.8436 (46) – 44.4217 (47) + 19.5781 (48) + 269348 (58) + 14, 1166 (60) – 41.9514 (61) – 32.4913 (66) + 7.7825 (67) + 24.7088 (69) The logarithmic values of the multipliers are as follow: Log I = 9.950.4678 — II = 9.6325438 + III = o-ooš657o + IV = o-'7835832 – v = o.7866830 — VI = 9.3045681 + VII = o-o/48563 + VIII = o'5874.408 — IX = 8.2550653 – X = o' 1799876 — XI = 9.864.4668 — XII = o-o862690 + XIII = o'o651282 – { : : : : : ; i º B'F JE'E AD JBF' CE Jº G' JFG D'IP QS O Q SD’ PPR MO NMI JKL LM1. Log (IoI (IoS) XV XVI XVII XVIII XIX XX XXI XXII XXIII XXIV XXV XXVI XIV = o' I458 Io9 — = o.o.og887o — = 9.2038683 + = 9.8621625 — = o'2231397 — = 9-ogó924o — = 9.3506273 – = 9.2090o 51 – = 9.682.7376 + = 9-1783546 – = 9. II73024 + = 9°37'95405 + = 8.336798o — |FIGURE 21. Notation. (4) B'P & G' B & (18) AG' (19) (25) DE" (26) (32) CD § (39) EA (40 (46) FC (47) (53) D'S (54) (60) PQ § § 3; ; 75 § N'S (82) (88) ML (89) ; NL (96) fo2) RN (103) Io9) L'N (110) Log B' Q JFA AF JDG' CA FK QA’ PB' O.K. SP JK'S AIN NL' A M L'R XXVII = 9.273.1265 — XXVIII = 8.80616Io — XXIX = 9. 1688924 — XXX = 9.0604901 – XXXI = 8.2076842 – XXXII = 8.904O258 + XXXIII = 7. 1870,128 + XXXIV = 8.544.4322 – XXXV = 8.7179146 — XXXVI = 7.87oo 567 + XXXVII = 8.1212923 — XXXVIII = 8.4427748 + XXXIX = 8.5068234 — (6) CG (13) FIB 20) BE § IX B (34) CF (41) EF (48) FIT (55) QB' (62) PII (69) OM (76) SO (83) K'O (90) ML’ (97) KO (104) LN (III) M'L CF AC BD DA JEG FB' A'Q QP PO OK? SK” R’ \ſ MK’ JKH JLM ALGEBRAICAL EQUATIONS OF CONDITION. 369. II. III. IV. VI. VII. VIII. IX. X. XI. XII. XIII. XIV. XV. XVI. XVII. XVIII. XIX. XX. XXI, XXII. XXIII. XXIV. XXV. XXVI. XXVII. XXVIII. XXIX. XXX. XXXI. XXXII. XXXIII. XXXIV. XXXV. XXXVI. O :…: JEquatioms. — I. 96o5 + (1 1) — (13) — (22) + (23) + o. 7348 + (9) — (II) — (2o) + (22) — (36) + (38) + 5-99o7 — (12) + (13) — (17) + (19) — (23) + (24) — I. 7529 — (15) + (17) + (2o) — (24) — (38) + (39) + I.4182 + (8) — (II) — (21) + (22) — (25) + (27) — 3.7588 — (16) + (17) + (21) — (24) — (27) + (28) — 4.5374 — (14) + (16) — (28) + (29) — (32) + (33) — 4.9481 — (14) + (I5) — (3o) + (33) — (39) + (4o) + 2-o758 + ( 2 ) — (7) — (42) + (43) + o. 2797 + (3o) — (34) — (4o) + (41) — (45) + (46) — 5-o7o7 + ( 7 ) — (9) + (36) — (41) — (43) + (45) — 4. II45 — (5) + (49) — (54) + (55) + 3-o329 — (77) + (78) — (8o) + (82) + 2:6955 — (53) + (72) — (78) + (8o) + 4*778I — (49) + (53) + (54) — (58) — (72) + (74) — 4-9495 — (56) + (58) + (6o) — (64) — (74) + (75) + 2. I 92 I — (4) + (5) — (55) + (56) — (6o) + (61) — II. I443 — (7o) + (71) — (76) + (77) — (82) + (83) — 4-2297 — (57) + (58) + (65) — (71) — (74) + (76) + 3-6534 — (63) + (64) + (66) — (71) — (75) + (76) — I. 6949 — (84) — (9o) + (9I) + (Io8) + 2.96o5 — (69) + (7o) — (83) + (84) + (86) — (91) — I. 2312 — (85) + (92) — (96) + (Io9) — 2.6938 — (84) + (85) — (89) + (91) — (92) + (93) + I.4675 — (87) + (9o) — (Io1) + (1o3)—(Io8)+(IIo) + 2. 1241 — (87) + (89) — (93) + (94) — (Io2)+(Io3) >- + 3-oo67 — (68) + (69) — (86) + (87) + (97) — (Io3) - - — 5-6584 — (2) + (42) — (47) + (4) — (61) + (63) — (66) + (68)-(97) + (99) — 5.85o8 — (87) + (88) — (Ioo) + (Io3) — (Io5) + (Io6) — I.4723 — (94) + (95) — (Ioo) + (Io2)—(Io4)+(io6) — o. 2615 — (95) + (96) + (Io4) — (Io7)—(Io9)+(III) a — 27.999 — 6.6342 (9) + 9.3845 (13) — 4-2127 (2o) — 3.8258 (22) + 8-o385 (23) 2o.869 I (36) — 44. I826 (37) + 23-3135 (38) 261.221 — o. 796 I (12) — 9.3845 (13) + 28.992o (17) — 44-o2I5 (18) I5-o295 (19) + 27-2974 (22) — 8-o385 (23) — I 9.2589 (24) 2o4.647 + 5-4o7o (15) — 28.992o (17) + 23-585o (18) + 4:2 127 (2o) 23-4716 (22) + 19-2589 (24) + 9.2397 (37) — 23-3135 (38) + 14-o738 (39) 2o2-55o + I 3-4865 (8) + 6.6342 (9) + 4-2I27 (2o) + 8-9 I Io (21) — I3-I237 (22) 2-o958 (25) — 3-o49o (26) + o. 9532 (27) — 2o.869 I (36) + 44. 1826 (37) 23-3I35 (38) - 918:817 — 1o9.282 1 (16) + 241. 1887 (17) — 131.9o66 (18) — 44*o815 (21) 146:9961 (22) — Io2.9146 (24) — 45-o347 (26) + 184. I9o6 (27) — I39:1559 (28) 3 A. - - . *-*- -H 37O PRINCIPAL TRLANGULATION. XXXVII. XXXVIII. XXXIX. XL. XLI. XLII, XLIII. XLIV, XIV. XIVI. XLVII. XLVIII. XLIX, LI. LII. LIII. *LIV. LW, LVI, . O == + ==– – = : O = -- * º . : I 455.221 + 15:4301 (20) - 59.4236 (21) + 43-9935 (24) + 139-1559 (27) 148.5888 (28) + 9:4329 (29) + 15:3329 (30) + 9.8467 (32) — 25,1796 (33) 83-4889 (38) + II.5.3664 (39) – 31.8775 (40) 367.623 + 78.8604 (1) – 9-7285 (6) + 14,9171 (10) 643.243 + 30.7023 (6) + 27-5493 (9) + 17.1498 (10) + 44.5404 (35) 106.2786 (36) + 61.7382 (37) 244-off I – 48-1713 (9) + 13.9364 (Io) + 56-3423 (14) — 80-5999 (15) 24.2576 (18) + 204.8841 (30) – 189:5512 (31) – 15:3329 (33) + 11o. 1816 (35) 27.5493 (36) – 59-71.97 (37) + 18.8506 (39) – 96.8618 (40). 635.050 – 92.6894 (30) + 94.4381 (31) — I’7487 (34) – 73.4662 (35) 45-o260 (40) + 28.4402 (41) + 67-5498 (44) - 84.97.32 (45) + 17:4234 (46) 1664,735 – 51.7756 (6) + 17.2433 (7) + 27.2562 (9) – 46-oo33 (Io) 29.4200 (35) + 57.8602 (36) – 28.4402 (41) + 81-1823 (43) — 166:1555 (44) 84.97.32 (45) 876,779 + 77.408o (1) – 12:1061 (2) — 22.8491 (6) + 17.2433 (7) – II.og33 (42) 81. 1823 (43) — 7o. 1490 (44) 194.682 + 45.5884 (5) – 9:2847 (49) + 63-ooog (52) + 7.3537 (54) - 7.3537 (55) 98.790 + 15.4324 (53) + 14:1283 (72) + Io:5889 (77) – 24.7172 (78) 20-9104 (82) 26.220 + 8.4042 (49) – 35-o218 (52) + 25.7371 (53) — 34.7932 (72) 20.6649 (74) + 14.1283 (78) + 7.6209 (80) - 3.570 – 13.8288 (80) + 31-4766 (81) — 16:5402 (82) 177.265 + 4,8761 (49) – 81.1416 (50) – III.3147 (51) + 20,6977 (53) 13:3035 (54) + 19. Io94 (58) + 16-970I (72) - 33-1774 (73) + 16-2073 (74) 32.4099 (59) 604.267 + 136-17oo (49) + 81.1416 (50) + 234,5767 (51) – 285-oo.58 (52) 154.3496 (54) 125-303–24.1273 (51)+20.6977 (53)+ 16-97.01 (72)-23:516o (73)+6.5459 (78) 60.3536 (79) – 32.8902 (80) 131.036+22.1689 (4)–67-7573 (5)-19-4831 (49)–81.4922 (52)+27.7700 (53) 17.9481 (60) + o-9062 (61) + 17:04.19 (64) – 5-o/22 (72) – 27.7608 (74) 32-8330 (75) . 154,720–9.7023 (2)+ 15:1719 (7)–45,8543 (42)+ 19.0886 (43)+26:7657 (48) 12:3358 (49) + 22.0381 (4) + 20,3636 (49) - 7.3537 (54) - Io. 9874 (55) 18-34II (56) + o-9062 (60) – 15.4042 (61) + 14,498o (62) I37.623+ 53.5071 (52)-68.9395 (53)+ II.3588 (57)— II.3588 (58)+ 12-6884 (65) I3-8077 (70) — 26.4961 (7I) + 25.7371 (72) — 25.7371 (74) – 14.6652 (80) 41-4873 (82) + 20.5769 (83) 121.885–2.3297 (56)—11,3588 (57)+ 13.6885 (58)+ 17-oA19 (60)+ 16.4394 (63) 33,4813 (64)— 12-6884 (65)–4, 1825 (66) + 16-8709 (71) 73°463+64.o.779 (3)–86-2468 (4)--22-1689 (5) + 18-3411 (55)–48.7946 (56) 30.4535 (57) + 22-og81 (61) – 30-2319 (62) + 8, 1929 (63) + 23.1319 (65) 48.0532 (66) + 24,9213 (67) 192.8oo--26.2888 (69)-4o-o965 (70)+13.8077 (7I)+4.6312 (76) – 15-2201 (77) Io.5889 (78) + 7.0443 (8o) + 2.92.15 (86) + 7.6174 (90) — Io.5389 (91) 12.3506 (Io9) tº | ALGEBRAICAL EQUATIONS OF CONDITION. 37I LVII. o = — 2o6*950-49-6832 (84)+67. I735 (85)+ 9. 9179 (92)—33. 2196 (93)+23-3o17 (96) + 94-399o (Io8) — 82-o484 (Io9) LVIII. o = + 76*9I2—7-7497 (93)- I5-552o (94)+23-3oI7 (96)+ 52-5564 (1o1)—66.539o(Io2) + I3:9826 (Io3) + 28. 7844 (Io8) — 82-o484 (Io9) + 53. 264o (IIo) LIX. o = + 357.962 + 27. 5o3 I (68)— 53-79I9 (69)+26.2888 (7o)+ 12.547 I (83)—3o.o374 (84) + 7-o955 (97) + 52-5564 (Io 1) — 59-6519 (Io3) — 65-6I46 (Io8) + 53-264o (IIo) - LX. o = + 2-ooo + 2o. 4823 (62) — 36.92 I7 (63)+ I6.4394 (64)-+-8. 1929 (66)— I2-o777. (67)- + 3-8848 (68) + 4I·777 I (75) — 46.4o83 (76) + 4.6312 (77) + 2o. 5769 (82) — 33. I24o (83) + I2-547 I (84) — Io-o94I (86) + 7. I726 (87) + 2.92 I 5 (91) — 53-9679 (97) -+- 46.8724 (98) + 7-o955 (Io3) • · · · · · LXI. o = — 32. I2I + 29-7822 (2)+36.468o (42)—47. 1654 (48)+ Io.6974 (47)—7I-822o (3) + 42.o398 (4) — 7-54oi (61) — 4*7493 (62) + 12.2894 (63) + 16.7284 (66) — 22.6236 (67) + 5-8952 (68) + 42:9876 (97) — 53.4156 (98) + Io.428o (99) LXII. o = + 184-8o9 — 7-2o56 (87) — 48:33o9 (88) + 55-5365 (89) + 35-9or3 (roo) — Io2.44o3 (Io2) + 66.539o (Io3) + 82:53Io (Io4)-95-o913 (Io5)+ 12.56o3 (Io6) LXIII. o = — IoI-784+ I7-49o3 (84)-+-24-o22 I (88)—3 I. 6395 (9o)+7-6174(91)-+- I3-7o8o(Ioo) — 37.9349 (Io1) + 24-2269 (Io3) — 18.57o5 (Io5) + I4-323o (Io6)+ 4. 2475 (Io7) + 38:4457 (Io8) — 38-4457 (I Io) + 23-o296 (I I I) The logarithmic values of the multipliers are as follow : Log I = o.o889695 — Log , XXII = I •oo44255 + Log XLIII = 9. 1856657 — II = o. 74I4385 — xxIII = o.4474535 + XLIV = o. 2679I88 + III = 9. I 598588 + xxIv = o.8o86689 + XLV = o. 222 I3I 7 -+- IV = o. 3I4483I — XXV = 9•7o22I54 + XLVI = o.37o3722 -+- V = o. 553 2633 + xxvI = o. 638829o + * XLVII = 8.4438869 + vI = o. I835627 + XXVII = o. 74396o5 + XLVIII = 7-84I 5347 -+- vII = o.o3I6456 + XXVIII = o. 2655749 -+- XLIX = 7.8332963 -+- VIII = 9.7I49I79 — XXIX = 9.85oo3I4 + L = 8. Ioο77 I 2 — Ix = o.23 I I78I — XXX = 9-755o39o -+ LI = o.o533o8 I + X = 9.7I I6I4I -* XXXI = o. 5 I5o7o3 + LII = 9:54o8247 -+ XI = o. 65o493 I - XXXII = 9•4543977 - LIII = o-o663444 + xII = I.oo6I77 I + XXXIII = 8. 3Ioo326 — LIV = o. 32o7788 + XIII = I. 5279569 + XXXIV = 9-o484-461 — LV = 9.6277542 + XIV = I •49476Io + XXXV = 9.4766255 — LVI = 9.4I88744 + XV = o-oo23475 — XXXVI = 7.8I4984 I — . LVII = 8.38o2I8I + XVI = I. 253576o — XXXVII = 7-36I7543 — LVIII = 8. 74I3799 — XVII = 9•2336458 -+- XXXVIII = 9. 2565835 + LIX = 8.72594o2 + XVIII = I. 298592o + XXXIX = 8. 5993786 + LX = 9•5Io5849 + XIX = o. 348847 I + XL = 8•o282628 -+- . IXI = 9-436483 I + xx = I •464992 I + xLI = 8. 27o786o + LXII = 7. 1515 Io8 + XXI = o. 2983o23 + XLII = 8.87 13732 + IXIII = 7.7I8773 I — 3 A 2 C O R. R. E. CT I O N S RESULTING FROM THE PRECEI).ING EQUATIONS. IFIGURE I. Correction tº From To to ob d * Correction }. From To º south EMD or BASE. Slieve Snaght — coºl S.1 WEL Cuilcagh . + &ogy, 3. Point . — o'4376 Slieve Snaght - O-9424 un tham + o-oš52 North End of Base | + o-6IOA. §§ + o-3869 Mount Sandy — o'5706 orth End of Base | + o-2616 ICnocklayd . — o-oS25 NonTH Eyp of BASE | Sawel . . . . – I-958o || .." i .# i. Hºus * -º-º: o:28o3 Slieve Donard +- § rung Point . + O-I * ~~~~ { Slieve Snaght -- ...; Vicars Carn . + o-8522 Cundtham . . . . o.o.587 |*****4* : Sawel . . . — o-756,o Mount Sandy • + o-or 25 Mount Sandy + 1.8215 : | Slieve Snaght — 1.6367 I).I. UNG POINT Mount Sandy — o-6496 Trostan • + o-4362 North End of Base -- o-2683 Divis — I.2198 South End of Base + o-517I | TROSTAN . . Sawel . . . . . . -- o-8335 CUNDTHAilſ Slieve Snaght + o-ol.25 jº. | | T 3.0660 Mount Sandy • + o-4012 Divis y • * * : + § ICnocklayd . . — o-4166 Slieve Donard iº ...; North End of Base — o-1746 9 South End of Base|| -- ozöö4 |** Vicars Carn . . . -- o-2120 Sawel . . . . . -- o°5953 Sawel tº dº tº Hºmº o,6775 Slieve Smaght - O - III2 lſ() UAVT SANDY - Sawel . . . . . -- o-I355 ICnocklayd + o-6690 North End of Base + o-og5o Trostan : — o-8289 South End of Base tºmº o°5424. Slicve Donard —- o:343o Drung Point . + o-2400 || VICAIRS CAIRV Cuilcagh . . . . — 3.1312 Cundtham • + o°5423 Šawelº. tº º timsº 3 312 Slieve Snaght º º o:2585 Divis • 2-O329 ICnocklayd . — o'5o vis . . . . . 4 o'ooA5 54 Slieve Donard . + o-'9675 | SLIEVE SYA G.IIT • Cuilcagh . – c.16co | SLIPTE Pow-tºp Cuilcagh . — o-3776 Knocklayd - 4.5o'79 Vicars Carn + I. Io.48 Mount Sandy -- 6.6135 Sawel . + O'3445 Cundtham . . . -- 1:05.13 Trostan º + o-225o hºnºus + sº Divis – O-5175 roStan • – 2.68% - * * : : -;|* §º smººt | ºf South End of Base | + o-1429 §. c . . . ] -- O'og73 Sawel . . . . -- o-9528 sº. {lr11 = + I-4I39 eve Donard — I-7017 CORRECTIONS FROM PRECEDING EQUATIONS. 373 FIGURE 2, Correction Correction IFrom To to observed From To to observed - Dearing. Bearing. Z/ */ CUTLC-1 GII • Keeper . . . . — o-4289 || KEEPER—continued Rippure . . + 2-oz 17 Nephin . . . . -- o-o/86 IXnockanaffrin — o'5632 Slieve League — o'o647 - Rippure . . — 3-ol 28 KyocKAYAFFIRIV Baurtregaum . . . — or 1896 Croghan • + 1-4682 - ICeeper • + o-2I59 º IGippure º — 2.2030 SLIEVE DOA.II? D ICippure + o-5816 Croghan . . — o-2957 | BA UIETIREGAUIſ . IBencorr . . - o'7474. ICeeper - I-433.I AIP PURE • Knockanaffrin -- I-2093 Knockanaffrin + o-4I2O IKeeper . . . . – o 94.25 - Croghan tº º + I-4031 || BEYCOIRR . . . . Baurtregaum • + I.oro7 Cuilcagh . – 3.9239 Nephin • - O - I 2.2 I Slieve Donard - O-3403 ICeeper ſº • — o-2646 CI?0 GII A.M - * * Reeper . . + I-5402 || WEPIIIM . . Bencorr • + o-8503 Cuilcagh . + 5.4.228 Slieve League • + I-6855 Slieve Donard — 2.2389 Cuilcagh . – o'4.185 IKippure • — I.5178 ICeeper – 3: I 5ol Ji EAEPER Hºm . . . . § SLIEVE LEſgue. | Nephin. . . . . . – o'4587 * Slieve Snaght + I-8829 Nephin . . . . . -- o-6893 Cuilcagl s". + O-I'73 I Cuilcagh + I. Io90 ullcagn . . . . 73 Croghan . . . . — o.o.444 || SLIEVE SY.1GIIT . . | Slieve League • — o'ol.47 FIGURE 3. A/ wº AIPPURE . Galtymore . — 5-7867 | BAUIRTREGAUJI Caherbarnagh ' | + o-5254 (continued.) IHungry Hill . . — o'IoAo JīA OCR.A.W.AFFRIN Doolieve . . . . . -- o-3653 - Knockmealdown • + o-olz. T.I.U.R . . . . Caherbarnagh — or 1267 Taur . . . . . -- 2.5485 Baurtregaum . . . – o-o/85 Galtymore . . . . . -- o'4027 Reeper . • + o-4345 * Galtymore . . . ] -- o'5238 JTEEPEI2 . . . IKnocknaskagh — o'5079 ICnockanaffrin – 4:5896 Caherbarnagh — o'32.44 IXnockmealdown — o'868o r- Taur . . . . . -- I -1729 Inocknaskagh + o-3830 IKnockmcaldown — o-8584 Galtymore + o-5676 KyocKYASKAGII • Doolieve . . . . . ; – o'2974 Carrigfadda . -- o-2088 J3.1 UIR TREGA U-21 . Galtymore . . – 3.3516 Caherbarnagh ' | – o'4778 Taur . . . . + o-7909 Baurtregaum . . – o'+B. Knockmealdown. | + o-7808 Taur • • + *:::::: Knockmag. • mºs I-98.23 IXeeper e e s 1 - 2.966 374 PRINCIPAL TRIANGULATION. FIGURE 3–continued. Correction Correction From To to observed From To to observed Dearing. Bearing. z/ # / RyocKNASRAGII . . . Galty more — o'6327 CAIIER HARMAGIF Galtymore + I-5694 (continued.) IKnockmealdown . -- 1.8638 (continued.) IKnockmealdown. || -- 3:390o - Knocknaskagh + o-2863 DOOLIEVE • * Carrigfadda + O. I323 Doolieye - — I.4789 | Caherbarnagh -H O'9473 Carrigfadda º o-og'76 Knocknaskagh — o'o.227 Galtymore + 2.8879 IIvyGIPI ITILL Daurtregaum + o-oog6 Knockmealdown — o-8486 Caherbarnagh + o-'7932 Enockanaffrin + 6.4890 Carrigfadda – o-2775 C.íITER BARNA. GII Hungry Hill . — o'817o CARIRZGFA.D.D.ſ Hungry Hill. + o-3346 Baurtregaum ' ' | – I'oZ95 Caherbarnagh + o- 1628 Taur . . . . -- o-2658 Doolieve . . . . — 1.0588 Reeper + 2.7334 FIGURE 4. f/ Ryoor(IAID . . . . Merrick . . . –12%183 MERRICK–continvited Sca Fell + o-o.468 Elack Comb . + o-I302 J) I WIS • * Morrick — 1.6858 South Berule . — o-5780 | SOUTII BERULE . Rippure . . — I-6019 i Howth . + 3-oo.94 | TRoSTAN . . . . . Merrick + 3’5449 Slieve Donard - O-3433 Divis • + 2.4595 SLIEVE DONARD - | Merrick • | + o- I?5o Trostan + o-8993 Criffel . . . . - O-3329 Merrick . . . . — I-52OI Sca Fell • + I-9194 Criffel . + o-5292 South Berule . — o'6820 Sca Fell . . . — o-8793 Snowdon - — o'4843 Black Comb . – o-6319 Howth . + o-I67I Ingleborough . + 2-4597 * Snowdon . + o-3038 HºpPURE • s Howth . . . + o-312I South Berule. – 3.9389 CRIFFEL . Sca Fell . + o-3022 Snowdon . . . — o-3871 IBlack Comb . + 4:4464 South Berule . - o'4I 94. IrO TV'THI · · · Kippure – o-2239 Merrick — o-2780 Slieve Donard + o-95 I2 SCA FELL - Black Comb . -- o.O482 3rERRrdx . . . . . South Berule. — o-2676 Snowdon . + 4°3755 Slieve Donard + o-8982 South Berule. — o-5789 Divis . . . + o-'760o Merrick • -- I-295o Trostan - O-3509 Criffel . . . . . – 2.6692 Inocklayd • + o-2O24. Great Whernside + o-4044 Criffel . . . . — or 1390 Ingleborough . + 2.9812 CORRECTIONS FROM PRECEDING EQUATIONS. 375. FIGURE 4—continued. Correction Correction From To to observed From TO to observed Dearing Bearing. f/ Z/ SCA FELL–contimwed| Pendle. + 1-oo79 || PENDLE—continued Great Whernside — or 5576 Whittle *— I-7864 Holme Moss • – o'8033 - Axedge + I-3799 B.J.A.C.H. COMB . Snowdon . — I-8o94 Whittle – I'o 515 South Berule • + O. 9525 Merrick + I-81.45 IVIIITTLE • . . . . Axedge + o-6523 Criffel . – o-9644 Mowcopt . + 6.4766 Sca Fell - I -og43 Snowdon . . . . . + 1.2829 Ingleborough . + o-6939 Black Comb’. ‘. .”— 'o.4058 Pendle . + o-9586 Sca Fell — o' 1711 Whittle – 2.91 IA. Ingleborough . + o-ol. 66 r Pendle . . . . . -- o-1726 SVO IV.D.O.W. “ Kippure º — o-82Oo Great Whernside + o-2387 Howth. + I-2I49 Holme Moss . – o'58.39 Slieve Donard + 3-9207 South Berule . + 3.6531 || AroTV.coPT . . . . . Snowdon ' ' ' ' ' ' | + o-98.23 Sca Fell + 1-7229 Whittle ſº — O'9457 Black Comb . — o-88.44 | Holme Moss . + o-3225 || Ingleborough . - 2'4'IQ4. Axedge . . . — or 1818 Whittle — 1. 138o Axedge + 1.7656 |AXEDGE . . . . . Mowcopt . — o-2621 Snowdon . – o-2264 GREAT WHERNSIDE | Whittle • — o-6678 Whittle + I-3566 | Pendle . • + o-3813 Pendle . + 2.5745 Ingleborough . . . -- o-og28 Ingleborough . + 2.3305 || Sca Fell & • | – O-4964 IHolme Moss . — I-9697 Holme Moss | + 1.5275 ITOLME MOSS • * Axedge º — I-2792 PENDLE . . . . . Snowdon . . . . — 2.2990 Whittle . " . + I •ol 16 Black Comb . . . -- 1.6505 Pendle ;... . . . . . . 4 o'1235 Sca Fell . • + o-o917 Great Whernside || – o:2974 Ingleborough . + o-orga. - IFIGURE 5. - &/ Af l/ERIEICK • . . . Hart Fell . . – 2.0541 | SCA FELL . . . . . Hart Fell + 4:3461 Wisp . . . • + o-O477' Wisp . . . + I-6895 - Cross Fell • — or 6502 Cheviot • + 5°7597 - Cross Fell. . . ] -- I-87 II CIPIFFEA, . Eſart Fell . — o-7285 Water Crag . . – 2:4748 l)unrich . . . . — 2.4089 - • tº tº Wisp . . — 1.3396 || GREAT WHERNSIDE | Cross Fell — 2.4252 Cross Eell . - 3-6593 Water Crag • — o'3423 *. IBotton Head — I •4OO4. 376 PRINCIPAL TRIANGULATION. FIGURE 5—continued. Correction Correction From To to observed From To to observed Dearing. Dearing. f f M/ IL1RT FELL ſº Criffel . + 2.5777 S.1 FIPS Li Wºº-cont. . . Cheviot — o'or 51 Morrick + o-57Oo - Dunrich — o-6895 || CIIEVIOT . . . . . . . Cross Fell . + o-o] 49 Sayrs Law + o-8013 Sca Fell + 2.288o Cheviot – O'553 I Wisp . . . — o.o.723 Wisp imº o:63 47 IHart Fell º º + o-2277 Cross Fell — I-5806 Dunrich – o'o603 Sca Fell + o-3700 Sayrs Law . + o-2463 Lumsden . . — o-8838 WISP e e s e Criffel . . . -H I.8705 Blackheddon – I'5242 Hart Fell . — o-5697 Easington . . . — o'o687 Dunrich • + o-3515 Wordeslow . — o-8625 Sayrs Law – o-6244 Botton Head . - O - 22 OO Cheviot - I-5334 Collier Law + o-2 176 Cross Fell — 1.3660 - - I? L.A. CAIIEDDON a Cheviot + o-8279 CIPOSS FELL, * * Sca Fell . . . . + 3-1672 Q. Dunrich — 1.3858 Criffel . - 2.944I Sayrs Law — o-3220 Merrick — O'9523 Lumsden . + o-2Io5 Hart Fell . + o-2619 Wisp . . . . . — 1.0519 || LUISDEY . Sayrs Law • + o-5038 Dunrich . . . . . . . ,-- 4:4155 Blackheddon . + o-8132 Cheviot . . ) + 2.7016 Cheviot – o-6911 Collier Law . + o-4182 + iº Botton Head . – 2.0497 | COLLIEIR LAW Water Crag . — o'7879 Water Crag + o-48 Io Cross Fell. + o-5428 Great Whernside — 2. I688 Cheviot . — 1.5IoI Ingleborough . — 2.2879 Wordeslow — o'2246 * • * Easington . . . . -- o'41.58 WATEI? CRAG • Sca Fell . . + o-'7176 Botton Head. . . . . . — o-o/23 | Cross Tell . — o'3718 * Collier Law • — o-3719 | TVOI: DESLoſſ' .. Great Whernside – o 1809 Wordeslow . — 2.7750 Water Crag • – 2.5964 Easington'. . . . . 4- o'78 Io Collier Law • + o-6654 Botton Head + I.og Io Cheviot . . . . — o-3117 Great Whernside – I-4403 Easington . . . . -- o-2 181 Botton Head . + o-o835 D UNTRICH e e Criffel . . . . . -- o-68oo Hart Fell . . . . — 1.4663 || DoTToy IIEAD . Great Whernside — o-6276 Sayrs Law . + o- 1997 Water Crag . + 1.3896 Blackheddon". '- O-3334 Cross Fell . . . . + o-6183 Cheviot + O-OI2O Collier Law . + o-6727 Cross Fell — o'o681 Wordeslow . . . -- 2.2806 Wisp . + o-6017 Easington . . - o'4799 SA FRS LA TV Wisp . – o-9644 | EMSI.YGTON Botton Head . + o-o/22 Hart Fell tº º + 2.9960 Water Crag • - || -- I-3327 Dunrich . . . — o-3946 Collier Law . . . — o-3754 Lumsden . . . -i- o-o825 Wordeslow . . — o-o856 Blackheddon . . ] – o 1185 Cheviot . . . | + I.33 II CORRECTIONS FROM PRECEDING EQUATIONS. 377 FIGURE 6. Correction Correction From To to observed From To to observed Dearing. Bearing. £f f/ JºAIR ISLE Foula . . . o.4936 IRONAS • Foula . – I'oo84 Ronas . - I.3974 Saxaford – o-o?93 Brass — I-5170 Fetlar . – 2-235o Yell + I'oon 5 JFOUL.A . Ronas . . + o-4069 Brassa . + o-3377 Yoll + o-4I5I Brassa • + o- 1584 FETLAI: Brassa . – o 1983 Fair Isle — o-3182 Yell + o-3324. - r; Ronas . + o-51.57 IPIEASSA I'air Isle . + o-9467 Saxaford — o-3647 Foula i.e. – or Ioa 7 Balta + o-2332 Ronas . — o-7071 Yell . + o- 1628 || BALT4 . Fetlar . — o-6720 Saxaford — o' I'704 Yell . . . + o-Io98 Fetlar . + o-o]. I.4 Saxaford + o-248I FELL Brassa • – o'o.243 S.A.A.A.FORD Fetlar . . . . . -- 1.2001 Foula + o-3148 Drassa • • – o-275o Ronas . . . – o I35I Yoll — 2.81oo Saxaford . + o-7227 Ronas . + 2.5483 Balta . . – o'24.Io Balta – o 1731 Fetlar . – o'3469 FIGURE 7. * J/ fº JBIEN CLIBRIG IFashven — o-oš99 || BEM IIUTIG-cont. . . Ben Cheiſt + o-3237 Ben Hutig – o'4570 Scarabin - — o-4692 Fitty Hill . . . + o-6511 | Ben Clibrig . + O.91.95 Wart Hill Hoy . — 1.1637 Dunnet Head - – 2.74Io | SCARADIY. Ben Clibrig . — o-o811 South Ronaldshay + 1.1713 Ben Hutig . . – o III.5 Ben Cheilt — o'9785 Wart Hill Hoy - + o-o499 Scarabin — o'o606 Dunnet Head — or 5682 South Ronaldshay + 1.8724 FASIry:Ey. Wart Hill Hoy — o-9556 Den Cheilt - O-I453 Dunnet Head - O - 22 I2 -- -- rººf Ben Hutig + o-oo:26 || BEY CHEILT . Scarabin . — O II22 Ben Clibrig . + o-2783 Ben Clibrig . + I-9325 * Ben Hutig + I-4488 BEV IIUTrø . I’ashven – 3.9326 Wart Hill Hoy . — o-7504 Titty Hill. • — o-3810 South Ronaldshay – 1:3038 Wart Hill Hoy . -- o-A377 South Ronaldshay — o-6483 | DUMNET IIEAD . Ben Cheilt – o 1868. Lunnet Head – o' 1505 Scarabin. • + 2.7982 3 IR 378 PRINCIPAL TRLANGULATION. FIGURE 7–continued. Correction Correction From To to observed From To to observed IBearing. - - - Bearing. - &/ ſ/ DUMNET HEAD–cont. Ben Clibrig . . . . . -- o'o632 | STRONSAY Deerness . . . . . – o 2004 Ben Hutig – o'3065 Wart Hill Hoy – o'o633 Fashven . • + 2.0636 Fitty Hill. • + I-213o Wart Hill Hoy . + o-o/70 N. Ronaldshay Deerness . . . – 2-7I16 Lighthouse. . . . -- o-1753 South Ronaldshay — o'o.443 Start Lighthouse. — o-2688 | Fair Isle - o'4I29 TVAIET FIXER, ITOY Ben Cheilt + I-474o - --. f Dunnet Head - — 3.2921 | FITTY HILL : Wart Hill Hoy + o-4390 Scarabin + 3-ol 18 Ben Hutig – o-org1 Ben Clibrig + o-84.54 Foula . . . . . — o-1916 Fashven + I.333 I Fair Isle . . . -- I. Io97 | Fitty Hill. • — o-1696 N. Ronaldshay N. Ronaldshay Lighthouse. — o-oogo Lighthouse. — o-org7 Start Lighthouse — o-3208 Start Lighthouse — o-6875 Stronsay . – o'2509 Stronsay . . . + 1-1836 Deerness . . —'o-5027 Deerness . . . — o-6991 - South Ronaldshay -- o. 1059 || FAIR ISLE Stronsay . . . . . . -- o-2941 - -- * Start Lighthouse — o-3441 SouTII RONALDSHAY | Ben Cheilt + o-2861 N. Ronaldshay Scarabin – I-3744. - ...Lighthouse – I. I84I Ben Clibrig . . . – 2-oo.55 | Fitty Hill . . . . . .- o.4009 Dunnet Head — O'3243 Foula . + o-4936 Ben Hutig . . . — 1.4648 Wart Hill Hoy . — o-2179 || FouzA . Start Lighthouse | + 1.8031 Deerness . . + o-5690 N. Ronaldshay - - - Lighthouse.” - || 4 o'9799 J) EER WESS South Ronaldshay | – o'5238 Fitty Hill. .. — o-2382 Wart Hill Hoy - + o-6399 Fair Isle . — o'3182 Fitty Hill. • | + o-5751 --- - Stronsay . . + o-I64I FIGURE 8. Af - */ new Tanzerm ' ' |Ben Heynish ... + 67136|new arone, Arviz . Ben Tartevil . – o-97.05 Ben More, Mull . + o-3592 Ben Heynish . + o-2428 Jura • — o-3762 Ben More, S. Uist || – o 4327 - Storr . . . . . -- o-2793 J UIFA Ben Tartevil . + I-5959 Den Nevis + o-32O2 Ben Heynish : . . – o 75% Jura . . . + o-I994 JBen More, S. Uist || – o-oš7I - Ben More, Mull. — o. 1412 || BEV IIEYNISII •. Ben More, S. Uist — I. 1740 Pen Nevis + o- 1862 Storr . . . . . — 3-1756 CORRECTIONS FROM PRECEDING EQUATIONS. 379 RIGURE 8—contimwed. • * Correction Correction |From To to observed From To to observed Bearing. Bearing. &/ f/ BEV IIEYNISII-cont. Ben Nevis . . . . . -- 1:54.97 storm—continued Ben Nevis . . . . -- o'o668 | Ben More, Mull. — o-3863 Ben More, Mull — I-2307 Jura . . . . . -- o'7883 s Ben Tartevil . – o'4092 || It U REA Storr — o'547I * Cleisham • + O. 2953 PEN AWE WIS • . Jura . . . . . . -- o'2429 Monach + o-8504 * *. Ben More, Mull — o-9049 Cnocghiubhais . + o-1552 Ben Heynish . + o-68o2 - JBen More, S. Uist + 1.2782 cleISHAMſ Ben More, S. Uist || + 2.7278 | Storr . . . . — o'5965 North Rona . + 2.7912 Mamsuil – o-o225 Monach – o-3563 Scournalapich – o-og83 Cnocghiubhais + 1-384.5 * Fashven + o-5908 MIAJISUIL - Ben More, Mull . | – o-o/96 Ru Rea – O-2534 Ben More, S. Uist – o 7437 Scournalapich + 2-4404. Storr . . . . . — o-6562 Mamsuil + 5.0870 Cleisham . + o-7449 Storr – I-2232 Scournalapich + o-6832 Ben Nevis . . — o-Io99 || MoMACII . Cleisham . + o- 1895 i. * North Rona . – o'5398 ScouTAALAPICH - || Mamsuil . . . . . — 1.2697 Cnocghiubhais + o-oz68 Ben More, S. Uist || + o-o261 Pashven — I-5262 Cleisham • — o-288o Ben Clibrig — o-o/84 Monach . . . . -- o-4968 Scournalapich – I-4714 Ben Clibrig . + 1.3066 Ru Rea + o-2097 Ben Nevis . . . . + o-4676 Storr . . . + o-5960 BEW iſoHE, S. UIST | Cleisham . . . . — ooz62 | DEy CEIBRIG Scournalapich – o'3829 - Storr – o'o684 Storr — o-1182 | Scournalapich + o-Io&I Monach + I-5460 Mamsuil . . . . . . . – O. I274 - * *** * | Ben Nevis . . . — o:3583 || FASIIVEN . Cleisham . + 6, 1978 Ben More, Mull. + o-41.4% Monach — 1.32O2 Jura . . . . . . — 1.2131 Cnocghiubhais – 4:5296 || Ben Heynish . + o-6544 North Rona . – 2:4222 STORE • , . . . . Ben Heynish . – I.org3 || BEV IIUTIG . . . Cnocghiubhais | + o-9905 Ben More, S. Uist + o-2576 North Rona . + o-4766 Cleisham . • | + O.5594 * Monach – I'3489 || CVOCGIII UBITATS Monach • — o'7031 rºy ºf Cnocghiubhais — o-7851 North Rona . . – 3-2460 Tu Rea . . + o-7025 Ben Hutig . . . -- o-oooo Ben Clibrig . – o'9119 Fashven . . . ] -- o'87oo Mamsuil . . . . . . . -- 1.2632 - -** ~ *- : *-*-- - - - - - - - - - . . . * ~ * ~ *-* *s, ** --- ... — s 3 B 2. 38o PRINCIPAL TRIANGULATION. FIGURE 9. Correction Correction From TO to observed From To to observed Bearing. Bearing. | BEN IIUTIG . Ben Wyvis — I-2593 || BEY MACDUI-comt. Scarabin – 6:1 509 Ben Cheilt + o-6 III I} EV CLIBIRIG Ben Wyvis – I-5917 Corryhabbic . – o-4664 Corryhabbie – I'Oo34. Mount Battock - || -- o-o233 Ben Macdui — I. 1723 Glashmeal. — O'o623 SCAIR.A.B.I.Y - Ben Macdui . + 2.4383 coſtlerſ.(BBIE Glashmeal. + o-o263 Ben Wyvis . + 5. Io99 Ben Macdui . + o-286I Mormonth + o-38o3 Ben Nevis + O.2423 Cowhythe . + o-3836 Mamsuil — o'987.9 Knock • tº — 2-6693 Scournalapich + o-334o Corryhabbie — o'4787 Ben Wyvis + o-2017 Ben Clibrig — 1.6290 JR EN CHIEILT" - IXnock • º + 4.7148 Scarabin . . . . . . -- o'I278 Corryhabbie . + 2.96 II Ben Cheilt + I-7074 Cowhythe . + o-o982 I} EV IVITPIS • Ben Nevis. - I-435I Knock . + o-I36o Mamsuil — I • II O2 Mormonth — or 1237 Scournalapich + I-5olo Mount Battock -- o-o/o2 Ben Hutig — I-7747 Ben Clibrig — o-oa 98 || KVOCI Ben Cheilt + o-8828 Scarabin + 3-693o Cowhy the — o-2218 ICnock . + o-37.59 Mormonth • — o-o868 Corryhabbie . — I'ool 8 Mount Battock + 1.5499 Ben Macdui . — o-o238 ** { CO IVIIYTHE IKnock . ſº + o-2634 SCO URNALAPICII Ben Wyvis . + o-2323 Corryhabbie . – O'4749 Corryhabbie . + 1.7802 Scarabin – 2:4843 Ben Macdui . + o-5976 Ben Cheilt + o-6037 Aſ Allſ.SUIL • * Ben Wyvis . – o-9867 || MoRMoMTIr . Mount Battock + o-2567 Corryhabbie - — o'5169 Corryhabbie . — o-1617 Ben Macdui . — o'5327 Knock . + o-5484 Glashmeal. — o-og.92 Scarabin • — o-'7848 IBen Lawers • – o'o.433 Ben Cheilt . . . -- o'7634 B EV WEVIS ... • |Ben Wyvis tº * O-4851 BEN LA WEIRS Jura . . . . . . ]. -- o,7287 Corryhabbie . . .] -- o:6854 Ben More in Mull — o.o.487 Ben Macdui + O-436I IBen Nevis + o-3307 Ben Lawers . – o-ooo? Mamsuil – o'5979 º Ben Macdui . — o-2,507 | BEY MACDUI Ben Lawers . + o-2,503 Glashmeal. + o-o990 * Ben Nevis + o:5884 º - Mamsuil + o-o837 || GLASII.M.E.A.L. . . . Ben Lawers . . . 4 o'5oo9 Scournalapich – I, IIo5 Ben Macdui . + I-4984 Ben Wyvis + o-2676 Corryhabbie . — o-3762 Ben Clibrig & — o'2268 Mount Battock . . — o:7742 CORRECTIONS FROM PRECEDING, EQUATIONS. 381 FIGURE 9—continued. Correction Correction From To to observed From To to observed Bearing. Bearing. Af # / AſOUNT B.ITTOCA: Glashmeal . . . + o-2950 || BEV iſoſt E, MULL • Ben Lawers . — 3.0967 | Ben Macdui . — o-I56o Corryhabbie . — o'3067 JUIA • Ben Lawers . – o-4408 IGnock • + o-of $3 Mormonth — o-oo:29 FIGURE Io. * & f f/ irov.A.T. BATTocſ . . . Dudwick . + o-'7456 | DUDIVICK–cont. Mount Battock | – I-5933 - Blue Hill . – o-3830 - Corryhabbie . — o-o466 + -- ICnock . — 1.2138 I? EN JLi CDUI • Dudwick . + o-4439 Mormonth + I-8233 - Little Stirling + o-6318 CORIPY II.1.B.B.I.E • Dudwick . + o-3190 * I}L UE IIILL Mount Battock • + o-5059. TAWOCA'ſ Dudwick . + 1-or Ig Mormonth + 2.490I * - Dudwick . — o-2684. JIOI?][OATII : * ~ * Dudwick . — o-6358 Little Stirling – o-4858 Elue Hill . . — o'7068 Little Stirling – o-4390 || LITTLE STIIRLING IBlue Hill . + o-7589 º Dudwick . - O-5397 | DUD TVICRI - Blue Hill . + o-6514 Mormonth . . . + 1-oSo? FIGURE II. & V Af SLIEVE SAVA. GIIT • Ben Tartevil . – 5:348o | MEIRIRICK • Jura . . – 1.0859 Jura – 6.9694 Goat Jºell . . . – o 1874 - - Ben More, Mull | – I.o.276 WOCATLA FTI) • Ben Tartevil . – o-2057 JBen Lomond . . - I-4036 - Jura tº — o'o676 Ben Lawers • - I-9774 Ben Lomond • + 1.8246 Ben Cleugh . - I.O259 Goat Fell . + o-8683 y º IIART FELL . . . " Goat Fell . . + o-8327 TROSTAN . º Tartevil . - 2.5430 Ben Lomond • + § Ulſa, “ s + I-3123 Ben Lawers • + o-6308 Goat Fell . + o-2272 Ben Cleugh + 2 -off 22 J) I WIS • Goat Fell . — 7, 1948 º D UNIRIC II • IBen Lomond — o'8744 GRIFFEL, e. Goat Fell . + 4,6193 Ben Cleugh . . - o'3°55 382 PRINCIPAL TRIANGULATION. FIGURE II—continued. Ben Lomond . I-9522 Correction Correction From To to observed From To : | to observed Dearing. Bearing. SA FRS LA TV • Ben Lomond . – 3:494I | BEY LOMOND Goat Fell . . . . .-- £6334 Ben Cleugh . – o 2071 ICnocklayd — O'24.24 Ben Lawers . — o'7081 Jura -- . . . . . . 4 o'4391 Glashmeal. - I-2755 Ben More, Mull – o 1339 Mount Battock • + 1.671 I Ben Nevis – 3:3754 | Ben Lawers • — o'8798 I, UMS DEA" - Glashmeal. + 2.888o Ben Cleugh . + o-5048 + Mount Battock • + I-5803 Dunrich – o-2464 Hart Fell . + o-8872 GOAT FELL • Slieve Donard *-* ...; - Divis T 9.93° pry crevair Merrick . . . . — 1.1591 ºyi . . . ; Goat Fell . + o-3769 Slieve Snaght + o-I993 Ben Lomond . – I'o636 Jura . . . . . . . . -- o-o838 Ben Nevis • + o-91.95 IBen More, Mull . — o.608o Ben Lawers. º + o-ogó5 Ben Lomond. + o-I438 IBen Macdui . + o-3035 Ben Lawers . – o-6798 Glashmeal. . . + o-2267 - Mount Battock + o-4346 Ben Cleugh . — o-o/o? S Law Hart Fellº. — o-2918 ayrs – I-4998 Criffel . + I. I 828 Dunrich, ' ' ' | — o'o619 Merrick - o-I475 Hart Fell . . . + o-7851 South Berule. – o'4428 I? EAW LA TVERS Merrick . . . . . 4- o'5098 BEN TARTE WIL s Slieve Snaght + o-6429 Goat Fell . . . . . 4- 2.8665 Trostan + I-Io'78 Bén Lomond . . . . -- o-3338 Inocklayd | + I-9964 Sayrs. Law. . . . . . — 1.6033 Ben Cleugh . — o-4892 JUIRA e • * Trostan • . – o'9348 |... Hart Fell. + o-7974 ICnocklayd . . -- o'4948 || –––––––lº, . I;|nºwraopuz. Ben Cleugh . . . ]. -- o-6698 Ben ionoid º + o-I754 Sayrs Law • + o-6974 Goat Fell . + o-'7348 - Merrick + I-717 I | GLASHMEAL • IBen Cleugh . -- 2 - I2OO BEy Aror B, Arvi.1, Ben Lomond . + o-II 78 h . Goat Fell . . . . .38% arouxT Bartook #.º. T §§ IPEV NEWIS • Ben Cleugh . – o 2003 Sayrs Law . + o-1994 CORRECTIONS FROM PRECEDING, EQUATIONS. 383. EIGURE 12. f : Correction ad Correction . . From To to observed From To to observed - Bearing. Bearing. - &/ & f | GRADLE . . . . . . . Dunkery . . . – o'2584 || HIGH WILHAYS . Precelly . . . . + O. II.79 § Paracombe . — o.o.839 (continwed.) Paracombe + 1-5518 Precelly + o-2732 Dunkery . – o-7437 Mendip + o-24I6 Mendip - O-4399 . Pillesdon . . – o I30I PRECELLY" . . . . . Cradle . — o-2708 Ryders Hill . — o'o669 # Dunkery . – o-og74 # Paracombe + o-15Io | Iey DERS IIILL Deadman . — o-2738 High Wilhays + o-o920 Hensbarrow . + o-I944. * Lundy Island + o-5585 Brown Willy + o-4792 | º _sº High Wilhays – o-o849 - Pillesdon . + o-238 LUNDY ISLAND . . . . . Hensbarrow . + o-3988 * 387 Trevose Head tº-º-º: .#. Barrow Hill . + o-o272 | Precelly tº i º o-o84o * d : Paracombe . + o-o804 || BAIRROW IIILL : Hensbarrow . – o-'9035 High Wilhays — o-7008 .# Maker Tower – O.3957 Brown Willy. + o-3819 Ryders Hill . — o-o/82 w Pillesdon . + o- 5273 JPARACOMBE - inh Wi — n.6n&- * macome #º s ſºme ; MAKER TOWER . . . Deadman . — o'427o Lundy Island + I-5597 - #º. º + o-2488 ... Tº igh Wilhays – o-ogg I Precelly . . — o.804o Barrow Hill 62 ! Cradle . -H o,8123 {ll'l’OW Ill tº - O - IOO2. º Dunkery . 9.5°55 | promºy Irizzy . Deadman . + 1.8665 • ' * { * * * . i • . Hensbarrow . *— I •o'742 DUNKEI.Y. . | High Wilhays – I-4389 Trevose Head + O'4432 Brown Willy. + I-2060 Lundy Island — 3.8892 Paracombe + o-4I74 Paracombe – 5-2824 | Precelly + o- 1509 High Wilhays + o-4723 Cradle . – or 5615 Ryders Hill . — 2.9672 * Mendip .. – o-o.223 - 3. * - tº ſº. Pillesdon . — o-o275 | TREVOSE HEAD . Lundy Island + o-2926 - . . ; Brown Willy . + o-O436 | *NDIP . . . . . . Pillesdon. + O.OO44 Hensbarrow . — I.3863 | -- | High Wilhays + o-7598 - * { | Dunkery — o-ošor IIENSBARIto W. . . . Trevose Head + o-3798 Cradle . - O - 2 IO2 - Lundy Island + O-4.559 º º i Brown Willy. – 2,4705 PILLESDON . • Barrow Hill . – o'o689 High Wilhays — o'7249 - * - ºr High Wilhays – o 1830 | Maker Tower – 3•og35 Dunkery . + o-ošo8 |Barrow Hill . + o-52OI Mendip + o-3628 Deadman . + O'24.23 III.G.II WILITAI's . Deadman . – o'7365 | DEADMAN - Hensbarrow - — I. I227 Hensbarrow . . -- o'8342 Brown Willy. — o'7722 Brown Willy . . . . 4 o'2441 -High Wilhays + o-934o : Lundy Island . + o-1336 fyders Hilſ . . . 4 o’3356 384 PRINCIPAL TRLANGULATION. PIGURE 13. Correction Correction From To to observed From To to observed Bearing. Bearing. Af Z/ IIENSIBAIPI’0 W Goonhilly . . . — o-2565 KAIN GALVEI: " . IKarnminnis ' ' ' ' ' + 1.562 I ICarnbonellis . + 3-ol 18 (continued.) Hensbarrow – 4,2636 Pertinny . + o-8779 * * ICarnbonellis . . -- o-oo;2 IXarnminnis -- I - IO2O Goonhilly . — o-4766 St. Agnes' Beacon | + o-9432 PEIRTI.V.VI" . Wolf Rock_... . . . – o 2398 JOEM DMAN - Goonhilly . — o'4872 St. Agnes' Light- ICarnbonellis . – I-4458 house ... . .] – or 1425 St. Agnes’ Beacon | – 2.3356 Peninnis Windmill — o-oš II Telegraph Tower | – o 1681 TRE WOSE HIELí D - St. Agnes’ Beacon | – o 6766 St. Martin's Head -- 1:4326 ICarnminnis + o-3462 Beacon Hill, Tres- IKarn Galver . — o'5612 cow . . . . . . – 2.0989 . IXarn Galver . — o-6195 GOONIIILL Y - Wolf Rock + o-o.482 Karnminnis | – I-3931 tº Pertinny . — or IIo5 Hensbarrow . + o-3938 IQarn Galver . + O'3275 IKarnbonellis . + I'O424. Karnbonellis . + o-3267 Goonhilly . . . . — o'5084 Hensbarrow . — I-2O62 Deadman . + o-5516 || PENINNIS WINDMILL | St. Agnes' Light- house . . . ] -i- or II.2.1 A.MIPWR 0NELLIS • Karnminnis + o-8271 Beacon Hill, Tres- St. Agnes’ Beacon | – o-o423 COW - • – O.3504 Hensbarrow . + o-6969 Telegraph Tower – 3.21.15 Deadman . — o'5487 St. Martin's Head | – 2.7183 Karn Galver . + 3. I379 ST. AGNES’ DEA colv. IXarnbonellis . . . -- 5. Io97 Pertinn — I-57 Io IKarnminnis — o-'9814 Wolf Rock – 4:53II Trevose Head + 3-3729 . . . Hensbarrow . + o-oroö TELEGIAPIr: ToIVER Peninnis W. Mill — o'7145 Deadman . – 4'O3 I4 St. Agnes' Light- house . . . – o-9377 | H.M.IPNI/INNIS • * Pertinny . . . -- o'68 II Beacon Hill, Tres- IQarn Galvér . — o'57.26 cow . . . . . . -- 3:5862 St. Martin's Head — o'9688 St. Martin's Head — 1.4489 Trevose Head — 1.6787 Karn Galver'. . . — 1.1198 Brown Willy. — o'4708 Pertinny . + o-91.96 St. Agnes' Beacon -- o-Oo39 Wolf Rock -- o: 9233 Hensbarrow . + I.OI 14. • * * º Karnbonellis . . . 4 o'o645 sq. MARTIN's IIEAD Peninnis W. Mill + 1.5066 • 1 Telegraph Tower | – o-og65 KARN GALVER • | Pertinny • . . . -- 2:0139 Beacon Hill . — I-8862 St. Agnes'Lighth. + o. 1823 ICarnminnis – o I325 Peninnis Windmill + o-og43 Karn Galver . + o-6532 Telegraph Tower | – 1.8798. Pertinn — I. I925 St. Martin's Head + 1.1657 Wolf Rock + o-3936 Beacon Hill, Tres- r cow . . . . . – o-8377 | BEACON IIILL, TRES- || St. Agnes' Light- Trevose Head + o-oo?4 CO II’. house • + o-4495 CORRECTIONS FROM PRECEDING EQUATIONS. 385 TIGURE 13—continued. * Correction Correction From To to observed From To to observed Bearing. Bearing. f/ */ JPACON IIILL, TRES- Karnminnis — o-8327 | BIRoſſly IVILLP . Karnbonellis . – 3: IIo2 C0 W-Comtimwed. IQarn Galver . + 1-892.4 St. Agnes’ Beacon – 7.7507 Pertinny . . . . — o'6758 ICarnminnis . – I-9101 St. Martin's Head + 1.7751 - Telegraph Tower — o-8773 || RITDERS IIILL Goonhilly . – o 1859 Peninnis W. Mill + o-4698 FIGURE I4. - £f f JB.E.1 CON IIILL . . Wingreen . . + o-8302 | STORE IIILL : • Wingreen . tº sm coz;3 Westbury Down + o-1483 Westbury Down. o-o/66 Stoke Hill - o'4091 Milk Hill . - O-3243 Milk Hill . + o-9153 Inkpen. • – o'3977 Inkpen . — O'o614 Beacon Hill . . . -- o'352I Dean Hill. – o'5064 Dean Hill . . . . -- o-5223 D.E.I.Y IIILL • , , Wingreen . • — I'8301 || IIILM IIILL Wingreen . + I-42O4. Westbury Down. + o-9520 Stoko Hill + I.O297 Stoke Hill – o. 5273 Westbury Down. + o-og82 Milk Hill . . - O-9475 Upcot Down • — o'2398 Beacon Hill . . . . . -- o-oš81 Inkpen • - || + o-2325 Inkpen • + o- 1605 Beacon Hill . — o'6358 Dean Hill + o-'7095 WIYGIREEN . . . Westbury Down — o.2921 Inkpen . . . . -- o-q81 - r T: i. Hil. . . ." §|Arrº #...ºn . . . ; Dean Hill. -- o'5954 º, tº 34 * W. D ſº T O'oï59 WESTBURY: Do IVy | Upcot Down . + O. 234o estbury y OWI) • o-o'755 \!. Hill . --> ...; Upcot Down . — o-6IoI Stoke Hill . — o-I?75 - Inkpen . . + o-2177 | Upcot. Do TVN . Milk Hill . + o-I418 Beacon Hill . + o-3832 Stoke Hill — o'5996 Dean Hill. – o'o.460 Westbury Down. + o- 1827 Wingreen . — I •oboo Inkpen . . . . -- o'46 II iº- | FIGURE 15. +r- f / f f lſ ILIT IIILL Mendip — o'I 189 || BEACOM IIILL Coringdon. — 2.5579 Swyre Barrow + o-'9975 UPCOT DOJWA" Mendip — o-oogó Mendip . + o-o566 Butser Hill — I-8433 IATPEN . . . . . . Mendip . . . – I-3194, Dunnose — o'564o Butser Hill . + o-5919 Dunnose . . + o-3389 || DEAA IIILL . . Coringdon + o-2718 3 C / 386 PRINCIPAL TRIANGULATION. FIGURE I5—continued. Correction Correction From To to observed From To to observed Dearing. Bearing. & Z Af DEAN IIILL —comt. Swyre Barrow — 2.7977 | COIRINGDON.—cont. . . Butser Hill + #4588 Horton's Gazebo. + 1.0438 Dunnose . — 1.1838 Butser Hill . . -i- or II.66 Dunnose . • — 1.2125 | SWYRE BAIRI:0W. High Wilhays — 2.2790 | - Black Down . -- I • II2. I WING REEV Pillesdon . + o-6396 Pillesdon . + o-2062 Mendip . + 1-offo.4 Wingreen . . . . . -.o.4936. Butser Hill + 1-o&31 Horton's Gazebo - 5-34ol Dunnose . • + 2.265 IBeacon Hill . + o-3646 Horton's Gazebo + o-5043 Dean Hill. + o- 1707. Coringdon. + o-3 Io? Coringdon — o'7091 Swyre Barrow + o-9484 Dunnose . . + 1-3656 | WESTBURY: Do WW . . Mendip . . + o-'7776 || BLACK Do WW . Barrow Hill . — o'2667 - Ryders Hill – O-O4O4. J} UTSAEP IIILT, e Dunnose — o-o873 High Wilhays + o-o/61 * Coringdon — I-3128 tº Pillesdon . • — o-7582 Wingreen . . — 1.3068 Horton's Gazebo. — o-3o48 Dean Hill . . . + 1.5oE.6 Dunnose . . . . . . -- o-2832 Beacon Hill . + o-8748 Coringdon – or 1791 Inkpen . . + o-518o Swyre Barrow + o-o?43 I) UAVNOSE • . Swyre Barrow — o-2204 || MENDIP Inkpen. + o-3144 -- Coringdon . + o-4842 Westbury Down. – o j628 Black Down . – O'.4395 Beacon Hill . . + I-7603 Horton's Gazebo. + o-91.25 Wingreen . . . + o-II 32 Wingreen . . . + o-o/65 w - e i Dean Hill. — o'5291 || PILLESDON . . . Wingreen . + 1.6762 Deacon Hill . — o.4603 Coringdon . . . -- o-8o06 Inkpen . + o-3749 Swyre Barrow — o'6319 IButser Hill + o-5568 Black Down . + I-66 II COPINGDON . Swyre Barrow + o- 1932 || BARROW IIILL : . Black Town . - I-4390 Black Down • — I'o'752 * - Pillesdon . + o-oo?5 || RPDERS IIILL : . Black Down . . – o 1648 Wingreen . + o-olog Swyre Barrow 1.6258 Horton's Gazebo. + 2. 1795 r Deacon Hill . + o-O405 || IIIGH TVII, IIA FS • Black Down . . . . 4- 1.7199 Dean Hill. + o-I577 Swyre Barrow - || – o 901; TIGURE IG. A/ - ; : f/ CRA DLJJ Malvern + o-S230 || ArizK IIILL : ' ' ' ' | Whitehorse Hill. + 2.1644 Broadway Tower — o-3887 i Whitehorse Hill. – o 8134|| VPCoT poſſy ' ' ' ' | Whithorse Hill . . – o'orge Aſ EVIDIP s • * Malvern . . . . + 1,8119 |IVKPEN . . . . . . . . Whitehorse Hill. -- o-org4 i Whitehorse Hill . | + I.oggó | Leith Hill Tower | + o-2504. CORRECTIONS FROM PRECEDING EQUATIONS, 387 FIGURE I6—continued. *** -ºs º-sº - - - --→ *-*. … . 2.9947 | - Correction Correction From To to observed From To to observed * - Bearing. Bearing. f / # / BUTSER HILL Leith Hill Tower o-4745 | EPPING CUPOLA Dunstable . . . . . -- o-7579 Ditchling . . . . — o-4846 (continued.) Wrotham . – 2.3769 BUNYoSE . . . . . . Ditchling . . + 1-5858 CIIING FORD . St. Paul's . . . — o-o/93 Beachy Head . + I. I 529 Leith Hill Tower | – o 2700 * , Berkhampstead + o-2,563 MAL VERY . . . . . Mendip . . + o-3738 Wrotham . — o-5638 | * * ~ : - - - - - -- - “Cradle' ºr ". . . . – o'4074 Severndroog . + o-224I Arbury Hill . + I.oro8 Broadway Tower — o-4655 SEVERYDI:00G . Leith Hill Tower | + o- 2 IoS Whitehorse Hill + o-7445 St. Paul’s . • + o-og45 Berkhampstead - I'o644 WHITEIIoIRSE HILL | Mendip . – 4,2465 Chingford . – o-ogó6 - Cradle'. + 2-4566 Epping Cupola – o 2013 Malvern — I-9652 Wrotham . + o-2072 Broadway. Tower -- 1.7912 34 Arbury Hill . + O. IO22 || WR OTHAMſ Crowborough . — o'7070 Dunstable . — o-6184. Ditchling . . . – o-2315 Leith Hill Tower | – o'6796 Leith Hill Tower | + o-og?7 Inkpen . . . . – o 6354 St. Paul's . • – 1:3096 Upcot Down . + 2.4OIo Severndroog • - O - I 2.2.2 - Dunstable . – 2.5686 BI:0ADWAY TOWER • Cradle . + O. 2594 Berkhampstead - o'944I Malvern • + o-3619 Chingford . + o-4858 Arbury Hill ... • — o-3849 Bpping Cupola + I-4866 Whitehorse Hill. — o. 1894 Fairlight . + o-31 Io | ARBURY HIzz Broadway Tower | – 1.7692 || LEITH HILL To WER | Butser Hill — o-7884 Malvern • | + o-o'782 Inkpen . . . – I-5763 Dunstable. . . . . -- o.2628 Whitehorse Hill | + o-6463 | Dunstable . + I.4773 JDUNSTABLE • Whitehorse Hill. + o-4790 Berkhampstead — o-4687 ... " f Arbury Hill . + o-og29 St. Paul's . + o-4729 Epping Cupola • – o 2021 Epping Cupola - O. 2433 Berkhampstead — 1.5237 Severndroog • — o-I575 Wrotham. . . . . – o 7478 | Wrotham • + o-I379 | Leith Hill Tower — o-4014 Crowborough . – o'3051 - g Beachy Head . + o-,5739 BERKHAMPSTEAD | Leith Hill Tower | – o 8734 Ditchling . + I-2I92 * * Dunstable. – o'3071 * - -y - º : : CEO WBO ROUGHT • . . Hººve, 1. ; 'sºg º + o-'9647 Fairlight — o'9823 "ºt r = St. Paul's . . + o-2760 airlignt 9 -- Apprwg oveoza {} Severndroog • – o 1403 || FAIRLIGHT . Beachy Head . . . – o-I651 * * * | Leith Hill Tower — o-3577 - Ditchling . . . . - or 1423 . . St. Paul's . • + I-6958 || Crowborough . . -F o'2% # , .2 Berkhampstead . | – *Wrotham • — o-o267 *** *** ***. * * * *** -ar.º. -º-, + º-º-º-º-º-º: -*** xx, - - ººm- - * *m' +* *** * * * * ~ * * * * * * * 3 C 2 388 PRINCIPAL TRIANGULATION. FIGURE 16—continued. Correction Correction From To to observed Erom To to observed .* Bearing. Bearing. f/ f/ J)ITCIILING . . . Dunnose – o 825o DITCIILING—cont. . . Beachy Head. – o-oo:34 Butser Hill . . -- o. 2400 Ilcith Hill Tower | + o- 12 II || BEA CII, IIEAD Dunnose — o-oğ92 Wrotham . – o 1809 Ditchling... . . . — 1.6566 Crowborough . – o'963.5 Leith Hill Tower — o'oš41 Fairlight . + I-3548 Fairlight . . . O'54II FIGURE 17. f / # / A.IIPPUI? E • Ballycreen -- 1:4287 | BALLI-CIEEEy—comt. Snowdon . + 2. II 58 > Procelly — o-82.49 Precelly – I'5099 Tara – I-8999 Tara • – o'325o CI2OGILí N - Mount Leinster . — o-8402 | PRECELLP I'orth . • + I-9766 Mount Leinster . + 8-3726 ICEEI2E12 Mount Leinster . + 2.2976 Tara — o-4281 Kippure — 1.2920 A YOCR.A.N.A.FFRIN Ballycreen — o'7703 Snowdon . + I-5496 Mount Leinster . — 1. 1894 Qader Idris + o-3299 l'orth . º + o-'7923 Plynlimmon . + o-4179 | SNO TV DON - Precclly + 1.2779 || CIRADLE Plynlimmon . + o-4277 Tara . . . . . -- I.4776 Cader Idris — o-616I Cyrn-y-Brain + 1.5386 Snowdon . — 2-o/87 Longmount Pole | + 43691 Longmount Pole + o-1864 Plynlimmon . + o-6365 Cader Idris + o-21.71 MALVERN . . . . Longmount Pole + 1.6678 Bardon • – o 3150 I'OI2TH - ICnockanaffrin + o-3253 Mount Leinster | + o-o2 Io | BIROADWAY. To WER. Bardon — o'5079 Ballycreen – I-9150 Tara . . . ~ O'2 I42 || Alº B UI” I* IIILL • Bardon + o-8985 | Precelly . . + O'4435 Loygl)rovyT Pozz - | Cradle . . . – o'7323 TARA - Forth : . . — I. 1821 Plynlimmon + o-o/67 Mount Leinster – o 8278 Cader Idris + o-I64I Ballycreen + 4.5583 Snowdon . . . . . -- 2:3109 Kippure º e + o-911o Cyrn-y-Brain + o-ogg3 Snowdon , * I ammºn 5-4284 Mowcopt * • + O-5026 Precelly * * * | – 2.7265 Axedge tº º tºmº I-8or 7 | Bardon . . . . -- 1.6388 DALL YOREEN Forth . . * | + o-3954 Malvern . . – o 8901 Mount Leinster . – o 643 - . º ICnockanaffrin – o-4838 || BARDoy . . . Broadway Tower — o'9428 Keeper . . . . 4. o,6466 | Malvern • + o-252 I Kippure . . . – o 6725 Longmount Pole | + 1.4504 CORRECTIONS FROM PRECEDING EQUATIONS. 389 FIGURE I7—continued. Correction Correction From To to observed From To to observed Dearing. Bearing. | º £ */ BARD0 y—continued Mowcopt . . # = º 3.296 3 || Moſycopt—cont. Cyrn-y-Brain — o-oo.47 : Axedge . . + 6.8833 Bardon * — I-4838 Arbury Hill . + 3.9590 Aſ X EDGE Longmount Pole + 1.6702 CITIRN- Y - BRAIN . Snowdon . – 3.7 428 Cyrn-y-Brain + o-292 I * Axedge + 2.39.13 Bardon + 3-4806 Mowcopt . • + I or 56 Longmount Pole — o-99.45 IIoEME MOSS . Cyrn-y-Brain — 2. Io99 Aro ſycopt ' ' ' | Longmount Pole | – I-4401 || IFIIITTLE . . . . . . Cyrn-y-Brain – 2.0999 FIGURE 18. £f £/ EPPING cupol.4 Danbury . — o-488o | FIRITTEYFIELD–cont. Paddlesworth . — O'74O4 Gads Hill — o-2037 GADS ITILL Severndroog + o-o88o SEVERY DROOG • Gads Hill — 2.2889 St. Paul's . . + I-43oo * Epping Cupola + o-3481 WIPOTHIAMſ Danbury . -- o'982O Danbury . . — o-6057 S. Hill . - I.3974 Norwood . . — or II 18 orwood . + +9998 || Monroop Wrotham + o-o;77 | * * tº .." L'-'t &LIII e º 'º •o 577 IFrittenfield iºmº o°4749 Gads Hill ſº tº -- § * 7/] [[r 7.7 * : Danbur + I.O.O4 LEITII IIILL TOWER Frittenfield + I-7540 Walton º Cl” h — I-18 ; tº St. Peter's Church + o- 1412 JB.E.M CHI Y HEAD • Frittenfield + I. I947 Tower J'AIR LIG IIT Frittenficló . + O'3254 Frittenfield — 2.3975 Paddlesworth + o-3193 DANDURY. . . . . Gads Hill — o'6595 Wrotham . + o-38Io PADDLESIVon TII Fairlight . — O'3099 Severndroog . — 2.2587 Crowborough + o- 2754 Iºpping Cupola + 2.0703 Frittenfield -H. I.- IOOO Walton Tower + o-O553 Walton Tower — or 1363 St. Peter's Church + 2-ol.12 St. Peter's Church — o-ogo; Tower Tower Norwood . . — I. Io91 Trittenfield • + I-4768 JFIRITTENFIELD . Fairlight . . . . . -- o'7913 º Beachy Head. — 2.8566 | ST. PETER's CITURCII | Paddlesworth — or 1468 ** Crowborough + o-2520 | TOWER Frittenfield . + 1-4266 Leith Hill Tower — o'o.462 Norwood . . + 1-ogóo Wrotham . + o-5969 Danbury . — 2.3227 Danbury . + I. 1803 Walton Tower + o-6924 Norwood . + 1, 1878 Walton Tower — o'oon 5 || WAZToy To WER • Danbury. . . . . . .H o,4262 St. Peter's Church — o-o;99 St. Peter's Church – 3: I 790 Tower Tower 390 PRINCIPAL TRLANGULATION. TIGURE 19. Correction Correction From To to observed From To to observed Bearing. Bearing. ſ/ f/ I) UAVSTABLE • Tharfield . — o-4073 || 0TLEI" . Stoke Tower . — 2.2213 | Naughton . + I-97.79 13 ERKHAMPSTEAD Thaxted + 3. I319 | Mickfield . . + o-4631 | Walton Tower + o-I940 EPPING CUPOLA Tharfield . – 2, 1634 ,- Thaxted – o 2408 || MICKFIELD Naughton . – 2.4587 Lawshall . • — I-2752 J)AMP UEF" Thaxted • + o-o873 South Lopham + 1.7766 Lawshall . . . . — I-7571 Otley . - O-2355. Naughton . + I-507 I ** * . ** = < Stoke Tower . + 2. 1301 || LA WSHALL Thaxted — o-oš28 Balsham • + o-I892 IVALToy To WER Stoke Tower . + o-3083 IBrandon Tower + o-4964 Naughton . - O-I244 Swaffham . — I-6863 Otley + o-4736 South Lopham + o-5348 Mickfield . + o-6503 THAIR FIELD " Berkhampstead + 2.4306 Naughton . — 2.2726 Dunstable . — O'8353 Stoke Tower . + o-o918 Ely Minster . – 2. I245 # . Brandon Tower º -- o-2O73 IBA LSIIAllſ • Tharfield † + o'o609 - Balsham . . + I. IO4O IEly Minster . + o-4963 Thaxted . . . . . . — o-6971 Swaffham . — o-8967 Epping Cupola • + o-2572 Lawshall . . – o 1824 Thaxted . + o-2275 THAITED ~ * * Epping Cupola • + o-418.4 Berkhampstead . + 1.2733|ELY MINSTER • Tharfield . + o-57I3 Tharfield • — I-7992 - Swaffham . + o-I238 Balsham — o'4772 Brandon Tower — o'5259 Lawshall . . – I-4400 Balsham . . . — o-2713 Stoke Tower . . . . -- I-9423 Danbury . — 2.4726 SWAFFITAMr . . . . Brandon Tower — 2.4476 - Ely Minster . + I-3217 SToxE ToIVER • Danbury . — o-6301 | South Lopham – I-37II Lawshall . - O-4242 Lawshall . – o 2076 Naughton . — o-8302 Otley . . . . . — o-oz81 | SouTIſ Lopil.Allr. Lawshall . . + o- 1272 Walton Tower . + o-2015 Brandon Tower . — 1.014.4 - Swaffham . +. I.3853 AAUGIITON • Stoke Tower . - O.O.5oz. 1Mickfield . . . — o'7567 Danbury + 2.2618 Thaxted — o-38or BRANDow ToyBIt Tharfield . . – o-3385. Lawshall . . + o-6763 Ely Minster . + o-7434. South Lopham + 2.4O23 Swaffham . . + o-4387 Mickfield . + 2.3793 South Lopham — I •o68o' Otley º º - o.O458 - Lawshall & C º-º-º: o:3183 Walton Tower - I • 222. I CORRECTIONS FROM PRECEDING EQUATIONS. 391 ** EIGURE 20. Correction Correction From To to observed From To to observed Bearing. Bearing. f / Af | TVA ETON TOWER Orford Castle . . . -- 1.4656 | DUVIVELL–cont. Laxfield + o- 1817 | LA WSHALL . . . Hingham . — o-'9536 IIINGHAMſ. Brandon Tower . — 1.7186 t + r Swaffham . + 1.4600 DIRANDoy To IVER . Hingham . — o'8044 | Baconsthorpe . + 1-o/73 * - Bunwell — 2.917.3 Norwich Spire + o-og S3 - Bunwell . . . . – o'5570 OTLEF • * Laxfield + I-5357 South Lopham - I - IIo.4. Orford Castle . + I-2519 * SOUTHWOLD . Orford Castle. + o-7582 Aſ IORTFIELD - • Bunwell • – 2.97.28 Laxfield – 3:3163 Laxfield • – 3.5772 Tofts Tower . + 1-oo73 . , - . Gorleston . — o'ozA6 SOUTH LOPEIAAſ Hingham . • | + o-8659 - Bunwell . . . . . . -- 1.7025 || Torps To WER Laxfield — o'22.99 Laxfield + 3’54O4. Bunwell — o-6854 Norwich Spire + o-3354. S WAFFIL! ºf Baconsthorpe . . -- o-6942 Happisburgh . — o-Igó9 Hingham . • - I.O.O.44 Gorleston . + o-o273 - * * Southwold . . . — o-o'77o ORFOR D CASTLE Walton Tower + I-2096 + - - Otley . — I-34oz NOI. WICII SPIRE Bunwell + I-7127 Laxfield + o- II.4o Hingham . . + 1-4839 Southwold . + o-7665 Baconsthorpe . – I-3605 sº- Happisburgh . - 4-24O2 * Gorleston . . -- 2 OOQ: L.A.A.FIELD Otley . . . . . . ] + o-6672 "ovºrov, 93 \ºid tº tº- : § º º Wel" . f 2°5794. s i. º + I-9533 | fuxile o-og 55 IBunwel — o-7528 * Tincr tº ſº Norwich Spire sº ; JBA CONSTEIORPE • §. * + º 3. Tofts Tower . — o' 1263 fia ii. l •o949 appisburgh . — o-o/87 Southwold . + o-3O33 Norwich Spire -- O - 3 I 3 I Orford Castle. + o-2353 p 313 GOI2EESTON - Southwold - 2 - IOIO il. BUN WELL . . . Mickfield . — o-4607 Tofts Tower . + o-6II.4. . . . . - South Lopham + o-86.79 Norwich Spire — o.o.397 Brandon Tower + o-3978 Happisburgh . + o-O457 Swaffham . — o'6723 º, -- Hingham . — o-5723 || IIAPPISBURGII . Norwich Spire + 1 .26oo Baconsthorpe . — o' 1633 Baconsthorpe . — o-2O34. Norwich Spire • + o-oš32 Gorleston . — o'747o Tofts Tower . + o-2786 Tofts Tower . + o-2225 ... --- - --~~~~------- *** * 392 PRINCIPAL TRLANGULATION, TIGURE 21. Correction Correction From To to observed IFrom To to observed I3earing. Bearing. &/ Af JPA 18 DOM - Back Tor , + 4-444i CLIFTOM BEACON Crowle . . . — o'o'747 i Lincoln Minster. + I. 1644 (comtimwed.). Lincoln Minster + I-2414 Buckminster . + 2.8175 i Tilton . . . . . -- 3:4813 || LINCOIN MINSTER • Bardon . . . . – 19848 Naseby Church + 1.3486 Axedge . . . . -- 1.6626 Tower Back Tor . . . – 3.7351 Clifton Beacon + I-3892 | A.Y.E DGE • Back Tor . – o-4030 Crowle . – o'3037 Lincoln Minster + 6.8877 Boston . . . . . . -- 5.2840 Buckminster . . – o-565o IIOI, IIE JIOSS . . . Garſorth Cliff – 4:0704 |. Clifton Beacon + 8.535o | ARBURY ITILL . . Naseby Church — o'3277 Back Tor . + o-8877 Tower Hanslope Spire • – o-ogo1 GREAT WHERNSIDE York Minster + 2.4675 ozysz, pze . Hanslope Spire . . -- I-9403 * * * Naseby Church + 2.7417 Boq"Toy ITEAD . . . Acklam Wold • — I 1278 Tower - York Minster – 3.8752 IKeysoe Spire • + 2.4500 A. C.R.I.A.Aſ WOLD - Crowle . • | + o-5809 || YASEBY CITVRCII Arbury Hill . . – 3-7734 Clifton Beacon + I-5598 TO IV.E.12 Bardon . . . . -- 2:or72 Garforth Cliff + 1.3310 Tilton . . . . — 2.1849 York Minster + 4-og'79 Easton Tower + 1.5oS8 Great Whernside — o-6772 Keysoe Spire . + 6.4331 Botton Head . — o-8II6 Hanslope Spire • + 2.56Oo I’O.R.R. M.I.YSTEZ2 . Clifton Beacon + o-4066 TILTON . Naseby Church – 1.9796 Garforth Cliff — I. 1763 Tower Great Whcrnside + 2. I452 Bardon . + 2. I631 Botton Head . — 2.2370 Buckminster . . – o 8136 Acklam Wold – o-5709 Easton Tower + 11.785o * * Reysoe Spire • + O.7355 GARForTII CCIFF . Holme Moss — 1.6076 Great Whernside + 5-ol Io EASToy Tom ER . . . Naseby Church + 1-oš58 York Minster + o- 1905 Tower Acklam Wold + 1-7878 Tilton . . . . . . . . -- 8-1934 Crowle . . + I-4939 Buckminster . . + 1.ogº; - Boston Tower + 1-or 32 CI2O JWLE • * * Clifton Beacon + o-6454. Walpole St.Peter's – 1.568.7 Back Tor . . . . . – 2.9347 IEly Minster . – 5-82 II Garforth Cliff — 1.4626 Keysoe Spire . – 3.4798 Acklam Wold + 2.6186 ºr Lincoln Minster + o- 5484 || KErsop SPIRE Dunstable . . . . — o:91.94 Hanslope Spire • | + o-4534 CLIFTOY BEAC0N Back Tor . . . . — o-634o Naseby Ch. Tower | + 1.7314 Holme Moss . + 8-2329 Tilton . • + o-'7781 Great Whernside + o-3563 Easton Tower – 2:4992 York Minster . — o'3081 | Ely Minster . + 3.5184 Acklam Wold . — 2.07.08 Tharfield . . – o'5046 CORRECTIONS FROM PRECEDING EQUATIONS. 393 FIGURE 21—continued. Correction Correction From To to observed From To - to observed Dearing. Bearing. Af - W/ TILLIFIELD . . . . Hanslope Spire — 1.5585 LYMy To WER—cont. Docking Tower | – I-1794 Keysoe Spire. + o- 1694 Swaffham . . . — o' 1851 BALSIIAAſ . . . . . IGeysoe Spire . + o-7971 BoSTOV To WE1: . Easton Tower — 3.678o | Buckminster + 1.81 og lºl, Y MINSTEI2 - ICeysoe Spire + I. I 594 Lincoln Minster + 4.4909 Easton Tower + 2.945I Docking Tower . – 7.967% f Walpole St.Peter's + 1-oš20 Swaffham . - 3-9.543 Lynn Tower. . + 1-82 18 Lynn Tower . - 2'544I Walpole St. Peter's — 1.5316 WALPozī, ST. PETEIt's Easton Tower • 2 I Q2 rºº Boston Tower f †: DOCATIA G TO TWER Lynn Tower,' ' | + o-6245 Docki * sº Walpole St. Peter's — o-2060 ocking Tower + o-'7483 Boston Tower º Lynn Tower . – I'512 I i. l OWCl + o-495o Swaffham . • + o- 1791 aconsthorpe — 2. I58o Elv Mi * * * | – 0 ° y Minster *7*|sizippſ.ur . . . Walpole St. Peter's + 5.7977 * Lynn Tower + 3.9192 | LINY TOWER • , | Ely Minster . – I'o613 Boston Tower | -- 3.7631 Walpole St. Peter's + 2.2323 Boston Tower + 2.6426 || BACONSTITOIRPE . Docking Tower | + o-4040 C O N N E CT I 0 N 0 T S P E CIAL POINTS WITH THE GENERAL TRLANGULATION. ' The corrections given in the preceding pages, 1,554 in number, enable us to determine the most probable relative positions and distances of 218 principal points; before proceeding, however, to the calculation of the triangles, there remain the extremities of five base-lines, and several sector stations and observatories, whose positions with reference to the above points must be accurately determined. We proceed to give the Equations of Condition necessary for these determinations, and the corrections to the observed bearings that have thence . resulted. * †. HounsLow HEATH BASE. The triangulation for the connection of this base-line is shown in Figure 22. The points in this figure that are already fixed, are Leith Hill, Wrotham, Severndroog, Epping, Chingford, and St. Paul's Cathedral. Those to be fixed are Banstead, St. Ann's, Hanger Hill Tower, and the extremities of the base, Ring's Arbour and Hampton Poorhouse. The station here called Leith Hill is not identical with that used by Captain Kater in 1822, nor with that of General Roy in 1795; their relative positions will be found at page 25. The station Wrotham is identical with that of Captain Kater, but at a considerable distance from Generallroy's station of that name. The stations Severndroog and Chingford are identical with Captain Rater's stations of 1822; the former is a few inches distant from General Roy's station (page 35). The station Banstead is 6.2 feet south (more exactly, 35.7° 7') of the old station of that name; and from the station on Hanger Hill Tower, the old station of Hanger Hill (1792) is distant 504.8 feet in the direction 269° 4' 24”. The remaining points, King's Arbour, Hampton Poorhouse, and St. Ann's Hill, are identical with the points so called in the first volume of the “ Account of the Trigonometrical Survey.” - Instead of writing the geometrical Equations of Condition at full length, it will be sufficient to indicate them thus: ABC prefixed to an algebraical equation indicates that that equation arises from the sum of the angles of the triangle ABC being necessarily equal to a known quantity, and A : BCD prefixed to an algebraical equation indicates that the equation arises from the necessary relation— - AB . AC. AD sin ACB sin ADC sin ABD AC AD AB T sin ABC sin ACD sin ADB T An inspection of the table of calculated corrections following the equations, will show to which bearings the symbolical corrections (I) (2) (3) . . . . . are respectively attached. I Dºuations of Condition. I. MD'B' o = + 2*9782 - (3) + (5) + (9) — (17) II. MD'C' o = - 2'4845 - (5) + (8) — (15) + (17) III. G.F. B' o = - o'6694 – (2) + (4) + (18) — (24) IV. GMB' o = - 3’8794 - (2) + (3) — (9) + (13) + (18) — (25) V. G D'E' o = - 2'4362 – (2) + (7) + (18) — (23) VI. LGB' o = + 2*7352 — (1) + (2) — (18) + (20) — (27) + (30) VII. LMB' o = + 4’3151 — (1) + (3) — (9) + (Io) — (29) + (30) VIII. LKM o = - 3'2068 – (10) + (11) – (26) + (29) + (31) — (33) Ix. HRL o = + o' 2864 – (26) + (28) + (31) — (32) — (34) + (35) x. FIL G. o = + 2 '906o — (19) + (20) — (27) + (28) — (34) + (36) XI. B. : MC'D' o = - 308'675 – 202: o300 (5) – 291 5474 (8) – 180°6479 (9) + 95.2285 (15) + 85'4194 (17) CONNECTION OF SPECIAL POINTS. 395 XIII. XIV. XY. XVI. XVII. XVIII, XIX. XX. XXI. A' Jſ : PI : MB'D' : MA'D' : B' GF M : JB' G D’ : MGD' LGB’ : D’G B' : MILG: : HIGL MILG : + II ‘4121 (23) – 63 '8654 (25) + 115°oGo5 (22) — 122 1792 (23) + 7. 1187 (25) + 41 6167 (25) + Io' 1682 (27) – 31 '91.96 (29) + 2 I-7514 (30) — 38.6782 (20) + 14' 3673 (23) + 3 '8094 (25) + 59' 4385 (26) – 62 “oj48 (27) + 2 - 5963 (29) – 21 5652 (28) — II 4592 (34) + 19.998o (35) – 8'5388 (36) + 27' 2417 (25) + 44°ol II (27) — 70°3338 (28) + 26-3227 (29) The logarithmic values of the multipliers are as follow: - 17° 312 + 147 5334 (3) + 9' 16oo (5) – 79-8601 (9) + 41' 2690 (14) + 38°591 I (17) - 80'636 – 101-6736 (5) + 70°5458 (14) – 203: 3259 (16) + 132.78or (17) + 39'243 + 29'6466 (2) — 68: 1250 (4) + 2 - 4314 (18) + 74°9657 (23) – 77° 3971 (24) + 184' 150 + 40'4729 (2) – 192'2492 (3) — 216.6342 (5) + 14.6042 (7) + 52.4533 (18) - 269'889 + 9' 16oo (5) – 106°oo36 (7) + 30°5365 (13) — 69' 1276 (14) + 38° 5911 (17) + 72°835 + 13°oo42 (1) – 40°4729 (2) + 27°4687 (3) — 52°4533 (18) + Io'8366 (20) +44'579 – 26 or 23 (1) + 35'2999 (2) + 74° 1309 (6) – 45'5851 (7) + 24°3109 (18) — 135°588 +44' 6263 (10) – 84-6437 (11) + 4o' or 74 (13) — 68.9615 (20) + 65. 1521 (21) + 312.936 – 23:348o (19) + 68.9615 (20) – 45-6135 (21) – 4o'4696 (26) + 62-oj48 (27) + 330-607 -- 42° 1516 (10) – 84-4427 (12) + 42 2911 (13) — 72°2598 (19) + 45 or 81 (20) Log I = 9'668or 21 — Log VIII = o' 260408o — Log xv = 8*7385372 – II = o'6784650 + IX = o' 2341499 + xv.1 = 8-2067635 — III = o' 3401836 – x = o' 3096631 — XVII = 8.707238o — IV = o' 7208430 + XI = 8.4608365 + XVIII = 7' 4672759 + V = o' 68.93755 + XII = 8-84-18597 — XIX = 8*7842O41 — VI = o'4823861 + . XIII = 7'9748855 — xx = 9°oo I437I — VII = o' 64II409 — XIV = 8-4566329 + XXI = 7-9454IIo — Resulting Corrections. From To Symbol. 3. IFrom . To sº §. Leiri Hill. Toren | St. Ann's Hill . (I ++. 1774 HANGERHILL ToweR | Leith Hill Tr. . . (18 +c" 5454. Hanger Hill Tr. (2) —o. 5529 Hampton P. Ho. (19) +2 '3278 Banstead (3) +o 1792 St. Ann's Hill . (20) —o'4229 r Ring's Arbour . (2 I +3 Ioo7 WROTHAM . Hanger Hill Tr. (4) —o. 4329 St. Paul’s 22) –o 5320 - Severndroog 23) | –o'72OI SEPERNDnoog ToweR Banstead . . . (5) +o. 9881 Wrotham . 24) –o "ooq I St. Ann's Hill. . . (6) +o 1951 IBanstead 25) —o'8976 Hanger Hill Tr. (7) +o. 6179 ST. ANN’s HILL IGing's Arbour . (26 + o' 37.59 CHINGFond . Banstead (8) —o. 7888 Hanger Hill Tr. (27) —o'8157 Hampton P. Ho. (28 +o 6242 BANSTEAD . . Leith Hill Tower (9) —o. 3736 Banstead . . (29) +o'5661 --- St. Ann's Hill . . (Io) —2: 2721 Leith Hill Tower (30) —o'8523 lºing's Arbour . (II + I 3993 Hampton Poor- RING's ARBoun St. Ann’s Hill . " 3. —o" o224 house . . . . (12 +o 1720 Hampton P. Ho. (32) –o'6049 Hanger Hill Tr. (13 + 1 3308 IBanstead (33 +o 6324 St. Paul's . I4) || – I ‘9324 • 7706 Shingford . 15) —o-8478 || HAMPTON Poonhouse St. Ann's Hill . (34) | †.7%; Pºpping Cupola. (16) || 4-o-668o Ring's Arbour . §§ L.; Severndroog I7) +3°4135 Hajor Hiii Tr. (36) |-o'824 a D 2 396 PRINCIPAL TRIANGULATION, MISTERTON CARI. BASE. The connection of this base-line with three fixed points in the triangulation, Crowle, Clifton Beacon, and Lincoln Minster, is shown in Figure 23. The points to be fixed are Gringley and the extremities of the base- line. The station here named Crowle is not identical with the station of 1806, of which no trace could be found in 1842, the date of the selection of the present station. JEquations of Condition. 1. CB’G o = — I '8284 + (3) — (4) — (5) + (8) II. GB'S o = + 2 '8655 – (2) + (3) — (5) + (6) + (10) — (12) III. NB'G o = + 9°2523 — (1) + (3) — (5) + (7) + (14) — (15) IV. WB'S o = + 5°4855 — (1) + (2) — (10) + (11) – (13) + (14) v. L’: GCB' o = — 236-220 + 80° 5504 (3) + 30-2328 (4) — 43' 8473 (5) – II '9960 (8) + 55'8433 (9) VI, B' : SNG o = — 169' 185 + 9:47.06 (5) – 16: 9378 (6) + 7.4672 (7) – 13 'o613 (10) + 3'3060 (11) + 9-7553 (12) — 12 or 54 (13) + 6' 2.883 (14) + 5°7271 (15) The logarithmic values of the multipliers are as follow : * Iog 1 = o' 1583.086 + Log III = o' 2579842 – Log v = 8' 7200391 + II = o' 1512869 + IV = 9.782681.5 + . v1 = 9' 1805777 -- Ifesulting Corrections, From To symbol. 3. From To symbol. 3. f CLIFTON BEAcON | North End of Base (1) +3°482 5 || GRINGLEY BEAcox, Lincoln Minster . (9) || +2'2469 South End of Base (2) —6' 3974 | Gringley Beacon. (3) | +o'8954 | Soºn END of . Clifton Beacon . (10) || –1 .7512 BASE. North End of Base (11) | +2-2655 Gringley Beacon . (12) +o 1331 Choirle . . . Gringley Beacon . (4) +o'4861 GRINGLEY BEAcox | Clifton Beacon (5) —o'7334 || Wolſtii END of South End of Base (13) | –o. 7918 South End of Base § –9°oo73 BASE. Clifton Beacon I4) -o'4I4 I North End of IBaso 7) —4’ 1688 Gringley Beacon . (15) +2'8156 Crowle Beacon (8) | +o'6858 | RHUDDLAN MARSH BASE. The triangulation for connecting this base-line with the points Snowdon, Cyrn-y-Brain, and Delamere” is shown in Figure 24. Besides the extremitics of the base, the points Great Ormes Head, Gwaunysgaer, Garreg, Moclfre Issa, Llanelian, and Arrenig are to be fixed. The relative positions of the old and new stations at Delamore are given at page 16. There is some little doubt resting upon the re-finding of the exact centres of the old stations at Arrenig and Llanelian, and this circumstance must necessarily diminish the weight of the calcu- lated length of the base-line. * The fixation of this Sector Station will be found at page 405, CONNECTION OF SPECIAL POINTS, 397 IV. W, VI. VII, VIII. II. III, Equations of Condition. CD'GL o = -7°6136 – (2) + (3) + (6)–(9) — (14) + (16) RøſſW o = + 6'8669 — (19) + (20) — (24) + (26) — (32) + (33) I, WM o = + 6'5616 — (19) + (21) — (25) + (26) — (27) + (28) F WR o = + o'o.248 – (24) + (25) — (28) + (30) — (31) + (33) C. : D'S'G o = - 193°947 + 60°4897 (3) + 41°3003 (5) – 27°o415 (9) — 14'2588 (10) 4 : GCL o = – 98'936 + 17° 1817 (1) — 16'2414 (2) — o'9403 (3) — 36'5312 (4) + 20°2082 (6) + o'9403 (9) + 15' 3827 (Io) + 16° 5508 (II) — 3 '7613 (14) — 12" 7895 (16) J. : MC'G o = – 604’ I 53 + 124°4269 (6) – 102’6215 (7) – 21 ‘8054 (10) – 34°5855 (12) — 5o'oZI4 (14) + 2 Io'5186 (15) – 125'8617 (16) – 233° 5353 (17) + 112'3243 (18) + 121 °21 Io (22) 0 : MLI: o = — 173° 193 + 14° 1428 (12) – 46' 1351 (13) + 31 '992.3 (15) – 3'4333 (17) – 41 °6479 (18) + 45°o812 (20) – 28°7795 (32) + 28°7795 (34) IV: MOR o = — 1297°611 + Ioo' 1486 (18)-III '3413 (19) + 1 I 1927 (20)-193'5255 (23)+ 107-885.1 (24) + 85’ 6404 (26) + 52 '9804 (32) — 234' I 192 (33) + 181 1388 (34) L. : MIRGC, o = + 995'867 – 30'8920 (6) + 9°o866 (8) + 21 '8054 (10) + 90' 1718 (13) + 3' 1454 (14) – 219 1789 (15) + 125'8617 (16) + 165° 1722 (17) – 43'961.2 (20) — 121°211o (22) W: EMI: o = + 27°641 + o'9403 (19) – 11’ 1927 (20) + 10 2524 (21) + 24'9075 (27) – 37046 (28) – 21 2029 (30) + 46'7787 (31) — 52 '9804 (32) + 6' 2017 (33) M. : WEO o = - 102'353 – Io'6528 (18) + 85'6404 (19) — 74°9876 (21) + 77°6606 (23) + 5°3451 (25) — 83°oo57 (26) + 71°2472 (27) + 24'9075 (28) — 96' 1547 (29) The logarithmic values of the multipliers are as follow : Log I = 9-9.186648 + Log v = 7.7652387 -- Log IX = 7-8oi6327 -- II = 9'8749473 – VI = 8 of 36344 + X = 8' 3408568 — * III = 9° 5291529 - VII = 8*ogzo;61 — XI = 8.25oog68 + IV = 9'8522429 + VIII = 8'5043912 — XII = 6'5666154 + Resulting Corrections. From Calculated { Calculated To Symbol.] §. IFrom To Symbol] &. LLANELIAN. MoELFRE ISSA . CYRN-y-BRAIN. DELAMERE . . . GARnEG MoUNTAIN • Llanelian . . (17) — I 6643 #4 Arrenig . . . ( 3 +o 2574 || MoELFRE ISSA—cont. Gt. Ormes Head (18) + * 1798 Llanelian . . (2) —3 ‘8456 West End of Base (19) || --o'3241 Gwaunysgaer . (20) —o'6642 Garreg Mount". (3) | +2 of 56 East End of Base (21) —o. 5256 Cyrn-y-Brain . §: + I 3557 Arrenig . . . § —o'3624 * Snowdon . +o'4564 || WEST END OF BASE Gt. Ormes Head (23) | –2.3856 ) * 5 Llanelian . . (6) +o' 1281 Gwaunysgaer . (24) +o '92 II Gt. Ormes Head (7) || +2'22.98 East End of Base §§ +2-6876 Gwaunysgaer . (8) —o'o.239 Moclfre Issa . (26) | – I'6218 Delamore (9) — I '8607 Cyrn-y-Brain . . (Io) —o I 158 EAST END of BASE Moclfre Issa . (27) + 1 IIII West End of Base § --o' 2915 Arrenig. . . . (II) +o 6586 Gt. Ormes IIead (29) —o I262 Gt. Ormes Head 12) -o- or 68 Gwaunysgaer . (30) || +o' 8o37 Gwaunysgaer . § —5'2266 - Garreg Mount". (14) —6'4526 || Girau NysGAER . . . East End of Base (31) +o'50% Moelfre Issa . 15) -i-o-o/84 Moelfre Issa . (32) | +o’956: Cyrn-y-Brain . §§ —o'7091 west End of Basel (33) | -2 °379% g 34) + I 'o658 Gt. Ormes Head 398 PRINCIPAL TRIANGULATION. BELHELVIE BASE. The triangulation for the connection of this base-line with the already fixed points Inock, Mormonth, Little Stirling, Blue Hill, Mount Battock, and Dudwick is given in Figure 25. The points to be fixed with relation to these, are the extremities of the base, and Over Hill and Brimmond. VIII. XI. XII, XIII, XVI. XXI. XXII, B Q'M’ B Q'D' OBD’ TOB TOD" LOT J.B.T. J. D'T JD' : Q BM’ JK' : BM'Q' R" : BD'Q' Q' : OD'B R! : B O Q' O : I?’ B.D.’ M7: OBD’ O : TBD" R! : OTB R! : BTQ' S’ - O TD’ O : LD'T' O : TLB I?' : D’BL : O O O O O O O O O - O O = O F. O -: O E Jºquations of Condition. - 2' 3354 – (21) + (23) + (29) — (30) – 2 o203 – (21) + (24) + (29) – (33) — 1 5922 – (14) + (17) — (24) + (25) - (32) + (33) + o'8103 – (3) + (4) + (14) — (20) - (25) + (27) + o' 2971 — (4) + (5) – (17) + (20) — (31) + (32) — o'4056 – (4) + (6) — (9) + (11) – (19) + (20) + 1 : 1426 – (3) + (6) — (9) + (10) – (26) + (27) + 3'5664 – (5) + (6)–(9) + (12) + (31) - (34) – 247.283 + 39° 1804 (21) + 141 '7549 (23) – 180°9353 (24) - 95. + 85*4037 (30) 2818 (29) + 57 o'S5 + 1 .4653 (21) + 16' 6345 (22) — 18’ ogg8 (23) – 16' 2795 (29) – 6' 3921 (30) + 99-644 + o- 3464 (21) — II '7652 (24) + II '4188 (28) + 75' 1326 (29) + 80' 3070 (33) + 81-650 – 148' 5797 (14) + 12o'o695 (15) + 28' 51oz (17) — 73'8633 (21) – 39° 1804 (24) + 113° o437 (25) — 42° 2861 (32) + 74°4481 (33) - 54-401 – 6: 9738 (13) + 92: 3495 (14) — 85' 3757 (15) + 64-6122 (21) – 68' 5470 (25) + 3’9348 (28) + Io'8668 (29) – 908' 360 – 77. 9768 (13) + 23-6762 (14) + 171' 7322 (17) – 117.4316 (18) + 65'9659 (24) — 85.3609 (25) + 19' 3950 (28) — 273'30.92 (32) + 1 II 6674 (33) + 126.308 – 31. 1333 (14) — 18o 2022 (16) + 211' 3355 (17) + 98-8721 (23) – 141 '7549 (24) + 42.8828 (25) - Ioz' 3938 (32) + 51°3437 (33) — II '897 -- or 5633 (3) - 37° 7397 (4) + 37' 1764 (5) + 65'9659 (24) — Io9'0459 (25) + 43 o8oo (27) + 158' 2223 (31) – 269'8897 (32) + 111 6674 (33) – 151'350 + 41.9536 (1) - 16:4673 (3) — 25°4863 (4) — 66-6603 (13) + 28-0837 (14) + 38' 5766 (20) – 4:281.2 (25) - 5'4662 (27) + 9.7474 (28) + 450-446 + 8:7522 (1) - 122°0134 (2) + 113° 2612 (3) + 97° 1403 (21) – 91 3277 (27) – 5.8126 (28) — 21 6613 (29) — 45' 178 – 15' 1957 (4) + 45'8695 (5) – 30:6738 (7) – 43.7005 (17) + 32-8938 (18) + 10.8067 (20) – 6'8515 (31) + io'ogo4 (32) + 99; 330 – 15-2531 (4) + 37' 1764 (5) – 21.9233 (6) – 24: o359 (9) + 13 oz.55 (11) + 11 oro4 (12) + 158' 2223 (31) — 76-4505 (32) — 81.7718 (34) *. – 41.8°781 – o'5633 (3) + 22:4866 (4) — 21.9233 (6) – 24: o359 (9) + 88.2288 (10) — 64’ 1929 (11) – 152*2404 (25) + 195' 3204 (26) – 43 oboo (27) + 133'349 - 98.7183 (3) + 35'7819 (10) + 62.9364 (12) + 11.7652 (24) – 19683 (26) – 9:7969 (28) - 80' 3070 (33) – 114-4305 (34) The logarithmic values of the multipliers are as follow: Log 1 = 9'9921867 + II = 8-85040II + III E IV = V = v1 = 9.4474726 -- VII = 9'9774388 + Log VIII = o' 2037.114 — Ix = 8. 1880672 +, o'7343735 -- x = 8° 5203934 – 9° 2550312 – XI = 7' 6353852 + o'oZ24357 – XII = 8: 98.28544 – NIII = 9’ o822298 — XIV = 8. 2626347 -- XV = 8.4699649 — Log XVI = 8* 1952064 — XVII = 8' 5173020 + XVIII = 7' 6938.474 — XIX = 7' 91 15076 + xx = 8-1528886 + XXI = 7'9674738 + XXII = 7' 632.7530 – CONNECTION OF SPECIAL POINTS. 399 Resulting Corrections. IFrom To Symbol. §. From To Symbol. §. f/ #! TARBATHY . Blue Hill . . . (1) | +o. 626o | OrER HILL–cont. Layton . (19) —o'og31 Mount Battock. : +2' 3953 Tarbathy (20) || 4-o'70oo Brimmond . § —o' 31.56 Over Hill 4) +o 2145 || BRIMMOND . , Mount Battock. (21) — I 38o3 Dudwick { 5) +o '4518 I(nock (22 —I '7604 Layton . (6) —o' 3048 Mormonth . (23) | + I 514o Stirling . § –6' 9ooI Dudwick 24 —o 203 I Over Hill 25) +o ‘ I 195 LAYTON JBlue Hill : +o 1563 Layton . § + I '8779 Tarbathy 9 —o 3382 Tarbathy 2 ; —o' o23 I Brimmond . IO +o "4094. Blue IHill § +o I572 Ovor Hill I I —o: 2064. Dudwick ; — I 5416 || MoUNT BATTock IBrimmond . (29) || –o 2.293 Over IIILL Blue Hill 13) | – I 6679 MoRMONTH . Brimmond . (30) +o 3296 Brimmond . . . (14) —o'4978 Mount Battock. (15) —2-2019 | DUDIVIck . Tarbathy (31) —o. 6098 Mormonth . (16) +3. Io98 Over Hill (32) -o- 9,153 Dudwick (I7) +o 9289 Brimmond . (33 —I of 24 Stirling. (18) —4'434o Layton . (34) +o'9966 The triangulation for connecting this base-line with the work will be found in Figure 26. The points that SALISBURY PLAIN BASE. have to be fixed are the south end of the base, Old Sarum Castle, Four-mile Stone, and Old Lodge: these are connected with eight points already fixed. * I. II. VII. VIII. IX. X. XI. XII. A. GFN GLF J.FN JINF MNL MNG JHLN JILM JHFN JENF JEMF JEHL xIII. - DNF XIV. IXV. XVI. IXVII, XVIII. XIX. DND, CDL CDN" CEM JF : G LWT N : GMF. " i JEquations of Condition. o = -4° 5659 — (1) + (3) — (6) + (7) — (33) + (35) o = – 4'5034 + (1) — (4) — (7) + (8) — (19) + (23). o = – 2 2453 + (3) — (4) — (20) + (23) – (33) + (34) -: : = – 6 or 32 — (2) + (3) — (9) + (12) — (33) + (37) = — 7'o';12 – (9) + (14) — (18) + (20) - (34) + (37) – 2: o360 – (5) + (6) — (9) + (13) — (35) + (37) = — I 3763 – (16) + (20) — (27) + (28) — (34) + (36) — or 9189 – (14) + (15) – (16) + (18) — (26) + (28) — o'oj90 + (3) — (27) — (33) + (36) + 1 . 7207 – (3) — (31) + (33) + (45) — I'5514 – (2) — (10) + (12) + (44) — I 1934 – (16) + (22) + (28) — (43) — o'8053 — (3) — (30) + (33) + (42) = — o' 5029 – (20) + (21) — (30) + (34) – (41) + (42) + o'7411 – (21) + (24) — (39) + (41) — 1 - 1233 – (30) + (32) — (38) + (42) + 1 : 5208 — (10) + (II) — (40) + (44) + 19.438 – 1'4826 (6) + 27-3128 (7) — 25'83oz (8) — 8-2595 (19) + I – 7:5826 (23) – 27.7686 (33) + 35-4188 (34) – 7' 6502 (35) o = - 11 o46 + 47.3029 (1) — 50-8765 (2) + 3'5736 (3) + 11 9574 + I'4826 (7) + 12'3456 (9) — 3' 1670 (12) — 9' 1786 (13) 5.8421 (20) G) – 13.44% (6) PRINCIPAL TRIANGULATION. I': MNL XXI. N : LFII xxII. M. : LFIT y- A. J& : : LFH LNET YXIII. 2xxIV, xxv. F : NEMſ F J. : MEFI : NEIT XXVI. XXVII. XXVIII. XXIX. NXX. XXXI. XXXII. XXXIII, : END : LD II : FCN : FC MI : LCHſ : DLC o = + 27′487 + 3' 1670 (9) – 30:6904 (12) + 27: 5234 (14) + 8: 1507 (18) — 15'8421 (20) + 7°6914 (23) + 3o 1965 (33) — 35-4188 (34) + 5.2223 (37) o = + 6-oA7 - Io' 62oo (3) + 2 - 2976 (4) — 3’ 1852 (16) + 19 oz73 (20) — 15'8421 (23) – 12 or 3o (27) – 13’5438 (28) o = - I '898 – 14:2289 (2) – 6: 1389 (4) — 9'55.05 (16) + 17:7012 (18) — 8: 1507 (23) — II 4825 (26) – 12.81.23 (28) ºmº * tºº sºmº — 26'4032 (29) + 32 2428 (34) – 5'8396 (36) = + 5°2223 (37) – 44' 3032 (44) + 4o '7227 (45) =: + 24*7208 (43) + 52 'o624 (45) O O = + 45'551 + 1 .7052 (4) – 11 6424 (16) + 17'9274 (17) – 6.2850 (23) + 3'9796 (28) + 162'935 – 11:6424 (16) + 68°4474 (17) - 56-8050 (20) + 22:2231 (27) + 3.9796 (28) + 39' 392 + 3' 1670 (9) – 6'8276 (10) + 3' 6606 (12) — o'9544 (31) – 4:2679 (33) + 32: 349 + 6'8276 (10) – 5’ 6744 (12) — I 1532 (15) + 24' 2948 (26) + 44' 3032 (44) + 79-797 -- 13’5438 (27) + 5’ or 12 (28) — 13 8440 (31) - Io'o'777 (34) + 23 '92.17 (36) + 26°492 + 4'3268 (29) – 4:3931 (30) + o'o663 (31) – 19° 3664 (42) + 20'3015 (45) + 65' 330 – 11 6424 (16) + 29'8065 (17) – 18 1641 (21) + 3 '9796 (28) — Io'4597 (41) o = + 1 . 922 – 12 - 1246 (3) — 25° 2167 (31) + 24'2623 (32) + o-'9544 (33) + 16' 9555 (38) o = + 30' 170 – 2 7545 (2) – 2 I '8287 (10) + 28: 6563 (11) – 6'8276 (12) + 13:2990 (40) o = + 5°205 + 7° 7785 (16) + 17' 2367 (21) — 25 or 52 (24) — 14. 7235 (28) — I 5972 (39) o = - I 3 '834 + 2 org4 (21) + 14' 5298 (24) — 16° 5492 (25) + 13:8698 (39) — 30 '8693 (41) The logarithmic values of the multipliers are as follow : Log I = I 1487492 + Log XII = o' 5700743 + Log XXIII = o' os'73730 — II = o' 7389172 + xIII = o' 581 II 30 + XXIV = 9° 24′oIoII + III = o '9214591 + xiv = 9 7969399 + XXV = 9°4525308 — IV = o'7388908 + xv = 9'47.91740 – NXVI = 9'489.1452 — y = o' 3201681 — xv.1 = 9 9653536 — XXVII = 9 'o621382 + VI = o' 4899.136 + xvii = o' 756762 I — XXVIII = 9: 2432695 + VII = o' 79142 12 + xviii = 8'5855937 – XXIX = 8-89265 Io — VIII = o' 2554530 + xx = 9°3038867 + xxx = 8*o836523 + IX = I I 1972 I4 — xx = 9'4042583 + XXXI = 8* 9263.399 — X = o' Iozo 325 — XXI = o' of 37402 + XXXII = 8'383361 I – XI = o' 8295361 + XXII = 9 79 12589 — XXXIII = 8° 3293730 + Ifesulting Corrections. IFrom To Symbol. $. From To sº galalaga Cl10n. *-* *--- : Correction. f / : : di Beacox AEIILL , | Old Sarum Gun () +o-o;17 | Old Sanvy Castle | Beacon Hill (12) +o’8947 Old Sarum Castle (2) —o. 82.56 (continued.) Sarum Gun (13) | +2' or 73 Tour-mile Stone (3) | +o. 1558 Old Lodge . (14) +o '88oo Old Lodge . . . (4) —2:4124 Dean IIill . (15) +1-2727 | OLD Sanvaſ Gwy. Sarum Qastle . . (5) —o-o816 | Old Lodge Dean IIill . 16) +o' 3796 º Four-mile Stone (6) —I 2689 Wingreen . . º *:::::: Beacon Hill (7) || +o. 32.18 Sarum Castle . (18) –o '9646 Old Lodge . (8) | + 1 . 1703 Sarum Gun . § —or 4642 tº Four-mile Stone (20) + 1 - 1887 Ozo Sanvaſ CASTLE | Four-mile, Stone (9) | –2.3624 Westbury Down (21 + o' 3851 Stoke Hill . (Io) +o 1.48% Stoke IIill . . (22) +o'34oo Milk Hill . (II) | –o 9789 Beacon Hill . (23 +o. 7266 CONNECTION OF SPECIAL POINTs. 4OI Ičesulting Corrections—continued. From To symbol. $. From To symbol 3. J/ --o Ioz6 —o Ioz6 Milk Hill Inkpen . OLD LoDGE—cont. DELN HILL . . . Sarum Castle Four-mile Stone Old Lodge . ( ( { — 1 'o672 MILK IIILL - ( Wingreen . . { ( : ( ) ) ) ) —o' 1774 ) ) ) +o '8o32 34) —o'64oo Old Lodge . ‘(35) || +2 °og2O Sarum Gun Foun-MILE STONE . (continued.) Four-yſILE STONE . 29) —2 2853 || WESTBURY Don'N . Westbury Down (30) || – I 6408 Stoke Hill . 3I) | –o 29.13 Milk IIill * ; —o' 41.47 | STORE EIILL JBeacon Hill 33 —o '779 I Dean Hill . . . (36) —#9533 Sarum Castle . (37) || --o'9956 Four-mile Stone (38) +o 2021 Old Lodge . . . (39) | +o 2524 Sarum Castle . (40) +o' 373 I Old Lodge . . § —o: 2062 Four-mile Stone (42 +o’ ogg4 Old Lodge . . (43) | –o'4298 Sarum Castle . § -:::::: Four-mile Stone (45) — I'oz72 SouTHAMPTON SECTOR STATION. In Figure 27 will be found the triangulation for connecting the Station at Southampton and Nodes Beacon in the Isle of Wight with Dunnose, Blackdown, Coringdon, Swyre Barrow, and other points to the north already fixed. The trigonometrical station at Southampton is Io.8 feet distant from the point over which Airy's Zenith-Sector was placed, and bearing Io9' 53' from the south, Equations of Condition. I. PPAD' = — 2-8745 — (1) — (13) + (14) + (22) II. HI’NA’ = — I '9338 — (1) — (11) + (14) + (2 I) III. H'NB = + 1 1817 — (1) — (Io) + (14) + (20) IV. II"NC" = — 4, 1867 — (1) — (9) + (14) + (18) v. II’NE” = + 3 5068 + ( I ) — (5) + (8) — (14) VI. IPNG! VII. IPNI." VIII. NOB' IX. NO II’ X. II’: B’ND’ XI. B’: IPNA' xII. N. : B'C' H' XIII. N : II'G'C' XIV. N. : IPFC XV. N. : FIPE" XVI. O : NB'II' + o' 3907 -i- (1) — (3) + (7) — (14) + or 2591 + ( I ) — (4) + (6) — (14) = . + 4o 1532 (19) + 22 '962 I (20) * The logarithmic values of the multipliers are as follow: Log I = 9.6655159 + Log vi = o'3642156 + II = 9°oy29042 — VII = 9°7705224 – III = o' 1871984 – VIII = 8* 1755 156 — IV = o' 31 19478 +. IX = 8*7059959 + y = o' 1372274 – xi = 7.8064977 – X = 7-88.1270.5 + . + 5'6692 – (10) + (12) — (15) + (16) - (19) + (20) – 4: 5398 — (1) + (2 ) — (12) + (14) + (15) – (17) + — 95'915 + 9°o871 (10) + I5'4088 (13) - 24°4959 (14) – 47' 1343 (20) + 39'7747 (22) + 142.910 + 22 '9091 (1) + 88°oo70 (Io) – 78'9199 (11) – 9: o371 (14) — 72° 5905 (21) + 17o 22 I – 34°4336 (1) — I 12 - 1703 (18) + 46' 3174 (20) - + 233.628 – 165'7842 (1) — 138°7887 (3) — 157.8349 (18) — I 11'555 – 144' 5296 (I) – 144°9775 (4) — I48'9335 (18) + 153.798 – 70'8826 (1) + 98-3132 (4) — 372 '7796 (5) – 48-575 -- 15'4743 (1) + 91 ‘8374 (2) + 35'8519 (10) - 38°4673 (12) + 2-6154 (14) Log xu = 8:4188703 + XIII = 8. 2726883 – xty = 7-97.16727 4- xv = 7.630.1458+. xvi = 7.7409708 + 3 E 4O2 PRINCIPAL TRLANGULATION. Resulting Corrections. T Symbol, Qalculated Calculated | From O * Correction. From To Symbol: 3. DUNNOSE . Nodes Beacon . ( 3 –6. 1889 MoDES BEAcON-cont. Butser Hill. 13 —& 3I29 Southampton (2) +o’ 1755 Dunnose I4) +o '8155 | Coring DON . Nodes Beacon . (3) | +o'5975 | SouTHAMPTON . Nodes Beacon . . . (15) | +2'4890 # Dean Hill . 16) —o. 6091 SiyynE BARROW Nodes Beacon . (4) — I '7658 | Dunnose 17) —o. 6132 Black Doirs. Nodes Beacon . (5) –o' or 72 WINGREEN . . . Nodes Beacon . . (18) +1. 1532 MoDES BEACON Swyre Barrow. 6) I — I o206 || DEAN HILL . Southampton . § +o 1274 Coringdon . . 7) + I 2 II2 Nodes Beacon . (20) || – I o228 IBlack Down . 8) —2 51.96 Wingreen . . 9) || –2 o292 || INKPEN . , Nodes Beacon . (21) +2 o256 Dean Hill . . . (Io) || + I 1633 Inkpen . . . 11) | + 1 - og 62 | BuTSER HILL . Nodes Beacon . (22) + 1 5572 Southampton . I2) | –o 2577 ISLE of WIGIIT SECTOR STATIONS. The four Zenith-Sector Stations in the Isle of Wight are Dunnose, Week Down, Boniface Down, and Port Valley, which latter is a point 263 feet distant from High Port Cliff, in a line between it and Boniface Down South-east Station. The points Shanklin Down, Wroxall, Littletown Down, and Boniface Down South-east Station, serve to establish the connection, which is shown in Figure 28. Equations of Condition. I, DA'B' o = + o' 1107 + (1) — (4) - (9) + (11) II. DFB' o = — or 3205 – (2) + (4) - (II) + (12) - (21) + (25) III. CB'F o = + 6' 1973 – (2) + (5) – (7) + (8) — (24) + (25) IV. CB'D o = — or 3236 — (4) + (5) + (6) - (7) — (10) + (11) V. EB'F o = – 2:3424 – (2) + (3) - (16) + (17) — (22) + (25) VI. DGIF o = – 48-3409 – (12) + (13) + (21) - (26) — (28) + (31) VII. EGF o = – 24-6503 – (17) + (18) + (22) — (26) – (29) + (31) VIII. HGD o = + o-8488 - (13) + (14) - (27) + (28) — (33) + (35) Ix, HGF o = – 42-98oo + (20) - (26) – (27) + (31) — (34) + (35) x. III.G o = - 35' 6206 + (27) - (32) - (35) + (36) – (37) + (38) - xi. B' DFA' o = - 1349'567 - 17°5700 (1) + 319'5749 (2) + 11.7741 (9) + 28.3884 (11) – 40: 1625 (12) + 6'5023 (21) + 324'3476 (23) – 330-8499 (25) xm. B : DFC o = - 694.875 + 18, 1673 (6) – 24-7280 (7) + 6. 5607 (8) — 152.5544 (10) + 192.7169 (11) — 4o' 1625 (12) + 6'5023 (21) + 55'4766 (24) – 61 ° 9789 (25) xIII. C.; FB'E o = + 282 '900 – I 2785 (2) + 7.8o32 (3) — 6'5247 (5) – 56' 1162 (15) + 61' 1924 (16) * - 5'9762 (17) - I'8799 (22) + 57.3565 (24) — 55'4766 (25) xry. D : FA'G o = + 377°806 – 28' 5552 (9) — 378- 1601 (12) + 406'7153 (13) + 406'3232 (21) – 414-7268 (23) + 8’4036 (26) – 438-3480 (28) + 448- 1660 (30) – 9.818o (31) xv. F: GECD o = + 2151'766 - 13'1078 (6) + 13'1078 (8) — 29°4922 (10) + 4oz'8037 (12)–373.3115 (13) + 67°4359 (15) – *59'5944 (17) + 92'o685 (18) + 62'3597 (22) – 62.3597 (24) – 9'8180 (28) + 15:3688 (29) – 5-5508 (31) CONNECTION OF SPECIAL POINTS. 4C3 XVI. F: HGD o = - 1470°573 – 224, 1672 (12) + 373. 31.15 (13) – 149' 1443 (14) + 2*4680 (27) + 9'8180 (28) — 12'2860 (31) + 12:8278 (33) + 38-8799 (34) — 51-7077 (35) XVII. F : HGE o = - 250-397 – 68-7506 (17) + 92'o685 (18) — 23.3179 (19) + 3' oo;1 (20) – 3'oo31 (22) + 2 °4680 (27) + 15:3688 (29) – 17: 8368 (31) + 51 '7077 (34) — 51 ‘7077 (35) The logarithmic values of the multipliers are as follow : Log I = 9'7478919 + Log VII = 9'6302700 – Log XIII = 8.1545226 – II = o' 261 1427 -- v111 = o' or 89.828 + XIV = 6' 98.55190 — III = o'o.800907 — Ix = 9'66or 518 + XV = 5' 60IoI64 + IV = 9'814ool 2 + X = o' II.42 154 + XVI = 7' 5705988 + V = 9°4175 or 4 — XI = 7. 2841 168 + XVII = 7-8327489 + VI = o' 3644958 + xII = 7. 1206394 + Resulting Corrections. r From To Symbol. §. From To . Symbol. 3. Nodes Beacon . Week Down . (1) + *20 33 || Boxiface Doryn , Littletown.Town (20 +4.6860 Week Down . (2I +2' 1265 DUNNOSE . . . . Boniface Down. 2) +o '92 I2 - Wroxall Down 22) —o' 5526 - Wroxall Down 3) | –2 6523 Nodes Beacon . (23) +7°4302 Week Down . 4) + I 6406 Shanklin Down (24) +4.768o Shanklin Down 5) —2 '7956 || Dunnose . . . . . (25) +3°7729 Doniface S.E. . . (26) |–14:318o SIIANKLIN DoſyN , | Week Down . . (6) + 1 2636 Dunnose . . . (7) +o 1612 | Box1FACESouTII-EAST Littletown.Town (27) — I ‘os36 IBoniface Down (8) | – I 3242 STATION. . Weck Down . (28) —o. 5361 Wroxall Down 29) |+ 17' 1924. WEEK Dorn . . . Nodes Beacon . (9) — I'4285 - Nodes Beacon . (30) — I '8388 Shanklin Down (Io) || –4° 7593 Boniface Down. (31) +24' 3836 Dunnose . . ; (II) – I IoI9 High Port Cliff. (32) |–12 - 7821 | Boniface Down I2. +3* I.472 -- - * Doniface S.E. . . (13 +3.8295 || LITTLETown Don'N Weck Down . (33) —o'9876 Littletown Down (14) +2 '8044 Boniface Down 34) | +o I324. gº *. Boniface S.E... (35) — I 3288 WnoxALL. Dorn , | Shanklin Down (15) +3°4034 High Port Cliff. (36) +13.9381 Dunnose . . . (16) —2'59.13 * Boniface Down 17) — I ooog | Higir Pont CLIFF . . Littletown Down (37) —6' 1837 | Boniface S.E. . . (18) +2' 6928 Boniface S.E. . . (38) +2'4415 Littletown Down (19) —o'6719 FEAGHMAAN SECTOR STATION. The triangulation for the connection of this point with the general triangulation will be found in Figure 29. Besides the sector station, the points Brandon, Knocknadober, and Knocknagante, which establish the con- nection, are to be fixed with reference to Bencorr, Keeper, Taur, Caherbarnagh, and Hungry Hill. Equations of Condition. I. C. F. K. o = - I ‘4391 – (4) + (8) — (17) + (19) II. C. HK ° = + 8, 1817 – (8) + (10) — (16) + (17) — (24) + (25) III. LC'F' ° = - 7: 1742 – (6) + (7) — (13) + (14) 4O4. PRINCIPAL TRIANGULATION. IV. VII, XIII, L C K . O = GC'I, O E GKL O = C : A'B'DT'Ho = C. : FIID' O = C. : HE D' O = II : F. KC’ O E I. : C KF' O = II : J. C. G. O = JK : LGITC’ O = – 4: o360 – (7) + (8) — (12) + (13) — (17) + (18) – 3:8048 – (7) + (9) — (11) + (13) — (21) + (23) – 18°4752 – (11) + (12) + (15) – (18) — (22) + (23) + 96°605 + 105 oSoz (1) + 59' 5653 (5) – 16-3272 (10) - 796'762 – 298'5307 (2) + 59' 5653 (5) + 97'o640 (10) + 736'846 + 298: 5307 (2) + 477-9250 (3) — 290.8889 (10) - 122°857 - 116°oč33 (4) — 161 61oo (5) – 16:8556 (8) + zo. 1323 (10) + 56-3207 (16) - 14° 1594 (17) — 42° 1613 (19) + 293:867 – 82°o215 (4) + 137°7556 (6) + 114' 3530 (7) – 32.2475 (8) – 4:0585 (17) + 67.7502 (18) — 63-6917 (19) - – 386-063 — 16:8556 (8) + 19 ogog (9) — 2' 1953 (10) + 8:6014 (15) + 5° 5580 (16) – 14: 1594 (17) – 6'8451 (20) + 27° 1517 (21) — 20° 3066 (22) + 1 196'363 + 32° 2475 (7) — 49' 1031 (8) + 16-8556 (Io) + 4o'7761 (II) – 49' 3825 (12) + 8'6064 (13) + 52 '7960 (15) — 52 '7960 (16) + 73° 1026 (20) – 98' 1280 (22) + 25' o254 (23) + 6' 5977 (24) – 6'5977 (25) The logarithmic values of the multipliers are as follow : CAIIERBARNAGII . Brandon . . . (2) -2 °4204 TAUIt . . . . . Brandon . . (3) | + o' 1466 Drandon . . I6 +o'7062 Baurtregaum 17) —3'8oo5 Hungry IIILL . ICnocknadober . § +o'4769 Inocknagante . . (18) —2 7960 | T}randon . . . (5) + o' 773 I Hungry Hill . . (19) —2'42.05 : Inocknagante . . (6) -o' 2573 - FEAGIIMAAN . Drandon . . . (20) — Io' 7509 JBAURTREGAUM . Inocknagante . . (7) || – I 5931 Daurtregaum . (21) +9° 7576 Inocknadober . (8) +o 5360 ICnocknadober . §: —o' 5748 Feaghmaan . . . . (9) | – I '7127 ICnocknaganto . (23) | +o'og3o Brandon . . . (Io +o 2899 BRANDON . . . . Baurtregaum . (24) + 1 3482 KNOcKNAGANTE Feaghmaºn . . . (11) – 11.8933 IXnocknadober . § 5 —2 o807 Inocknadober . (12 +o' 7434 Log 1 = 9'6812744 – Log v = o' oo78131 — Log X = 6' 64492.29 – II = 9°2907549 – * VI = o'oZ92531 + XI = 7'7249087 — III = 9.408or 46 + v11 = 7.7063062 — : XII = 8: 513o445 – Iv = o' 1332.116 + v111 = 7: 94.17825 + XIII = 7° 7374582 – Ix = 5'8854839 + I?esulting Corrections. From tº sºlº ºn To symbol. 3. BENconn . . . . Brandon . . . (1) —#312 5 KNocRNAGANTE, cont. Baurtregaum . (13) +* 6958 Hungry Hill . (14) |+10:2658 RNOCKNADoDER . | Feaghmaan. . . (15) +2' 3747 CONNECTION OF SPECIAL POINTS. 4O5 DELAMERE SECTOR STATION, The point Delamere is fixed by its relations with Whittle Hill, Holme Moss, Mowcopt, and Cyrn-y- Brain, shown in Figure 30. The old station of Delamere, over which Ramsden's Zenith-Sector was placed, is calculated by the method given at page 69 to have been 3-7 feet distant, and bearing 201° from the present station. sº Equations of Condition. I. C.’ DMI’ o = + o'946o + (1) — (4) + (5) — (7) II. PV’DM’ o = — o' 5723 — (2) + (4) — (5) + (6) re - III. C.’ : D W’M7 o = + 26, 140 – 54-2793 (1) + 37'955o (2) + 16-3243 (4) — 39' 6697 (5) – 101.9365 (6) Iv. II : D W’M’ o = — 214-648 + 41 ° 2902 (2) — 56.4688 (3) + 15 1786 (4) — I 4771 (5) – o 1330 (6) The logarithmic values of the multipliers are as follow : Log 1 = 9 'ogoş823 - Log II = 9'46.271.76 — Log IV = 8'4532300 + III = 7' 5892 119 — Resulting Corrections. Calculated I'rom To Symbol. Calculated Correction Correction. From To Symbol. DELAMERE . . Cyrn-y-Brain {} § +3°o;34 | Morcorr . . . . Délamore . . (5) +30623 Whittle Hill . 2. o' oozó i , , - H.M. º § *:::::: P’HITTLE IIILL . Delamere . . . (6) +o 3154 Mowcopt “ . . (4) +o'4127 | CYRN-y-Bitary . Delamere . . . (7) | +o. 6289 TAWNAGIIMORE SECTor STATION. The connection of this station, together with Slieve More in Achill and Rnockalongy, is shown in IFigure 31. The points already fixed are Slieve League, Cuilcagh, Nephin, and Bencorr, - Equations of Condition. I. LKI o = + 7°2449 + (5) — (7) — (12) + (14) - II. MLI o = – 3 ‘8552 – (6) + (7) — (14) — (15) + (16) III. M.III o = — 8°4733 + (6) — (9) — (16) + (17) IV, ILP o = + o-3053 – (7) + (8) — (13) + (14) — (18) + (19) W. PLK o = + Io' 5268 – (3) + (5) — (12) + (13) — (19) + (20) VI. PKO’ o = – 6' 1889 — (1) + (3) — (zo) + (21) vii. L. : O'KI o = — 117' 52 + 99'5073 (2) — 52° 2846 (5) – 18 9328 (7) * VIII. I : HMLKO'C o = + 296'742 + 46'4689 (5) + 22 1679 (9) + 7'8985 (II) – 3'3945 (12) — 4' 5040 (14) sº + 2.0-42.5o (15) – 26" 7772 (16) + 6’ 3522 (17) IX. Aſ : KIL o = — 457-424 – 333-0297 (4) + 275' 1799 (5) + 22’6879 (6) – 9.9567 (7) + i 12°2873 (11) - — Ioa. 3888 (12) — 7'8985 (14) * X. I : PKO’ o = — 87-910 – 111-9432 (1) – 40'3273 (3) — 56-4753 (18) + 12'3876 (20) +44'0877 (**) xI. P : LIK o = + 189'480 – 23-8447 (3) — 16:4826 (5) – o'5770 (7) – 33 1687 (8) – 20°2765 (**) + 36: o375 (13) — 15'82 Io (14) + 390-145 – 53-7198 (8) + 22, 1679 (9) + 132-4011 (10) + 7.8985 (11) + 15.8°(3) — 23.7195 (14) + 20:42.5o (15) – 26.7772 (16) + 6:3522 (17) – 26°4784 (*) + 26’4784 (19) g xII, I ; HMLP O – 406 PRINCIPAL TRIANGULATION, The logarithmic values of the multipliers are as follow: Log 1 = o'8166955 + II = o' 3720919 + III = o' 3425474 + Iv = o'7ooI880 – Log v = o' 6667926 – VI = o' 6126070 — VII = 7°2344059 — VIII = 9' 1318820 — IResulting Corrections. Log Ix = 7'2996482 + x = 8'9464007 -- XI = 9°2677854 – XII = 7'3198985 — - Calculated - From To Symbol. č. From To Symbol, $. CUILCAGII . . I(nockalongy I –3. 5282 || BENCORR-cont. Knockalongy (Io), — 1" 3630 * Tawnaghmore . 2) — I '8539 º ſº * Tarnaginone . Slieve. More in : | SLIEVE LEAGUE . . Inockalongy (3) + 5°8432 Achill . § 1) +3'o685 Slieve More in Slieve League . . (I2) + I 4294 Achill (4) —5'8126 Inockalongy § – I '993 I Tawnaghmore . . (5) -6°or 55 Nephin . 14) +o'8613 NEPIIIN . . Slievo Moro in SLIEVE MoRE IN | Tawnaghmore . (15) —o' 3724 Achill 6) –o 31.75 AcIIILL. Nephin . . 16) +o. 2768 Tawnaghmore . 7 †: Bencorr . . . (17) +6'4220 ICnockalongy . *) | ***3* || Kroczaroway . . Nephin . * § +o '4554 : * Tawnaghmore . . (19) || –3°oj90 JBENCORR . . . slºº II]. (9) —2'6456 Slieve League . (zo) || +1-6754 ſº tº 9 Cuilcagh 21) — I 5070 GREAT STIRLING SECTOR STATION. The fixation of this point is shown in Figure 32. The Reform Monument, though not observed from, affords two Equations of Condition. Wo Lq. Equations of Condition. I. M'L'P o = – 14:2612 — (1) + (3) - (9) + (10) II. L'FS O = - 1.6486 – (3) + (5) - (6) + (8) + (9) — (11) m. L. : PSRM' o = + 252.311 + 77: 1848 (1) - 119°8638 (2) + 39:9464 (4) — 51.7746 (5) + 54.59.13 (6) — 47.6097 (7) – 6'9816 (8) - 80°3874 (9) – 9'8101 (10) + 90' 1975 (11) iv. It : PSL'M' o = + 282-338 + 194'6150 (I) - 32°3970 (2) – 30-5347 (4) + 13-8407 (5) – 4: 1649 (6) — 163’5483 (7) + 167'7132 (8) - II 2030 (10) + 118: 1442 (11) – 106.9412 (12) The logarithmic values of the multipliers are as follow : Log II = 8'9688224 + III = 6'7896507 + Log 1 = 9' 1060989 + Log IV = 6'36485 12 — IResulting Corrections. From To Symbol. 3. From To Symbol. 3. | MoRMONTH Peter Head W. M. (1) || –é.o 508 Sector STATION.— | Reform Monum! 7) | +& 3675 Reform Monumt 2 +o'ool 3 (continued.) IPeter Head W. M. (8 + I 74.44. Lirrte STIRLING . . Peter Hººd W. M. (3) | +2.7253 | Peter Head Wind- Little Stirling . (9) —2.2698 IReform Monum: 4. +o'9695 MILL, Mormonth . . . (Io +9° 2153 Sector Station . 5) +o "414o Sector Station . (11) –2. 3326 tº * . *- Reform Monum (12) | + 1 of 58 Sector STATION . . Little Stirling . . (6) —2° 1527 | CONNECTION OF SPECIAL POINTS. 407 GERTH OF SCAw SECTOR STATION. The connection of this point by means of Nive Hill to Saxavord and Balta is shown in Figure 33. Dguations of Condition. I. B’NS' o = - 8'3169 + (1) — (4) — (5) + (6) II. S'B' G. o = + 2 I 1177 + (2) — (3) — (8) + (10) III. S.NG o = + 19.2024 – (3) + (4) — (6) + (7) — (9) + (10) f IV. S. : WB'G o = – 534'705 + 56°ošzo (I) – 43.6463 (2) — 25'4248 (5) + 9:82.16 (6) + 15-6032 (7) + 4’3343 (8) — I'ogo.3 (9) – 3:2440 (Io) The logarithmic values of the multipliers are as follow : Log I = 7'99.17438 - Log II = 8*8154413 – Log IV = 7°495.5424 + III = 8'8318146 – Resulting Corrections. From To symbol. 3. | From To symbol. 3. BALT4 . . . . . Nive Hill . . (I +3. 505 I | Nu E HILL–cont. | Saxavord . . § +4.7737 Gerth of Scaw. (2) —7'2309 Gerth of Scaw . 7) —o. 6265 SAxayond . . . ] Gerth of Scaw. § +6° 5262 || GERTII of Scary . Balta . . . § +1-6262 Niyo Hill 4) — I 5538 Nive Hill 9) + I '9877 Saxavord . . . (Io) -5°7344 Nrre HILL . . . Balta. . . . . (5) | – I 4843 GREENWICH ToyAL OBSERVATORY. The Transit is fixed by observations from Epping Cupola, Chingford, and Severndroog. From the latter point the Dome was taken, but the plan of the building affords the means of calculating the angle subtended by the Dome and Transit at Severndroog; thus the observation is reduced to the Transit. IPutting (1)(2)(3) for the corrections upon the three observed bearings, the Equation of Condition is— o = 44' 572 + 126' 1686 (1) — 86-7897 (2) — 7'o'837 (3) Whence there results— * * | Calculated From To Correction. &M DPPING . . . . . Greenwich . . . —o. 2257 CHINGFORD . . . 3) . . . --o' 1833 SEVERNDRoog 27 . . . --o'o.267 408 PRINCIPAL TRIANGULATION. EDINBURGII Roy AL ODSERVATORY AND RELLIE LAW SECTOR STATION. The connection of these points is shown in Figure 35. The trigonometrical station” on Calton Hill, selected and observed from by Major-General Colby, is 6.85 feet distant from the centre of the Altitude and Azimuth Instrument or of the Dome with the bearing 27° 27'. The Zenith-Sector Station on Kellic Law was 201.1 feet from the trigonometrical station, bearing 302°53'. The fixation of these points involves that of Last Lomond; and in order to diminish the labour, this latter point being well observed from cight points, and observing them reciprocally, was first fixed independently of its connection with Calton Hill and Kellie Law. The equations and resulting corrections for the station East Lomond are as follow : Bºuations of Condition. 1. DLK, o = + 7.7463 – (7) + (8) + (15) – (16) II, DCK7 o = + 2.9042 + (1) — (7) — (9) + (15) III. D.B.E." o = + 1 2148 – (2) + (3) + (10) — (II) IV. D.C.E" o = + 4'4970 — (1) + (3) + (9) — (11) v. DCC’ o = + 2 '9093 — (1) + (4) + (9) — (12) VI, DC B' o = + 1 3886 – (4) + (5) + (12) — (13) VII. DI’B' o = — 4°ojo8 - (5) + (6) + (13) — (14) vim. B : K.D.L. o = - 146'679 – 15 '2690 (2) + 14-7352 (7) + o'5338 (8) – 31 of 39 (15) + 17° 3759 (16) Ix, C : K'DL' o = – 240°876 – 14' 3095 (1) + 11 - 1506 (7) + 3' 1589 (8) — 49' 6088 (15) + 42.8057 (16) x. C : EDB o = + 649 250 + 143-7954 (1) — 169' 4997 (2) + 25'7043 (3) - 264. 1193 (10) + 41 '8914 (11) xi. C. : CDE' o = — 189: 727 - 26-8082 (1) – 25.7043 (3) - I Io39 (4) – 41 ‘8914 (II) +44'2920 (12) xir, D : K.CB' o = – 60’945 – 48,4158 (9) — 121 '994I (13) - 78°9163 (15) xum. D : I'K'B' o = + 38'907 -i- 21 '9845 (13) – 44'238o (14) + 38'8947 (15) The logarithmic values of the multipliers are as follow : Log I = o' 2004674 + Log v = o' 3639746 – Log x = 9' 1666089 — II = I 5853962 + VI = 9' 4995 I94 – XI = 8* 7652974 – III = I 5519484 – tº VII = 9° 4461661 + xII = 8*625oz.52 — VIII = o' 594.8687 -- Ix = o' I 50I 222 — Iy = 1 - 5628928 + XIII = 8° 36992.61 + I?esulting Corrections. From To symbol. 3. | From To symbol 3. JºAST LOMOND . Ben Cleugh (1) | +o. 9711 || BEN LAirens . East Lomond (II) || – #. 6184. I3en Lomond (2) | +o'4215 - IBen Lawers (3 -4'4394 || GLASIIMEAI. 33 33 (12) -o'4533 Glashmeal . . (4 — I 6866 Mount Battock. (5) —o. 9080 || MoUNT BATTock 39 33 (13) | + 1 .7139 Lumsden § + o' 5319 r Sayrs Law . (7) || + I 5999 || J.U.MSDEN . 3y 33 (14) —o'897o Dunrich. (8) — I or 80 g SArms LAir 35 32 (15) –2 98.93 BEN CLEUGII . Last Lomond (9) —o'7049 : ºr DUNIticii 3? 33 (16) +2' 1481 BEN LoMOND . East Lomond (Io) +2 o276 * Astronomical Observations made at the Royal Observatory, Edinburgh, 1835. CONNECTION OF SPECIAL POINTs. 409 East Lomond being thus fixed, we have for the fixation of Kellic Law and the Observatory on Calton Hill the following— - Equations of Condition. I, EDI’ o = + o' or 52 + (2) — (5) – (16) + (20) II. EDK' o = - o'6466 + (2) — (6)– (16) + (21). III. EDC' o = -4°5696 – (2) + (3) + (16) – (18) IV. EDB’ o = + o-6085 – (2) + (4) + (16) — (19) * V. FCL o = - o' Io24 – (7) + (9) + (13) — (15) VI. FCB o = - 5'6433 – (8) + (9) + (14) — (15). VII. FCD o = – o 'o';33 – (9) + (11) + (15) – (17) VIII. FED o = + 4* Io42 — (1) + (2) — (11) + (12) — (16) + (17) - Ix, P : EIB o = – 319. 111 + 20-2577 (2) – 1 'o687 (4) — 19:1890 (5) + 61:2850 (19) + 73.4896 (26) x. D : PEK: o = + 166'745 – 16:3905 (2) + 19. 1890 (5) – 27985 (6) – 73.4896 (20) + 37-8999 (21) xi. D : BCE o = + 210-528 – 11 3470 (2) + Io-2783 (3) + 1-oë87 (4) + 56.9.186 (18) — 61.285o (19) xii. C. : J/FB o = - 55' 315 + 14'8885 (7) + 62-5075 (8) — 77° 3960 (9) — 39' 5247 (13) + 76-4695 (14) xiii. C : FBPP o = - 90°676 + 62-5975 (8) – 79.9131 (9) + 17:4056 (11) + 76-4695 (14) + 2-2390 (17) xiv. P : FCC’ſ o = + 269°480 + 16'9925 (1) – 27-2768 (2) + 10.2783 (3) + 17:4056 (9) – 41.1570 (11) + 23°7514 (12) + 20-5834 (15) + 56.9.186 (18) xv. P : FPC o = + 745'523 – 112'0793 (9) + 137.3678 (Io) — 25°2885 (11) + 56'7490 (15) + 13'8048 (17) The logarithmic values of the multipliers are as follow : Log I = o' 8270589 — Log v1 = o' 4820265 + Log XI = 8* 97.775.15 + II = o' 6344.166 + VII = 9'8612972 — XII = 9°oš12482 – III = o' 32032 18 + VIII = 9' 742 of 9o — XIII = 8'9888977 + IV = o' 2005oz2 — IX = 9 32.397.55 + XIV = 8:8161620 — v = o' 6026239 – X = 8* 7643532 — XV = 7'7249571 — Resulting Corrections. I'rom To Symbol. 3. From - To Sy º 3. JKELLIE JAir . . . Calton Hill. (1) –6778 3 || BEN LOMOND . . . Calton Hill . . (14) +3. 7611 East Lomond (2) | +3° 3533 - Glashmeal . (3) | + 1 . 6226 || BEN CLEUGII . . , , . . . (15) -o'7.185 Mount Battock. (4) | –o 3835 Lumsden (5) +o 2844 | EAST LOMOND . . . ICellic Law . . ] ( º + 5°ooş4. Sayrs Law . (6) — I 7997 Calton Hill. . . (17) | +o'o687 CALTON IIILL . . . Dunrich (7) | +1.8469 || GLAsixteal. . . . Kellie Law . . . (18) | – I'2950 Ben Lomond (8) –2 1404 sº Ben Cleugh (9) || +o o233 || MoUNT BATTock . 23 ,, . . . (19) + 1 ‘877I Den Tawers (Io) –4°9592 * * Iºast Lomond (II) +o '8638 || LUMSDEN . . . 33 ,, . . ] (20) || + I '9212 ICellie Law . (I2) -2 °4353 SAYIts LAIV . . 33 ,, . . . (21) | +o'4990 Pºmon . . . . Calton Hill. (13) | + 1 . 2076 3 F 4 IO PRINCIPAL TRLANGULATION. DUBLIN OBSERVATORY, The Dome of this Observatory is observed from Kippure, Lyons Hill, and the Hill of Howth, which stations were also observed from the Dome. The connection of Lyons Hill and the Observatory with the fixed points Rippure, Croghan, and the Hill of Howth is shown in Figure 36. The centre of the Dome is 57.25 feet east and 17.3 feet south of the centre of the Transit. - Equations of Condition. – 3 '7082 – (2) + (4) — (6) + (7) — or 6551 — (1) + (3) — (Io) + (II) III. LK'D o = — I'6260 — (1) + (2) + (5) – (7) — (9) + (II) IV. LK'C' o = — o'7292 + (1) + (8) — (II) – (12) === v. K. : DLH o = + 1 370 + 30-4833 (3) — 14, 1657 (4) — 16' 6022 (5) – 2' 1920 (6) + 187942 (7) – 2 '9654 (9) + 12 5418 (Io) – 9°5764 (II) R! : CLH, o = – 210-226 + 30-4833 (3) — 30 oz77 (8) + 12'5418 (10) + 17°4859 (II) + 129' 1318 (12) I, DH' K' O II. LK'H' O WI. The logarithmic values of the multipliers are as follow : Tog I = o' 4701389 + Log III = o' 2843.241 + Log v = 8: 1286971 + II = o' 3619191 + IV = o' 7273617 -- VI = 8*7623300 + Resulting Corrections. From To Symbol. §.: Erom To Symbol. S. I KIPPURE Lyons Hill . . 1) +: 1173 DUBLIN OBSERVATORY Kippure. (7) +é91 I4. Dublin Obsy . § —o' 3707 JLyons HILL Croghan . (8) +o'8908 PIILL of Hong'TII Lyons Hill . (3) | + I 1352 Dublin Obsy . (9) || –2° 3457 | Dublin Obsy (4) | + I 2577 Hill of Howth . . (Io) || – I'og35 Rippure . . . (II) —o'4563 DUBLIN OBSERVATORY | Lyons Hill . . (5) +2 I359 ' Hill of Howth . . (6) | – I 1685 CnogliaN . Lyons Hill . (12) | + I '7352 | CAMBRIDGE OBSERVATORY. The Dome of this Observatory is observed from Dly Minster and Balsham; a Heliostat near the Dome was also observed from Brandon : the reduction to the Dome is given with the observed bearing. If (1) (2) (3) represent the corrections to the observed bearings from the three stations in the order above named, the Equation of Condition will be found to be— ° = - 188'892 + 36'994 (1) + 15-924 (2) – 74-764 (3) Whence there results— {} { Calculated JFrom To 3. DLY MINSTER Cambridge Obser- a * I : BALSIIAMr. vatory p OD10 ſº ::::: # J3RANDON . 3 y —2 2672 The Dome is 45.4 feet east of the Transit, and in the same parallel of latitude. CONNECTION OF SPECIAL POINTS, 4II wº DURHAM OBSERVATORY AND BURLEIGH MooR SECTOR STATION. The triangulation for the connection of these two points with Collier Law, Wordeslow, Easington, and Water Crag is shown in Figure 37. The Dome of the Observatory, which is the point observed from Collier Law, Brandon, and Merrington Church, is 12.5 feet west of the Transit, and in the same parallel of latitude. I, CMA' II, CMB' KA'M A C/M RC B' JE' BB' M. : C'A'B' Aſ : C KA' IV. : MC'B' : KMC" : KO'B' B : B'C'E' : KBB' . : + O Equations of Condition. + 8:4899 + (2) — (6) — (Io) + (11) — 2 o251 + (6) — (7) — (II) + (14) + II '8765 — (1) + (2) — (Io) + (12) + (15) — (21) + 5°9767 – (4) + (6)– (11) + (12) + (16) – (21) – 3: 7947 -- (4) — (8) — (16) + (17) 1 '9697 -- (9) — (22) — (23) + (24) – 218: 675 – 136 oAoz (2) + 31 7070 (6) – 61 ° 9052 (7) – 44' o80 – 91 '6903 (1) + 64'6847 (2) + 66'4055 (4) — 69'9643 (6) – 7:4661 (15) — 16' 1379 (16) + 23 '6040 (21) – 772°303 – 126'8517 (4) + 66'4055 (6) + 40'3874 (7) — IoI 1351 (8) + 30° 1361 (11) - 41 ° 5154 (12) + II : 3793 (14) = – 618-628 + 207-3126 (3) — 258-7950 (4) + 51-4824 (6) + 7.6329 (II) – 29'9223 (12) + 22 2894 (13) + 59' 6767 (16) — 52 '8214 (18) — 6'8553 (21) + 399' 136 — IoI 4627 (4) + 6.6551 (8) + 75'4569 (16) – 15' 3465 (17) – 60’ IIo4 (19) + 120°862 – 382 Io97 (5) + 95-2763 (9) — 52' 3924 (22) — 171o. 260 + 54' 6117 (8) + 57'2923 (9) — 63' 3031 (17) + 25o'ozo8 (19) – 186'7177 (20) + 29°2867 (23) – 29-2867 (24) == = The logarithmic values of the multipliers are as follow: Log I = o' osog327 – Log v = o' 4824777 -- Log x = 7' 0329938 + II = 8-8127808 + v1 = 8*9146314 – XI = 8*4917703 + III = 9:7361491 + VII = 8.4028697 -- xII = 7:3867.015 — IV = 9° 5780705 — v111 = 8.7283164 + XIII = 8' 2431481 + - Ix = 8' 57578.11 + I?esulting Corrections. IFrom To Symbol. &. From To Symbol. 3. WATER CRAG . Brandon Down (I –3. 6415 | MERRINGTON CHURCH Durham Obsy . § +8.5255 Merrington Ch. (2) — I 2887 (continued.) Wordeslow . . . (14) | + 1 '4656 CoLLIER LAiy . Durham Obsy . 3) | +o '2487 | BRANDON Down Water Crag (15) +o 1.188 Brandon Down 4) — I '7849 Collier Law (16) — I 6148 * Burleigh Moor . . (5) +o 3654 Wordeslow . 17) | + 1 3321 Merrington Ch. (6) + 1 . Iozo Durham Obsy . 18) –o 342 I 7. Easington . . (I9 +6'9942 PPond ESLory Merrington Ch. (7 —o. 1361 Burleigh Moor. (20 —o. 6079 IBrandon Down 8) —2' 6328 Merrington Ch. (21) || +2 3594 Durleigh Moor. § +o 2398 JºAsiNGTON . Burleigh Moor. (22) +o'oZ82 MERRINGTONChunciſ Water Crag (Io) +6'7779 * Collier Law 11) || +o. 6785 | Bundergii Moon Wordeslow . § +1. 3% Brandon Down I 2 –4° 2 Io9 - - Dasington (24 —o' 7b4o 3 F 2 4I2 PRINCIPAL TRLANGULATION. MoRDINGTON AND BURNSWARR. These points were originally omitted in the calculation of the most probable corrections for the parts of the triangulation where they would naturally fall, as they were not necessary for the connection of the principal triangulation. Subsequently, however, it was considered desirable to add them, on account of the azimuthal determinations made at those points, that at Burnswark having a probable error of only o”.33. The stations Wisp, Dunrich, Sayrs Law, Blackheddon, and Cheviot are observed from Mordington, while Mordington is observed from the last four of these stations: these are the data for the determination of the position of Mordington. Tirst, from the observations at Sayrs Law and Cheviot determine an approximate position, M', of Mordington; then, using the corrected bearings and relative positions of the five fixed points, and denoting them by their initials, we have by exact calculation the following angles:— Corresponding tº Angle. Calculated Angle. Observed Angle. Difference. O 4 O. f { { M’CS 43 5ſ 34*7837 || 45 51' 34*7837 | +6-oooo MPSC 44 34 23° 2749 44 34 23'2749 +o'oooo ASDM’ 22 37 16' 5216 22 37 19: 6103 || –3'o687 CBM1" | 117 11 38-8915 117 11 42.8922 —4-ooo.7 CM'S | 89 34 5'4769 89 34 4'430o + 1 oA69 JPM'S 52 20 42 offo3 52 20 42°41oo -o'3492 DM'S 26 56 24'6539 26 56 25'50oo —o'8461 SM'B | 122 15 48' 2929 122 15 47° 55oo +o '7429 Trom the differences shown in the last column the correct position of Mordington must be determined. Let it be defined by co-ordinates a, and y originating at Ilſ', Slſ’ being the axis of a, and the positive direc- tion, y being measured perpendicular to Slſ’ and northwards, then we have the following equations for deter- mining a, and y:— I 6628 y . . . = o Weight = 2:44 + I 7oo3 as - o'oroá. 3/ . . . = o 3, F 5' 26 + o' 3807 a - o'7491 y – 3: o387 = o , - o' I2 + 2 °5492 a + 1 '6093 y — 4-ooo? = o , - II " II - **70°3 w – I-6524 y + 1-oſé9 = o , - 2 ° 22 – o'6127 a - I Igoo y – o' 3492 = o , F I " 47 ~ o'3807 w – o'9136 y – o'8461 = o , = 1 69 - 2'5492 a - 3 272 I y + o-'7429 = o , - I 22 Whence by the method of least squares— 104'610 a + 64'81o y – 120° 445 = o 64'810 a + 58' 947 y – 77° 137 = o ..". Q: E + I 'o68 : 3/ = + o' I34 CONNECTION OF SPECIAL POINTS. which determine the exact or most probable position of Mordington. The resulting corrections upon the observed angles are as in the adjoining table:— Angle. Correction. Angle. Correction. Angle. Correction. Angle. Correction. | AICS | + “8152 | CMS . —6991o | SDM . —#7822 | DMS . —#3752 MSC —o. 2227 | PVMS . — I 1632 || CBMſ . — I'o616 || SMB . —2'4189 If 2 be the correction upon the bearing of Sayrs Law as observed from Mordington, the corrections to the four other bearings will be, 2+ o-991o, 2+ I-1632, 2+ I-3752, and 2+2:4189, whence the most probable value of 2 = — I’’. Ioo3, and the corrections to the bearings will be as follow :- Resulting Corrections. { Calculated { Calculated IFrom To Correction. From To Correction. ſº A f ſº ! MondingTow . Wisp . +o'o624 | DUNRICII . . . . Mordington. –2" 7822 Dunrich. . . +o 2744. Sayrs Law . — I Ioo? | Clierior . . 33 . . . -- I '8152 Blackheddon + 1-3181 Cheviot . —o Io98 || BLAckIIEDDON . . 33 . . . — I'o616 SAyns Lary . . . Mordington. . –o'2227 The station Burnswark is observed from Hart Tell, Cross Fell, and Criſſel; and Criffel, Merrick, Hart Tell, Wisp, Cross Fell, and Sca Fell are observed from Burnswark: these are the data for the fixation of Burnswark. IProceeding in the same manner as in the fixation of Mordington, the corrections contained in the annexed table were obtained. Jēesulting Corrections. # =- Calculated w Calculated From To orrection. IFrom To Correction. FIART FELL . . Durnswark . +o" 9424 || BURNSIPARK, cont. | Merrick. . . . — o”8 573 Hart Tell . . . —o: o370 Citoss FELL . 22 tº +o. 6203 Wisp . . . . —o'8479 Cross Fell . — I'4778 CRIFFEL . . . 33 tº –4." I294 Sca Fell. . +o'835o BURNSIVARK Criſtol + I ooo; 4I4 PRINCIPAL TRIANGULATION, A TABLE SHEWING THE MEAN AMOUNTS For THE DIFFERENT STATIONS OF THE CORRECTIONS To THE BEARINGS OBSERVED WITH THE LAIRGER INSTRUMENTS, No. Asºº g|... Sum of ... Mean No. Average ź 3 tº Sum of | Mean Names. of | Recip. ;5|Squares of Value of Names. of | Recip. |###|Squares of Value of Bear- of £6.3 Correc- |Correc- Bear-|_ of |É53| Correc- |Correc- ings. Weight.:*T tions. tions. ings. Weight.:**| tions. tions. Arbury Hill . 6 | I oo | 8 4. 12 o' 26 || Coringdon . . . . Io o'72 II 9'86 || 1 , oo Axedge . . . . II I 23 || 7 || 8o 50 || 2 71 || Corryhabbie . . . . I4 o’ I 5 || 35 7'oo o'71 Baconsthorpe Tower. 5 o' 24 8 1 : 56 o' 56 || Cowhythe . . . . . 4 o°33 27 | 6'83 I 31 | Ballycreen . . . 9 o' 15 31 8: 15 o' 95 || Cradle . . . . . . 12 o' 58 7 6.21 o'72 Balsham Tower 8 o' 32 20 I '77 o' 47 || Criſſel . . . . . . Io 3' 88 || 6 || 62.96 || 2:51 Balta. . . . . . 3 o' 54 Io o' 53 o°42 || Cnocghiubhais . . 5 5*44 || 8 || II '79 || I'54 | Banstead . . . . . Io o' 49 || 12 25' 61 I 6o || Croghan . . . . 6 5' 7o 5 || 42 '81 2' 67 Bardon Hill . . . II o' 73 || 5 || 1 14' 35 | 3: 23 || Cross Fell . . . . 13 || 2 77 || 6 || 62 II || 2 19 Darrow Hill . . . 5 o' 72 15 3' 33 o' 82 || Crowborough . . . | 3 || o' I I 20 I'o6 o' 59 Baurtregaum . . . . I 3 || 2 ° 33 { 25' 39 I ‘40 || Cuileagh . . . . . II 3'44 13 33' 15 I of | Beacon Hill . . . . 15 o' 20 28 19: 76 I 15 || Cundtham 6 o' 97 II o:76 o' 36 Ben Cheilt . . . . 7 || 1 '45 || 6 || 39 II || 2:36 || Deadman. . . . . 7 o' 54 18 Io. 62 I-23 Ben Cleugh . . . . I 3 o' 39 19 7.66 o'77 || Dean Hill . . . . 16 o' 48 || 14 | 18.81 I og Ben Clibrig . . . . . I4 I 4o 15 19' 60 I 24 || Deerness . • , || 4 || o' 24 9 I oA o' 51 Bencorr . . . . . . . 6 I '96 || 8 || 11 69 || 1:40 || Delamºre . 5 o' 92 || 5 || 13° 38 I 64 Ben Heynish . . . 6 || 1 - 21 12 || 14-81 I 57 Ditchling • º 7 o' 58 13 3° 55 o '71 Ben Hutig . . . . I I 2.69 7 26-21 | 1.36 || Divis. . . . . . 9 || 2 °32 I4 56: 71 || 2:51 Ben Lawers . . . 13 or 14 || 26 || 15.71 || 1 - 19 || Docking Tower 4 o' 39 || 6 5' 33 I ‘ I 5 Ben Lomond . . . 11 o'98 || 7 || 46.72 2 'o6 || Doolieve . . . . 6 4'94 || 7 || 52 'o6 || 2: 95 Ben Macdui . . . . I4 o' 25 | 24 3:52 or 50 || Drung Point . . | 3 || o' 28 16 o'76 o' 50 Ben More, Mull . . . g . o. 81 | 16 || 11 off 1 II || Dublin Observatory . 3 o'78 Io 6-76 || 1:50 Ben More, South Uist || 8 || o' 30 30 2 23 o'53 || Dudwick . . . . . g o'83 || 7 || 11:51 | 1.13 Ben Novis . . I 3 o' 3 I 24 8 of o'79 || Dunkery Beacon . 6 o' 59 II 4' od o'82 IBen Tartevil . 6 o '86 16 6' 35 | I of || Dunnet Head . 8 I o8 || 4 || 19° 58 || 1 : 57 Ben Wyvis 9 || 2:23 || 4 || 23-48 || 1:62 || Dunnose . . . . 17 | 1:42 || 1 || || 24.56 || 1:26 Berkhampstead 7 I '84 14°os | I '42 || Dunrich . . . . . 12 || 1:20 | 16 || 16.67 o. 92 Black Comb . 8 7:43 || 6 || 19:47 I '56 || Dunstable . . . . . Io o'80 || 8 || 20.77 || 1:44 | Black Down . 9 o' 43 I5 o'86 o'32 || Easington . . . . 6 o'47 11 3' 9o o'81 Blackheddon . 5 o' 14 16 2’75 o'74 || East Lomond . . . . Io || 1:27 | 8 || 53-40 || 2:31 Blue Hill . 4 o' 69 || 7 6'76 I 39 || Ely Minster . . . 9 o'2; 15 15. 13 || 1:30 Botton Head . . g 2.29 || 6 || 24'87 I '66 || Epping Poorhouse . 11 | 1.66 11 23-28 || 1.46 Brandon (Suffolk) 8 I • I I I I I II 26 | I 19 || Fair Isle , tº ſº 7 o' 62 Io 6'26 o' 95 Brandon Down (Dur- Fairlight . . . 6 o' 31. 24 o' 20 o' 17 ham) . . . . 9 I 33 || 7 || 59' 36 || 2 57 || Fashvon 7 4: 16 || 7 || 67' 58 || 3: 11 IBrassa . 6 o' 49 | 12 I ‘48 o' 50 || Fetler . . 5 o' 24. 4. I - og o' 47 Brimmond 8 || 1:18 || 8 || Io'91 || 1:17 || Fitty Hill . 8 o' 46 14 I '87 o' 48 Broadway . . . . 5 o’ II 30 o' 64 o' 36 || Forth . 7 I '95 | .9 4'oz o'76 Bunwell Church Tower| 9 || o' 34 II 2 ” O4 o' 48 || Foula . 7 I 17 II 4'73 o'83 Burleigh Moor 2 I '79 7 2 ° 45 I II || Four-mile Stone . 9 o°44 23 I5' 66 I 32 Burnswark 6 o' 20 15 3 ‘84 o'80 || Frittenfield Io o' 72 I2 | 12 56 || 1 - 12 Butser Hill Io o' 54 14 9'61 o'98 || Gads Hill º 5 o' I 7 14 2 55 o'71 Caherbarnagh . . . . . . 2. 26 || 6 || 31:46 | 1. 69 || Garforth Cliff 6 || 3: 74 || 9 || 33-16 || 2:35 Calton Observatory . 6 I 61 | 18 39'26 2.56 || Garreg . 7 I 17 | 9 8 - 81 | I • I2 Carrigfadda 3 o' 99 || Io I 26 o'65 || Glashmeal 7 o' 88 || 8 9.61 || 1 - 18 Cheviot I3 o' 23 17 9° 30 o'85 || Goat Fell . I5 O'23 I5 7' 27 o' 69 Chingford. 7 o’ I 5 42 I 17 o' 41 || Goonhilly . 5 o' 4o I4. I ‘99 o' 65 Cleisham . 8 4'85 | 8 || 51 of 2.53 || Great Whernside 8 o' 95 || 5 || 17-22 | I 47 Clifton Beacon To 2 or || 7 || 128 Io || 3:58 || Gringley . . . 5 3' 19 20 | Ioa. 56 || 4' 57 Collior Law. . . . . Io O' 75 I 7 8'oz o'89 || Gwaunysgaer 4 I '96 || 6 || 16’ 40 2 : o3 MEAN AMOUNTS OF THE CORRECTIONS FOR THE DIFFERENT STATIONS. 415 Np. º 33 #| Sum of Mean No. Average 33 t; S Sum of f vº. f O ecip. $2.É|Squar {llli(? y f l?ccip. ; ; ; Ej Squares of Value 0 Names. Bear º # g sº f . Names. Bºº. º £5 g §. Correc- ings. Weight. ### tions. tions. ings. Weight. ăgº tions. tions. Hampton Poorhouse . 3 o'46 || 6 I 39 o:68 Pertinney . . . 9 o '87 13 Io' 39 I of Hanger Hill Tower . 8 o'87 | 12 || 17-12 | 1.46 || Pillesdon . . . 8 o' 54 16 6-78 o' 92 Happisburgh Tower . || 4 || 1 '68 || 5 2 24 o' 75 || Precelly . . 14 o'77 | 6 || 78'98 || 2:38 Hart Fell . . . . . I3 o'46 || 17 29'98 || 1 : 52 Rhuddlan B D. end| 4 | I or || 6 7'97 | I 4. I Hensbarrow 12 I 38 || Io 28' 88 I 55 **ase iw.end 4 2.16 || 5 I '98 || o'71 High Wilhays I2 o' 49 II 8'28 o'83 || Ronas . tº ſº 5 o' 55 I 2 7° 14 | I 20 Howth Hill 4. o '68 12 3 ‘83 o' 98 || Rue Rea . 4 o' 4 I I9 I ‘ I 3 o' 53 Hungry Hill . 6 | I - og | 6 I 6o o' 52 || Ryders Hill 9 o' 34 I3 3 * 12 o° 59 Inkpen II 2 25 | Io 17' 27 | I 25 || St. Agnes Beacon , || 5 || 3: Io 5 || 54' 64 || 3:31 Jura * 13 o' 35 | 17 | II 22 o '93 || St. Anne's Hill 5 o' 34 || 5 2 24 o' 67 Rarnbonellis . 4 | I 65 5 I '47 o' 61 || Sarum Castle . 7 o' 51 I4 I 3 '82 I 4o Karnminnis 8 o' 64 || 9 5'8o o '85 || Sarum Gun . . . 4 o' I I 35 3 o9 o' 88 Reeper 11 || 2 - 13 II 14'89 I 16 || Sawel . . 9 I 36 | Io 2 '94 o' 57 IXellio Law 6 o' 71 || 22 || 17-95 || 1 61 || Sayrs Law 14 o'86 || 8 || 36'63 | 1.62 Kings Arbour 3 o' 22 || 4. o' 77 o' 51 || Sca Fell I4 || 3' 17 | 6 || 105-76 || 2 75 Rippure I4 o' 96 II 76'8o 2: 34 || Scarabin . I2 I ‘43 | 19 || 43’50 I '91 Inock . . . | 4 | I '96 || 9 3'24 o' 90 || Scour-na-lapich Io o' 33 20 5'84 o' 76 Knockanafirin . . II o’90 || 14 || 14' 36 || 1: 14 || Severndroog . II o' 34 4o 7'85 o'84 Knocklayd 9 I '8o 21 || 179°25 || 4:46 || Slieve Donard I3 o' 5o 18 6-78 o. 72 Inocknaskagh 8 3'22 || 7 || 13:45 i-30 || Slieve League 6 || 4' o4 || 6 || Io? '90 4'24. Lawshall Tower . 9 I o? | 8 9° 92 I os || Slieve Snaght 12 || 2 of | 8 || 146'73 || 3'50 Laxfield 8 o' 38 15 7- og o' 94 || Snowdon . . I7 || 2 26 || 5 || 70°53 2 o4. Layton . 5 o' 96 || 6 2 : 73 o' 74 || South Barule . . . II o' 92 || 17 28' 5o | I : 61 Leith Hill I6 o' 57 16 12 '96 o' go || South Lopham Ch. Tr. 7 o' 56 || 9 || 19:71 || 1 : 68 Lincoln Minster . . | 7 || 3:24 || 5 || 50' 31 || 2 '70 || South Ronaldsha . . | 7 || 1:20 9 8 : 62 | I II Llanelian . 6 || 2 '89 || 6 || 28°47 || 2: 18 || Southwold Tower 4 o' 48 Io 12 59 I 78 Long Mount N . 9 I ‘O2 || 9 || 12 9o | I .# §: IHill. 9 o' 27 25 2 : or o'47 4 so ſ N. end. 6 o' IO * O * 5 I Stoke Tower . . | 5 || o' 28 || 12 I 31 o' 5I Lo, P. Base S. end . 5 ...?. I6 3.}; o' 28 || Storr Hill . . . . . Io o' 47 22 8'28 o'91 Lumsden . . . 7 o°4o II | 16'72 | I 55 || Stronsay . 6 o' 51 | 12 I '79 o' 55 Lundy Island. 7 o' 24 13 9 : o3 I 14 || Swyre Barrow Io I '77 | Io 4o '88. 2 o2 Lynn . . 5 o'66 || 8 || 14' 50 | 1:76 || Tara . . 7 o'86 || 9 || 6o' 59 2 94 Lyons Hill • 4 I oš 9 7° 7o I 39 || Tarbathy . 7 || 4' 56 || 5 || 54° 18 || 2 78 Maker Church Tower 5 o' 46 | 19 o' 27 o'22 || Taur . . . . . | 8 || 1:37 || 9 || 22:46 || 1 '60 Malvern . . 7 o' 68 || 6 4'98 o'84 || Tharfield . . . . 9 o' 99 || 9 I5' 39 I ‘3 I Mamsuil II o' 5o 23 3’54 o' 57 || Tilton . . . . . 5 I '86 || 6 || 148°69 5:45 Mendip Io o' 61 | II 8.64 o’93 || Tofts Tower . . 6 | I 12 | 12 o'66 o' 33 Merrick . 18 o'84 || 2 || || 15:52 o' 93 || Trevose Head. 6 o' 47 19 2 '90 o' 69 Milk Hill . . . . I2 o' 59 22 9 oA o'87 || Trostan tº 9 || 1 '78 || 13 31 : 56 I '87 M. Carr Base [Nºnº | 3 | "30 5 8.73 || 1 : 71 || Upcot Down . 6 o' 29 18 o' 63 o' 33 t { S. end | 3 | I '89 || 8 8'21 | I 66 || Vicars Cairn . . . | 4 || 5' 71 || 4 || 14-87 I 93 Moelfre Issa . . . 6 I 67 || 5 6.82 I o? || Walpole, Saint Peter's Monach . . | 8 || 4'44 | 12 5' 23 o' 81 Church Tower . 6 o' 70 II | 15' 36 1:60 Mordington . . . | 5 || 6’27 21 3: o3 o'72 || Walton Tower . . | 6 || 1:45 || 7 | 12 77 I 46 Mormonth. • II o' 39 I9 4. 12 o' 61 || Wart Hill IIoy . . 11 1-62 || 8 || 26'98 || 1: 57 Mount Battock . I3 o' 20 18 7.85 o'77 || Water Crag . . 9 o' 70 Io 20 '87 I 52 | Mount Sandy . . . 5 || 1:21 | 16 o' 99 o' 33 || Westbury Down . Io o' 3o 2 I 2 - 18 o°47 Mowcopt • . . . 7 O'34 || 2 I 6’44 o' 96 || Whitehorse Hill . 9 || 1:29 || 9 || 38' 15 || 2 oô Nephin . . | 6 | I '90 || 9 || 15-27 | I 6o || Wingreen . 12 o' 54 12 II '76 o'99 Qld Lodge . . . Io i o 24 28 7'47 o'87 || Wisp Hill . . 6 5' 22 || Io 8' 55 I 20 Qrford Castle . . 4 o' 56 | Io 3' 86 o' 99 || Whittle Hill . II | 1.68 || 3 || 49' 17 || 2 II º Hill . . 8 I 23 || 5 || 38' 57 || 2: 20 || Wordeslow . . 9 o' 53 II | 1.4° 37 I’27 addlesworth . 5 o' 57 II 6-68 || 1 - 11 || Wrotham . . . . . 15 o°38 22 | 16.85 / I'o6 #."; Ç 6 I 14 || 12 6 o8 | I or ||. Yoll ſº 6 o' 55 I3 o “82 o° 37 €II (110 lill 9 || 4' 59 || 6 || II '98 || 1 - 15 || Yorkminster . . 5 o.71 15 11-48 || I'52 416 PRINCIPAL TRLANGULATION. A TABLE SHEWING THE MEAN AMOUNTs AT THE DIFFERENT STATIONS CORRECTIONS To THE BEARINGS OF THE OBSERVED WITH THE SMALLER INSTRUMENTS. *: *. żg tº S Sum of f V. f No. Average 33 g Sum of Mean O ccip. 3, 2°E Squares of Value o of ip. 32.É * Names. Bear-) of p #3 É !. Correc. Names. Bear- Hºp £33 S. f Y. ings. Weight.: ‘s tions. tions. ings. Weight. #5 tions. tions. Acklam Wold. . . | 6 || 4:20 || 4 || 22'45 I '93 || Little Stirling 3 I 30 5 2 *oq o'83 Beachy Head . 5 | I I5 2 I 4' 48 o' 95 || Littletown Down . 5 |29' 65 || 8 || 197'o'; 6:28 Deacon Hill, Trescow 7 o' 72 19 9 of I 14 || Merrington Church 5 7'79 || 13 | 66'56 || 3:62 Boniface Down . . . | 7 || 9 || 1 || 7 || 323.97 || 6-80 || Mickfield Tower . 6 I og 22 || 32 °52 2 °33 Boniface Down, S.E.. | 6 |Io'70 || 6 |1058-30 |13-28 || Naseby * * * 6 || 5'45 || 7 | 73°29 || 3 5o Boston Tower. . . | 7 || 2 of 9 || 124° 92 || 4'23 || Naughton Tower . 8 2'48 II | 18-65 I 53 Brandon Hill (Ireland) || 2 |Io'76 || 6 6- 15 I '76 || Nive Hill . . . 3 28°46 19 || Io' 29 I '85 Brown Willy . Io | I 26 || 13 | 130°28 3' 61 || Nodes Beacon Io I 67 | 12 17.81 I : 33 Carn Galver . 12 || 1 ‘83 || 15 30' 54 || 1 60 || Norwich Spire 7 | 6’ 35 || 4 || 35' 66 2'26 Crowle . . . 7 || 5 o8 || 4 | 18° 56 I 63 || Norwood . . . . . 6 o' 91 16 || 17. 19 || 1 69 Cyrn-y-Brain . . . 6 || 4-22 || 17 41 oS 2’62 || Q. M. O. Southampton | 3 |30'18 12 6'94 | I 52 Danbury Spire 12 || 3:83 12 27'34 I ‘51 || Otley Church Tower. 6 || 1 of 17 | 13. 62 | 1.47 Faston Tower 7 || 2: 14 || 8 || 112-96 || 4'oz || Peninnis Windmill 6 || 4-79 22 5o '68 2 '91 | Feaghmaan . . . . . 4 (80-85 || 3 || 2 II 14 7°27 || Peterhead Windmill ; 4 |44. 73 || 9 || 96° 59 4'91 Gerth of Sciw . 3 |30-46 || 36|| 39-48 || 3:63 || St. Martin's Day Mark | 6 || 6-82 17 7-86 || 1 - 14 Gorleston Tower . 4 4°8o 9 4-79 I Io St. Peter's Church Tr. 5 || 2 °46 9 9 * I 3 | I 35 Great Stirling 3 ||38°43 II 7.81 I 61 || Saxayord . . . . 5 o' 61 | 8 || 15.93 | 1.79 High Port Cliff 2 || 3:31 || 11 44'21 || 4-70 || Shanklin . . . . | 3 | I Io | 8 3° 38 || 1 'o6 Hingham . . . . . 6 || 3 29 || 8 7-80 || 1 14 || Slieve More in Achill || 3 || 1.66 || 9 || 41.56 3.72 | Holme Moss º, tº 8 3 of 5 97' 45 3 '49 Swaffham Tower. 9 || 3 °43 Io 74°29 || 2 87 Reysoe Church Spire 7 | 1.77 || 8 || 23: 53 | I '83 Telegraph Tower. 6 || 1 '34 19 | 19:30 | I '79 | ICnockalongy . . . . 4 || 5'96 || 8 || 14-76 I '92 || Thaxted Spire 7 || 2 41 || 15 17' 21 I 57 IXnocknadober § 5.78 || 5 || 34-27 || 2: 62 || Week Down . 6 || 3’ 72 || 9 || 58' 34 || 3:12 ICnocknagante 4 |36. 16 || 7 || 249 of 7'89 || Wroxall 2 4' 59 || 5 || 27°oo 3' 67 SECTION VIII. TRIANGLES AND DISTANCEs. CALCULATION OF DISTANCES. In the preceding section we have given the results of the calculations for determining the most probable corrections to be applied to the observed bearings for the principal triangu- lation. These corrections being applied to their respective bearings, the process of calculating the distances is sufficiently simple: if ABC be the angles of any triangle, s the spherical excess = A + B + C – 180°, then any one side c being given, we have a = c sin (A tºº ..) COSEC (c º #) b = c sin (B iºs #) COSCC (c- #) It remains now to consider, what is to be taken as the absolute length of any one side of the triangulation? For this purpose, we have the measured lengths of six base-lines, and from any one of them we might calculate the whole of the distances; but as in general each base-line should have weight in the final distances, we may proceed as follows: Let A, A, A, . . . . be the measured lengths of the bases, and let g, g, g, . . . . be the ratios of their lengths to that of any side in the triangulation as determined by the calculation of the triangles, and let v be the most probable length of this side; then if a., w, w, . . . . be the weights of the measurement of the bases, a must be such that w, (gia – A,) + w, (g,” – A,) + w; (g,” – A,) + . . . . shall be a minimum. The differential coefficient with respect to a being put = o, we have {C E wig, A, 4 a. g., A., + as g. As + tº ſº º w; g,” + wag,” + w; g,” + . . . . which gives the most probable length of the side required, and the scale of absolute distance. To determind the weight of v, put the denominator of the fraction = v, and let w be the weight of w; them - I. {-º L 49, 91 \* . I a'a 92\* I (* g) # =# (º ++(*) + i. V _* gi" + °, gi" + æs g; + . . . +Lºmº V2 { • W = w g,” + w, g,” + w, g,” + . . . . . . . " - 3 G 418 PRINCIPAL TRLANGULATION. If the side a coincide with one of the base-lines A, , then g = i. and = *, *. + °. g. A, 4 o', g, A, + . . . . w; + wag,” + wag,” + . . . •. a – A = * g. (A - g. A.) + æ, e. (As - e, A.) + . . . . w; + wag,” + wag,” + “ . . . Ø which is the correction to be applied to the measured length of the base-line A,. If L, L, L., . . . . be the logarithms of the measured lengths, and L. L. L.' . . . . be the corresponding logarithms given by the triangulation (using the measured length of A, as the standard), then it will follow that the correction to the logarithm of any side will be o, A,” (L, - L.') + w; A,” (L, - L,') + . . . . w, A,” + wa A,” + wa A,” + . . . . . In the application of this principle to our triangulation, we are stopped in the outset by the impossibility of ascribing with any kind of accuracy the proper relative weights to the measurements of the base lines. Two different methods of measurement have been employed, namely by steel chains of Ioo feet in length, and by the compensation bars. The relative value of the two methods might approximately be ascertained by repeated measurements of the distance between two points on the ground; such experimental measures have not however been made, nor would the relative weights thus obtained enable us to assign weights to measures made under different circumstances of ground, and with different degrees of carefulness and experience. If the relative precision of the compensation method be at all proportioned to the complication of the apparatus and tediousness of the process, the weight of a chain measurement will be comparatively small,—and that the former method is much more accurate there can be no doubt. In the absence of any means of ascertaining the comparative value of the old bases, the absolute distances have been made to depend upon the Lough Foyle and Salisbury Plain compensation bases. The relative weights of the measurements of these two bases it would be difficult to assign. The ground in the former case was very much more favourable than in the latter, while on the other hand, the measurement of the line on Salisbury Plain was more perfect, from the circumstance of the compensation microscopes having been frequently and regularly examined and compared with the standard brass' scale: in the measure- ment of the Lough Foyle base these comparisons were either very few or not generally recorded. It follows from the theory of accidental errors of observation, that their influence to be apprehended in the measurement of a line is proportioned to the square root of its length; and hence the absolute length of any side in the triangulation has been taken, such, that the apparent errors of the measured lines at Lough Foyle and on Salisbury Plain as compared with their lengths in the consistent triangulation shall be proportioned to the square roots of their lengths. - CALCULATION OF DISTANCES. 4I9 The logarithm of the measured length in feet of the base line on Salisbury Plain is 4.5632182708, and the logarithm of the length as calculated from the measured length of the Lough Foyle base is 4.5632136242, the former exceeding the latter by -ooooo.46466. Let A, and A, be the measured lengths of the bases, A, + v VA, and A, -- a VA, their lengths adopted in the triangulation of which the ratio is given, then A, - a w'A, Log A,- log (A, A, TºyA. = •ooooo.16466 = M & MA # ** w/4,4, Also, if w be the correction to the logarithm of any distance as calculated from the measured length of the Lough Foyle base - w = log At # *VA, e Ma — A. WA, • *. = -ooooo.46466 —“*— = •ooooo.2248o A/A, + WA, since VA, = 204-06 and VA, = 191.25: also a = -ooro563, and consequently the apparent errors of the measured lengths will be - Feet. Inches. . Lough Foyle Base . . . . -- o'2155 = + 2.586 Salisbury Plain Base . . . . – o 2020 = — 2.424 The difference between the lengths of the Salisbury Plain base as measured (M), and as calculated (C) from the Lough Foyle base, is given by the equation M – C Lo g M + C = 2 (Modulus) = 'ooooo.46466 ; “. M – C = M × -ooooo.46466 (Modulus) M = C + 4.6956 inches = '3913 The probable error of this determination depends upon the probable errors of the mea- surements of the two lines, and also upon the probable error of the ratio of the two lines as derived from the triangulation. The calculation of this last probable error is possible, but quite impracticable. It may, however, be interesting to ascertain the amount of error that might be expected to result from the errors of observation of the triangulation, supposing one single chain of triangles 3.G 2 . . 42O PRINCIPAL TRIANGULATION. only to connect the two bases. For this purpose, take the triangles contained in the fol- lowing table. No. Names. Angles. §. t No. Names. Angles. .#. South End . . 6; t 37 J& i Precelly . tº 4% sº 7 Jº I | North End . 84° 25 —o'32 9 | Dunkery . g 62 52 | +o'oz Slieve Snaght 27' 57 | | Cradle . 7o'o North End . 92°4 I Cradle . . 46’41 2 | Sawel . . . 32°57 —4'o6 Io Mendip . . 68°32 +o 13 Slieve Snaght 54 ° 2 I Dunkery . . 64'46 Slieve Snaght 40°3 | | Dunkery . . . 41 °48 3 | Cuilcagh . . 20°20. +2 o8 || II || Pillesdon . . . 76. 39 –o 26 Sawel . I 19° 36 Mendip . . . 61:32 Sawel . . . . 82 - 15 Pillesdon . . . 44'42 4 | Slieve Donard ... 43°6 + I oy | 12 || Wingreen . . . 61.27 –1-62 Cuilcagli . 54'38 Mendip . . . 73°5o - Cuileagh . . . 48° 27 w Mendip . . . 36:36 5 IXippure . . . 53° 34 || – I 31 I3 13eacon Hill . . 43 - 16 || +4' 61 Slieve Donard . 77' 58 Wingreen . . 1oo. 7 Slieve Donard 59' 12 Wingrocn . . . . 3o° 13 6 | Snowdon . 40°36 —5'83 || I4 Dean Hill . . . 82°56 —4'95 IXippuro 8o II Beacon Hill 66.50 IGippure . . . 48' 2 Dean Hill . . . 39°29 7 | Precclly . . . 57. 30 + 1 30 I5 Four-mile Stone . 72°5 —o°62 Snowdon . t 74° 27 Deacon Hill . 68.25 Snowdon . (48° 58) Four-mile Stone . 70'2 8 || Cradle. º 68.30 Notobserved 16 | Old Sarum Gun . 85'58 —4.57 Precelly . . . 62-31 Beacon Hill 23'59 If 2, 3, represent the first and second angle of any triangle, s (cota + cot'8) = 30.04 S (cot’a -- cota cotſ + cot'6) = 39.46 The ratio of the lengths of the base-lines, putting 2, 0, for the first and second angles of the nº triangle, is expressed by the equation A, sina, sin a, sin a, . . . . . . sin 2,6 A, T sin 3, sin 3, sing, . . . . . . sin 3. Suppose a, + was 3, 4 y, to be the true angles, – w, and – y, being the errors of observation corresponding to the observed angles a, 6,5 then A. sin & . . . . Sin &I6 * sin 3, . . . . sin 3,6 ( +2, cot 2, -3/, cot 3, 4-ac, cot «,-4), cot 6, + ' ' ' + æ,6 cot &,6-y,6 cotá.) A, - CALCULATION OF DISTANCES. '42 I If now v. J. &. J. be all independent, that is, supposing two angles only of each triangle to be observed, the probable error of A, will be + A, v/ ( (a,’ cot a,) + (y,' cot 6,) + (a,’ cot a,) + (y,' cot a,) + . . . . J a',' y,' being the probable values of w, y,. If we assume a mean quantity, 0, as the probable error of observation of a bearing, the probable error of observation of an angle will be 04/2, and the probable error of A, will be Q + A, 6 M2 w/> (cot” 2, -- cot” (3.) or, expressing 6 in seconds and putting A, = 36578 feet, we have Probable error of calculated length of Salisbury Base = + 36578 wº, sin I". 9 vs. (cofa, Toot, 8.) = 1.370 feet, which depends entirely on the value we choose to assign to 0. If the angles were well observed, so that 6 might be taken as = o”. 5, the probable error would be + o-68, or 8 inches. If the three angles of each triangle be observed, and s, e, . . . . . be the errors of the sums of the angles, then the probable error of A, will be” + ;A. v/ (cot. c., + cot 2, cot 3, -- cot” 3.) e,” + (cot” cº, + cot cº, cot 3, -- cot” 5.) 8,” + “ . . or if s be the mean value of the quantities e, e, . . . . . + # A. V S (cot. 2, 4 cot c., cot 3, + cot” 3) or, expressing the quantity s in seconds, . -E I2193 sin I”.s Vs (cot a. + cota, cot 3, + cot? É) The sum of the squares of the quantities s for 15 triangles in the above table is 129. 16, so that we may put s = 2.93: also the value of the quantity under the radical being = 39.462, we have, - Probable error = + 1-op feet. If instead of restricting s to its value, as resulting from the particular triangles under consideration, we put s = 0 V 6, 9 being still the probable error of observation of a bearing, should have had, Probable error = + o-91.6 feet. - which would be the probable error of the length of the Salisbury Plain base as calculated from the Lough Foyle base, on the supposition of there being no other means than the single chain of triangles contained in the table, and of the three angles of each triangle being observed in each case with an even probable error of 04/2. * Laplace : “Théoric Analytique des Probabilités: Deuxième Supplément.” Paris, 1847. 422 PRINCIPAL TRIANGULATION, If + 2, A, and + o-, A, be the probable errors of the measurements of the Lough Foyle and Salisbury Plain bases, and + R the probable error of the ratio, R., of the two bases given by the triangulation, the probable value of the discrepancy will be, expressed in feet, + 36578 W &,” + 2,” -- sº If g, g, be the ratios (as given by the triangulation) of the two bases to any side in the triangulation, the absolute length, ×, of that side is º x = A.V.A., + A.V.A. g, VA, + g, VA, If instead of assigning to each base an error proportional to the square root of its length, the errors had been assigned as the lengths directly, the absolute length of any side would have exceeded the above length in the proportion of I g, A. - 9, A. ** = x^s . . + ...A. -- g, A, WA. H. WA, " or, substituting the values of º A, and A, in the proportion of I. ooooool 73 to unity, equi- 2 3 valent to an increase of one inch in a hundred miles. CoMPARISON OF BASES. The annexed table contains the lengths of the bases as measured and reduced to the same standard, and their lengths as shown in the triangulation, in accordance with the adopted scale of linear measure. The last column of the table shows the discrepancies. Length in Terms Length in Terms { } Date. Bases. mºsasons ano. TÉ. Difference. . . 1791 || Houns.oir HEATII 27404 24 27406; 190 27406. 363 +o 173 1794 | SALISBURY PLAIN 36574° 23 36576'83o 36577.656 +o-826 18or MISTERTON CART: . 26342 19 26344'o60 26343.869 –o 191 1806 || RHUDDLAN MARSII 245 14-26 24516°ooo 24517. 596 || + 1 '596 | 1817 | BELHELPIE . 26515.65 26517' 530 26517: 770 | +o 240 | 1827 | Lough FoxLE 41640.887 41641 - 103 || +o. 216 | 1849 SALISBURY PLAIN. 36577.858 36577.656 | –o 202 We may now estimate the difference that would have resulted in the absolute distances, if the first five bases measured with the Ioo-feet chain had been allowed to have a weight in the determination. Suppose these bases to have an equal weight represented by unity, while the weights of the compensation bases are represented by w. Let 3, 3, ... represent : CALCULATION OF DISTANCES. 423 the differences in the last column of the table, A, A, . . . . representing the lengths of the bases. Now, if I + r be the multiplier by which all the distances should be increased, the quantity - 3. (A, a + 8,) + (A, a + 8,) + . . . -- w (As a + 8.) + w(A, a + 8,)” must be a minimum with respect to a ; this gives _ A, 3, 4 A, 3, + · · · + w A3 36 -- w A, 8, A,” + A,” + . . . -- w A6” + aſ A,” a = – 7-5499 + 9:1593 * 40845 I + 3070I2 w from which it follows, that if we give all the bases equal weight, the assumed absolute dis- tances would have to be multiplied by o-99998924 : log = 9.99999533 By assigning double weight to the compensation bases, the absolute distances would require to be multiplied by * 3C E o-999992.31 : log = 9.99999666 The alteration in the former case would be at the rate of — 5.8 feet in every hundred miles; in the latter case — 4. I feet in every hundred miles. And in general, leaving w indeterminate, the correction to any distance, as given in the triangulation, will be at the rate of — .27396 47:34 + 4 feet I.33 + w to one hundred miles; or the correction to the eight-figure logarithm of the distance will be 47-34 -- w – 22.53 I.33 + w The following table shows the apparent errors, in inches, of the measurements on the suppositions of w = I, w = 2, and as actually assumed. Giving *Wºn: to all Giº to Aims d as most probable. Bases. - Error Error Error Error Error Jºrror of Measure. per Mile. of Measure. per Mile. of Measure. per Mile. | SALISBURY PLAIN + 7' 15 + I of + 5°8o + o-'84 + 2 + 42 + o-35 Lougir FoxLE + 2 -80 | + o' 36 | + 1 24 | + o- 16 || – 2'59 — or 33 IIownslow HEATH + 1-46 | + o-28 || + o-45 | + o-og | – 2: o3 — o'40 ! MisTERTON CARR. + 5°72 + I 15 + 4*7I | + o'94 + 2* 29 || + o'45 BELHELPIE + o' 55 | + o- 12 — o' 43 — o'o6 — 2 '88 — o' 57 Salisbuny.(OLD) . — 5:18 — o'74 – 6'54 — o'94 | – 9'91 | – I ‘43 *Upplan Mansil . —15'99 || – 3:43 —16-89 | – 3.63 — 19:15 – 4-12 *an Amounts . . . 4: 7.29 | # 1.45 | # 7.39 || 4- 1:49 | # 8:40 | + 1-69 424 PRINCIPAL TRIANGULATION. From the last column of this table it would appear that the last five bases, measured with Ramsden's Steel Chain, are in defect by the average amount of 1.21 inches per mile. This might be attributed to an error in the comparison between the standard measure used in reference to these bases, and O, ; but the individual differences are not sufficiently regular to give much probability to this hypothesis, which would in reality rest almost entirely upon the comparatively large error shown in the Rhuddlan Marsh base. In examining the fixation of this base-line, page 396, it will be observed that for the determination of 34 corrections there are only given twelve equations between them. The general pro- portion of the number of equations to the number of corrections or observed bearings in any part of the triangulation is nearly as 6 : Io, consequently the number of Equations of Condition for the fixation of the Rhuddlan Marsh base should be 20. The connection of this base-line is therefore defective in this respect. It has also been stated that there was Some uncertainty with respect to the refinding of the centres of the old stations at Llanelian and Arrenig at the time of the new observations at Cyrn-y-Brain in 1852; the centre stone of the latter station was then found in good preservation. The measurement of the Salisbury base-line in 1849 exceeded the old measurement with the chains in 1794 by 12.33 inches. Part of this difference may be owing to a small displacement of the guns marking the extremities of this base-line during the fifty-five years that elapsed from their first being sunk and their being revisited in 1849. The errors shown by the remaining bases are sufficiently small, and do not call for special notice. º TABLE SHEwing RELATIVE DISTANCES OF BASE-LINES, IN MILES. Names. Hounslow. Salisbury. |Misterton, Rhuddlan. Belhelvie. Lough Foyle. JHouxstory . 62-48 || 142 '93 183:22 | 406. 10 370.78 SALISuvny 62'48 166-68 166'59 |422:52 349-13 MISTERTON 142.93 166.68 108'97 262-26 269. 15 IRIluppl.A.N. 183'22 166'59 Io8'97 279-78 187-58 JBELIIELITE 406. Io 422. 52 262-26 279-78 241 ° 39 JLougli Foyle 37o'78 349' 13 269' 15 187-58 241 - 39 . PRINCIPAL TRIANGLES OF THE ORDNANCE SURVEY OF GREAT BRITAIN AND IRELAND. 3 H TRIANGLES, ITIGURE I. | - tº tº Dist * sº Names of Stations. Corrected Angles. Log. Distances. # 3.11CCS º: Fº of | South End of Base ......... 53 36 53.209 4-62.32 I.693 || 41996.870 | 8.o & I | North End of Base ......... | 73 37 18.656 4.69996493 || 5or 14,676 9.5 || – I-40 Drung Point............. jº º º tº 52 51 48.529 4.61952222 - 4I641. Io9 7. 9 18o o O-394 South End of Base ......... 53 30 52.415 || 4-66834381 || 46595'482 8.8 2 | Drung Point.................. 66 37 60.557 4.7259 1989 || 532OI or I Io. I || -2.77 Mount Sandy ............... |_59 5* 7:53° 4.699.96493 || 5ol I4,676 9-5 | I8o o o'504 * South End of Base ......... | 67 37 37.739 || 4-9246.1702 || 84965:35 | 15.9 3 || Mount Sandy ............... | 76 33 17.344 || 4.946,53490 || 88416.82 16.8 || -o.84 Slieve Snaght & a º a s a tº t e º 'º º ºs º ºs 35 49 5°939 4.72591989 532OI •ol IO - I | 18o o 1,022 South End of Base ......... 67 37 38-534 4.9146 IIoI || 82150-651 | 15-6 4 | North IEnd of Base ......... | 84 25 14.637 4.946,53490 || 88416,822 | 16.8 || -o-32 Slieve Snaght ............... 27 57 7.629 4.61952.222 || 41641. Io9 7.9 180 o'o.800 Slieve Snaght ............... 54 21 6.969 5-ob895548 || 122731-34 23.2 5 | North End of Base ......... | 92 41 50-595 5-17859.199 || I50866-2I 28.6 || -4.06 Sawel........ tº ſº tº ſº º tº e º 'º e º O & tº º º & © tº | 32 57 4-8o3 || 4.9146 IIol 82150-65 15-6 18o o 2.367 Mount Sandy ............... 84 7 14:736 5-178591.99 || 150866-2I 28.6 6 | Slieve Snaght ............... # 62 I3 5-279 5: I.2769166 || 134181.20 25.4 || -o-92 Sawel........................... 33 39 42-622 || 4-9246 1702 84O65-35 | 15.9 i i80 o 2,637 - Sawel........................... 76 42 31.28o 5:35557,056 || 226762. I5 42-9 7 Slieve Snaght tº tº ºn tº dº º ſº tº ſº º iſ º º 62 56 25-90.I 5.317o I 186 2O7497'oz 39°3 -5-44 Rnocklayd..................... 4o 2 I 9.979 5-178591.99 || 150866-2I 28-6 18o o 7,160 Sawel........................... ey º r) ºf fºr . { } 43 2 48.658 5' 1544.4656 || J42707:42 27°o 8 Mount Sandy {, } @ tº ſº º e º 'º - º 'º - tº 97 I ; 5.317o 1186 2O7497.02 39'3 —3-71 ICnocklayd * * * * * * * * * * * * * * * * * * * * * 39 55 38.037 5-12769166 134181.20 25°4. 18o o 4.466 Sawel........ * * * * * * * * * is e s e s e e s e e 6o 21 12-157 5.262682Oo || 183097.33 34-7 9 || Knocklayd..................... 39 36 57-704 || 5-1281.8857 || 134334.81 25.4 |supplementary. Cundtham ......... tº Q & G G & º 'º g º º 8o I 55.832 5-317o II86 || 207497.02 || 39.3 * I8o o 5.693 - Sawel......... tº D C tº ſº e º 'º e º 'º ....... 16 21 19-123 || 4-649912.18 || 43743.365 | 8-3 Io | Slieve Snaght ......... tº tº e º ſº tº º 59 51 I9'30I 5. I281.8857 || 134334.81 25-4 33 Cundtham ......... tº º ſº tº º º ſº tº tº º C. § Io9 47 22.917 5'17859.199 I50866-2I 28.6 18o o 1,341 | TRIANGLES. FIGURE I—continued. Dista +. ºrror of sº Names of Stations. Corrected Angles. Log. Distances. # In CCS == | º Mount Sandy.................. 73 36 46.865 4,75776118 || 57248-113 Io.8 & - II | South End of Base........... 42 42 50.952 4.60637539 || 40399.444 7-7 || - I-22 Cundtham ..................... | 63 17 22.669 || 4-7259 1989 || 53261 or I Io. I 18o o o-486 W | Mount Sandy ................ 73 59 49.727 | 4:5892.3649 || 38836. I79 7.4 - I2 | Cundtham ........... tº ſº e º ſº tº tº tº e tº I6 37 33-674 4-off 295444 || II559.9 Io 2-2 || + o-II North End of Base ......... 89 22 36.704 || 4-60637539 || 40399-444 || 7-7 || 18o o o, IoS Sawel........................” 13 5 8.947 || 4.672O7372 || 46997.387 8-9 I3. Knocklayd..................... 7; 31 47.368 5:39842277 || 203433-64 38.5 | + 1.74 Trostan ........................ 88 23: 5.931 || 5-317o II86 || 207497.02 || 39.3 | 18o o 2.246 l Sawel................. tº tº $ tº e º 'º e º 'º 89 47 40.227 5-40283536 252833-93 47.9 * I4 - Slieve Snaght * * * * * * * * * * * * * * * 53 34 23:265 5.30842.277 203433-64 38.5 – I-35 Trostan ............. * * * * * * * * * * * 36 38 3-721 5-178591.99 || 150866-2I 28-6 i 18o o 7,213 Sawel.......... * @ 8 º' tº º e º tº it tº tº ſº tº E tº º 68 20 8.138 5:50512565 || 319982-08 || 66.6 iº. I5 | Trostan ....... * * * * * * * * * * * * * * * * * | 75 26 59.030 5-52278501 || 333261.40 63. I | –o:/2 Slieve Donard ............... | 36 13 7.640 5:30842277 || 203433-64 # 38.5 18o o 14.808 Sawel.......... tº tº º & tº tº tº º ſº tº ſº º & 8 & © tº 82 I5 28:4I4 5-60738062 || 404930.62 76.7 I6 | Slieve Donard ............... 43 6 32.532 5-4460 II36 || 2792.61.72 || 52.9 || + I of Cuileagh........................ | 54 38 20.731 5-522785ol || 333261.40 63-1 - 18o o 21,677 Sawel............. tº e º 'º tº e º ſº º tº ... II9 36 43-221 5-5767.2864 || 377336-34 71.5 * 17 | Slieve Snaght ............... 4o 2 55.977 5-4460 II36 || 27926 I-72 | 52.9 + I o8 Cuilcagh................... tº 0 & 0 & 20 20 29.411 5-178591.99 || 150866-21 || 28.6 18o o 8.609 Sawel........................... 62 44, 3-ol 5 5.4186 1291 || 262188.06 49.7 - 18 Cuileagh ..................... 46 2 51.007 || 5'32704220 || 2 12345-oš 40.2 || – I-65 Vicars Carn .................. 7I 13 18:368 5-4460 II36 || 2792.61-72 52.9 - I8o o 12.390 Sawel........................... 44 33 11:948 5.22524141 || 167973-75 31.8 19 Vicars Carn .................. 72 57 49. I 87 5-35968.473 || 22892O-52 43.4 || – I-32 ivis ........................... 62 29 6.88I 5.32704220 || 2:12345-o8' | 40-2 - I8o o 8.oſ. 6 tº Piwis........................... 54 54 Io.809 || 5-178567-19 || 150857.60 || 28.6 * 2O. fears Carn .................. 59 27 I2.323 5-20083103 || 158792.88 - 3o. I | +o.79 Slieve Donard ............... 65 38 41.998 || 5-22524I41 || 167973-75. 31.8 || I8o o 5-130 Sawel... . . . . . * * * * * * * * * * * * * * * * * * * * > . . . 43 18 21.590 5.20757696 || 161278.68 || 30-5 2 I º * * * * * * * * * * * * * * * * * * , , , , , , 76 47 38.959 5-35968.473 || 228920-52 || 43.4 —o-26 IVIS • . . . . . . . . ....... * * * * * * * * * * * 59 54 6-958 5.30842277. || 203433-64 || 38.5 I8o o 7.5o'7 3 H 2 PRINCIPAL TRIANGULATION. FIGURE I—continued. I)istances in Names of Stations. Corrected Angles. Log. Distances. Fº of : Feet. Miles. ſº Sawel........................... 56 23 36,537 5.316o 9989 || 207061-75 || 39-2 &/ Knocklayd..................... 67 2 14-284 5.35968.473 || 228920-52 43.4 || – 2:58 Divis ........ tº 9 º' tº 0 ° tº e s is e is a e º e º 'º º 56 34. 24.476 5-317o II86 || 207497.02 || 39.3 18o o 9.297 Knockluyd..................... Io'7 23 24-263 || 5.54382 III || 3498o 1.06 | 66.2 | Divis ........................... 38 I3 2.48o 5:35557,956 || 226762. I5 42-9 || + 1.30 Slieve Snaght ............... 34 23 43.787 5.31609989 || 207061-75 39.2 18o o Io. 530 FIGURE 2, Quilcagh......;...........“ 48 26 57,849 5.5758.7896 || 376598.83 71.3 Slieve Donard ........... tº º ſº º 77 58 57.091 5,692.15523 || 4922.15.44 || 93-2 || – I-31 Rippure........................ 53 34 40. I23 5-60738o02 || 404930-62 76.7 18o o 35-odd I Cuileagh........................ 5I 55 I4.884 || 5-6560.5572 || 452955-69 | 85.8 Rippure...... “.............. & 69 I7 30-429 5'73roof.49 || 538271-62 |IoI-9 || –o-52 Reeper º e g º º º O & © tº tº ſº e s ∈ C C 0 & 0 & 0 & tº 58 48 3.718 5-6921 5523 t 4922 IS-44. 93.2 18o o 49-031 Cuilcagh........... tº º 'º º ſº tº ſº º ſº dº ſº tº º 31 9 50:633 54864-1948 || 306492.21 58.0 IKeeper ........ tº dº ſº tº C tº ſº e º 'º tº C tº e º 'º 34 Io 38.462 5.522O6794 || 3327II-6o 63-O || —o.84 Croghan........................ II4 39 52-693 5'731ool.49 538271.62 IoI-9 18o o 21.788 Quilcagh....................... • || 20 45 24-251 5-33464833 || 216096-8o 40-9 Rippure...................... tº º 33 4 5.583 5.522O6794 || 3327II-6o 63-o || + 7.79 Croghan........................ || 126 Io 43.809 5-692.15523 || 4922.15.44 | 93.2 18o o 13.643 Quilcagh........... • . . . . . . . . . . . • || 69 12 22. Ioo 5-626423oo || 42308o.49 8o-I Slieve Donard ............... 47 19 26.318 5.52266794 || 3327II.6o 63-o || +4.57 Croghan....... tº tº Q & Q ºn tº e º 'º º ...... || 63 28 4I. I88 || 5-60738062 || 404930-62 76.7 18o o 29.606 Kippure......... tº C C & C & d e º 'º º •... 86 38 45.707 || 5.626423oo || 42308o.49 || 8o. I Slieve Donard ........ tº º ſº º ºs e is 3o 39 30-773 5-33464833 || 216096-80 | 40.9 || + I-90 Croghan........................ 62 42 2-621 5-5758.7896 || 376598.83 71.3 18o o 19.1oo Rippure...................... tº ſº. 36 13 24.846 5-4864-1948 || 306492-2I 58.0 ICeeper ........................ 24 37 25-256 5-33464833 || 216096-8o 40.9 || –7-47 Croghan........................ || 119 9 23.498 || 3.6560.5572 || 452955.69 | 85.8 18o o 13.600 Cuileagh........................ 68 22 o'878 5.71622432 || 520264.65 98.5 Keeper ........................ 37 32 47-704 || 5.5328.2660 || 341056.71 64.6 || + 1.81 Nephin C º º O ſº tº 0 tº C & C G Q & Q ſº tº g º is g g tº 74 5 51.538 5'731ool.49 53827I.62 IoI-9 180 o 40-120 TRIANGLES. 429 FIGURE 2—continued. f | Distances in Error of s: O Names of Stations. il Corrected Angles. Log. Distances. | A | g : ! Feet. Miles. i. Cuileagh...................... ... 52 5 58,287 5.43524IIo 27242 I-32 5I-6 f/ 9 | Nephin........................ . . 46 5o 19.546 5-401 Io94o || 251827.64 || 47.7 || + 2.88 Slieve League ............... 81 3 58.098 5.5328.2660 || 34Io56.71 64.6 I8o o 15.93 I Cuileagh.......... tº e º $ tº e º e º 'º e º $ tº 64. Io 57.961 5:545oo251 || 350753-90 | 66.4 Io | Slieve Snaght ............... 4o 15 51.475 5-401 Io94o || 251827.64 47.7 || + 2.46 Slicve League ............... 75 33 30.67o 5-5767.2864 || 37.7336-34 || 71.5 | 18o o 20. Iod IXeeper e e s e e º e s a se e s ∈ e º 'º º e º ºs º º a | 22 47 43-7 IS 5-3149275o 2O6503.54 39. I II | Nephin ..............---------- 54 38 31.770 5-638.I 9669 434797'o6 82.3 || –3.76 Bencorr ... . . . . . . . . . . . . . . . . . . . . . | Ioz 34 5-II.8 5.71622.432 520264-65 98.5 18o o 20.601 Keeper s e º e º 'º e º 'º e º e º 'º e º e º 'º e s e º º 68 58 9°994 5-67626133 474527:44 89.9 . 12 | Bencorr........................ | 52 ió 23.595 || 5-60433034 || 402096:55 76.2 || – I-68 Baurtregaum .................. 58 46 4.774 5-6381 9669 || 434.707-06 || 82.3 I8o o 38.363 Keeper ........................ 103 7 55-176 || 5.7028355o 504470. I9 || 95.5 13 Baurtregaum............ § C & s º º 25 57 18.935 | 53554562o 226702-44 42-9 || -2.5I Inockanaffrin ...... ........ 56 55 6.765 5-60433o44 || 402096:55 76.2 | 18o o 20.876 Keeper ....... tº º tº ſº tº º ſº º Q & Q º 'º e º 'º | 68 45 19.695 5-6302 or 98 42.6777.96 || 80.8 I4 Kippure....................... | 29 46 39.868 5:3554562o || 226702:44 || 42.9 || +7°16 IKnockanaffrin ............... | 81 34 22.941 5-6560.5572 || 452955-69 85.8 18o o 22.504 Nephin ....... tº ſº C tº ſº tº G & C & G T G. ... || 121 9 37.343 5:57.018541 || 371693.88 79.4| I5 | Slieve League ...... tº $ tº tº e º a s & 19 59 55.616 || 5-1718,5971 || 148545-57 28. I supplementary. Slieve More ............... ... 38 5o 35-182 5-43524IIo || 27242 I-32 51.6 18o o 8-141 Nephin ....... • * * * * * * * * * * * * * * * tº 63 15 39.8o3 5.2847.2087 || 192628.64 || 36.5 I6 Bencorr........................ 43 31 35-853 || 5-1718,5971 || 148545-57 28. I || -7.50 Slieve More .................. 73 12 50-785 5-3149275o || 206503-54 || 39. I 18o o 6441 Nephin ...................... ... 143 36 58-584 5.52591909 || 335675:07 || 63-6 || 17 CI1001°r . . . . . . . $ tº tº t t e º 'º º tº º e º 'º - {º º 14 58 53.019 5.1651.7958 || 146278.19 27-7 |supplement” Knockalongy.................. 21 24 12.610 5-3149275o || 206593:54 39. I I8o o 4-213 Slieve League 628 8 6278. 27. , - ~~~o “* * * * * * * * & C & 9 º' tº e e 27 34, 5-638 5. IG5I 795 146278.19 27.7 s - I8 Nephin * * * * * * * * * * * * * > . . . . . . . . . . 31 57 44.271 5-22353502 || 167315-oj | 31°7 +5-73 Inockalongy... * * * * * * * * * g e º 'º e s I2O 28 I5-ošo 5-43524.I Io || 27242 I-33 51-6 I8o o 4.959 43O. PRINCIPAL TRLANGULATION, FIGURE 2—continued. Di g # No. of Names of Stations. Corrected Angles. Log. Distances. iStanceS in | Error of A. Feet. Miles. } A• Slieve League ............... 53 25 54,460 5-3078.8538 || 203182.07 || 38.5 Af I9 Cuileagh........................ 4I 26 52-863 5-22353502 || 1673 15-off 31.7 || – 5.95 ICnockalongy .................. # 85 3 22.638 5.401 Io940 || 251827.64 47.7 18o o 7.961 Nephin ........................ 64 41 30-619 5-1566.2611 || 143425.41 27.2 20 | Slieve More .................. 45 52 15.459 5:05643344 || 13876-32 21-6 || –3.86 Tawnaghmore ............... 69 26 17.517 5-1718,5971 || 148545-57 28. I I8o o 3’595 | - Slieve League ............... 24 22 27,433 5.05643344 || II.3876:32 21-6 2 I Nephin . tº s tº $ tº tº ſº tº ſº º 'º £ tº º is tº º gº tº º 56 28 6.724 5-36175872 23ooI6.36 43-6 || + 5. Io Tawnaghmore ............... 99 9 31.922 5-43524IIo || 272421.32 51.6 º, 18o o 6079. Slieve League º, º ºr e s a s g º º º ſº G is s 5 I 56 33-o? I 5.2622 I 507 I82900-57 34-6 22 | Inockalongy e e º ſº º e º e º e s is º ºs º is a tº 8I 58 49'3 I4. 5-36175872 23ool 6.36 43-6 + IO-53 Tawnaghmore tº e º is a tº e º is tº º ſº tº ſº º 46 4 44.738 5' 22353502 I67315.05 3I-7 18o o 7.123 Slieve League ............... Ioš 26 25-531 5:5839 oso2 || 383621:57 | 72.7 23 Cuileagh........................ 35 18 28.889 5-36175872 || 230216:36 43.6 |supplementary. Tawnaghmore ............... 39 15 18.703 5.401 Io940 || 251827.64 47.7 18o o I3. I25 Croghan is g g º a s e º 'º º is º e s e º e s is e º e º ºt i 9 I5 37.297 4:7822.5756 60570-oo II.5 24. Rip UTC - . . . . . . . . . . . . . . . . . . . . . . • 25 46 38°584 5-2I4o 1486 163687.25 3I.o + 2.19 Lyon's Hill .... ............. I44 57 45-547 5:33464833 || 216096-80 | 40-9 18o o I-338 Rippure ........................ 86 8 49,445 5'ozó67635 || Iot,335.03 || 20.1 25 | Howth ........................ 34 38 I-609 || 4-7822.5756 60570-oo II.5 || – I. 19 Lyon's Hill .................. 59 I3 IO-247 4-96.17 I958 91.562.91 I7-3 I8o o 1.301 IKippure:: tº e º is ſº tº sº g º C tº º tº º it tº ſº tº E tº C tº 46 I6 I9-602 4:746I 6279 55739.46 Io.6 26 Lyon's Hill .................. 8I 59 I'559 || 4-88298225 7638o.46 14.5 || – I.63 Dublin Observatory ......... | 51 44 39.625 || 4-782.25756 || 60570-oo II.5 - I8o o o,786 IGippure........................ | 39 52 29.843 || 4-770994.59 || 590.19-37 II-2 27 Howth © tº º is ſº tº ſº ſº tº tº $ tº tº º ºs s a s e º e s a e | 56 4. ; 4-88298225 7638o.46 I4°5 -4-24. Dublin Observatory ......... 84 3 25.520 4.96.17 1958 9I562.91 17.3 t I8o o I'o64. TRIANGLES, 431 FIGURE 3. * * * - IDI - in N. of Names of Stations. Corrected Angles. Log. Distances. iStanceS in Fº of ſº IFeet. Miles. * O / / / - - - a Keeper ........... * * * * * * * * * * * * * | 51 39 17.491 || 5.4990 6554 || 315548-oS 59.8 I | Baurtregaum.................. 36 I9 48-og I 5.3772 2386 || 238354.77 45 I | +3. I3 ICnockmaskagh ............... 92 I I2. 154 5-60433034 || 402096:55 76.2 18o o 17.676 Keeper ........................ 36 47 37.871 5-2III 3297 || 162604-65 30.8 3 || Knocknaskagh ............... 81 48 47.332 5-4293io26 || 268726.35 | 50.9 || + 1.99 Taur .......................... 61 23 43.818 || 5.3772 2386 || 238354,77 45.1 18o o 9.oz.I sº Keeper ........................ 22 43 41-547 | 5.2036.1750 || 159814.99 || 30-3 3 | Baurtregaum ............... 53 4I 37.208 || 5'5229 oo.4I || 333349.96 || 63. I || -5.79 Caherbarnagh ............... Io9 34 53.423 5-60433O34 || 4ozogó.55 76.2 18o o 12,178 Caherbarnagh. ..... § tº tº dº tº e º 'º º º 74 52 13.875 5:1991 of 88 I58163.36 30.o 4. Baurtregaum .................. 27 51 37.325 4,884.03598 || 76566-oo 145 || - I'13 Taur ............... tº dº tº tº º 'º e º 'º e º º 77 16 11-578 5.2036.1750 || I59814.99 || 30-3 18o o 2.778 Caherbarnagh ............... 65 52 5,807 || 5.27887967 || 1900.55-16 || 36|o 5 | Baurtregaum.................. 64 o 43.921 5.27230051 || 1871.97.70 || 35.5 || +o: Iz Hungry Hill.................. 5o 7 I6-694 5-2036.1750 || I59814.99 || 30-3 18o o 6-422 Caherbarnagh ............... 55 34 37.441 5.20264660 || 159458-II 30.2 6 || Hungry Hill.................. 48 : 3. 5-1631.7630 || 145605-oo 27.6 || + I-96 Carrigadda tº º ſº tº º ºs & C tº tº $ tº G * Q & Q & 75 33 13.838 52723 oošI | 187197.70 || 35-5 18o o 5.288 Qaherbarnagh ............... 92 13 32-116 5.35787605 || 227969:13 || 43-2 7 | Carrigfadda .................. 48 6 57.683 || 5.230.06366 || 169849-26 32.2 surplementary. Inocknaskagh ............... 39 39 36.013 || 5-1631.7630 || 145605-oo 27.6 | 18o o 5.812 Caherbarnagh ............... 7 52 39.805 5.06448245 || 116996:53 22.0 8 ićnockmaskāgh * * * * tº dº ſº tº ſº $ tº C º 'º º % 5. #: 5.26690429 || 184886. II 35-o || +3 or Doolieve........................ 64 1 9.700 5-2300.6366 || 169849-26 32.2 I8o o 4-534 Carrigfadda .................. 27 44 48.646 5-06448245 || II6ooô-53 22-o 9 || Knockmaskagh ............... 38 26 39-oló 5, 1901 2015 || I54924.52 29.3 |Supplementary.| Doolieve ...... tº $ in º ºs º ºs e º 'º e º 'º tº tº º I 13 48. 36.205 || 5.35787605 || 227969. I3 43-2 || | ** 18o o 3.867 - Caherbarnagh ............... 57 Io 33-062 5-3415.4065 || 219553-64 || 41-6 19 Doolieve....... * Q & º 'º º 'º C tº º 'º º º ſº º ſº 77 46 57-ol I 5.407 14005 || 255352.46 || 48.4 35 *altymore..................... 45 2 39.257 5.26690429 || 184886. II | 35-o 18o o 9.33o . Doolieve .8 | * * * * * * * * * * * * * * * * * * * * * * * * 3o 24 3.031 5-134992.47 || 136455.95 || 25 II º: * * * * * * * * * * * * * * * * * * * 95 5 32.26o 5-4290.9338 || 268592-19 50.9 53 nockanaffrin ............... 54 3o 31.727 | 5-3415.4065 219553-64 || 41-6 ºm- 18o o 7.or 8 4.32 PRINCIPAL TRIANGULATION. FIGURE 3–continued. No. of Names of Stations. Corrected Angles. Log. Distances. Distances in Error of A. Feet. Miles. A. - Keeper .............. tº tº Q tº º C tº º tº Q 68 26 66.645 5'5729 o'763 37.4031-02 70.8 & ſ | I2. Baurtregaum .......... tº C tº C & G & º 2O 39 62.232 5. I52O6064 I.4.1925'57 26.9 |Supplementary. Galtymore ...... * - ſº tº C tº ſº tº º ſº tº tº º 90 53 9-695 5-60433034 || 402096.55 76.2 18o o 12-482 Keeper ........................ Io3 26 14.226 5'70342878 || 505159.79 || 95.7 13 | Kippure................. º e º ſº tº dº ſº I5 51 35-444 5’ I 5206064 || I41925-57 26.9 33 Galtymore..................... 6o 42 25-o33 5-6560.5572 || 452955-69 || 85.8 18o o 14.703 - Knocknaskagh ............... || Io9 37 21-166 5-33641560 || 216977-95 41.1 14 | Taur ............. tº º g g g ∈ G tº ſº tº º ſº tº º 29 37 55.249 5.64290.510 || 110383-74 20.9 33 Galtymore..................... || 46 44 47.687 | 5-2 III.3297 || 162604-65 30.8 I8o o 4. Ioz ; Doolieve........ º º ſº tº it tº ſº tº º, º º ſº º tº C & 98 26 18-724. 5-4663.2376 || 29.2633-31 || 55. I5 | Caherbarnagh ............... 42 52 61.94I 5.30387912 || 201316.38 38. I 35 ISnockmealdown ............ 38 4o 48.894 5-26690.429 184886.1 r ſ 35°o 18o o 8.659 Taur ...... .................... 16 3I 34-ol I 5°og453556 I24318.44 23.6 16 Rnockmealdown ............ 2I 5o 32.286 5-2III 3297 162694.65 30.8 35 Knockaskagh.................. I4I 37 56-653 5:4334.2053 271281.72 51.4 I8o o 2-950 | ICeeper ........................ 2O 2 50-495 || 4,892I 78o3 78ol 4'98 || 14.8 17 | Knockanaffrin ........... tº ſº tº 64. 53 51783 5.31408139 || 206 IoI.61 | 39-o 35 ICnockmealdown ..... tº e º 'º C & ſº 95 3 2 I-578 5:3554562o || 226702-44 || 42.9 18o o 3.766 i Taur ........................... 49 52 12:526 5:3554562o || 226702.44 || 42.9 | I8 | Keeper ................. º tº º 88 I6 I5-556 5:539461.70 || 346307-34 65.6 || +5.62 IKnockanaffrin ...... tº ſº tº g º º ſº tº tº 5o 51 46.237 5-4293 Ioz6 || 268726.35 50.9 18o o I4-319 * - Caherbarnagh ........... ... || 141 19 23.399 || 5-63263909 || 429.179:62 | 81.3 19 | Bauriregaum ................. § 25 I3 I7:305 || 5-4663.2376 || 29.2633-31 55.4 ||Supplementary. Inockmealdown ............ 13 27 26.17o 5.2036.1750 || 159814.99 || 30-3 18o o 6.874 Baurtregaum ............ tº ſº tº º 'º º 84. 4O 47.623 5-67698o34. 4753I3-7I 90.o . 20 | Bencorr ........................ II 34 43-677 4,9814oo24 || 95807.66 | 18. I Brandon............ tº º & tº e º 'º º º ºs 83 44 39.345 5-67626133 || 474527.44 | 89.9 33 I8o o Io. 645 Baurtregaum.................. 98 52 49:474 535335987 || 225610.79 || 42. 21 | Hungry Hill........... II º 'º º is º º 24 48 36.836 || 4,9814oo24 || 95807.66 i8.1 33 Brandon........................ 56 20 40-922 5.27887.967 || 196055.16 || 36.0 I8o o £333 TRIANGLES. 433 FIGURE 3–continued. Di tº { sº of Names of Stations. Corrected Angles. Log. Distances. iStan CeS in Fº of tº Feet. Miles. * Baurtregaum ....... * * * * * * * * e s e 5i 13 16.454 4.95488778 90I33.82 17. I f / 22 | Brandon............ * * * * * * g º ſº e º 'º 72 36 2.591 5-04208481 || IIoI 75.44 20.9 || +8. I8 Knocknadober ............... || 56 4 42.893 || 4,98140624 || 95867.66 | 18.1 18o o 1.938 , Baurtregaum.................. 47 31 30-ozo 5-15029738 || 141350-51 26.8 23 Hungry Hill.................. 35 5 33-773 5-o4208481 || IIoI75:44 20.9 || - I-61 Knocknadober ............... 97 22 59.84o 5-27887.967 || 1900.55-16 || 36-o : * 18o o 3.633 Baurtregaum .................. 33 8 32-259 || 4-81339779 65972.54 || 12.3 24 || IKnocknadober ... . . . . . . . . . . . . 79 5 25-o.15 5-off77 I328 || II6872 76 22-1 || –4.og ICnocknagante ............... 67 46 4.352 5'o.4208481 || IIoI75:44 20.9 * 18o o 1,656 Baurtregaum .................. 14 22 57.761 4.91458716 82I46. I4 15-6 25 | Hungry Hill....... tº tº e º e º 'º, º ſº. tº 2O 41 £º 5-0677 1328 || 116872-76 22.1 || – 7.35 IXnocknagante © tº º º ſº º º ſº e º 'º ºn g º º I44 55 I8-990 5.27887.967 I90055. I6 36.o 18o o 1.298 Burtregaum.................. 36 36 6.460 4.9699.1349 || 93306-82 | 17-7 36 Knocknagante ............... 95 4 53.559 5-1927.7728 || 155875-29 29.5 || -3.8o Feaghmaan .................. || 48 19 3.336 || 5 of 77 1328 || II6872-76 22.1 I8o o 2.555 Bauriregaum.................. 47 51 42.253 5-off.4I 5052 || II5917.90 22-o || 27 Brandon $ ſº tº º ſº tº tº º e º e g º e s tº * * * * * * * * 94. 2O 26.494 5. I927 7728 I55875-29 29'5 |Suprementary. Feaghmaan ...... ........... 37 47 53.858 4.9814oo24 95807.66 | 18. I I8o o 2-605 ICnocknadober ............... 112 36 38.190 4.9699.134o || 933có-83 || 17-7 28 IGnocknagante .......... tº ºn tº º 27 is 49.267 4,66632685 || 46379.58 8.8 || – 18-48 Feaghmaan . . . . . . . . . . . . . . º, C & © _40 4. 33.258 4,81339779 65072.54 I2.3 18o o O-655 Brandon:".... tº C & b & © tº ſº º e º 'º º º 45 36 45,116 || 52723 ooj I | 1871.97.70 || 35-5 29 || Hungry Hill.................. 74 55 53-530 5'40303105 || 252947-89 47.9 |Supplementary. Caherbarnagh tº tº tº tº tº ſº ſº tº C tº º ſº ſº tº tº 59 27 3O'947 5-3533,5987 2256Io. 79 42.7 18o o 9:593 Brandon........ § 3 º' tº º is is C & Q ſº tº º & tº ſº 17 24 40. I33 4.8840.3598 76566-oo || 14.5 3o Caherbarnagh......... “....... 81 I6 48.736 5-40299659 || 252927-82 47.9 33 Taur ........................... 8I 18 35.633 5.40303 Io5 || 252947-89 47.9 I8o o 4.502 IFIGURE 4. * I jºrd “............ || 1 or 57 56.384 5-70396709 || 59.5786.34 95.8 || S § i.” 31 17 7.841 5-4288,9806 || 368471-48 || 36.8 || + 1-oš Outh lierule.................. 46 45 19-o29 || 5-5758.7896 || 376598.83 || 7 I’3 I8o o 23-254 3 I +- 434 PRINCIPAL TRIANGULATION. FIGURE 4—continued. |- * * Nº. of Names of Stations. Corrected Angles. Log. Distances. Distances in B. of tº Feet, Miles. -. Slieve Donard ............. 103 43 26.353 5-65738687 || 454346-17 | 86.0 f/ 2 Trostan ........................ 35 29 35-366 5-4288 98oo 268471-48 50.8 lºw- South Berule.................. 43 47 18. I23 5'5951 2565 || 319982.08 || 60.6 18o o 19.842 Slieve Donard ............... 94 23 6.459 5-61787735 || 414836.87 78.6 3 | South Berule.............. ..., || 45 25 53.857 | 5'47.186881 || 296.393.59 56.1 33 Howth ........................ 4o II 18.335 5-4288,98oo || 268.471-48 || 50.8 --- 18o o 18.651 Slieve Donard ............... 59 12 33.636 5,696.42725 || 497981-19 || 94.1 4 Kippure........................ 86 II #7.873 5.75693663 || 570212.36 Io8-o || -5-76 Snowdon ..................... 4o 36 21:921 5:57587896 || 376598.83 713 I8o o 43.370 - Kippure.............. . . . . . . . . . . 54 55 5-491 5-6539 1288 || 459726-28 || 85.4 5 Snowdon ..................... 9 34. I2-og5 4-96.17 1958 9I562.90 I7.3 |Supplementary. Howth tº e º e º is tº g º e º ºs º dº º º º º ſº tº ſº tº º II.5 3o 51-230 5-696.42725 - 49708I. Io 94. I 18o o 8.756 Slieve Donard ............... 55 33 27,ood 5.7319958I. 539505-42. Io2-2 6 Snowdon ..................... 63 48 46.282 5-76867715 || 587052.78 III.2 33 Sca Fell.............. • . . . . . . . . . 6o 38 51.612 5’756o3663 || 5702:12-36 Io8.o 18o o 64-900 Slieve Donard ............... 38 23 29.264 5-56181329 || 364597-17 | 69. I 7 | Sca Fell........................ 52 33 15-339 5-66849586 || 466 II 7-98 || 88.3 35 Merrick............... tº dº º ſº tº º 'º - e. 89 3 55.34I 5-76867715 || 587052.78 III.2 | 180° o 39.944 Slieve Donard ............... | 49 31 52.830 5:55025292 || 355ozo.o8 || 67.2 8 Trostan ........................ 87 II II.499 || 5-66849586 || 466I17.98 || 88.3 || +5.14 Merrick ........................ 43 17 22-341 5'505I 2565 || 319982-o8 60.6 18o o 26.670 Knocklayd..................... 75 40 14.648 5'57879591 || 379136-77 71.8 9 Pāvis. ........................... 7, 22 65.235 | 5:571664:io || 372961-58 || 70.6 || -8.79 Merrick ........................ 31 56 57.702 || 5.31609989 || 207061-75 39.2 : 18o o 17.585 Merrick • * * * * * * * * * * * * * * * * * * * * * * * 53 I5 67,768 5.52296.532 333399.79 63-1 Io | Divis ........................... 61 2 27.428 5.56108339 || 363984.92 | 68.9 || + I-84 South Berule.................. 65 41 50.8oo 5'57879591 || 379136-77 71.8 I8o o 25.996 Snowdon ..................... 37 46 29. I4o 5:5193.6549 330647.69 62.6 11 Sca Fell........................ 5o 16 6o-o/6 5-61827517 || 415217-05 || 78.6 || + 5.70 South Berule....... ſº º º º ſº tº ſº tº a tº º 91 56 63.043 5.7319958I || 539505:42 | Ioz.2 | 18o o 32-259 Snowdon ..................... 38 o 12:582 5-46199301 2897.29-69 54-9 I2 South Berule.................. | 8o 4 35.246 5-66609198 || 463545.08 87.8 H +o.84 | Black Comb .................. 61 55 4o-o32 5-61827517 || 415217.05 || 78.6 18o o 27.860 * TRIANGLES. 435 FIGURE 4—continued. Distances i 4 sº of ... Names of Stations. Corrected Angles. Log. Distances. istanceS in * º of º Feet. Miles. i. South Berule................ tº º 7: 58'53.338 5-60444615 || 4022O3.78 || 76.2 & f 13 | Merrick............ ſº tº º e º e º 'º e º e s 44 5 19:572 5-46199301 || 2897.29-69 54.9 || – I-35 Black Comb ........ ſº tº tº ſº ſº º º tº dº tº 6o 56 9-032 5.56Io9339 || 363984.92 | 68.9 * 18o o 23.942 - Slieve Donard ............. º 1839 7.082 5.27979903 || 190457-92 || 36:I. I4. ºrick ........................ Io9 56 56,667 5.74834,132 || 569197.73 |1961 ||*. Crittel........................... 51 3o 15.88o 5-668.49586 || 466 II.7.98. 88.3 I8o o 19-629 Slieve Donard ............... 19 44 22-182 - 5-297.53558 || 198397-22 || 37.6 - I5 | Sca Fell........................ 72 28 12.844 5.74834I32 || 56ol.97.70 || Ioë. I 33 -- Criffel........................... 87 47 51.081 5-76867715 || 587052.78 III-2 --- 18o o 26.107 South Berule....... ſº tº tº $ tº ſº º ºs e º 'º 3o 20 40.289 5.27979903 || 190457-92 || 36. I I6 * • * * * * * * * * * * * * * * * * * * * * g e º 74 45 52. I42 5-56081440 363759-55 68.9 — 2-off Crittel ........................ 74 53 43.291 || 5.561.08339 || 363984.92 | 68.9 * 18o o 15.722 South Berule............... tº C. 44 38 I5.o.49 5-4106.6981 || 257436-31 || 48.8 17 | Critiel........................... 52 15 20.994 || 5-461993OI || 28.972.9-69 54.9 || + 7.94 Black Comb .......... Q ſº ſº Q tº g º º 83 6 41-363 5-5608 I44o || 363759-55 | 68.9 18o o 17.406 Snowdon ...................., || 49 24 27-109 || 5:5466 1849 || 352961:47 | 66.7 18 Sca Fell....... tº º tº º tº e º tº ſº tº e º 'º & tº ... || 56 I4 54.032 5:65474726 || 451593-05 || 85.5 || + I-85 Whittle ........................ 83 21 I5-986 5.7319958I || 539505:42 Io2.2 * 18o o 37.127 *, Snowdon ...... tº ſº tº c is tº it tº ſº tº º ſº e º e 4o Io 43-666 5-49764190 314515:39 59.6 I9 Black Comb ............... tº tº . 67 52 Io. 962 5:65474726 | 45.593-25 85.5 + o-84 Whittle ............ L C tº dº ſº º G & º 'º º ſº. 71 57 37.121 || 5-66609198 || 463545-oS 87-8 I8o o 31-749 Snowdon ..... • * * * * * * * * * c e s tº e e 32 5 21-632 5.4.1995ogg 262.997:12 || 49.8 20 | Black Comb .................. 78 28 53.572 5.68585 Io; ; 485.122-09 || 91.9 |supplementary. Pendle Hill .................. 69 26 12.879 5-66609198 || 463545-ob 87.8 18o o 28.083 Snowdon ..................... 32 18 65-o/5 5.4622 1444 289877.46 54-9 21 | Sca Fell:".................. . 63 27 5I-357 5.68585105 || 485 I22.99 || 91.9 33 Pendle Hill .................. 84 13 36.461 5.73199581 || 539505:42 Ioz.2 18o o 32.893 22. i.e. ....................... 29 34 39:388 5.388o4552 244368-67 46.3 endle Hill .................. 7I 57 18:571 5.6727 910.4 470750-77 | 89.2 23 edge ..... .... tº tº e º O ſº e º 'º e º ſº e º 78 28 28.54I 5.68585 Io; 485.122-og 91.9 18o o 26.5oo Snowdon I 2 | .8 wº tº e º 'º e s a e s º 2I 29 17-353 5.237944I5 I72959:39 32 23. W. * * * * * * * * * * * * * * * * . . . . . . . . 85 3o 21.331, 5.67279104 || 470750-77 | 89.2 || -5° 8° “............. tº e º e º 'º e 73 o 39.623 5:65474726 451593-oš 85.5 18o o 18.307 : 3 I 2 436 IPRINCIPAL TRLANGULATION. FIGURE 4—continued. i Nº. of Names of Stations. Corrected Angles. Ilog. Distances. Distances in Error of * Feet. Miles. A. Snowdon tº e º 'º tº º 'º º 'º º ſº tº a tº e º is e º 'º g 26 32 ºz., 5:304984II | 2O1829.25 38.2 Af 24 | Whittle ........................ 65 7 52-996 || 5-61266289 || 409885-81 77.6 supplementary. Mowcopt .......... tº G º º s e º ºs e s e 88 20 I5-272 5:65474726 || 451593.05 || 85.5 18o o 19.442 Mowcopt ..................... 56 36 35-974 5:237944.15 I72959:39 || 32.8 25 | Whittle ................ iº & e º 'º º tº º 20 22 28-334 4,858o3603 7212o.o.5 13.7 || —8.22 Axedge ............ tº ſº tº g º is tº e º 'º C tº 103 o 58,549 5-3o4984II || 201829-25 || 38.2 # 18o o 2.857 South Berule.................. i 73 20 20-844 57338.0915 541762.76 Io2.6 26 Snowdon ..................... § 25 38,538 5.68742.159 || 486879-61 92.2 supplementary. Ingleborough......... . ....... 17 14 46.133 5-61827517 || 415217-05 || 78-6 18o o 45.535 Snowdon ......... & e º e e º e s is tº a tº 4O I4. 35.065 5'54975463 354612.98 || 67.2 27 Axedge .................. “ ... || 8o 43 18.447 5,7338o315 || 541762.76 192-6 33 Ingleborough.......... . . . . . . tº 59 2 45.221 5:67279 IoA || 470750-77 89.2 18o o 38.733 || Axedge & is ºn a tº º ſº tº º, º 'º º ſº tº $ tº a ſº e º z dº º tº O 42 18-904. 4-97.94 oz Ig 95.367.8 18. I 28 Whittle ................ * * * * * * * * . 7, 25-366 5-oš2Oo814 .### 2I-3 || –o.2O Holme Moss ......... tº º 'º º ſº ſº º ... || 112 Io 18.071 5’23794415 || I72959:39 || 32-8 18o o 2.34 I IHolme Moss ................ .277648o 80 RIG. º sº ... || 54 20 3.441 || 5.27704803 || 1895:0-94 35.9 29 S.W.tº ſº º tº C & is ........... rói 32 7.157 5.35999:53 228.5%:#8 || 43-3 || +4.33 reat Whernside ............ 24 7 53.565 || 4:9794O2.19 95367.89 | 18. I 18o o 4. IG3 - Sca Fell........................ 25 12 32.633 5-ogó13514 || 124777-17 || 23-6 30 Pendle Hill ...;............. tº 73 7 8.441 5:44768611 || 28o340.67 53-1 || +o-92 Great Whernside............. 8'ſ 4o 27.062 5:4622 1444 || 289877.46 || 54.9 18o o 8-136 Great Whernside tº ſº tº ſº tº dº e º 'º º tº º 37 33 18:824 5. I7696826 || 150303-21 28.5 31 Holme Moss .................. 3o 23 54.619 5.09613514 || 124777-17 || 23-6 || + 1.81 Pendle Hill .................. II2 2 50-644 || 5.35900153 || 228560-68 43.3 18o o 4.087 Pendle Hill ........ tº C & © tº C G s ſº tº 3I 3o 3-952 4-97.94.O2.I.9 95367.89 18. I 32 #. Moss .................. 23 56 8.822 4,86952I3o 74O49°35 I4. O + 1-89 little • - - - - - - - - - - - - - - . . . . . . . . • || 124 33 48-593 5-17696826 || I50303-2I 28.5 18o o 1.367 W. * * * * * * * * * * * * * * * * * * * * * * * * 57 29 53.701 || 5.23228182 || 17of 18.99 || 32. 33 ...'" * * * * * * * * * * * * * * * * * * * * * 28 6 28-548 || 4-97.94.o.219 95367.89 | 18. I supplementary. Holme Moss .................. 94 23 41.567 5:304984II || 201829-25 || 38.2 18o o 3.816 } Great Wººl * * * * * * * * * e º e 6o 13 6-942 5-o.44724.46 IIo847. Ig 21.0 34 Pendle º * * * * * * * * * * e s e º e e s a 42 5 42.333 4.93255067 || 85615-16 | 16.2 33 Ingleborough.................. | 77 41 12-905 5-0961.3514 || 124777-17 || 23.6 18o o 2. 18O TRIANGLES. 437 FIGURE 4—continued. s: of Names of Stations. . Corrected Angles. Log. Distances. Distances in Fº of :- Teet. | Miles. { } - Sea Fell........................ 23 33 1£862 5:26642265 || 184681.18 35-o # f 35 Whittle ........................ 26 4. 6.868 5-30768300 2O3O87-41 38.5 |Supplementary. Ingleborough.................. I3o 22 43.987 || 5'5466 1849 || 352061.47 | 66.7 18o o 6.717 Sca Fell........... tº e º 'º º e º 'º tº $ tº tº 78 24 26:517 | 5.33541592 || 202039.03 || 38-3 Ingleborough.................. 21 37 II-69; 4.8827.3675 || 75986:55 14.4 33 36 | Black Comb .................. 79 58 25.338 5-30768300 || 203087.4I 38.5 18o o 3-553 s FIGURE 5. Sca . s & a e s is tº e º e º 'º º is º ºs s tº dº e º º º 39 4 I 47. I4.I 53859;ror 243192.97 46. I I | Merrick........................ 67 3 48.82 I 5-5448814o || 350656. Io 66.4 || – 5:35 Hart Fell .................... 73 14 43:230 5-56181329 || 364597-17 | 69. I 180 o 19. I92 Sca Fell........................ 36 56 29.804 || 5-418384.51 || 262050-2I 49% 2 Hart Fell ..................... 89 31 53.433 5-6395 IA94 || 436028-56 | 82-6 || -o-28 Cheviot ........................ 53 31 58.359 5'5448814o || 35oG56. Io | 66.4 - 18o o 21.596 Sca Fell........................ 65 34 23.775 5.5oG54O47 || 32 Ioz6. I9 60.8 || - 3 || Hart Fell ..................... 3o 25 54-700 5-25184402 || 178584.6I 33.8 || +3.43 Cross Fell ..................... 83 59 54.925 5-5448814o || 350656. Io 66.4 I8o o 13.400 Cross Fºll tº e º dº º 'º º 'º tº e º 'º e º 'º e º 'º º ſº º 5o 20 Io. 790 5.418384.51 || 262o.5o-2I 49-6 4 || Hart Fell ..................... 59 5 58.732 5-46552.539 || 29.2095,85 55-3 || – I-62 Cheviot ........................ 7o 34 7.443 || 5.5oG54047 || 32 Io26. I9 || 60-8 18o o 16.965 Cheviot ........................ 22 II 22.577 5-o-;42.9778 110738:28 2 I •O : 5 Cross Fell ..................... 62 47 33.977 5-41627822 || 260782.37 || 49.4 || +4.54 Collier Law .................. 95 I Io.207 5-46552.539 || 29.2095,85 55-3 18o o 6.761 * Qheyiot......................... 25 38 38.770 5-o/787782 || II 9640.39 22.7 6 | Collier Law .................. 83 44 42.245 5.4399.2784 274807.03 || 52-o || – I-39 Wordeslow..................... 7o 36 46.273 5-4162 7822 || 260782.37 49.4 -- 18o o 7.288 - 3. Fell..................... 95 24 46.768 5-6536 9439 || 450499.58 85.4 7 $.” * † ºn tº ſº tº e s tº a g º º ſº tº e º tº º tº ſº tº $ tº 44. 23 18. I65 5.5oo4 1761 || 316531.99 59.9 |supplementº otton Head........ tº tº tº C tº º tº C wº 4o I2 16:70I 5-46552.539 292995.85 55°3 I8o o 2 I-634 Cheviot zº * * * * * * * * * * * * * * * * * * * * * * * 9 48 58.809 || 4.89.099059 77801.97 || 14-7 8 fººd * * * * * * * * * * * * * * * * * * 7o 58 52. I4I 5-63494 IIo 43.1460-56 81.7 33 { & “Y” “* * * * * * * * * e s e º e s - e e s e e s 99 12 16.839 5-65369439 450.499.58 85.3 18o o 7,789 | 438 PRINCIPAL TRLANGULATION. FIGURE 5—continued. - - - - - º Distances in Error of No. of Names of Stations. Corrected Angles. Dog. Distances. A. --- Feet. Miles. A. Botton Head.................. 4; 34 18496 || 3:34957552 || 22365341 42.4 || " | 9 | Cross Fell..................... 42 38 5.731 5-3316 off01 || 214588.73 | 40.6 || –2.15 Great Whernside ............ 92 27 47-O45 5.5oo41761 || 316531.99 || 59.9 18o o II. 272 Sca Fell........................ | 52 5I 18. I43 || 5.34957552 || 223653-41 42°4. Io Great Whernside ............ 39 31 49.451 5:25184402 || 178584.61 || 33.8 || – 1.94 Cross Fell.............. tº tº tº º is tº tº 87 36 61.786 5.4476861o || 28o340.67 53.1 18o o 9:380 * Botton Head.................. 90 27 52.478 5:445987 Io || 279246.09 52.9 II | Great Whernside .......... tº º 39 19 25-542 5.2478.7858 || 17696.I.4I | 33-5 Supplementary. Wordeslow...... tº g º e º e º ºs e º ſº tº C tº º 5o I2 50-906 5-33160691 || 214588.73 || 40.6 18o o 8.926 - - - - Botton Head.................. 62 48 27-791 || 5:32042514 || 209134.24 39.6 I2 Wordeslow........... º e s tº e s tº a tº e 68 22 27.960 5-33959240 || 218570.93 || 41.4 || – 2.02 Water Crag .......... © tº º O ſº tº º ſº 48 49 12-336 5-2478.7858 || I76961.41 33.5 18o o 8.087 Botton Head........... © a º º g º º 27 39 24,687 5-or 536998 || Io96oz-22 | 19.6 13 Great Whernside ............ 78 18 40-502 || 5-33959240 || 218579-93 41.4 || + 1.51 Water Crag .......... tº tº º 0 tº e º e 74 I'59.929 5-33160691 || 214588-73 40.6 18o o 5. II.8 Wordeslow............... º tº tº e º is 94 26 39.466 5.43743696 || 2738oz.22 || 51.9 I4. ſater Crag .................. 35 57 31.926 5:2075.2595 || IGI259.74 30.5 || +o,68 Easington ..................... 49 35 56.512 5°32042514 || 209134.24 || 39.6 18o o 7-904 Water Crag .................. 66 32 34.273 || 5:4098.9214 || 251705-17 | 47.7 I5 | Easington ..................... 27 Io 61.262 5-o981 I.393 || 125347.oo 23.7 || +1.96 Collier Law .......... tº ſº tº º ſº e º º 86 I6 31.866 5.43743696 2738oz. 22 5I-9 18o o 7.401 | . Water Crag .................. 52 19 57-450 5-o-;4297.78 || IIo738.28 21.o 16 | Collier Law .................. 64 1 53.810 || 5-o99585.14 || 125772.34 23.8 || – 1.39 Cross Fell ................... ſº tº 63 38 II.673 5'og81 1393 || 125347.oo 23.7 I8o o 2-933 Cross Fell ..................... 99 I4 8.636 || 5-36986766 || 234351-46 44.4 17 Sca Fell........................ 31 59 I4-7I4. 5.ogg,585.14 I25772:34 23.8 + 2.75 Water Crag * * * * * * * * s s a s a e e s e. e. 48 46 4I-86 I 5-251844O2 I78584.61 33.8 180 o 5.211 | Cross Fell ..................... 22 20 50.261 4.9325.5oG7 85615-16 | 16.2 I8 Great Whernside * * * * * * * * * * * * 6o 59 9'572 5.294.281.58 1969.16.26 37.3 Supplementary. Ingleborough.................. 96 4o 4. Io9 5'34957552 || 223.653.41 42.4 - 18o o 3.936 Cross Fell ..................... 65 16 11.525 5:30768369 || 203087.41 38.5 19 || Sca Fell....;................... 6i 43 32-240 5294281.58 || 1969.16.26 37.3 25 Ingleborough............... ... 53 o 23-743 5:25184402 || 178584.61 || 33.8 I8o o 7:508 * . TRIANGLES. 439 ) 3. 18o o 8.300 | FIGURE 5—continued. -- Di tº - sº of Names of Stations. Corrected Angles. Log. Distances. iStanceS in º of tº .* Feet. Miles. • Sea Fell........................ 53 46 4474 5.5oz.29433 || 317902.78 || 60-2 & f 20 | Merrick.::........... * * * * * * * * * g e 53 I 50-609 || 5.48789.407 || 307534.66 58.2 supplementary. Wisp Hill ..................... 71 17 46.681 5-56181329 || 364,597. I? | 69. I 18o o 21.764 Wisp Hill ........ º g º O & 6 & 8 & © tº º 35 20 26,746 5-25184402 || 178584.61 || 33-8 2I Sca Fell......... & G e s tº e º & 0 & tº º º º tº 49 35 26-442 5:3712 2258 235083-73 44'5 33 Cross Fell.................... ſº 95 4 16-641 5-487894oz || 307534-66 58.2 .." 18o o 9.829 Cross Fell..................... 39 15 49-073 5.26735943 || 185976-14 || 35.1 22 | Cheviot ........................ 53 30 11-483 5:3712 2258 || 235083:73 44.5 || –3.83 Wisp Hill ............ . . . . . . . . . 87 IA. 9-658 5.46552.539 292995.85 55-3 i8o o Io-214 Wisp Hill e e s tº e º e s e s a s is º e º e º e º 'º 5o 36 I6-471 5.237660.58 172846.50 32.7 23 | Cheviot ....... tº $ $ 8 tº º º ſº tº ſº tº º e º 'º º q 73 33 31.168 5.3314734o || 2I4522.77 | 40-6 || + I-54 Sayrs Law..................... 55 5o ig-571 5.26735043 || 185076.14 || 35' I 18o o 7.2 Io - Cheviot ........................ 6 2 .209 || 5.34303500 || 22031O-43 4I-7 24 Hart Fell ....... .............. 3. : #. 5.23766058 || I72846.5o 32.7 || –I.66 Sayrs Law..................... 82 39 5-271 5:418384.51 || 262o.5o-2I 49.6 18o o 8.875 Cheviot ........................ 85 8 34.105 || 5'54337483 || 349441:78 | 66-2 || - 35 | Cross Fell..... tº 6 & Q & Q tº dº º º sº º ... 38 27 47.776 5.33872431 || 218134-48 || 41.3 || + 1.84 Dunrich............ tº ºn tº ſº º 'º e º 'º t e C 56 23 53'O4o 5.46552.539 29.2095-85 55°3 - I8o o 14.921 - -. Cheviot ........................ 41 55 8.547 5-16467961 || 146 Io9'89 27.7 26 Sayrs Law..................... 85 51 58.796 5.33872431 || 2:18:34:48 41-3 || + o-49 Dunrich......... ............... 5% a 38.582 5.23766058 || 172846.5o 32.7 I8o o 5.919 - Cheviot ........................ 3I 38 22-622 5:05853271 II.4428: II 21.7 27 | Dunrich................... ..... || 58 2 32-970 5.26735043 || 185076.14 || 35. 1 || + 1.25 Wisp Hill tº e º 'º C & G e º O & G & C G & © 2 & ſº º 90 I9 9-385 5.33872431 218134-48 4I '3 I8o o 4-977 Wisp Hill • * * * * * * * * * * * * * * * * * * * * 4O 4. 33°31 I 4.87436661 7488o. 13 I4-2 28 Dunrich........................ 6o I4 39-2I2 5-oo.42 og I5 || Ioog73-90 I9. I || + I •og Hart Fell ............. • - - - - - - - 79 4o 49-225 5-oš853271 || II.4428. II 2I-7 - 18o o 1.748 Wisp Hill ..................... 73 41 34.357 5-4081 6348 || 255954'92 || 48.5 *9 |9-9ss Fell ..................... 44 29 4.562 5.27153407 || 186867-63 || 35.4 || –2.81 * 9 iſſol........................ ..., || 61 49 30-990 || 5:3712 2258 || 235083:73 || 44.5 * 18o o 9-909 Cross Fell ....... - * .o.o. a 7.6 , or , T ~ ** * * * * * * * * * * * * * * * * * * * * * 5o 35 12-of 9 5:297.53558. I9839722 || 37 +- 30 | Crittel........................... 44 3 42.811 5.25:18.4402 || 178584.61 33.8 || -2°33 Sca Fell.......... * * * * * * * * * * * * * * 85 21 13-410 || 5-46816348 || 255954.92 || 48.5 44O PRINCIPAL TRLANGULATION. FIGURE 5—continued. Distances in { sº of Names of Stations. Corrected Angles. Log. Distances. F * CéS Mil Fº of º €6t, IlêS. * > O Af f/ Wisp Hill ..................... 68 43 33290 5.24840969 || 17777.96 || 33-6 - 31 | Crittel.......................... . || 32 3 55'949 5-oo.12 o'915 || Ioog73-90 | 19. I || –o-I6 Hart Fell ..................... 79 I5 34,892 5.27153407 || 186867.63 || 35-4 18o o 4. I31 \ Hart Fell ..................... 1934° 37'931 5-6495.5355 || 446224.64 | 84.5 32 | Cross Fell .......... tº ſº º O ſº ºn tº ſº tº tº dº 31 58 36,354 5-38355ioi || 243192.97 || 46.1 || –4.77 Merrick.............. tº e º 'º e º 'º e º 'º 44 20 63-644 5,5065.4047 || 32io26.19 || 60.8 18o o 17.829 Hart Fell ..................... 59 58 37'o62 5.27979904 || 190457-92 || 36. I 33 || Merrick........................ 46 1647-495 || 5.24840969 || 177177.96 || 33-6 || + o-54 Criffel........................... 82 44 43.290 5.38595ioi || 243192-97 || 46. I 18o o 7.867 Criffel........................... 87 4o 29.63o 5.54337483 349441.78 66.2 34. Cross Fell ..................... 45 I 7 5-859 5:39.535683 248.517:42 47. I –6.86 Dunrich ........................ 47 ° 39'448 5-408; 6348 || 255954.92 48.5 I8o o 14.937 *. -- Cheviot e g º sº tº e s tº a s tº º is tº e º 'º tº º ſº º ſº º º 75 58 I4. I3o 5' 232 I 6557 170673.29 32°3 35 Sayrs Law..................... 24 45 26.793 4-8672 9673 73671.og I4 -o + 2.82 Blackheddon ................ tº º 79 I6 2I-98o 5.237660.58 sº 172846.5o 32.7 18o o 2.903 Sayrs Law..................... IIo 37 35-584 || 5-41639562 || 260852.87 49.4 36 | Blackheddon ................. 31 36 60.734 5.16467.961 146 Io9'89 27.7 || –o.o.6 Dunrich....................... 37 45 39°497 5:232.16557 || 170673:29 32-3 180 o 548.5 Sayrs Law..................... 39 25 54.889 5-05541698 || 113610-11 || 21.5 37 | Blackheddon .................. 33 9 24.962 || 4.956.46774 || 97829-03 18.5 || –o-o2 Lumsden ..................... Ioz 24 42:04: 5:232i 655; 176673.2% 32°3 | I8o o 2.492 Sayrs Law.............. • * * * * * * 64. II 3:6.2 5'IQ653829 I5723 I.O.4 29.8 38 Cheviot a c e s a e º e s e e s e s • * * * * * * * * * 34. 3 53-370 4'990.46774 97829-og 18.5 + o-og t Lumsden ............ . . . . . . . . . 8I 44 48.525 5.237660.58 172846.5o 32.7 18o o 3-577 Botton Head.................. 3° 13 5: I.33 5-og81 I.393 || 125347.oo 23.7 : 39 Water Crag .................. 79 24 I4.683 5.3638o38o || 23 IIo9.64 43.8 || +o.og Collier Law .............. tº º tº º 68 22 46.514 5-3395924o 218570.93 4. I*4. 18o o 6. 33 o Wordeslow..................... II 18 46.521 || 4-6261 1735 || 422782.84 || 8.o 4O Easington • * * * * * * * * * * * * * * e s is e º e 37 7 26.607 5. II42 or 3o I3oo77-24 24.6 +2-27 Burleigh Moor ............... 131 33 47.839 || 5.2075.2595 || 161259.74 || 36.5 18o o o'967 TRIANGLES. 44I. 3 IC 4– FIGURE 5—continued. s: of Names of Stations. Corrected Angles. Log. Distances. Distances in Fº of -. Feet. Miles. i. O f A/ f/ Wordeslow..................... || II5 20 39.996 || 5:32.4458.41 || 21 Io85.5o 4o-o 41 Collier Lay .................. 33 5o 36.08o 5.1142 or 3o || 1300.77-24 24.6 |supplementary. Burleigh Moor ............... 3o 48 47.230 5-o/787783 || 119640.39 22.7 g 18o o 3.306 Wordeslow..................... 96 13 38.257 5-1783.8689 || 150794.98 || 28-6 42 Burleigh Moor ............... 24. 44 1.612 || 4,8025484o 63467.06 | 12-o 33 Brandon Down............... 59 2 22.060 5-II.42 or 3o || 1300.77-24 24.6 18o o I-929 Wordeslow a s is º is e º e º 'º e º is tº º is a º º 'º º Io'7, 32 24-779 5-2793.6422 I90267-33 36.o - 43 | Easington ..................... 18 32 44.963 || 4-8025484o 63467-oG | 12.o 35 Drandon Down ............... 53 54 52.612 5.2075.2595 || IGI259.74 || 3o:5 18o o 2.294 * Wordeslow..................... 46 39 3.372 4.94236764 || 87572.48 16.6 44 || Collier Law …................ 36 47 56.636 || 4-85813977 72I33.96 I3-7 || –2-92 Merrington Church ......... 96 33 7.467 5-o/787783 || II964o:39 22:7 I8o o I-475 Collier Law .................. 8o 24, 23. Too 5-1474746o || 140434.75 26.6 45 Water Crag .................. 37 56 31.103 || 4.94236764 87572.48 | 16.6 || +8.91 Merrington Church ......... ‘. 6+ 39 8.341 5-og81 I.393 || 125347-oo 23.7 18o o 2-544 Collier Law .................. 8.267 5, 1703 IA57 || 148or 8-or 28-o 46 | Water Crag .................. % 5. ; 4.8ooč4730 63189,85 I2-o || +3-ol Brandon Down............... 56 59 32.407 || 5-og8II.393 || 125347.oo 23.7 I8o o 1,844 Water Crag .................. I2. .933 || 4:52308453 || 33349-131 | 6′3 47 | Brandon Down ............... 7o § ; 5.14747460 || 140434,754 26-6 || + II-88 Merrington Church ......... 96 35 go.é51 5-17031457 || 148orbor.3 28.o 18o o I.ogg Brandon Down ............... I .872 4.520843.35 || 33177.477 6.3 48 Merrington Church ......... % 5 57 5. 4.30275839 || 20079-754 || 3-8 supplementary. Durham Observatory ...... 2 53 6o.o.2 4:523O8453 || 33349-131 || 6-3 º 18o o 150 Merrington Church ..... tº ſº tº º 7o 4 24.567 4.9159 Io90 82396.905 I5-6 49 | Collier Law .................. 22 14 37-693 || 4:52O84335 || 33177.477 | 6′3 33 Durham Observatory ...... 87 4o 58.382 4.94236764 || 87572.478 || 16.6 | 18o o o-642 Cheviot * * * * * * * * * * * * * * * * * * * * * * * * 45 51 36,599 || 5-09357859 || I24O44-81 23:5 5o §: * * * * * * * * * * * * * * * * * * * * * 44 34 33.498 || 5.08389616 || 121369-86 23-o || -9.79 910 ington .................. 89 34 3.439 5.23766058 || 172846.5o 32.7 | I8o o 3-536 442. 12RINCIPAL TRIANGULATION. FIGURE 5––continued. N% of Names of Stations. Corrected Angles. Iog. Distances. Distances in Error of: —l- - Feet. Miles. | A. - Dunrich. tº e º ſº tº e º 'º º º ſº tº tº º ſº tº tº º º ſº e º 'º 23 3% 16.828 5-0935785 ," * // - * 357859 || I24O44-8I 23.5 5I §:"............... *3. .. 22.288 5-3899.6909 i 24.5453.42 46.5 +4.73 115uvai - - - - - * † tº ſº tº . , tº tº e º 'º - 26 50 24. I25 5. I6467.961. - I46Io9.89 27-7 || 18o o 3.241 Wisp ............. tº dº º e º C & C & © tº º $ tº 27 (441.834 5-og357859 || 124044.81 || 23.5 52. Sayrs Law.................... tº IOO 24. 43-off.8 5'42.57 o'54I 266505-og 50-5 |Supplementary. Mordington .................. 52 20 41.247 5'3314734o 2I4522-77 | 40-6 *, 18o o 6,149 | - §. * * * * tº dº ſº º tº dº e º 'º - e. ſº º tº dº tº º º 3o 6 37.531 | 4.8351.86 Io 68420-49 || 13-o 53 i. ington .................. ! 32 41 41-392 4.8672 96.73 7367I'o6 I4.o || +6.66 ackheddon .................. 117 II 41.830 5-o&38961o || 121309-86 23-o : | 180 o 1,053 Merrick ........................ 27 27 45.4420 || 5 of 871642 || 1171.43.02 || 22.2 54 || Hart Fell ..................... 79 19 32° 1676 5.3972.82.55 || 24.9621.82 47.3 |supplementary. Burnswark............ º, º e º ſº tº e º 'º 73 I2 48-9703 "5385951or || 243192.97 || 46.1 18o o 6.5799 Merrick................... ..... 39 35 63-3789 5-37014383 || 234,500-53 *. * 44°4. 55 | Sca Fell........................ 42 43 46.3578 5.3972.82.55 || 2496.21.82 47.3 33 Burnswark..................... 97 4o 23-8977 5-56181329 || 364597-17 | 69.1 iº 18o o I3-6344 Merrick ....... tº gº tº dº º ſº e º ſº e º C tº C & º º I6 53 18-2019 5-3417 9186 || 2:1968o.68 | 4 I-6 56 Cross Fell ..................... I9 I6 29-6726 5-397.28255 || 24.9621.82 47.3 * Burnswark................... ... || 143 59 19.7305 5-6495.5355 || 446224.64 | 84.5 18o o 7.605o Mºrrick................. ſº gº tº ſº ºn tº º 13 2 5 47.2301 || 4:9771 6804 94878-55 | 18.o 57 | Wisp ........................... 37 39 52-51.22 || 5.3972.82.55 || 24962 I-82 47.3 3? Burnswark..................... 128 54 24:5894 5:50229.433 || 317902.78 6o-2 18o o 4.3317 º * Merrick ........ º, º ºs e s tº tº tº º ſº tº ſº tº e º 'º 18 49 2-oš31 4,96680087 92.640.4 * '49 |. I'7.5 58 * tº º e º 'º tº ſº tº º C tº º ſº º ſº tº e s º º 4I 32 I?.3722 5'27979904 I90457-92 36. I 33 * * * * * * * * * * * * * * * * * * * * * * * * * * * II9 38 44, 1786 5.3972.8255 || 24.9621.82 47.3 I8o o 3.6039 I'IGURE 6. ** —H·- | ſ E. • * * * * * * * * * * * * * * * * * * * * * * * | 45 46 32.409 5:26057665 || 1822II.86 34.5 | I | Foula ........................... | 67 39 7.723 5.37.138595 || 235172.18 44.5 || +3.54 IBrassà. . . . . . . . . . . . . . . * * * * s tº e s s e | 66.34 29.999 || 5:36798827 || 233312.64 44.2 | 18o o 9:231 | TRLANGLES. 443 - \ FIGURE 6—continued. ' ' . * +* * * * * * * * * - * * * * * * * = Distances i | Fºr Nº. of Names of Stations. | Corrected Angles. Log. Distances. 1StanceS 111 – Fº of Q. Feet. Miles. º O / £ - - - - - -r- in Brassa.............. & tº e º e º a c e s tº e 65 2I 32:398 5:26945531 || 185975.32 35.2 | 2 | Foula.......... * * * * * * * * * * * * * * * * * 51 42 2.991 5:20567031 || I60572. I& 30.4 || +2.20 Ronas........... * * * * * * * * * * e º e s º e 62 56 30-654 5-26057665 || 1822II.86 34.5 18o o 6.243 Foula * * * * * * * * * * g e s ∈ e e s e e º 'º e º e s e e 119 21 Io.7.15 5.55956106 || 3627.II-28 | 68.7 3 | Fair Isle........................ 26 32 47.869 5-26945531 || 185975°32 || 35.2 surplementary. Onas . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 6 Io. 295 5.36793.827 || 233312.64 44-2 18o o 8.879 | * Ronas........................... 7o 54 44 II6 5-18244724 || 1522II:42 28.8 4 || Brassa......................“ 23 34 54.2 Io 4-8091.2521 || 64435.5o | 12.2 || –o. Io Yell........................“ 85 3o 23.969 5.20567031 || IGoś72-18 || 30-4 18o o 2.295 Ronas........................... 133 51 I4,770 5-37153330 || 23525I-99 || 44-6 5 i Foula ........................... II 23 3o-oo& 4,8091.2521 || 64435.5o I2-2 || + 2.45 Yell ..... * * * * * * * * * * * * * * * * * * * * * * 3445 17.25o 5-26945531 || 185975:32 || 35.2 18o o 2-oz8 Prassa........................... 36 9 I4.478 5-og844808 || Io9256.70 || 20-7 r 6 Ronas........................... 83 43 48.8o3 5.26502,522 || 184087-89 || 34.9 || – 2.97 Petlar........................... 6o 6 60.813 5.20567031. I60572-18 || 30-4 . I8o o 4'og4 Fetlar...... tº tº tº º ſº tº a tº e º ſº º ºs e e º c e º 'º e 43 o 10. IoI 5, 18244724 || I522II'42O | 28.8 , 7 | Brassa ...... tº º º sº º 'º e i t t e º $ tº tº e º is iz 34 20-269 4.68643895 || 48577-934 9-2 || -o-70 Yell ........................... 124 25 31.062 5.26502522 || 184087-889 || 34.9 I8o o I-432 Brassa...... tº º $ tº tº tº t e º 'º º e º 'º e º º e tº tº Q 33 Io 62.367 5-18362746 || I52625.63 28.9 8 Ronas........................... III 39 36.007 5,413584I3 259.169-64 49' I –3.78 Saxavord ....... tº e s ∈ S. & tº º e s tº e º 'º 35 9 36.973 || 5.20567031 || 160572-18 || 30-4 I8o o 5.347 Fetlar........... * * * * * * * * * * * * e s p → Io9 41 48.661 5-18362746 || 152625-63 28.9 9 || Ronas........................... 27 55 47.204 || 488941605 75939-46 14.4 || +o-66 Saxavord ..... * * * * * * * * * * * * * * * * 42 22 25.969 5-og844808 || Io9256.70 | 20-7 18o o 1,834 k Saxavord ..................... 22 3 20.248 || 4-8091.2521 || 64435.5o | I2.2 - Io Ronas........................... 4o 44, 51.891 || 5-0492.4262 || II2OO6-34 2I-2 || -7.30 Yell ........................... 117 11 49-368 5-18362746 || I52625.63 28.9 18o o 1.5o'ſ - Saxavord ...... & 8 º' tº e º e º 'º e º s e e . || 42 45 1.693 || 4,96615055 || 925OI-878 17.5 II *ell ........................... 12 31 43.186 4,4707 1871 || 2956o:972 5-6 || +3:46 Dalta ...................... || 124 43 15-649 5-o492.4262 || II2006:347 21.2 18o o o-528 Saxavord - * * * * * * * * * * * * * * * * * * * * * 22, 2 4. 4.69808366 || 49898.060 9°5 I2. 㺠* * * * * * * * * * * * * * > . . . . . . . . . . . º I3 ; ::::: 4,4707 1871 || 29560-972 5-6 –2-89 * “..................... I44 3o 8.48o 4.88041605 7593o463 I4°4. 18o o o-201 3 IC 2 444 PRINCIPAL TRIANGULATION. TIGURE 6—continued. | i - Distances in IE f No. of Names of Stations. | Corrected Angles. Iog. Distances. rror O A. Feet. Miles. A. O f A/ f / Saxavord ..................... | 52 37 8.644 4’37988539 2398.I-999 4'5 I3 Balta ........................... | 25 45 3: Igg 4. I 1767665 I31I 2.233 2.5 || + 2 I-I2 Gerth of Scaw ...... tº £ tº g tº gº tº $ tº | 101 37 48.22% 4'4797 1871 || 29560-972 5-6 18o o o-o/2 - Saxavord ..................... 33 34 46.31o 3.95553oô7 9926-734 I-7 I4 Gerth of Scaw ............... | 92 57 43.698 4:21.215114 || 16298.632 || 3-1 || + 19.20 Nive Hill ..................... |_53 27 30-ozo 4-11767665 || 13112:233 || 2:5 180 o o-o28 Saxavord ..................... I9 2 22:334 4, 17954288 || 1511.9-690 2.9 75 Balta ........................... | 20 35 19-365 4.21215II.4 || 16298.632 || 3: I | –8.32 Nive Hill ..................... 14o 22 18:338 4,4707 1871 || 29560-972 5-6 | 18o o orogº TIGURE 7. Ben Clibrig ......... tº º ſº º it tº º ſº tº 90 9 20.248 || 5-36738588 || 233016.07 44. I I | Ben'Cheilt..................... 3o 9 44. IG6 5-off.847.423 || II.7.077.71 22.2 || + o-41 Ben Hutig..................... 59 4o 61. II6 5:30352254 || 20II.5I-I6 38.1 18o o 5:530 Ben Cheilt..................... | 68 59 55.733 5.3461 1286 || 22 1877-30 || 42-o 2 | Ben Hutig....... tº $ tº º ſº e º ſº º ſº º ſº tº c. | 32 21 15.504 || 5: Ioa 4.3731 || 1271.85:41 24.1 supplementary. Dunnet Head ............... | 78 38 55.26o 5.36738588 || 233016.07 || 44.1 |Tºgo o 6,497 Dunnet Head ............... 64 47 9.415 || 5.33083134 || 2I4205-85 | 40-6 3 || Ben Hutig..................... 45 38 32.831 5-2286 1358 || 169283.og 32. I || +3.88 Scarabin........................ 69 34 25.733 5.3461 I286 || 22.1877-30 || 42-o 18o o 7,979 Dunnet IIead ............... 27 22 3-970 5-od847.423 || 117077-7I 22.2 4 || Ben Hutig..................... 92 2 16.62o 5.4057,3309 || 254526.55 48.2 || + I-57 Ben Clibrig .................. 6o 35 45-500 || 5.3461 1286 || 22 1877-3o 42-o 18o o 6.096 Ben Clibrig .................. | 88 59 52.329 || 5-46853oI2 || 294.123.77 55.7 5 Dunnet Head ............... 3I 5 37°42O 5, 18160562 I51916-74 28.8 +o. 17 Fashven........................ 59 54 39°330 5-40573309 254526.55 48.2 | 18o o 9-o'ſ 9 Dunnet Head * * * * * * * * * * * * * * * * e s IO4. 43 I 2-514 5:4097.5785 256896.30 48.7 ; 6 Ben Hutig..................... 18 37 46-422 || 4-92.86.42O6 84848-09 | 16. I supplementary. Wart Hill Hoy............... 56 39 5-34o 5.346 II 286 || 22 1877-30 || 42-o | 180 o 4.276 Dunnet Head g tº º ºr º ſº dº º ſº tº it is º º tº IOO 59 39.063 5 50689488 ; 32.1288.28 60-9 A-y Fashven & s e s e s is e º e º a tº e º e º 'º e º 'º s is e. I5 I 3I '954 4-928.64206 84848.og I6. I –3:37 * ; i : Wart Hill Hoy...... & C & tº gº tº ſº º | 63 58 54,735 | 5-46853012 | 294.123.77 557 18o o 5.752 TRLANGLES. 445 FIGURE 7—continued. No. of | Distances in | Frror of * Å Names of Stations. Corrected Angles. Log. Distances. * º A ſº | IFeet. Miles. | 4 Wart Hill Hoy............... 2: 36 3.548 sº I51916.74 28.8 ºf 8 Fashvon........................ 74 56 11.284 5.5ozo 1710 || 317699.88 6o-2 || -o-62 Ben Clibrig .............. i. e. g. ſº 77 33 57.236 5.5oG89488 || 32.1288-28 || 6o.9 18o o 11.068 Wart Hill Hoy............... 29 29 11.284 5, 19895844 || 15819976 29.9 9 Ben Clibrig ................. 5% 6 58.883 5.40343638 || 25318497 48-o || + o-93 Scarabin........................ 98 29 39.131 5.5ozoi 7or 317699.88 6o-2 || - 18o o 9-298 Wart Hill Hoy............... 38 30 7.281 5:30352254 || 20115I-16 || 38. I Io Ben Clibrig e e s is a e e s is a e º sº * * * * 4o 59 29.835 5:3262 2427 3, 1945:53 4O' I + 2.05 Ben Cheilt..................... Ioo 30 32.727 5'502917OI 317699.88 6o.2 18o o Io-923 Wart Hill Hoy............... 64 13 13.742 4,969.2 1802 91246.88 17.3 II | Dunnet Head ............... 58 55 15.349 || 4-9384.5147 86786.36 I6.4 || +3.41 Ronaldshay, South ....... tº tº 36 ºf 34.466 4,9286.4206 || 84848-09 16:1 18o o 1,557 { Wart Hill Hoy............... 71 12 54.646 || 5-3797.6783 || 2397.55-68 45.4 I 2 Scarabin........................ 2O 2. 30.293 4-9384.5147 86786.36 16.4 —5.88 Ronaldshay, South ......... 88 44 39.946 5.40343638 253184 oz 48-o 18o o 4.885 Ben Cheilt..................... 94 27 57.437 5'49235537 3,9495-54 58.8 13 Ben Hutig..................... 37 6 8.372 5.2738,563.I º 187869.5I 35-6 || +3.53 Ronaldshay, South ......... 38 26 4.39 5:36738588 233016.07 44.1 | 18o o Io. 248 Ronaldshay, South ......... || | 16.oir 5-0684.7423 || II.7977-7I 22.2 14 Ben Hutig..................... ; º ...; 5.5372.3354 || 344535-16 65.3 –3.74 Ben Clibrig. .................. 63 39 43.648 5.49205537 || 31°495'54 58.8 | * 18o o 8.477 Ronaldshay, South ......... . .8 5-05291349 || 112957-09 || 21.4 | I5 Wart Hill Hoy............... ! º : #: 4-8567 8282 71908-93 13.6 || —2.76 Deerness ..................... 36 12 7.33% 4-93845747 86786.36 16.4 18o o I-466 Deerness ..................... .358 4.92.86.42O6 84848-09 | 16.1 | I6 Wart Hill Hoy............... ... . ; ºš ſº 397 ºut. Dunnet Head ............... 4, 33 33.7% 5-05291349 || 112957-09 || 31.4 18o o 2.186 Peerness ..................... § 2 gº 5-18942889 || 154678.12 29.3 | I7 . Hill Hoy............... º: º ; 5-1180,5079 || 131235.34 24.9 || -o-36 *y Hill ..................... 45 37 58.632 5:05291349 || 112957-09 || 31.4 Fitt n 11 I8o o 3.407 *. ºtty Hill ..................... T., ry • 2 tº ſº ºf or 68 nſ. 8. 18 Wart Hill Hoy............ * : *9.3% ...; . . . . . Bon Hutio ... " " ''''''''' 143 36 1.552 5:59342.37 || 392:13:33 743 c * * * * * * * * * * * * * * * , , , , , , 13 35 34-239 5-1894.2889 || 154678-12 29.3 18o o 5-559 446 PRINCIPAL TRLANGULATION. FIGURE 7–continued. Di º Nº. of Names of Stations. Corrected Angles. Log. Distances. F istances == Fº of º feet, 116S, g | | Fitty Hill................ º e º 'º º II 55 48.461 5.off&474.23 || 117077.71 22.2 f / 19 || Ben Hutig...................” 124 15 37-289 5-67036496 || 468.128-30 || 88.7 |supplementary. Ben Clibrig .................. 43 48 43:168 5-5934o827 || 3921.1o.33 74.3 18o o 8.909 Fitty Hill ........... & e º 'º e º 'º e s a 29 36 49.318 4.81239323 64922.20 | 12.3 20 | Deerness ..................... 57 4o 36-off!} | 5-o454 I548 || IIIo23.65 21.6 || –o.75 Stronsay ..................... 92 4.2 36.303 || 5 II.8o 5079 || I31235.34 24.9 18o o I-690 Stronsay........................ 64 24 38.636 5, 1894.2889 || 154678-12 29.3 21 | Fitty Hill ..................... 75 14 47.970 5.21970505 || 165846-02 || 31.4 || -3-32 Wart Hill Hoy............... 4o 20 37.293 5-O4541548. || IIIo23.65 2I'o - 18o o 3,899 Stronsay • * * * * * * * * * * * * * * * * * * * * 75 30 51.888 5-06858792 I 17108.36 22 - 2 22. Titty Hill ..................... 37 51 5I-98o 4-87064032. 7424O-40 14. I Supplementary. Start Lighthouse ............ 66 37 18:ood 5-O454 I548 || IIIoz3.65 21.o - 18o o 1-874 Start Lighthouse * * * * * * * * g e º º 38 39 42-341 5. I8942889 154678. I2 29.3 23 | Fitty Hill ….................. ..] II.3 6 39.950 5.3574I459 || 2.27727.03 || 43.1 33 Wart Hill Hoy............... 28 13 41-622 || 5-off.858792 || 117108.36 22.2 I8o o 3.913 Fitty Hill ................... tº tº 6o 7 43’545 5°3754 II.90 237362-39 45°o 24 Stronsay ..................... 95 56 38-oo.4 5.43498 Ioo || 27.2258-22 || 51.6 || +3.68 Fair Isle .................... 23 55 44-605 || 5:0454.1548 || IIIo23.65 21.0 I8o o 6-154 Fair Isle e e º 'º e º g º a t t e º 'º º º § e º 'º I5 8 58.233 5-06858792 117108.36 22 - 2, 25 Titty Hill tº e º e º 'º º 'º e º 'º º tº 0 & 0 & © e º 'º 22. I5 5I-566 5.22988839 16978o.73 32.2 |*. Start Lighthouse ............ || 142 35 13.037 5.43498100 || 27.2258.2% 51.6 18o o 2.836 Fair Isle........................ 88 34 33-oS4 5'549I4673. 354116.96. 67.1 26 IFitty Hill • * * * * * * * * * * * * * * * * * * * * 4. I I I 55. I55 5:36793827 2333I2-64 44'2. –2.27 Toula........................... 5o I3 46.670 5'43498 Ioo 27.2258-22 51.6 I8o o 14-909 Foula ...................... © tº C tº º --mm º 31 5 2.61 I 5.22988839 || 16978o.73 || 32.2 27 Fair º * * * * * * * * * * * * * * * * * * * IO3 43 3I.318 5'5O442O33 319462.82 60.5 Supplementary. Start Lighthouse ....... “ || 45 II 35-105 5:36793827 || 233312.64 || 44.2 º I8o o 9-034 Foula • * * * * * * * * * * * * * * * * * * * * * * * * * * 32 9 3.228 5. I7479 Io9 I4955I-61 28-3 28 Fair Isle ....... * * * * * * * * * * * * * * 91 43 59-798 || 5-44.856687 || 280909.79 53.2 55 North Ronaldshay Lt.-house 56 7 5-163 || 5.3679.3827 || 233312.64 44.2 18o o 8, 189 Stronsay ..................... 67 24 23:412 5-ogoó4342 I23209-28 || 2 º ſº 3'3 29 | Fitty Hill .…....: * * * * * * * g e 59 17 43.338 5-oA539781 || 11joió.13 21.3 33 North Ronaldshay Lt.-house 56 17 55.922 5-O-4541548 II IO23.65 21-o 18o o 2.672 TRIANGLES. 447. FIGURE 7—continued. No. of * Distances in Prror of Å Names of Stations. Corrected Angles. Log. Distances. * A i ſº Feet. Miles. º North Ronaldshay Lt.-house 2% § 48732 5-18942889 || 154678.12 29.3 f/ 3o Fitty Hill .......... * * * * * * * * * * * I31 32 31.308 5.4043848o. 253737-6o 48. I supplementary.| Wart Hill Hoy............... 21 18 43.290 5-ogo.64342 | 123209-28 || 23.3 I8o o 3-350 IFIGURE 8. Scournalapich ............... 55 I 37-730 356389632 368o.41. Io 69-7 I Ben Clibrig .................. 75 37 45.849 5-63859075 || 435IoI-67 82.4 || – I-35 Monach e e º e º e s a e º s is a e s s > * * * * * * * 49 2 I 4-957 5.53246544 34O773.2 I 64.5 18o o 28.536 Ben Clibrig ........ tº t e º ºs e º ºs º º 44 19 I5.314 || 5:4475 I575 || 28o23o:72 53. I 2 Monach ........................ 22 15 26.978 5-18160563 || 151916.74 28.8 || + I-76 Tashven........................ II3 25 26.881 5.5658.9632 || 36804I. Io 69.7 I8o o 9.173 h Monach ...... * * * is e s e e s m e º s e s e s a 55 26 42.484 || 5-42795235 || 267887.44 50-7 3 Fashven................ ſº º ſº tº tº 65 4 14, 218 5-46977217 İ 29.4966. I5 || 55.9 |supplementary. North Rona .................. 59 29 19.285 5.4475 I575 || 28o23o.72 53. I 18o o 15.987 Monach ........................ 52 5I 20.257 5-4004.5o?3 || 251449-48 || 47.6 4 | North Rona .................. 57 54 38.462 5.426927or || 267255-72 50-6 33 Cnoc-Ghiubhais............... 69 14 I6.og'7 5.46977217 || 294966. I5 55.8 18o o 14.756 Fashven........................ 7 22.25o 5-66644394 || 463929-90 87.9 5 North Rona .................. % § : 5-63163719 || 4281.90-68 81. I 5) Cleisham ..................... 34 39 30. I3o 5-4279.5235 267887.44 || 50.7 I8o o 26.529 North Rona. .................. II 16 30.669 || 4:9578.4865 90.750'42 I7.2 6 || Cnoc-Ghiubhais............... 135 55 36.332 5:50903727 || 322877-12 61.2 33 Ben Hutig..................... 32 48 6.726 5.40045073 || 251449.48 47.6 18o o 3.728 Pen Hufig;...: º, º 'º e º 'º º t e º 'º t t e º 'º 4 41 3I '903 4'2534.522I I7924.7I 33.9 7 |-Cnoc-Ghiubhais............... 19 46 26.264 || 48700 oo40 || 74.131-09 || I4-O || – lo.32 Tashven........................ 155 32 1.962 || 4-9578.4865 || 9ozso.42 I7.2 18o o o 129 * -- ~~. -º-º-º-º: Cnoc-Ghiubhais............... 14 23 33-840 5-238423 Io || 173152:39 32.8 wº- 8 Monach tº tº C tº ſº º ſº g tº e º ſº tº ſº º ſº º tº º ſº º ſº tº C. I43 2. 55.783 5-62197495 418769-4I 79°3 Supplementary. leisham ................ tº C G D tº 22 33 36.910 5.426927oI || 267255-72 50-6 Cl Aft 18o o 6.533 eisham - r) • ; : " ":" . . . . . . . . . . . . . . . 46 4. 8. 42 5.49487oo2 3I25I4’39 59°2 9 gºliubhai * * * * * tº e s e º sº e s e e 28 46 %: .5°31.97 I 505 208792.58 39°5 35 * * “...................... Io 5 9 8.370 5-62197495 || 418769.41 79.3 I8o o 14-792 448 PRINCIPAL TRIANGULATION. FIGURE 8—continued. N* of Names of Stations. Corrected Angles. Log. Distances. Distances in Fº of i. I'eet. Miles. Cleisham ..................... 65 38 3$653 5.3371 6823 2I-7354-30 || 4 I-2 & f Io Monach ........................ 63 27 46-990 || 5-3197 I505 || 208792.58 39.5 || -o-64 Ru Rea '........................ 47 53 45-265 5-238423 Io || 173150-24 32.8 18o o 7.908 Cleisham ..................... 4o 49 18.700 5' 10171442 || 145115-71 27.5 II Ru Rea '....................... 69 2 9.412 5:31658955 | 207295.35 | 393 || –o-o2 Storr ........................... 7o 8 38.533 5-31971505 || 208792.58 || 39.5 18o o 6-645 | Cleisham ..................... 57 2 19:07.1 5.37556491 || 237446-93 || 45-o I 2 Storr ............ :.............. 75 52 4-812 5.43844Oo3 || 274435-35 | 52°o —4-2I Ben More, S. Uist............ 47 5 47.328 5-31658955 || 207295-35 | 39°3 I8o o I I-21 I * Cleisham ..................... 8 46 54.338 5.64708656 || 443697-o/ | 84-o I3 Ben More, S. Uist............ ź. 52 ; 5-608645or 4O61 II-24 76.9 - O - II Scournalapich e e s e e s is a º º is a tº a tº 37 2 I I 2.296 5.43844oo5 274435-35 52-O 18o o 25,678 4. Cleisham ..................... 74 5 36-48o 5-6338.562o 430384-o8 81-5 14 || Ben More, S. Uist............ 68 5 16:559 5-61824448 || 415187.71 78.6 || + o-97 Mamsuil........................ 37 49 32.699. 5.43844oo3 || 274435-35 | 52-o 18o o 25.738 Mamsºil.......:::.............. 22 Io 29.604 || 5.37556491 || 237446.03 || 45-o I5 Ben More, S. Uist............ 20 59 29.231 5:35288219 || 225362.78 42.7 || + o-97 Storr .................. º, tº G & C & © tº º 136 5o 9.764 5-6338562o || 430384-08 || 81. 18o o 8.599 wº Cnoc-Ghiubhais............... 26 55 35-561 5:31658955 || 207295.35 | 39.3 I6 Cleisham ..................... 86 54 17.442 5-66003063 || 45712o.43 86.6 supplementary. Storr ........................... 66 Io 27.356 5-62197495 || 418769.41 79.3 18o o 20-359 Ben More, S. Uist............ 25 29 6.924 . 5.32 Io 7834 2O9449'O2 39.7 17 | Scournalapich ............... 88 48 51.349 5.687.26718 || 486706.53 92.2 || + 2.22 Ben Nevis............. Q & tº $ tº ºn tº º 6542 23.553 5-64708656 || 443697.oz | 84°o 18o o 21.826 |Ben Nº. S. Uist............ 3o 2 52-102 5.38877.379 244778-79 46.4 I8 Ben R. Muji * * * * * * * is e s e e º e 54 32 55.283 5-6col 42O7 398237.43 75'4. —3.71 Ben More, Mull ............ 95 24 35-413 5.68726718 486706.53. 92.2 18o o 22.798 Storr ................... i. f ... . . . . . . . . . . . . . 6 5-48 II 5202 || 3O2797-31 || 57.4 19 || Ben More, S. Uist............ ; § §. 5.61456360 || 41 1683-63 78.0 || +o.or I3en Heynish * * * * * * * * * * * * , , , , , , 34: 49 30.568 5.37556491 237446-og 45'O 18o o 16.702 Storr ........................... .265.6 8 i. i. * , 26 I6 53.8 5-205097.57 || IS4373. Io 34.9 20 || Ben Heynish;* * * * * * * * * * * * * * 72 22 § 5'5986,3433 || 396857.26 75.2 || —3.04 Ben More, Mull ............ 81 21 10,636 5.61456360 || 41 1683-63 78.o 18o o 16.992 TRIANGLES. 449 FIGURE 8—continued. tº IDi * º s: of Names of Stations. Corrected Angles. Log. Distances. istanceS ill Fº of º Feet. Miles. º - Storr ........................... 26 16 23.684 5.25oS 5482 || 178055-26 33.7 £f 2I Mamsuil............. tº ſº º ſº tº º C ſº tº º I 19 39 19.684 || 5.54353474 || 349570-47 | 66.2 || + 1.18 Ben Nevis.................... * 34 4 24,824 5-35288219 25.362.78 42.7 18o o 8.192 Ben Nevis..................... 24 25 45-473 || 5-28072430 || 190864. 12 || 36.2 ** | Ben More, Mull ............ I23 32 29°349 5:5;29.190 38.4673. I9 || 72.9 || + o-94 Jura ........................... 32 I 54'327 5.38877.379 || 244778-79 || 46.4 18o o 9. I49 Ben More, Mull ............ 19 46 27.730 || 5-ox{59.4334 || IIII.58-67 21.1 *3 Jura .........................” 124 42 46.633 || 5:43:59942 || 279999:57 || 51.1 || +3.54 Ben Tartavil.................. 35 30 49.735 | 5-2807 2430 || I90864. I2 36.2 * 18o o 4.098 Ben More, Mull ............ 74 4o 28: II3 5:4532 1443 283932.06 53.8 *- 24 || Ben Tartayil.................. | 38 46 33.324 5-2656.9758 || 184373. Io 34.9 || -o-73 Ben Heynish........ 9 tº e º ºs e º 'º º e | 66 33 9-847 5.43150942 || 27oo90.57 || 51. I . | 180 o 11.284 Ben Nevis..................... 78 58 40-755 5-74794oD.4 || 55968o:39 Ioff.o 25 | Ben More, S. Uist ......... 42 25 43.455 5.585091.90 || 38.4673. I9 || 72.9 || -o-42 | Jura ........................... 58 36 18.964 5.6872 6718 || 486706.53 92.2 I8o o 43-174 Mamsuil............. & e º 'º e º 'o e º s º 59 43 41.956 5-6coI 4207 || 398237-43 75.4 26 Ben More, S. Dist gº tº c tº 8 tº s º it 5I I9 ; 5-55624Ooz 359948.2 I 68.2 |Supplementary. Ben More, Mull ............ 68 57 47.962 5-6338.562o || 430384-o8 81.5 || | I8o o 31.429 Ben Clibrig .................. 44 35 30-134 5'493IoI55 || 311244-40 || 59°o 27 | Monach ........................ 79 (7 65.465 5-639.13345 || 435645-72 82.5 —2.78 Storr ........... ſº e g º C G tº G & © tº 8 º' tº tº 36 6 53.83% 5.56589633 || 36804I-II 69.7 18o o 26.436 Jura............................ 73 53 29.532 5-60880215 || 406258-21 76.9 28 || Ben Nevis. tº º ſº º tº º º tº C & © tº º 0 & 0 & e º º º 4O 38 64.847 5-44006641 || 27546499 52.2 || -o-62 Ben Heynish.................. 65 27 49.539 5.58509190 || 38.4673. I9 72.9 l I8o o 23.918 FIGURE 9. Ben Lawers .................. 25 59 43.963 || 5-2807 2428 || 190864. II | 36. It * | Jura ....... tº tº º ſº º ſº tº it g º O & © tº º 'º C tº dº tº 56 58 8.26o 5.56240606 || 365095. I5 69. I || -2.22 Ben More, Mull ............ 97 2 24-ozó | 5,63568972 || 4322O4.94 81.9 I8o o 16-2 49 a #. ſº * * * * * * * * * * * * * * g º º e 36 47 39.289 5.38877377 || 244778.78 46.4 * H. §. Mull ............ 26 3o 5.323 5.26093366 || 182361.71 34.5 || +394 CIl NeWIS .......... tº $ tº º ſº a c e s a º II6 42 24,756 5.5624.0606 || 365095.15 || 69'ſ 18o o 9-368 3 L 450. PRINCIPAL TRIANGULATION. FIGURE 9—continued. | º g No. of . Names of Stations. | Corrected Angles. | Log. Distances. Distance S in Error of A. ! Feet, s Miles. A. Een Lawers tº Q tº ſº tº dº ſº tº $ tº C tº g º ºn g g ſº 89. 4. 2:329 5.4543.2436 284658-63 53-9 47/ 3 || Ben Nevis •:-------------...... | 51 5 47.o.53 5:3454.6930 || 22.1548.75 42-o || + o-68 Ben Macdui .................. |_39 5° I. IoS 5:26093366 || 182361.71 34.5 18o o 9-490 r | Ben Lawers .................. | 24 56 44.2 Io 4'9722 oo.47 93799.49 || 17.8 4 || Ben Macdui .................. 7o 5 2-833 5:32O36048 || 209,163.11. 39.6 || –1.63 Glashmeal ..................... | 84 58 17.547 5'3454.693o || 22.1548.75 42-o 18o o 4.590 Ben Nevis..................... 76 23:34,549 5.47441148 || 298.133.98 || 56.5 5 i Ben Macdui .................. 35 29 3.975 5.2505548o || 178055-26 || 33-7 || -o-38 Mamsuil........................ 68 7 33-049 5.4543.2436 || 284658-63 53.9 180 o II.573 - Ben Macdui .................. 42 11 9-501 || 5.32 Io?832 || 209449 of 39.7 6 || Ben Nevis.............. • * * * * * * 71 56 29.354 5-472O7618 || 296535-15 56.2 || + 1.36 Scournalapich e e º 'º e º e º ºs e tº e º 'º º 65 52 34°46o 5.4543.2436 284658-63 53-9 I8o o 13.31.5 - - Ben Macdui s tº º 'º e º 'º º º is a G e º 'º & © a IIo 41 34.864 5.56598393 || 3681 15-35 | 69.7 7 Scournalapich ............... 29 24 24.217 | 5' 1373,5653 || 13720o.77 26-o || + o-49 Corryhabbic ..... & ſº tº a tº e º ſº tº £ tº J 48 54 9.858 5-472O7618 || 296535-15 56.2 18o o 8.939 Mamsuil....................... 33 27 19:346 5:32936O48 || 209102. II | 39.6 8 Ben Lawers .................. 88 5 58.987 5'57876oo5 || 379105.47 || 71.8 supplementary. * Glashmeal ..................... 58 26 57.535 5'5095.2261 || 323238. I5 61.2 180 o 15-868 Corryhabbie .................. 71 29 II:826 5-45614422 || 285853.96 || 54. I 9 || Ben Macdui .................. 81 26 3.I.oré 5'47.436Oo3 || 298098.66 56.5 || –o.16 Ben Wyvis .................. 27 4 26.268 5-1373,5653 || 137200-77. 26.0 |Tºo To 9. IIo Ben Wyvis.................. tº º º 81 II 27.627 5.61442657 || 411553.75 77.9 Io | Corryhabbie ............ tº tº º is a tº 53 6 22-859 5.5225.25oz || 333061.99 || 63-1 || –o.70 | . Ben Nevis............ ... ...“ 45 42 32°560 5'47.436603 || 398098.66 56.5 18o o 23.046 Corryhabbie ...............” 43 28 54,526. 5:10806024 || 128250.85 24.3 II Glashmcal s s a º ºs º is a tº º ſº º º º º ſº tº º tº tº º 66 3 47'392 5.23133844 I70348-55 32°3 +-I-O4 Mount Battock............... 7o 27 22.918 5.2446.25or I75640.64 33-3 .# 18o o 4,836 | * - . Corryhabbie .................. 8o 4o 19424 5,44233125 || 276925-29 52.4 12 | Mount Battock............... 61 57 11.494 5.39385588 || 247663-ol 46.9 || -o-o8 Mormonth ..................... 37 33 38.86í 5.23133844 || 170348:55 32.3 I8o o 9.779 Mount Battock............. ... 31 46 41.142 5-16394,039 || 145831.40 27.6 : 13 | Mormonth ..................... §6 55 22:781 5:36565127 || 232087.24 44-0 || -1.86 Inock ....... t is 0 & 0 & 0 & 6 g c e º 'º e tº Lº 91 18 4.027 5:44233125 || 276905-29 52-4 18o o 7.95o TRIANGLES. 45 I JFIGURE 9—continued. - Di tº Frror of s: of Names of Stations. Corrected Angles. Log. Distances. ||-- StanceS in Fº of º - Feet. Miles. º O f & - Aſ Corryhabbie .................. Io8 28 53.985 5-55047146 || 355198.78 67.3 i I4 || Ben Wyvis .................." 18 46 24.802 || 5-oSIo 7412 || I2O524. I6 22.8 |supplementary. ICnock ....... * * * * * * * * * * * e s is e e is 52 44 50.217 | 5'47.436Oo3 || 298098.66 56.5 18o o 8-oo.4 Mormonth..................... 48 I 30.905 5.46788o09 || 293684-48 || 55-6 #5 I Knock ........................ IIo 18 29.68o 5.568.77.197 || 370486-14 || 70.2 35 Ben Cheilt..................... 2 I 4o 8.851 5. I6394,039 || 14586 I-40 || 27.6 18o o 9-436 Ben Cheilt..................... 7 24 -748 || 4.62977;or || 42635.465 8.1 I6 Knock ........................ 55 7 28.735 | 5.433878o8 ||27.1567-68o 51.4 35 Cowhythe ..................... II 7 28 31.930 5-46788o09 || 293684-476 || 55.6 I8o o 2.4.13 Ben Cheilt..................... 25 24, 28.264 K 5-2Io94747 || 162497.79 || 30-8 17 | Cowhythe...................... IoS 47 5.048 5-55457586 || 35857 I-58 || 67.9 53 Corryhabbie .................. 45 48 36.5ol 5.43387808 || 271567-68 || 51-4 18o o 9.813 Corryhabbie .................. 56 38 6.498 || 5.44947621 || 281498.58 53.3 I8 || Knock ....... tº ſº º ſº º ſº tº ſº tº ſº tº dº º ºs e º 'º Ioz 24 52-034 5.51742.292 || 329 I'72-O2 62-3 33 Scarabin............. ſº tº ſº ſº º & L → ; * * 2O 57 9.25I 5-oš Io 7412 || I2O524-16 || 22.8 || . 18o o 7.783 Cowhythe ..................... II 4I Io:258 || 4-7.4046625 || 55or 3.12 Io.4 I9 || Ben Cheilt....... tº C º º ſº tº 9 º' C. º. º. º. º º 79 18 25.241 5-4263.3525 || 266891.81 | 50.5 39 Scarabin........................ 89 o 27.949 || 5.43387808 || 27.1567-68 51.4 I8o .o 3-448 t Ben Macdui ..... * * * * * * * * * e º s e 4o 35 34,981 5-4403.3099 || 275632.86 52.2 20 | Ben Wyvis .................. 96 58 21.713 5.62375481 || 420489. I7 79-6 || + 1.47 Scarabin........................ 42 26 21.675 5-45614422 || 285853.96 || 54. I 18o o 18.369 Ben Macdui • * * * * * * * * * * * * * * * * * 2O o 34-795 5-31359330 205870. II 39°o 2I Ben Wyvis .................. I31 37 35-276 5-65297.290 || 44975 I-79 85.2 || +o.91 Ben Clibrig .................. 28 22 o'26I 5-45614422 || 285853.96 || 54.1 -r I8o o Io.332 º: -- Ben Macdui .................. 25 29 59.948 5:30352254 || 2011.5I-16 || 38. I 22 || Ben Qlibrig .................. 8o I4 35-o.46 5-663.23901 || 460509-95 || 87.2 supplementary. Ben Cheilt..................... 74 I5 45-947 | 5-65297.290 || 449751.79 85.2 || I8o o 20.941 Çorryhabbie tº º ſº ºn tº e º is s a tº t e is a e º 'º 22. Io 41.437 5' 19895844 || 158109.67 29.9 *3 Šarºbin........................ Iod I 23-948 5-60486868 || 4oz 595-28 || 76.2 || – I-2I Pen Clibrig .................. 51 48 6.365 5:51742.292 || 329.172.02 || 62.3 18o o II.75o + 㺠Ben Clibrig I w " . : :b • * * * * * * * * * * * . . . . . . 2 52 56.459 5-1685326o || 1474II.92 || 27.9 & 24. §. \; * * * * * * * * * * * * * e o e s e I48 58 38.609 || 5.532.46544 || 340773-21 64.5 || + ſ^4° Cournalapich ............... 18 8 28.606 || 5-31359330 || 205870. II || 39°o 18o o 3-674 3 L 2 452. PRINCIPAL TRIANGULATION. FIGURE 9—continued. i Distances i Nº. of Names of Stations. Corrected Angles. I.og. Distances. F sances == Fº of Tect. All IQS. º o 4 f/ Ben Macdui .................. 6 42 5-526 || 4:5414924o 34793-042 6.6 f/ 25 | Mamsuil....................... º 84 I I2.924 5'472O7618 || 296535-147 56.2 || +4.28 Scournalapich ............... 89 16 43.973 5'4744 II.48 || 298.133.981 56.5 18o o 2.423 Ben Macdui .................. | 35 57 9:374 5.25573050 | 180695-30 || 34.2 26 Mamsuil........................ | 68 18 61,754 5-45614422 || 285853.96 54.1 || +o.45 Ben Wyvis .................. 75 44 o'624 5.4744 II.48 || 298.133.98 || 56.5 i 18o o II.752 Corryhabbie .................. 75 28 33.206 5.27887692 || 199051.34 36-o 27. Mount Battock............... 44. 20 4-759 5. I373,5653 || I372Oo.77 26-o || –o.55 Ben Macdui .................. | Go iſ 27:350 5.23133844 || 170348.55 ; 32.3 I8o o 5.315 Mamsuil....................... * 26 42 40.808 || 5.244.62591 || 175640-64 || 33-3 28 Glashmeal e e º e s e e s is e s s e º e º 'º º " " " 77 I9 32-638 5-5812 oA.88 3.81245-64 7.2.2 Supplementary. Corryhabbie .................. 75 58 1.876 5:57876005 || 379105:47 71.8 - 18o o 15.262 Corryhabbie º e º & C tº gº tº $ tº º tº tº ſº tº dº tº ſº 8o 3I 9-os3 5'5774 o'724. 377926-41 71.6 29 Scarabin........................ 4O I6 9-671 5.3938,5588 Hi 247660.or 46.9 + I-73 Mormonth ..................... 59 13 o' I57 5'51742.292 || 329172-oz 62.3 180 o I 8.886 - Ben Lawers ................. , iſ 624, 45.841 5:55624ooo || 359948.20 | 68.2 3o Ben More, Mull ............ 52 56 52-773 5.5995.2261 || 323238-15 61.2 supplementary. Mamsuil.............. tº e º O ſº tº tº tº g tº | 64 20 46-o24 5.5624O606 || 365095.15 69-1 18o o 24.638 Scarabin..... tº g º C tº º ſº e º 'º tº º $ tº º ſº tº º ſº 8o II 18.935 5'5037.3052 318955-81 60-4 31 || Ben Wyvis .................. 41 26 7.708 || 5.33O83135 || 214205-86 40-6 || + o-54 Ben Hutig..................... 58 22 47.ozo 5'4403.3099 || 275632.86 52.2 18o o 13-663 TIGURE Io. | * Mount Battock tº º ſº tº º tº ſº tº tº g º is tº ſº tº r II.4. 20 18.822 5.54283857 3490Io-56 66. I I Ben Macdui .................. 35 55 2.869 5.35160461 || 224700-80 || 42.6 supplementary. . Dudwick s is º e º 'º º º is a g º g & tº E tº ſº º ſº tº | 29 44 47'449 5,2788.7092 | 19005I-34 36.o | 180 o 9. I4O # Mount Battock * * * * * * * * * * s a e ... 7o o 14-odz 5-36348.448 230932. I9 43.7 2. Corryhabbie * * * * * * * * * * * * * * * * * * | 66 6 53.981 5.35160.461 || 224700-80 || 42.6 || –2.35 Dudwick ........ * * * * * * * * * * g e a | 43 53 o'407 5:23133844 || 170348.55 32-3 I8o o 8.45o Mount * * * * * * * * * * * * * g e • 39 49 43.7io 5' 1924O428 || 155741.47 29.5 3 | Dudwick ..................... | 72 38 32.819 5:36565127 || 232087.24 || 44-0 || –I-60 Knock ........................ | 67 31 51.328 5.35160461 24700-80 || 42-6 18o o 7.848 TRIANGLES. 453 FIGURE lo—continued. y listances i 4 | s: of Names of Stations. Corrected Angles. Log. Distances. 1Stan CeS lil Fº of *: Feet. Miles. i. O M f / * & ſº Knock ........................ | 23 46 I2.698 4.79839.123 62862.44 II-9 | 4 | Dudwick ..................... 69 16 4.677 5-16394,039 || I45861.40 27-6 || —5.32 Mormonth ..................... | 86 57 44.774 5, 1924O428 || I55741.47 29.5 18o o 2. I49 Mount Battock............... | 36 9 60-760 5.27081059 || 186556-59 35.3 5 Mormonth..................... | 24 59 22: Ioa 5: I.2563052 || 133545.89 25-3 || -2°57 Blue Hill ..................... | II8 5o 42.264 5-4423.3125 || 276905-29 52-4 18o o 5-128 • | Mount Battock ............... 28 & 58.9; 5'99363745 || 124961-62 || 23.5 6 Dudwick ..................... 3o 28 59.885 5: I.2563652 || 133545.89 25-3 +4' I 5 || I}lue Hill ..................... 121 24 5.246 5.3516O461 || 224700-80 || 42.6 i 180 o 3.322 Blue Hill ..................... | 19 17 3424 4,83326885 68119-09 | 12.9 7 Mormonth. * * * * * * * * * * * * * * g & • . . . . 45 27 58.502 5. I674. I2 Io i I47032.08 27.8 | + 2.92 Little Stirling ............... 115 15 o.º.o.2 5-2768 Io59 || 186556.59 35.3 18o o 2.128 Mormonth................. ... 4o 24 58-613 4,658+3756 || 45513-220 8.6 8 | Dudwick ..................... 76 o 51-599 || 4.8332 6885 || 68II9-og2 12.9 || –o.23 Little Stirling ............... | 63 34 Io-440 4.79839I23 || 62862-440 II-9 18o o o-652 i Mormonth ..................... 73 6 46-589 5.2649366o I84050-33 34.9 | 9 || Knock .............. tº tº º t e º ºs s p is 57 34 14-210 || 5.2104,4796 || I62348-38 || 30-7 |supplementary. Brimmond............. tº tº tº t e º 'º º 49 19 4.525 | 5-16394039 || 14586 I-40 || 27.6 18o o 5.324 Mormonth ............... tº $ tº tº º 7 55 7.998 || 4-6O126469 || 39926.82 7.6 IO: Brimmond tº e º e º is e s ∈ C in tº s º is is e º 'º s ºl 26 9 I-455 5. Io928o'71 127726-41 24-2 53 Over Hill ..................... I45 55 51.218 5-2Io44796 || 162348,38 || 30-7 18o o o-671 Knock ...................... 33 48 I-5 II | 5-oro4.o.525 || Io2424.83 I9.4 II Brimmond * * * * * * is s u e s e s e º e s = e s e 57 45 57.637 5: I.224O428 || I55741-47 29.5 93. Dudwick ..................... 88 26 4.599 || 5.2649366o || 184050-33 34.9 18o o 3-747 Brimmond..................... 17 42 8.342 4-81639473 65523: 14 | 12.4 I 2. Rudwick & ſº ſº tº º ſº tº e º ºs º º ſº e º ſº tº a ºn tº Io 4o 40°433 4.6012.6469 | 39926.82 7.6 — I-59 Over Hill ........ tº º ſº tº e º 'º is t t tº $ tº 15I 37 11:517 5-oro40525 || Io2424.83 | 19.4 18o o o-292 | Brimmond - * r) i.” “................ 43 44 57.08o 4'9042,3596 802.11.38 || 15.2 || I3 #. * * * * * * * * * * * * * * * * * * * * * 18 15 #: 4:56039291 || 36340.67 6.9 || -o-49 *Pººlly -.................... II 7 59 35.298 || 5-oro.40525 || 1 oz.424.83 19:4 I8o o o-605 454 PRINCIPAL TRIANGULATION. FIGURE Io—continued. * --> * > ** x * , s : * * * * ºr . -- - * { Di * No. of Names of Stations. Corrected Angles. Log. Distances. istances in Error of A. Feet. Miles. A. O Af Z/ - - - - - --- - // * Brimmond tº º ſº tº ſº tº dº º ſº tº ſº tº ſº tº ºn tº g º º ſº tº | 26 2 48.738 || 4-243989.45 17538.38 3°3 I4. Over Hill ..................... 65 29 7.932 4:56039291 36340.67 * 6.9 + o-8I Tarbathy .......... tº C tº º tº ſº tº º ſº º º | 88 28 3.48o 4.6012.6469 || 39926.82 7:6 .. 18o o o 150 Brimmond............ tº tº C tº ſº tº e º 'º | 23 51 19:571 || 4-7396528o || 549 Io-17 | Io.4 I5 | Dudwick ..................... | 25 6 60-o21 || 4.76064885 5763o-93 Io.9 || +1.94 | Layton .................. tº tº º º 'º º | 131 1 40.969 5-oro40525 || rozłºś3 | 19.4 18o o o-561 Over Hill ..................... | 94 56 21.553 || 4,42353693 || 33517.7% 5-o I6 Tarbathy s g g g º e s is e º e s is tº e s tº e º 'º º º 5o 33-601 4.26568.559 18436.802 3'5 -o-41 Layton * - s e º e s is tº e s is º º ſº tº $ tº º º 'º e º is 4I I3 4'922 4,24398945 | - 17538.379 3'3 18o o o-o'76 - - Tarbathy ........ º g c e s is a s tº º is º is 24, 39 15.408 || 4.65813756 || 455I3-220 | 8-6 I7 | Dudwick ..................... Io8 I 30.898 || 5 or 5999.19 || Io.3752-647 | 19.6 *. Little Stirling ............... 47 19 14:510 || 4-9042.3596 || 802II-375 | 15.2 180 o o-816 Over Hill s & g º º ſº Q º 'º e º 'º º ſº $ tº $ tº # * * 25 43 25-og7 4,6581 3756 455 I3'22O 8.6 18 | Dudwick ..................... II5 36 18-693 || 4:9757.2518 || 94563-858 17.9 35 Little Stirling ............... 38 40 I6.842 4-816394.73 || 65523. I45 12-4 18o o o-632 Brimmond..................... II9 II 44.540 || 5-op363745 124061-62 23.5 19 | Dudwick ..................... 14. 41 28.096 || 4:55.680497 36O41.68 6.8 55 Blue Hill ................... ... || 46 648-121 5-oro40525 || 102424.83 | 19.4 18o o o-757 Mount Battock............... 9 58 32°569 || 4-81639473 65523. I4 12.4 2O | Dudwick ....... ſº º e º 'º º is e º 'º a tº º º 26 28 12-222 5-2268.4577 || IG8595.42 31.9 33 Over Hill ..................... 143 33 I6.751 |. 5.3516o.461 || 224700-80 || 42.6 18o o I-542 Over Hill ..................... 44 55 32.186 5.12563.052 || 133545.89 || 25.3 2. I Mount Battock............... I 8 8 25.623 4.769953o4 * - 58878.oo II • 2. 33 | Blue Hill ..................... 116 56 3.838 5.2268.4577.| 168595.42 31.9 - 18o o 1,647 Tarbathy e e º e s tº e s tº it s > * * * * * * * * * 5.I 58 14:958 4-5568o.497 36O41.68 6.8 22 Brimmond tº ſº tº º tº º tº $ tº $ tº $ tº C tº e º 'º º is tº 75 26 47.460 4.64628237 44.287.62 8.4 25 Blue Hill ..................... 2 34 57.880 4:5603929I 36340.67 6.9 I8o o o-298 Layton • * * * * * * * * * * * * * * * * * * * * * * * 30 28 26.413 || 4:55689497 ||.. 36041.68 6.8 23 Brimmond * * * * * * * * * * * * * * * * * * * * * . 95 2O 24.969 4,84978226 70759-og I3°4. 33 Blue Hill ..................... 3: 11 9.104 || 4-76.064885 || 57639:03 || 10.9 & r | 18o o o-486 i Qver Hill .........?........... 8 3 54,766 || 5 III.2.1217 | 129185-02 || 24.5 24 Brimmond..................... 169 26 58.520 5.2268.4579 || 168595-43 || 31.9 25 | Mount Battock ............... 3 29 6.936 4.6012.6469 || 39926.82 7.6 18o o o-222 TRIANGLES. 455 FIGURE Io—continued. Dista * . No. of Names of Stations. Corrected Angles. | Log. Distances. 1Stºln CCS 111 — Error of A. | Feet. Miles. A. O & f / & W Tarbathy. ..................... 39 51 29.829 5: I.2563053 || 133545.89 25-3 25 | Blue Hill ..................... 127 52 I5-oo.4 5.216I 4322 || 164491.4I 31-2 supplementary. Mount Battock............... 12 16 16.264 4.6462.8237 44287-62 8.4 18o o I.og7 Mormonth ..................... I5 I5 30-512 || 4-296.18278 || 19778-ol.9 || 3.7 26 Little Stirling ............... 49 45 23:245 || 4-7586.3866 || 57363.898 || Io.9 || – 12.74 Peterhead Windmill......... II4 59 6-485 4.8332 6885 || 681 19-092 | 12.9 18o o o-242 l Mormonth ....... tº ſº tº ſº tº º 'º º ſº tº ſº tº º 9 5 I-330 4-og II 4661 | I2335-212 || 2:3 27 | Little Stirling ......... § 0 tº C C tº 5I 35 25-719 4.7869 1679 61223.307 II-6 supplementary. Reform Monument ......... II9 ig 33.106 || 4,83326885 681 19-092 | 12.9 I8o o o-I55 Mormonth...... * * * * * * * * * * * * * * * 6 Io 29-182 3.8727 1433 7459'579 I'4. 28 Peterhead Windmill......... II8 I 7.62o 4.7869 1679 || 61223.307 || II.6 33 Reform Monument ......... 55 48 23.287 || 4-7586.3866 57363.898 Io.9 18o o o-o89 - - Little Stirling ............... 58 3o 53°oog 4.2496.7090 || 17769.324 || 3-4 f 29 || Peterhead Windmill....... tº º I3 8 22-283 || 3.67548028 || 4736-748 o.9 || – I-65 | Sector Station, Great Stirling| IoS 20 44,727 4.29618278 || 19778.org | 3.7 || - I8o o o-or 9 Little Stirling ............... 56 4o 50-535 || 4 oz 1492.13 || IoSo?:324 |, 2-o 3o | Reform Monument ......... 22 7 46.426 3.67548028 4736.748 o.9 |Supplementary. Sector Station ............... IoI 11 23.650 4.09: 14661 || 12335:212 || 2:3 r I8o o o-or I FIGURE II. Slieve Snaght .......... tº ºn tº º 57 24 II. I75 5-6 II6.6782 408947.75 77.5 I Divis ............... tº Q & C C tº C C C tº 76 29 53.716 5-6.7394491 || 472Oo3. I6 || 89.4 |Supplementary. Goat Fell ...... tº ſº tº $ tº º 'º C & © $ tº £ tº tº 46 6. 27.798 5.54382 III 3498or of 66.2 18o o 32.689 - - Slieve Snaght ............... 23 22 34’ I 54 5-29102774 I95446.43 37-o * Goat Fell .................. º, º º 49 59 18.204 5:57669069 || 377303-37 71.5 33 ** ........................... || Iod 38 24.245 5-67394491 || 472Oo3. IG | 89.4 i 18o o 16.603 r Slieve Donard 24. 46 67.6 . 367048 22.283 5. * Aſ -----f tº $ tº dº º ſº e º tº a tº a ſº a º 4. 46 67-63 I 5.36704874 || 232835-25 || 44' I 3 łºń* * * * * * e s a * * * * * * * * * * * * * * 98 9 58. I44 5’74O2 I994 | 5498.19-25 | IO-4. I 39 9* *911 ..................... 57 3 19.474 5-66849586 || 4661.17-98 || 88-3 18o o 25-249 456 PRINCIPAL TRIANGULATION. . * FIGURE II—continued. Distances in { sº Names of Stations.' Corrected Angles. Log. Distances. Fect. | Miles. º of *-* I ammºsºmsºm, g A/ i */ South Berule.................. 48 1; 43-623 5.61366,598 || 410833-62 77.8 4 | Criffel........................... 90 20 3-669 5-740601.23 || 550302. I5 IoA-2 ||Supplementary. Goat Fell ..................... 4I 22 47-834 5.56c8 1440 || 363759-55 | 68.9 18o o 35. I26 Rnocklayd..................... 38 32 59:263 5-36704874 || 232835-25 || 44.1 - 5 | Merrick ........................ 48 I 57.20o 5:4437.2440 || 277794-98 || 52.6 || + 12.47 Goat Fell ................... tº tº 93 25 18.709 || 5:57 1664Io || 372961:58 70.6 r 18o o 15-172 Trostan ........................ | 4o 44 44.948 5:36704874 232835:25 44' I 6 Merrick ........................ 54 52 35.863 5:46.5o.4540 291773-22 55-3 || -4-74 Goat Fell ..................... 84 32 53.137 5:55.025292 355020-oS 67.2 18o o 15.888 Slieve Snaght.................. 49 23 29.150 5:32166699 || 299733. II | 39.7 7 fºnocidayå. g is e º 'º e º e º 'º e º 'º & tº º & © tº 8 75 26 43-511 5:42.716461 267401.98 50.6 || – I-22 Ben Tartavil.................. 55 9 58.157 | 5'35557,056 226762. I5 42.9 18o o Io.818 ſº | Slieve Snaght.................. 58 45 31.786 5.4074,4775 255533.44 || 48.4 8 Trostan ........................ 63 28 12-oš3 5:42.716461 || 267401-98 50.6 || –2-72 Ben Tartavil.................. 57 46 29:745 5-40283536 252833-93 || 47.9 18o o 13.584 Trostan ........ • . . . . . . . . . . . . . . . 78 7 24.923 || 5-6264oo27 423°58.35 8o. I 9 Merrick ...... * * * * * * * * * * * * * * * * * * 46 4o 32.215 5'49760615 3I4489.5o 59-6 || + I-15 Jura ............. * * * * * g º 'º º dº º e º s 55 12 28.538 5'5.5oz 5292 || 355ozo-o8 67.2 18o o 25-676 Inocklayd..................... 79 5632-189 5.6264oo27 || 423058.35 80.1 Io Merrick ........................ | 39 49 53.612 5.4396.5052 || 375261.3% 52.1 |+15-39 Jura ........................... 6o 13 57.948 5-571664Io || 37.296 I-58 7o.6 I8o o 23.749 Slieve Snaght.................. 47 6 22-163 5:51315835 || 325955-52 | 61.7 II Jura ........................... Io 53 29.866 4'9246.1702 84O65-35 | I5.9 || – I-23 Mount Sandy.................. 122 o 13:432 5'57669069 || 377303-37 71-5 - 18o o 5-461 Merrick ........................ 53 42 37.218 5-63568972 || 4322O4.94 81.9 - 12 Jura ........................... | 74 12 39-198 5.71264579 || 515995.24 97.7 || -1.48 Ben Lawers .................. | 52 5 24.929 5-6264oo27 423058.35 | 8o. I * ! iſ 18o o 41.345 Merrick....... * * * * * * * * * * * * * * * * * 39 2 17.670 5.56240606 || 365095.35 | 69'ſ I3- Ben Lawers .................. 78 5 8-891 5.75374975 567217.67 Io'7.4 |Supplementary. Benmore, Mull ............... 62 53 16.752 5.71264579 || 515995.24 97.7 || 180 o 43-313 Jura ........................... 51 55 23-849 5-3728 I476 235947-16 || 44.7 14 | Goat Fell ..................... 87 22 55-16o 5'4762.8959 || 29.9426.06 || 56.7 || +3-57 Ben Lomond.................. 4o 41 51.816 5:29Io 2774 I95446.43 || 37'o 18o o Io.825 TRIANGLES. 457 FIGURE II—continued. | Distances in *::: Names of Stations. Corrected Angles. Log. Distances. Feet. Miles. Fº of O f £/ Ben More, Mull ............ 67 2: 19808 5.591or 976 || 389959-73 | 73.9 -15 Ben Lawers .................. || 52 52 36.395 || 3:52.748700 || 336889-13 | 63.8 || + o-oë Goat Fell ......... ............ || 59 46 36.468 5.56240606 || 365095. I5 | 69°r 18o o 26.671 Merrick........................ || 43 9 54.062 5,47628959 || 2994.26'96 || 56.7 * Jura ......................... tº º 61 - 42 26-og2 5.58592621 || 3854.12.87 | 73°o supplementary. Ben Lomond.................. 75 7 66.118 5.6264.oo27 || 423058.35 | 8o'I 180 o 26.212 Ben More, Mull ............ 5o 33 54,408 || 5.3690.8218 || 233927-98 || 44.3 17 | Ben Lomond............... “ 53 54 63.358 5.38877377 || 244778.78 46.4 || +2.4o Ben Nevis......... . . . . . . . . . . . . 75 31 15-257 || 54672,5744 293263 II | 55.5 | 18o o 13.023 Ben Lawers ............ ...... 53 19 7.829 5.57919191 || 379482-34 || 71-9 18 Goat Fell ........... * * * * * * * * * * 7i 11 36.558 5-65126997 || 447929-82 | 84.8 || -2.26 Hart Fell ....... * @ & © & C G & e º 'º º ... || 55 29 54,528 5-5910 1976 || 389959-73 | 73.9 I8o o 32.91.5 Ben Lawers .................. 29 22 59:461 5.34393505 || 230310:43 || 4-7 19 | Hart Fell .............. & © tº e s ∈ tº 64 39 42.75o 5-60835.552 || 40584o:33 || 76.9 || + I. I.4 Sayrs Law..................... || 85 57 38,746 5-65.120997 || 447929-82 | 84.8 180 o 20.957 Ben Lawers .................. 98 33 21.697 5,69059.228 || 490447-23 92.9 2O Sayrs Law............... tº Q º e º g 26 31 63.399 5'34546930 221548.75 42-o ||Supplementary. Ben Macdui .................. 54 g4 53.793 || 5-60835.552 || 405840.63 76.9 18o o 20.889 Ben Macdui .................. || 52 10 51.384 5-60522155 || 402922:52 79°3 21 | Sayrs Law............ tº e º e º e º e º " 21 52 39.656 5-27887.091 || 199951.33 36.o 33 Mount Battock....... tº º 'º º C tº € 9 Io; 56 46.865 5.69059.228 || 490447-23 92.9 I8o o 17.299 Ben Lawers .................. . 73 36 37.488 5.60278467 || 400068 or 75.9 22 Sayrs Law.......... © tº £ tº $ tº e º 'º tº º 36 2 47.162 5.32936O47 || 209193-ſo 39:6 33 Glashmeal..................... 76 20 54.478 5-60835552 405840.63 76.9 18o o 19.128 Glashmeal .................... º 81 48 47.957 5-60522155 || 402922:52 76.3 *3 Sayrs Law..................... 18 21 55.287 5. IoSoóo24 || 128259.85 24.3 33 Mount Battock............... 79 49 28.706 || 5-60278467 || 4ood68-ol 75.9 18o o II-950 Mount Battock............... 39 7 13.900 5:40924840 || 256595-12 || 48-6 24. Sayrs Law................ tº e º 'º º 58 4. I 35.718 5-54O9 I993 || 347472. Io 65.8 - + o-73 | Pen Cleugh ............ tº tº º º q & 82 iſ 31.136 5-60522155 || 402922.52 76.3 18o o 20-754 + - Mount Battock I 6 820. I8. * * * * * * * * * * * * * * * * 4 2. .896 4,990.46774 ... 97829-03 “5 ... Ayo 25. #." * * * * * * * * * * * * * * * * * s e s • 78 47 11.851 5-5973 7566 || 395708-76 749 + o-72 uſus(1911 ..................... 87 Io 50.337 5-60522155 || 402922.5% 76.3 18o o 9-o84 3 M 458 PRINCIPAL TRIANGULATION. FIGURE II—continued. Nº. of - Names of Stations. Corrected Angles. Log. Distances. Distances in Error of * Feet. Miles. A. Goat Fell ..................... 2: 13 6.169 5.2042 7464 I6oo56.99 3o-3 f/ 26 Ben Lawers .................. 66 4 31.836 5-55200635 || 356456.34 || 67.5 || –3.68 Ben Cleugh .................. 89 41 40-399 || 5'591o 1976 || 389959-73 || 73.9 18o o 13.404 Sayrs Law.............. tº º tº e º 'º º 75 40 45-477 || 5,46828 172 || 293955-59 55.7 27 | Ben Cleugh ........ tº dº ſº tº dº ſº tº ſº º º 46 34 4-6I5 5.34393505 || 22O3ro.43 || 41.7 || +2.17 Hart Fell ............... tº $ tº dº ſº tº 57 45 22:779 5:40924840 || 256595-12 || 48.6 18o o 12.871 Goat Fell ..................... 72 30 29.854 5:58195056 || 38.1900-79 | 723 28 || Hart Fell ..................... 36 6 20-206 || 5.37281476 || 235947-16 || 44-7 || -6. I2 Ben Lomond.................. 7I 23 3o-oo7 5.57919191 || 379482.64 71.9 I8o o 20-off 7 * Ben Lomond.................. II 18 23:364 || 4-87436661 74880-13 || I4-2 || 29 || Hart Fell .............. • e s ete e e 77 46 20-931 || 5-57204007 || 373.285-60 | 70-7 || +2-60 Dunrich....... º e º e g c e º e º e º 'º º & © tº 90 55 22:272 5-58195056 || 38.1900-79 || 72°3 18o o 6,567 || + Ben Lomond e dº º e º C tº º º dº º tº e º 'º 's s e 30 25 36.299 || 5-4051 og57 || 2541,57.88 || 48. I 3o | Dunrich........................ 24 16 40-849 || 5.24547749 || 175985-75 | 33-3 || + I-16 JBen Cleugh © tº e º 'º & C C C & G & © tº º ſº. C & II9 17 52-ol.8 5'572O4oo7 373284.60. 70-7 18o o 9-166 Ben Lomond.................. 2O 5 20.058 5-16467.961 I46Io9.89 27.7 31 | Dunrich........ tº e º 'º C º 'º e º 'º tº e º 'º tº e 98 34 26:964 5.62392,543 || 420654-40 || 79.7 |supplementary. Sayrs Law..................... 6I 2O 25-651 5-57204007 373284.60 70-7 18o o 12.673 Ben Cleugh .................. 32 39 I-97 I 5.27887o91 || 190951.33 || 36-o -- 32 Mount Battock............... 66 49 32.965 5.5Io942.99 || 323849-32 61.3 || – I'o9 Ben Macdui .................. 8o 31 39-326 5'5409-1993 || 347472. Io 65.8 - 18o o I4.262 Ben Cleugh ....... tº t e º 'º e s tº º C. C. 51 Io 5o. 184 5.45432437 || 284658-64 53.9 33 Ben Macdui ............... • * * 66 24 8.958 5'52479754 || 334809:32 63.4 || + I’33 Ben Nevis..... ................ || 62 25 20-704 || 5-510342.99 || 323849:32 61.3 18o o 19.846 Glashmeal ..................... 39 o Io.737 5-40924840 || 256595-12 || 48-6 34 | Sayrs Law..................... 4o 19 40-432 5-42136168 || 263852.78 5o'o supplementary. - Ben Cleugh .................. Ioo 4o 24,463 5-60278467 || 4ood68 or 75.9 - I8o o 15-632 Glashmeal ..................... I3 13 54.686 || 4,990.46774 || 97829-03 | 18.5 35 | Sayrs Law..................... 97 9 7-138 5-62747.262 || 424. Ioa 25 8o-3 23 ° Lumsden • * * * * * * * * * * * * * * * * * * * * 69 37 7-314. 5-60278467 * 4ooë68.or 75'9 18o o 9-138 ICnocklayd............... 49 33 70-797 5'58592621 || 385412.87 | 73.o 36 || Merrick ...............“ 82 59 47-674 5'701 19509 || 502.568.30 | 95-2 33 * IBen Lomond • * * * * * * * * * * * * * * * * * 47 26 35-I46 5'57 I664Io º 372961-58 70.6 I80 o 33.527 TRLANGLES. 459 FIGURE 11—continued. s: of Names of Stations. Corrected Angles. Log. Distances. Distances in Fº of º - - Feet. Miles. –*_ Ben More, Mull ............ 4; 1; 33723 537281476 233947-16 || 447 || " | 37 | Goat Fell .............. © tº G & º O O. 58 27 37. I72 5-4672,5744 || 293263. II 55.5 || +4.32 Ben Lomond.................. 78 I5 8.023 5-52.748700 || 336889. I3 || 63.8 18o o 15-918 Ben Lomond............------ 4o 59 3-ood 5.38897.096 || 244889.95 || 46.4 - 38 | Dunrich................“'• * * * 5o 28 14.673 5.45939397 || 288ooo-38 54.5 || —2.19 East Lomond..........-------- 88 32 58.889 5-57204007 || 373284.60 7o. 18o o 16.568 Ben Lawers .................. 63 33 4.963 5.36616147 || 232360.05 44-o 39 || Glashmeal ........ tº t t e º 'º tº º & G G G & 62 46 16-644 5-3631 6942 || 230764-72 43-7 || – I-99 East Lomond.................. || 53 4o 48.543 5.32636647 || 269103. Io 39.6 18o o Io. 150 Mount Battock............... 36 49 57.7II 5'38152139 || 240725-II 45-6 40 Lumsden ..................... 43 22 9.407 5-4405 1503 || 275749-69 52.2 || -5-23 East Lomond.................. 99 48 8.25o 5,597.37566 || 395708-76 || 74.9 18o o 15.368 Mount Battock............... 22 47 50-815 5.2627.2065 || 1831.13.62 | 34.7 41 | Sayrs Law..................... 35 4I 46-oro 5-4405 I503 || 275749-69 52.2 || -8-67 East Lomond.................. I2I 3o 33.289 5-6052.2155 || 402922.52 || 76.3 - ** 18o o Io. II.4. * . . . . . . . * º Dunrich........................ 26 11 33.824 5.05475167 || II3436.21 21:5 - 42 | Ben Cleugh ................... 72 20 25.063 5.38897.096 || 244889.95 || 46.4 || -5-o& Fast Lomond...... * * * * * 0 e º s e º e 81 28 7.569 5-4051 og57 || 254ij7-88 || 48. I 18o o 6.456 Mount Battock............... || 17 52 19:024 5:23295834. || 170985-12 || 32.4 • * 43 Lumsden ..................... 27 22 52.299 || 5.40865.187 || 256.242-91. 48.5 || – I-80 Kellie Law ......... • * * * * * * * * * 134 44, 55.988 5-59737566. 395708-76 74-9 . 18o o 7-3 II - * Battock............... | 18 57 38.687 4,95283913 || 89709-64. 17 o' 44 . . fºliº Law ................... 92 54 i8-103 || 5:44053503. 275749-69 52.2 || -2°or * Lomond.................. 68 8 8.603 5.40865187 ... 256.242.91 || 48.5 || M - 18o o 5.393 + ºr ount Pattock............... 75 59 16.578 5-41040858 257281.51 48.7 - A5 jºy • * * * * * * * * * ........ || 28 55 29.234 5-10806021 || 128250.83 || 24-3 || +4^* ashmeal ...... • * * * * * * * * * * * * * *- ... “75 5 21.679 5.4086,5187. ... 2562.42.91 || 48.5 18o 6 7.491 | . . . 3 M 2 46o PRINCIPAL TRIANGULATION. FIGURE II—continued. Nº. of Names of Stations. Corrected Angles. Log. Distances. Distances in IError of tº - Feet. Miles. A. º O f f/ f/ 6 }..." * * * * * * * * * * * * * * * * * e 34 46 24:426 || 4:99046774 || 97829.03 | 18.5 4. - llſ/lsCiCºl - - - - - - - - - - - - - - - - - - - - º 59 47 58-oğ7 5' I 70990.72 1482.48-64 28. I + I.oS Sayrs Law..................... 85 25 4o’934 5:2329,5834 || 170985-12 || 32.4 l 18o o 3-397 Ben Lomond. tº tº tº º ſº tº º tº e º e º 'º º ſº tº 2 I I 52-482 5. I45563 Io I398.18.oo 26.5 47 | Dunrich::::.................... 52 19 24-o';2 5'48996584 || 308365-54 || 58.4 || +4.91 Calton Hill tº º º ſº tº º tº e º 'º º 0 & C & Ioé 38 53. I?3 5'572O4oo7 373284.60 7o.7 180 o 9.707 Ben Lomºnd.................. 72 56 2 I-402 5,47942685 301596.88 57. I 48 Calton Hill .................. 29 15 17-971 5, 188ooo34 || I5417.9:14 29.2 |Supplementary. Ben Lawers tº e º G & 0 & © Q & Q J C & © tº & © 77 48 31.306 5.489.06584 308365-54 58.4 18o o Io. 679 Ben Cleugh ................... 45 38 57.376 5'oz2I 8970 || Ioš242. I5 I9.9 49 | East Lomºnd.................. 83 55 49-252 5.1653.9899 || 146352.09 27-7 || – I'73 Calton Hill .................. 5o 25 I6. I61 5-oš475I67 II3436.21 2I-5 18o o 2-789 º tº ſº tº Q º tº ºt tº tº º tº ſº tº © C tº º 4.I 33 20.721 4'95283.913 897.09.64 I7.o 5o . East. OIn Onſl., “ . . . . . . . . . . . . . . . . 87 20 55-303 5'13063390 || 135093-33 || 25-6 || +4. Io ICellie Law .............. •... 51 5 46.192 5'oz218979 || IoS242. I5 | 19.9 18o o 2.216 FIGURE 12. Precelly.......... tº e º 'º e º 'º º tº t t t t tº 54 9 6'992 || 5'51774790 || 329418.44 || 62.4 I Cradle ........................ 59 22 27.467 5'5437 I596 3497I6-37 66.2 -2'40 Paracombe..................... 66 28 50'476 5-571295.08 || 372644.82 70.6 18o o 24,845 Precelly....................... tº 32 7 28-868 5:270.16409 || 186279.09 35-3 2 | Paracombe........... * c e s e o e s so f54 31 33-o26 5:4552 7895 || 285285.of 54-o || + 1.79 Lundy Island .............. º 93 2 I Io:584 5.54371596 || 3497.16.37 | 66.2 18o o 12.478 #. º º tº ſº tº G & © g º e © C & © tº 86 50 43-672 5.4373 1551 || 273725-66 || 51.8 3 i.". © e º e º 'º e 5o 2I 5.897 || 5.32444565 || 2IIo79-30 || 4o-o || – I-71 TOWIl VY lily . . . . . . . . . . . . . . . . . . 42 48 19.667 5.270.16409 || 186279.09 || 35.3 I8o o 9.236 Lundy Island ............ 5o 4. I-7 26c8626 82,222. tº tº e º 'º 39 5-2008 6364 || Iö2332°31 34°5 4. #º; * * * * * * * * * * * see e. e. e. e. e. 78 21 45-188 5.3671 66oo || 232898. I3 44.1 || –2.91 19h WV 11Day 8 . . . . . . . . ....... 51 34 20.898 || 5-2701 6409 || 186279-09 || 35.3 18o o 7.825 Lundy Island ........... tº dº I 24 47 6-4II 5°oo5o I493 || IoII61 - Vſ: tº º C sº •42 I9.2 5 Brown Wºjº. * * * * g º º tº º ſº 94 12 20:998 || 5'38141360 || 240665-37 45.6 || +7.83 Trevose Head ..... * * * * * * * * * * 61 o 37,601 || 5°32444565 || 211079-30 || 46-o 18o o 5-olo TRIANGLES. 461. FIGURE 12—continued. Dist: * * & s: of Names of Stations. Corrected Angles. Log. Distances. * II]. E. of ſº Feet. Miles. i. Brown Willy.............. tº ſº tº ºt 4% 38'34'867 4,8927 1977 || 78II2.36 || 14.8 Aſ 6 | Trevose Head ............... 59 13 7.590 || 4-9581 5606 || 90814-68 || 17-2 || +2.76 Hensbarrow .................. 73 8 19-140 5-oo.5o 1493 || IoII6I'42 | Ig-2 18o o I-597 Hundy Island ............... 48 o 38.530 5.338o 8or 5 || 2:1781 I. I7 || 41.3 7 |"High Wilhays ............... 79 21 38.839 5.4594o875 || 288ojo.79 || 54.5 || + o-79 Hensbarrow .................. 52 37 54.359 || 5-3671 66oo || 232898. I3 44. I 18o o 11.728 Precelly........................ 47 7. 23.673 5-48689345 || 306826.91 58. I - 8 Cradle ........................ 7o o 37.032 5'5949.2094 || 393478-43 74.5 || + o-or Dunkery ..................... 62 52 24.568 || 5-5712 95.08 || 372644.82 | 70.6 I8o o 25-273 Precelly....... $ $ ſº e º 'º º ſº º e º t e º 'º e ſº 22 46 33’559 || 5-3oo83762 || 1999 II:43 || 37. 9 | Dunkery........................ Io? 35 36.450 5,6922 IoS9 || 492278-19 93.2 || -o-92. High Wilhays ............... 49 38 7.628 5:5949.2094 || 393478-43 74.5 18o o 17.637 Paracombe..................... I24 5o 22.808 5-4970.4166 || 31408.I.oo 59.5 Io Brown Willy.................. 9 29 35.276 4.8ool II 12 || 631 II.88 12.0 supplementary. Dunkery ..................... 45 4o 5.25I 5.4373 I551 || 273725-66 51. I8o o 3-335 Cradle ........................ 46 41 4-3oo 5:3799.5750 || 239859-82 45.4 II | Punkºry ..................... 64 46 25.679 || 5.4745.4951 || 298228.75 56.5 || +o. 12 Mendip ........................ 68 32 45.68o 5-48689345 || 306826.91 58. I I8o o 15-659 Punkºry ..................... 41 48 II-675 5.21569899 || IG4323-24 3I-I I2 - Mendi tº º is is tº e º e º º ºs e º e º e ∈ E is e e º is a 61 32 57.755 5.335955oo || 216747-95 4I'o || -o-25 Pillesdon ..................... 76 38 58.722 || 5.3799.575o || 239859-82 45.4 18o o 8. I52 Mendip ........................ 36 38 56-475 || 5,44130642 || 276252.63 || 52-3 13 Pillesdon. ..................... 132 33 21.276 5.59116789 || 390092.76 | 73.9 || – I-61 High Wilhays ............... 20 47 51.25o 5.21569899 || 164323:24 || 31. I 18o o 9.ool High Wilhays ............... 76 36 42.163 5-4294.9.205 || 268838.87 50.9 I4 Pillesdon ..................... I4 54. 25.788 4-8518 o'S5o 7Io90-oo 13.5 |supplementary. Ryder's Hill .................. '88 28 56-544 || 5-4413 of 42 || 276252.63 52.3 I8o o 4.495 - Pillesdon ............... Q & Q tº e G 22 28 57.538 5.o.4667169 || III.345-25 || 21. I *5 | Ryder's Hill .................. 90 6 33. Io9 || 5-464I 6083 || 29II79.5I 55.1 33 Parrow Hill .................. 67 24 36-395 5-42949.205 || 268838.87 || 50.9 18o o 7.042 Ryder's Hill - .8 tº tol, wrºn: “.. 56 9 I.o.46 5-15Ioos 18 || 141581.07 26 I6 i. Mºſs & © tº º 'º e º º º is s a º tº ſº 99 I2 I5-891 5.2260378o || 168282-off 31.9 +3.7o rown Willy...... 0 tº e º a º ºs e s a tº a 24, 38 45-400 || 4-85180850 7Io90-oo I3’5 I8o o 2.337 462. PRINCIPAL TRIANGULATION. FIGURE I2—continued. - ~. * No. of Names of Stations. | Corrected Angles. Log. Distances. Distances in Error of A. . : Feet. Miles. A. Ryder's Hill ......... tº ſº Q is e º e º s 103 5 38.407 5'4295 I546 || 268853.36 || 50.9 &/ 17 | Barrow Hill .............. .... || 53 7 2.275 5'34396994 || 22O785. I9 || 41.8 ||Supplementary. Hensbarrow .................. 23 47 24-951 | 5-o.4667169 || III.345-25 21.1 18o o 5.633 High Wilhays ............... 7o 49 II:94o 5:37384.198 || 236505.90 44.8 18 | Ryder's Hill .................. 92 41 I5'789 5:39816723 || 25oE30-84 47.4 || " +1.09 Deadman ................. tº º is tº 16 29 36.222 || 4-85180850 || 7 Io90-oo 13.5 18o o 3-9.5I Brown Willy.................. I4 42 17-739 || 4-7739 1845 59295-off II-2 I9 | Hensbarrow ............ ...... || 142 25 I-off3 5-15372540 || 142470-65 27-o || -o- 12 Deadman ..................... 22 52 41.971 || 4.958.15606 || 90814-68 I7.2 H 18o o o'773 | Hensbarrow .................. 6 53 5-554 5.08868212 || I22654. II || 23.2 20 | Barrow Hill .................. 8 20 56-618 5-1719.3237 || I48570-43 28. I || –4.48 Maker Church Tower ...... I64 45 58.955 5-42951546 || 268853.36 5o:9 18o o 1,127 | High Wilhays .......... ſº tº C º º 29 28 41.782 5. I7973892 151265. I6 28.6 : 2. I Deadman ........ * * * * * * * * tº C º g & 24 58 57.820 5. I 13357.70 || I29824.81 24.6 ||supplementary. Maker Church Tower ...... I25 32 24, 158 5:39816723 25oI30.84 47'4 18o o 3,760 FIGURE I3. Trevose Head ............... 65 43 55.940 4.987242O2 97Io5-09 | 18.4 I | Hensbarrow .................. || 67 6 7:276 || 4.99.177485 || 98.123.91 || 18-6 || +3.22 | St. Agnes’ Beacon......... tº C C 47 9 58-428 4,8927 1977 78II2.36 14.8 || 18o o I-644 Hensbarrow .................. 77 20 32-521 5°oo897351 || Iozo87.72 | 19.3 2 | St. Agnes’ Beacon............ || 34 31 IG-off3 || 4-7730 1844 59295-off II-2 || + 2*I3 Deadman ................. tº º º ſº 68 8 I2.733 4.9872.42O2 ..97 Toš'o9 I8-4. 18o o I-322 º Deadman ... . . . . . . . . . . . . . • * * * * 25 5I 23.420 4.6577.2987. || 45470-515 8.6 || | 3 | St. Agnes' Beacon.......... tº tº 75 51 56-605 || 5-oo.47755o || IoII95.667 || 19.1 || –7.74 ICarnbonellis ................ tº ſº 78 I6 41.034 5-oo89735.I Iozo87.722 || 19.3 18o o 1,059 Deadman º” ........ tº ſº tº $ tº e s ∈ C & 27 45 9-281 470/4211ol. 56982.5° 9.7 4. Karnbonellis tº Q & Q & Q * * * * * * * * e s e e 84 48 39.232 5-og757542 || Io9937-38 20-6 ||supplementary. Goonhilly ....... * * * * * * * * * * • * ~ * 67 26 12.695 5-oo.47755o. . . IoIIo5-67 || 19. I Tºo To TL. 253 || • Ryder's Hill .................. 17 18 27.430 5'1732.6057 || I49025-49 28.2 5 | Hensbarrow ......... * * * * * * * * * 136 32 31.974 5'53726361 || 344559.02 || 65.3 s, 1 Goonhilly .................... 26 9 6.820 5'34396994 || 220785.19 || 41.8 18o o 5°324 TRIANGLES. 463 FIGURE 13—continued. Di º . . . . . . . . I4O 36 47-169 5.o.44498or Ilo'789.349 2 I • O 1So o o-27o TRIANGLES. 467 TIGURE 14—continued. * * Dist º º Names of Stations. comes Auge. Log Diane. # == ** - - , - Pºº º ſº O f // W/ Dean Hill. • * * * * * * * * * * * * * * * e o e s e 4o 54 51.415 || 4-58096962 || 38 Io9-127 7.2 17 Beacon Hill ......... ſº tº ſº º 'º - O - C 45 57 2.32 I 4.62.133882 || 41815.647 || 7-9 — 1.18 Old Sarum Castle............ ,93 8 6.638 || 4-7641 1607 || 58091.965 II.o r I8o o o-374 Dean Hill..................... 58 4o 46.570 4,5935 6492 || 39225, 178 7.4 18 | Old Sarum Castle.......... ... || 55 43 Io. I63 4.5791 oozó || 37940.256 || 7-2 || -o'92 | Old Lodge......... tº ſº tº º tº 65 36 3.586 || 4.62.133882 || 41815.647 7.9 18o o o-319 Dean Hill ............... “... 39 29 I-595 || 4:5890.6622 || 38820.956 | 7.4 I9 || Beacon Hill .................. 68 25-59-202 || 4-75418305 || 56778,382 Io.8 || –o.62 Four Mile Stone ... . . . . . . . . . 72 4 59-696 || 4-7641 1607 || 5809 I-965 II.o I8o o o.493 Beacon Hill • * * * * * * * * * * * * * * * * * 96 I3 41.648 || 4-6839.0792 48295.639 9. I it " 20 | Four Mile Stone ....... “... 3o 43 47.919 || 4:39.48.9332 || 24825-232 || 4-7 || -2-25 Old lodge ... º tº º º is ſº tº º º is is e s s º e º e 53 2 30-658 4.5890.6622 | 38820.956 7-4 18o o o-225 Peacon Hill º dº ſº tº ſº tº º º ſº º ſº tº ſº º ſº tº º º 72 I4 - I - I'74 4-57307331 - 374I7.375 7.I i 21 | Old Lodge............. ........ | 68 34 52.961 || 4-5632 1587 || 36577.656 | 6.9 || -4.5o Old Sarum Gun ....... * * * * * 39 II 6-of 8 || 4:3948.9332 || 24825-232 || 4-7 - 18o o o-203 Beacon Hill ................ º 23 59 40-474 4, 19936067 || 15825-618 || 3:0 22 | Four Mile Stone ............ 7o I 57.751 4.5632 1587 || 36577.656 || 6-9 || -4-57 Old Sarum Gun ............ 85 58 2I-91 I 4.5890.6622 38820.956 7.4 18o o o 136 * + * * * * Four Mile Stone ............ 6 2. I6.6 .2591 o'7o || 1815-966 o-3 23 | Old Sarum Gun ............ 6o 24 ...; ; 15012. ITI 2.8 || –2. Io Old Sarum Castle............ 113 33 17.94% 4.19936067 || I5825-618 3'o - I8o o o-ood Milk Hill .................... 56 37 33.310 || 4,953.76577 || 8990 I-26 I7'o 24. Inkpen • s • * * * * * * * * * * * * * * * * * * * * * 67 58 6o-o/2 4'999'I 44I2 998o3-12 18.9 Supplementary. Old Lodge..................... 55 23 28.355 4'9474,5472 886.04.28 I6.8 | 4. 18o o 1,737 * * Milk. Hill ' tº ſº tº a • * * * * * * * * * * * * * * * * 22 5 4I-o/I 4:59356492. 392.25-178 7.4 35 – 9d Lodge.................., | 84.4; 44-697 5.61640672 || 163848:617 | 19.7 || -3-oš Old Sarum Castle.......... ... | 73 8 35-149 || 4,999.144r2 || 998o3-122 | 18.9 || 18o o o.917 | . . . . Milk Hill • * * * * * * * * * * * * * * * * * * * * - 57 43 2 I • 27 4' 445744, 88oz8.59 * - 16.7 - 36 |9|d Sarum Castle............ || 36 # ::::: #; -61641.24 11.7 || +o. 17 Stoke Hill................ ..., || 85 58 16,734. 5-ord 4oo72 || Io9848-62 || 19.7 : 18o o I-273 . . . *. 27- -], §: tº º e º ºs e º a g º e s a e 34 18 36.863 || 4-78987136 || 61641-24 II-7 || tº: 7 Stoke Hill * * * * *“.... tº ºn tº º tº ſº ºn tº '• * }} - 79 49 2.597 5-O319.5oor Io7634. I3 - 29.4 —t “43 * * = e s we s • * * * * * * * * * * * ~ || 65 52 2I-964 4'999'I 4412 '998o3. 12 18.9 - I8o o I-424 3 N 2 468 PRINCIPAL TRLANGULATION. FIGURE I4—continued. No. of Names of Stations. Corrected Angles. | Log. Distances. Distances in * Fº of A. Feet. Miles. O & M f £f * Old Lodge..................... 4o 5 14-298 || 4:89866534 79.189-og | I5-o 28 Milk Hill ................ tº C tº º tº 85 39 44.266 5:08.856667 || 122621-34 || 23.2 || +o.43 Westbury Down ........ tº ſº º º 54 is 3,299 || 4.99.914412 || 998o3-12 | 18.9 18o o I-854 t Old Lodge..................... 49 12 60-754 5-oo309963 || Ioo716.27 | 19.1 29 Westbury Down ............ 63 34 58-906 || 5-o/6ool 27 II 9124-55 22-6 ||Supplementary. Wingreen ................. tº ſº tº ſº 67 12 2.942 5.0885.6607 || 122621-34 23.2 I8o o 2.602 Westbury Down ........ ..., || 47 23 31.861 || 4-8792.3232 || 75723-78 I4.4 3o Wingreen ..... tº € g g º C tº dº ſº º ſº tº ſº tº º º 54 23 36.523 4,92246089 83649-03 | 15.8 33 Four Mile Stone ............ 78 I2 53-o/5 5-oo3o 9963 || Ioo716-27 | 19. I 180 o I-459 Westbury Down ............ 7o 26 30.336 || 4:973o 54.52 93984. I3 I7.8 -- 31 || Four Mile Stone ............ 52 33 27.296 || 4,89866534 79.189-og I5-O || - I'44 Milk Hill ..................... 57 O 3.836 4,92246089 83649-03 15.8 180 o I-468 - Tour Mile Stone ............ 4o 57 7'o'77 || 4-7898.7136 || 61641.24 II.7 32 Milk Hill...................... 51 9 22: 168 4.8648 of 33 73249-78 I3-9 || + o-o5 Stoke Hill..................... 87 53 31.817 | 4,973.05452 93984-13 || 17-8 18o o 1,062 FIGURE 15. Pillesdon ..................... 44 42 44'304 || 5 II9263.16 || 131602-20 24.9 I Mendip ..................... º, º ſº 73 49 49.971 5:25444.357 || 179656.77 34.0 || – I-63 - Wingreen ..................... 61 27 30-6 II | 5.21569899 || 164323-24 || 31.1 18o o 4.886 * Pillesdon .................. ... . .44 25 16:492 5-141454.21 || 1385oI-42 26.2 | 2 | Wingreen ..................... 7o 2 I 45-97 I 5-27038oo 5 || 186371-73 || 35-3 || +3:32 Swyre Barrow ............... 65 I3 3-ojo 5’2544.4357 || I79656-77 34°o - I8o o 5.5I3 Wingreen ... . . . . . . . . . . . . . . . . . . 56 32 62.233 5.3182 or 51 || 208066-19 39.4 3 | Swyre Barrow ............... 89 42 43-249 || 5:3968.3883 || 249366.92 47.2 || –o.84. Dunnose.................... 33 44 2 I-297 5' 141454.21 || 1385oI-42 26.2 18o o 6.779 Wingreen ... ................, || 31 58 21.912 || 5.14802983 || 14061441 26.6 4 | Dunnose::::.................... || 78 8 22-690 5-41478671 || 259888.29 || 49.2 || –o,44 Butser Hill .................. 69 53 23.471 5-3968.3884 || 2.49366'92 || 47.2 18o o 8-o'73 Wingreen • * * * * * * * * * * * * * * * * * * * * 42. 39 I5-982 5.2462 1308 176284.08 33.4 5 Butser Hill ........... tº e s m º ºs º 5o I 37-335 | 5:2996.8295 || 199380-62 37.8 || –rºg2 Inkpen ...................... ... 87 19 I4.942 5-4I478671 || 259888.29 || 49.2 18o o 8-259 TRLANGLES. 469 FIGURE 15—continued. Distances in sº Names of Stations. Corrected Angles. Log. Distances. Feet. Miles. Fº of º O & f/ (ſ/ Mendip ............. * * * * * * * * * * ſº 51 46 9.889 5.29968295 || 19938o.62 | 37.8 . | 6 || Wingreen ..................... 97 o 3.291 5-4012758o || 251927-63 47.7 || + I-58 Inkpen ........................ 31 13 52.946 5. I 19263.16 || 1316oz"20 24.9 I8o o 6. I26 Wingreen .............. º t e º ſº tº tº 71 51 45-342 5-22760874 || 168891.87 || 32-o 7 Mendip ........................ 6o 21 53-891 5-1888,5754 || I54474-76 29.3 supplementary. Milk Hill ..................... 47 46 25.311 || 5-119263.16 || I316oz"20 | 24.9 _{* * +5+ - Wingreen ..................... 45 51 52.656 || 5-2640.2736 || 183665-41 34.8 | 8 || Dunnose........................ 31 8 61-672 5-1218 1566 || 132377.95 25.1 || +3.56 Coringdon ..................... Ioz 59 II.245 5.3968.3884 || 249366-92 || 47.2 18o o 5-573 Wingreen .................... . || 41 17 5.510 || 5-26367907 || 183518-17 | 34-8 9 | Dunnose...................... tº º 22 25 23:334 5.02569.162 || Iodog4:20 20:1 || -o-45 Dean Hill ..................... II6 17 35-262 5.3968.3884 || 249366'92 || 47.2 I8o o 4. Ioff Coringdon ................ ..., || 74 II 33.776 5-37864326 || 239135°o7 || 45.3 Io | Dunnose........... tº e º ºs e º 'º e º 'º e ... || 58 9 47.605 || 5.32457447 || 2 III.4.1-92 || 4o-o || +4:16 Beacon Hill ...... tº e º 'º e º is tº t tº º tº 47 38 47.396 || 5-2640.2736 || 183665-4I 34.8 ºf 18o o 8,777 Coringdon ....... tº º º ſº e º 'º - e º C & C º 44 13 4.158 || 527048029 || 1864I476 35.3 II | Beacon Hill .................. 83 36 33.925 5-42430467 || 265646.85 50-3 || –2.89 Butser Hill .................. 52 Io 3 I-II 8 || 5°32457447 || 2 III.4.1-92 || 4o'o 18o o 9.201 Swyre Barrow .............. º 66 23 6.841 5.37864326 || 2391.35 oz 45.3 12, Dunnose........................ 6o 45 7.230 5-3573.9586 || 22.7717-22 || 43-I || -2.32 Beacon Hill .................. 52 5i 56.142 || 5.3182 of 51 || 208066. 19 || 39.4 18o o Io. 213 Swyre Barrow ............... 55 13 5.825 5.26367907 || 183518-17 | 34.8 I3 - | Dunnose........... * * * * > * * * * g e º s 56 5 44.631 5-26856279 || 185593:51 || 35.1 || + o-70 Dean Hill ..... ................ | 68 37 17:005 || 5.3182 on 51 || 208066. 19 || 39.4 18o o 7-461 Coringdon ................ tº ſº e s tº 63 Io 6,859 5.26367907 || 183518.17 | 34.8 14 | Dunnose....................... wº 53 34 25-oo7 5-2 1873952 || 165477-72 31.3 || + o-87 | Dean Hill ..................... 63 I5 34,514 5-26402736 || 183365.41 || 34.8 18o o 6.38o | Dunnose........................ 5I 7 36.757 5.27048029 || 1864I4.76 35.3 - *5, Butser Hill .................. 92 54 42.872 5-37864326 || 239.135-07 || 45.3 || -3.26 Beacon Hill ........ tº º tº e º C tº e º 'º 35 57 46.529 5-148o 2983 || 1406144'I 26.6 ! 18o o 6.158 Butser Hill - 27 o 17. 7 2228 852 tº 5.6 6. I ... • * * * * * * * * * * * * > . . . . 933 4-9307233 5255-09 || 1 16. #. Hill ...... * * * * * * * * * * * * Çr 69 5I 47-O48 ::::::::: 176284-08 33°4. + 2*39 Inkpen * * * * * * * * * * * * * * d a º e º e s e tº º 83 7 58.529 5-27048029 186414.76 35-3 I8o o 3.51o 47O PRINCIPAL TRLANGULATION. FIGURE I5—continued. IDI º 4 No. of Names of Stations. Corrected Angles. Log. Distances. istancCS in Fº of A. Feet. Miles. ... º., ºr O * ** (/ ". Wingreen * - C tº $ tº $ tº dº ſº tº ſº tº tº ſº º ſº tº G º & 74 37 37.894 5-4391 8596 274907. II 52. I 17 | Dunnose........................ 44 22 22-618 5.2996.8295 || 19938o.62 37.8 || – I-23 Inkpen 'º e s is a s is e º 'º e s s a e s is a e s is e º e 6I o Io. 765 5:3968.3883 249366-92 47.2 18o o II-277 Dunnose..... tº tº º ſº g º O s tº ſº tº ſº ſº º ſº º tº $ tº 55 42 59:356 5. I935 Io96 I56138.85 29.6 18 Butser Hill .................. 76 I2 8.199 || 5.26367997 || 1835.18.17 34.8 || – I-35 Dean Hill ..................... | 48 4 57.461 5-I48o 2983 || I4O614-41 26.6 | 18o o 5-org Butser Hill .................. 43 42 52.607 5-09747629 || 125163-19 || 23.7 || : 19 Dean Hill ..................... | 76 44 3,916 5.2462 1308 || 176284-98 33.4 || +4.95 Inkpen ........................ | 59 33 7.952 5, 1935 Io96 || 156138-85 29.6 18o o 4.475 Wingreen ..................... | 44 54 18.677 4,96943936 932O5.03 I7.7 2O Mendip tº s º g º e º 'º º e º º is e s is ſº tº º º sº ºn tº * | 49 42 5o. II6 5-Oo3o 9963 Ioo716.27 I9. I —I-18 - Westbury Down ............ 85 22 53-408 5-II 926316 I31602-20 24'9 - 18o o 2.201 Mendip • * * * * * * * * * s tº tº e s is a tº e º e º e s 36 36 57.863 5.osé88866 ... II.452 I'93 2I-7 21 Wingreen..................... Ioo 7. 2:47, 5-2765.1198 || 189321.84 35.8 || +4.61 Beacon Hill .................. 43 16 3-156 5.11926.316 || 131602.26 || 34.9 I8o o 3.490 - Mendip........................ 9 30 40.403 || 4-58880754 || 38797.840 7.4 22 | Milk Hill ..................... I24 29 30.739 5.28673225 || 1935.22.852 36.6 supplementary. Upcot Down .................. 45 59 50. I29 5,22760874 168891.866 32°o 18o o 1,271 Mendip tº $ tº tº ſº tº dº ſº tº C C C C C & 0 & tº º C & © tº º 2O 9 44' I 78 5-O44498or - IIo789-35 21.0 . 23 Westbury Down ........ ſº tº º tº I42 58 54.366 5.28673225 I935.22.85 36.6 39 Upcot Down .................. I6, 51 22.918 4'96943937 932O5°o3 17.7 18o o I-462 Pillesdon .............. tº tº ſº tº º ſº tº 39 25 29.705 5-1218 1566 || 132377.95 || 25.1 : 24 || Wingreen ..................... 81 2 55-549 5-31367885 || 2059:10.67 39-o || +o:32 Coringdon ..................... 59 31 40:273 5.2544.4357. 179656-77 || 34°o 18o o 5.527 Dean Hill ................. & Cº º 83 44 I-816 5,29403 II5 || 196802.75 37.3 a r 25 | Dunnose........................ 28 18 22:599 || 4.97.257616 || 93880.66 || 17.8 supplementary. Horton's Gazebo ............ 67 57 39.614 || 5,26367907 || 183518.17 | 34.8 18o o 4.029 - Horton's Gazebo ............ 129 2 9-920 5,49740321. 314342.58 59.5 26 | Dunnose........................ 2I 51 60-oi 2 5-17817534 || 15072 I-55 28.5 • Blackdown..................... 29 5 55.488 5.294031 I5 || 1968o2.75 37.3 I8o o 5-420 Horton's Gazebo.............. 46 33 45:948 5:03974802 || Io9584.22 || 20.8. 27 Blackdown..................... || - 4o 31 32. I79 4.99.150601 || 98063-19 | 18-6 || 2: . * , Swyre Barrow ............... 92 54 44-398 || 5-17817534 || 150721.55 28.5 - 18o o 2.525 - TRLANGLES. 47I FIGURE 15—continued. s: of Names of Stations. Corrected Angles. Log. Distances. Distances in º of tº I'eet. Miles. in #. Gazebo ............ 63 25 3% osó 5-II.876983 || 131452.8o 24.9 ** 28 3. .." tº tº C tº º * * * * * * * * * * * e s e e e 33 51 Io-ood 492;28768 . 84.195.27 | 15.9 |supplementary. Oring010n . . . . . . . . . . . . . . * * * * * * * 85 43 I5.5o.4 5. I7817534 || I5072I-55 28.5 18o o 2.596 i. 3. tº º ſº tº C & tº ſº tº ſº tº ſº tº ſº tº Q 6 4o 22.173 || 4-41413568 || 25949-900 4.9 29 oringdon ........ tº º tº ſº tº ſº tº g º º ſº º º 29 23 II-592 || 5.03974801 || Io9584:217 | 20.8 || +2-84 Swyre Barrow ............... I43 56 26.629 5-11876983 || I31452.796 || 24.9 || I8o o o-394 Horton's Gazebo ............ 85 31 58.766 || 5 oz.569.162 || Iodog+-20 20.1 - || | 3o Dean Hill ...................” 32 33 33.446 || 4-7579.3270 572.70.73 Io.8 |supplementary. Wingreen ...... . . . . . . . . . . . . . . . 6I 54 29-049 || 4:972.57616 9388o.66 17.8 I8o o I-261 Fºiſ". gº º ºs e º O L & tº C is tº § tº G & 20 I3 39-547 5-O-4667169 †:34:35 2I-I || 3I . #. & C ºf ſº tº tº º ſº º tº t t e º g º 'º º 81 42 55-049 5:50336687 || 318688.85 60-4 || + o-94 Ry CI'S e tº 0 º' tº e º O tº e º e s e º e º e 78 3 33-572 5.4984222I 315081 -oo 59-7 18o o 8-168 jºi. II 53 59-297 || 4-8518 ob49 || 7Io89-99 || 13.5 32. yder's Hill .................. || Ioo 3i 56.08o 5.530.15693 || 338966-62 64.2 || + I-74 High Wilhays ............... 67 34 9.863 5-5033,6687 || 318688.85 60.4 I8o o 5-240 - Pillesdon, ..................... || 148 1837.929 5-64996452 || 445722.46 | 84.4 33 || High Wilhays ............... 12 41 21.869 5-27038o05 || 186371-73 35-3 || – 2:16 Swyre Barrow tº e º is º e º ſº ºn s tº C e s is I9 O 6.565 5.44130642 2.76252.63 52-3 I8o o 6.363 Pillesdon...::................... || 133 24 12-141 5.62258805 || 419361 or 79.4 i 34 | Ryder's Hill ................. º i8 50 18.766 5-27038o03 || 186371-73 35.3 |supplementary. Swyre Barrow ............... 27 45 37.657 5-42949205 || 268838.86 50.9 18o o 8.564 - Barrow Hill .................. 14 18 18.654 || 4:8982.9760 7.9122-06 || I5-o 35 Pillesdon ..................... || Ioo 17 22.960 5.49842221 || 31508I.oo 59.7 +4.18 Blackdown dº tº ſº e g g g tº g g g tº º 0 º C. C. tº C C & 65 24 23.719 5-464I 6083 || 29II79:51 55. I * I8o - o 5.333 | - Dean Hill ..................... 72 9 II.471 5-236588oo || 172420. I4 32-7 || 36 §. Hill .............. º, º º º 48 18 23-694 § 135256-73 || 25-6 || + 2.67 odes Beacon ............. ... || 59 32 29-564 5, 1935 Io96. I56138-85 29.6 18o o 4,729 | Nodes Beacon , ºr 4.85; .6 ** º, º º ſº tº 0 & 0 & e º 'º e º is 3o 25 29-O49 || 4-8551 9932 71645.73 || 13 i 37 #. * * * * * * * * * * * * * * * * * * a s e 42 3I 9°30o 4,9805346o 95616.89 || 18. I +5.67 Outhampton ........... ...... | 167 3 23.192 || 5.13115887 || 135256-73 25-6 18o o 1,541 * r * ºr w rººm, as ºr "sº 472 PRINCIPAL TRIANGULATION. FIGURE 15—continued. No. of Names of Stations. Corrected Angles. | Log. Distances. Distances in Error of A. Feet. Miles. A. Ç & £f A/ Nodes Beacon ............... 82 55 Io:913 5-ozog.8936 || 117757.71 22.3 38 Southampton.................. 43 23 39:282 4.91127855 81522.70 | I5'4 || -4.54 Dunnose ..................... 53 41 II-625 || 4,9805.3466 95616.89 | 18. I I8o o I-820 Dunnose ..................... 98 18 7.766 5-23658800 || 172420. EA 32.7 39 | Butser Hill .................. 27 53 44.505 4.91127855 81522.70 | 15.4 || –3.52 Nodes Beacon .......... ſº G & º º 53 48 Io-398 5.148o 2983 || 140614.41 26.6 : 18o o 2.669 Wingreen ..................... 83 51 41.022 5.3994.9127 || 250894-58 47-5 40 | Inkpen ........................ 43 56 35.809 5.24332893 || I75Io9'19 || 33-3 || – I-26 Nodes Beacon ............... § 11 51.333 5.29968295 || 19938o.62 37.8 I8o o 8. I66 Nodes Beacon ............... 51 2 5 21.411 5'14145421 13850I-42 26.2 41 | Wingreen ..................... 47 18 59.io.5 5'1147.2837 || 130235-20 24-7 || + 2.49 Swyre Barrow ............... 8; 15 #3.678 5.2433 oë93 || 175Io9'19 || 33-2 I8o o 4, 194 Nodes Beacon ............... II 48 o'911 5-o:39748or || Io9584.22 20.8 42 | Swyre Barrow ............... 154 8 3.322 5'36881920 || 233781.53 44.3 || +4.29 Blackdown..................... 14 3 57.332 5'1147.2837 || 130235-20 24.7 I8o o 1.465 Nodes Beacon ............... 48 54 39-360 5-1218 I566 || I32377.95 25. I 43 | Wingreen ..................... 36 37 49.527 5-02O342.95 || IoA795-58 19.8 || +3.5o Coringdon ..................... 94 27 34,367 5.2433oS93 || I75Io9'19 || 33-2 I8o o 3.254 Nodes Beacon ............... 2 30 42-oš2 || 4-41413568 25949-90 4'9 i 44 Swyre Barrow .............. Io 11 36,693 5'ozo.342.95 || Ioa/95.58 | 19.8 || -o-77 Coringdon ...... tº tº e s tº e s tº G s ſº is tº ſº tº 167 17 41.396 || 5 II47.2837 || 130235-20 24-7 || 18o o o-I4I | | Wingreen ..................... Io 41 9-578 4-41413568 || 25949-90 4-9 45 | Swyre Barrow ............... 71 4 6.984 5-1218 1566 || 132377.95 25-1 || -o-25 Coringdon .......... . . . . . . . . . . 98 14. 44.238 5'141454.21 || rā85or-42 26-2 18o o o-8oo Dunnose............. tº £ tº ſº tº º tº º is tº in 53 49 45-700 4,877.37757 || 754or-oSo 14.3 | 46 | Nodes Beacon ............... 6 57 23.768 || 4-oš356865 || 1 1312-7.62 2.1 || + 1.11 Week Down .................. I 19 12 50-707 || 4.9112 7855 || 81522.698 || 15.4 -- 18o o o-175 Dunnose....... tº C. § º C G - e º 'º ſº º º ſº tº º tº 45 Io 21.329 || 3-924I 3940 || 8397.295 | 1.6 47 Week Down .................. 27 39 54,765 || 3:74O15289 || 5497-344 1-0 || –o.32 Boniface Down ............... | Io? 9 43.917 || 4-05356865 || 11312-762 2.1 | 18o o o-or I > TRIANGLES. 473 FIGURE 15—continued. Tº-m-m-m- Distances in : s: Names of Stations. Corrected Angles. Log. Distances. Feet. Miles. º of O A f / £f Dunnose........................ 4T 21 5-634 || 3:99439474 98.71-763 I-9 48 || Week Down ........... tº ſº tº C º . 7 51 33 Ioy || 3:3102.9796 || 2043-139 o.4 || -o-32 Shanklin Down............... 13o 47 21.262 4,65356865 || 11313.762 2.1 18o o o-oo:3 Dunnose............. tº º ſº e s tº $ tº ſº * * 99 o 7.03o 4.91677805 || 82561-591 | 15-6 49 | Nodes Beacon ............. tº º 3 46 I4.761 || 3:74OI 5287 || 5497.344 I-o |supplementary. Boniface Down............... 77 I3 38.313 || 491 I2 7855 || 81.522.698 || 15-4 | 18o o o- Ioa. * Boniface Down ....... tº ſº a c e º 'º º 29 56 5-604 || 4-87.737757 || 75.401-08o 14.3 5o Nodes Beacon ... . . . . . . . . tº e º 'º 3 II 9-ood 3-924.I 3942 8397.295 | 1.6 33 Week Down ... . . . . . . . . . . . . . . . I46 52 45-471 4.916778o3 || 82561-591 15.6 I8o o o-o81 Dunnose........................ I6 51 32.927 | 3.27675294 1891.267 O'4. | 51 Boniface Down ............... || IoS 40 57. I55 || 3-79784959 6278-409 I-2 || -2-34 Wroxall Down ............... 57 27 29-920 3.74oD 5289 || 5497.344 I'o I8o o o-oo:2 Dunnose........................ 69 39 54-037 3.77Oo 2323 5888.751 I • I 52 Wroxall Down ............... I8 59 8.675 || 3:3102.9796 || 2043-139 o.4 |supplementary. Shanklin Down............... 91 20 57.291 || 3-79784959 || 6278.409 | 1.2 18o o o-oo:3 || Dunnose ...... tº e º e º e e s tº e º s º º º 86 31 26.963 3.75947.588 5747-459 I• I || 53 Boniface Down ............... 20 46 59.275 || 3:3102.9796 || 2043-139 o-4 || +6-20 Shanklin Down............... 72 4I 33.765 || 3:740I5289 5497'344 I'o 18o o o-oo:3 Boniface Down............... || 52 36 38-990 || 3.88278522 || 7599,594 | 1.4 54 | Week Down............. {} {} º C & 8 2 13.882 || 3-13824451 I374-816 o-3 || —4-51 Littletown Down ........... . || I2I 21 7-220 3-924.I.394o 8397.295 | 1.6 I8o o o-oo.2 Boniface Down ......... tº C tº ſº º is I 13 14 32.375 || 3:33272617 || 2151,425 | o'4 55 Wroxall Down .............. ſº I2 52 57°o34. 2.71769678 522-O31 O - I –24-65 Boniface Down, South East 53 52 30-591 || 3:27675294 | 1891.267 o.4 18o o o-ooo Boniface Down............... || 52 5 25-662 || 3-1781 91.5o | I507,271 o-3 56 Wroxall Down ............... 46 I 31.499 || 3-13824456 I374,816 o-3 ||supplementary. Littletown Down ....... $ tº º º is 81 53 2-840 || 3:27675294 I891.267 o.4 18o o o-oor - Boniface Down............... 61 9 6.714 || 3-oS366949 I212.465 o-2 8 57 Littletown Down ............ 22 9 20.059 2.71769678 522-og I o, I || -42.9 Boniface Down, South East 96 41 33-227 | 3-13824456 1374-816 O'3 I8o o o-ooo Boniface Down, South East 8 25 67,720 | 3:42373085 || 2652-961 o'5 58 Littletown Down ........ ſº tº tº º %. ; § ::::::::: 2615-238 O-5 —35.62 Highport Cliff ............... 26 35 56.925 | 3:08366940 || 1212.465 o-2 I8o o o-oor 3 O 474 PRINCIPAL TRLANGULATION. FIGURE 15—continued. No. of Names of Stations. Corrected Angles. Log. Distances. Diane, in Iºrror of A. - Feet. 'I Miles. A. Nodes Beacon ............... 3. 57 464. 3'9347 2638 86O4.515 I.6 Af 59 Week Down .................. I59 6 33’708 || 4.91893.096 || 82971.886 15.7 suprementary. Boniface Down, South East 26 55 41.727 4,877.37757 || 75.401-08o 14.3 18o o o-o/6 FIGURE I6. Mendip ........................ 85 15 49.530 5.57766991 || 378155°oG | 71-6 I | Cradle ............. & D C C C C tº º º ſº tº 42 55 52.585 5:41236684 || 258444'23 || 48.9 || -9-07 Whitehorse Hill ............ 51 48 35.953 5.47454.950 || 298228.75 56.5 I8o o 18-off.8 Mendip ........................ 34 3 20.832 5.26738ozo || 185988-83 || 35. I 2. Cradle .......... tº e s g º e s is e º 'º e º 'º' 8I 29 II .358 5'51439222. 326882.91 61.9 —o.96 Malvern........................ 64 27 40-649 5.4745495o || 298.228.75 56.5 I8o o 12-839 Mendip .............. tº º C tº ſº tº º e 51 12 28-698 || 5-41557849 || 260362.54 || 49-3 3 Malyern.....:º::. . . . . . . . . . ſº tº C. 59 41 8-739 5-41236684 || 25844.4.23 48.9 || –1.20 Whitehorse Hill º e º 0 tº tº s tº tº O L tº 78 6 38.05I 5°51439222. 326882.91 61.9 * 18o o 15.488 Whitehorse Hill ............ 6o 22 39.897 || 5:4097.8719 || 256913-66 48.7 4 Malvern:::::................... 57 5I 57.924 5:3984oool || 250264.94 47.4 |supplementary. Arbury Hill .................. 6I 45 35.5ol 5:41557849 || 260362.54 || 49-3 18o o 13.322 Whitehorse Hill ........ ..., || 46 43 I2:389 5:30314247 || 200975-20 38. I 5 Arbury Hill • e º 'º e º e º 'º e º 'º e º 'º e º 'º 68 I4. 58-794 5-4089.3294 256408.81 48.6 32 Dunstable tº e º e º 'º e º 'º e º 'º e º 'º º 'º e º 'º º 65 I 59.804 5:3984ooor 25oz.64.94 47°4 - 18o o Io. 987 Whitehorse Hill ............ 47 49 63.475 5:46.425192 29I240-60 55-2 6 Cradle ... ... . . . . . . . . . . . . . . . . . 26 24 12-675 5.24236,128 I 74727.5I 33' I + o-64 Broadway Tower ............ || Io; 45 55.369 5'57766991 || 378155-od 7I-6 18o o II.5.19 Whitehorse Hill ............ 52 16 40.849 5.40435519 || 253895.63 || 48.1 7 Dunstable & C & C C C C C C C C C C tº º ſº tº º O C & 74 42 3I-34o 5.499.83617 || 309625. Io 58.6 || — 1.65 Leith Tower........... tº g º O & ſº tº 53 o 62-581 5.40893.294 || 256408.81 || 48.6 I8o o 14,770 Whitehorse Hill ....... tº C & tº 6 23 13.764 5-41262566 || 258598-30 || 49'o 8 | Leith Tower........ tº dº º º ſº tº e º 'º º : º: :::::: 4-92.766546 84657.5o | 16.0 || –2.5o Inkpen * * * * * * * * * * * * c e s e e s s e o e s a II9 54. Io. 517 5.490.83617 309625. Io 58-6 I8o o 4:464 Whitehorse Hill ............ 76 7 35-049 || 5-4012758o || 251927-63 || 47.7 : 9 || Mendip ............. tº º e º 'º e s ∈ g º e 19 2 37.175 4.92766546 84657.5o | 16.0 || +3.06 Inkpen tº º tº tº º tº tº º 0 º 'º º 0 ºn tº e º 'º e º 'º e s e 84 5o 2.773 5'4L236684 258444-23 48.9 I8o o 4:997 TRIANGLES. 475 FIGURE I6—continued. No. of Names of Stations. Corrected Angles. Log. Distances. Distances in Fº of A. Feet. Miles. tº - O A £ f Leith Tower.......... tº ſº tº º G & º º 38 34 14749 5-20474992 || IGo232-25 || 30-3 Io Dunstable ..................... 6o 20 46.311 || 5.34896601 || 223339.74 42-3 || + o-8o Epping Poorhouse ......... 8I 5 7.256 5.40465519 || 253895.61 || 48. I 18o o 8.316 Leith Tower......... tº ſº tº º ſº tº C tº 4o 47 2-631 || 5-165o 9373 || 146249-28 || 27.7 | II | Epping Poorhouse ......... 45 Io 45-199 5-20088075 || 15881 I.off 3o. I || -3.79 Wrotham ..................... 94 2 17-619 5-348966or || 223339.74 42-3 i 18o o 5.449 Leith Tower................. • l 79 2I 17.381 5.4369 og83 || 273470-og 5I-8 I2 | Dunstable ............ . . . . . . . . . 34 48 7-146 5-20088o/5 || 15881 I.off 3o. 1 || +3.66 Wrotham ...... . . . . . . . . . . . . . . . 65 50 44-794 5.404655I9 253895-61 48. I 18o o 9.32 I Leith Tower ............. § º C C º 56 Io 5.787 5-2688.4369 || 185713.59 || 35-2 : I3 Wrotham ..................... 78 34 13.718 5-34o 7 I5I5 219136.72 4I'5 + 2.86 Berkhampstead....... & º C º º º º 45 15 47.295 || 5-20088075 || 15881 I.O6 30. I 18o o 6.8oo Leith Tower.................. 23 II II-594 5-oo.42 Io'72 || Ioog74-27 | 19. I I4 | Dunstable ................. ..., || 58 41 61-o 2 || 5-3407 1515 || 219136.72 41.5 || +o:26 Berkhampstead............... 98 6 52-496 5.40465519 || 253895.61 48. I 18o o 5. I52 Leith Tower.................. 44 21 39.706 || 5. I2593061 || 133638.20 || 25.3 | I5 Wrotham .......... tº Q tº º 'º tº e º 'º º ſº 79 27 5-428 5.27394406 1879.07-48 35-6 supplementºr. Chingford e e º 'º e º is tº e º e s tº º ºs º ºs º º º is 56 II IQ-774 5-20088075 15881 I.06 3o. I 18o o 4-908 - Leith Tower.................. 8 46.6 5.off38748o || II.3267-39 21.4 I6 Wrotham ......... tº º ſº tº º tº $ tº e º 'º º § 9 *::::: 5.14do 9359 || 138968-18 26. I 33 St. Paul's ..................... 77 42 13.624 5-20088075 || 1588.II of 30. I I8o o 3.592 Wrotham ........ * * * * * * * * * e s a 2 13:346 4.9339515o || 85891.76 | 16.3 17 | Epping Poorhouse tº dº tº dº tº e s ſº º : ; 19.753 5-oš38748o || 113297.39 21.4 33 St. Paul's ..................... 93 31 29.184 5.1650.9373 || 146249.28 27.7 18o o 2.283 Epping Poorhouse ......... 72 52 32.749 || 4:94879239 88877.61 | 16.8 18 St. Paul's ..................... 39 4o 18.882 || 4-77357083 59370°52 II 2 33 Berkhampstead............... 67 27 9.515 4.9339515o || 85891.76 I6.3 18o o I. I.46 St. Paul's ..................... o 5 26. 4-7I7 IoI93 || 5213 I-705 9-9 I9 Berkhampstead. tº ſº º ſº º tº Q tº dº ſº º º tº º 3. s: ...; 4,69760379 || 498.42-956 9°4. 32 Chingford * * * * * * * > . e. e. e º t e º 'º e º 'º • || I2 I I5 57-586 4.9487.9239 88877,613 I6.8 I8o o o-523 Leith Tower 28 º ...a... " -- “. . . . . . . . . . . Q Q º º q 4" 24 4.875I 3762 75oI3. IQ I4. 2. 2O . * * * * * * * * * * * * * * * * * * * * * 65 & : 5-16066.432 || 144765-25 | 27.4 —o-o8 CWCrndroog .................. 86 24 7.714 5-20088075 || 15881 I-oG | 39:1 I8o O 2.549 3 O 2 476 PRINCIPAL TRIANGULATION. FIGURE I6—continued. IDI ſº | No. of Names of Stations. Corrected Angles. Log. Distances. Stan CeS in Error of A. Feet. Miles. A. Leith Tower.................. 28 23:34: 5-0566 2801 II3927°35 2I-6 º, 21 || Berkhampstead............... 36 4o 54.522 || 5-16066432 || 144765-25 || 27.4 || +2.77 Severndroog ....... tº º ſº ſº tº e º gº tº • || II5 I6 37.445 5-34oz 1515 || 219136.72 || 41.5 18o o 3-508 Severndroog ................ tº lº 3o 56 I7'o63 || 4-77357083 || 59370.52 11.2 22 || Berkhampstead............... 49 38 58-o/3 || 4:94452493 88oo8.56 | 16.7 |*. ISpping Poorhouse ......... 99 24 46.076 5-oš6628or || II3927.35 | 21.6 I8o o I-212 St. Paul's ..................... 89 16 4,203 || 4,80268862 || 63487,557 | 12-o 23 | Severndroog .............. tº º ſº tº 5i 43 20-649 || 4-69760379 || 49842.956 9.4 3? Chingford ............... tº dº º ſº tº ſº 39 o 35.617 4.60168807 || 39965-759 || 7-6 18o o o-469 Leith Tower.................. II 48 26,081 4,717 IoI93 || 52I31.70 || 9.9 24 Berkhampstead............. tº º 47 31 19.625 5.27394406 || 187907-48 || 35-6 32 Chingford ºn g c e º e º sº a s is e º 'º º 'º e º 'º wº I2O 4o 16.276 5-34o 7 I5I5 2I9136.72 4I '5 18o o 1,982 Leith Tower.................. 77 48 33-652 5.246.32215 I76328.35 33°4. 25 Wrotham ..................... 4O 3o 26-979 5.off.883549 II 71.75-I4. 22 - 2 - I • II Ditchling is º e º ºs ºn tº C C º tº º tº tº º is º º º C tº 6 I 4. I 3.648 5-20088o75 I5881 I.oé 3o-I I8o o 4.279 Leith Tower.................. 94. 9 57-502 5-3078.2811 203155-28 38.5 26 | Ditchling ....... tº º ſº tº ſº e º 'º tº dº ſº gº tº º 5o 43 3-oz1 || 5-19773428 || I57664.63 29.9 || +3-09 Butser ........... tº º tº G. C. C C C º C. • “ 35 7 3.81.1 5-06883549 II 7175. I4 22.2 18o o 4,334 Leith Tower.................. 41 56 28.702 || 5-2462 1308 || 176284-08 || 33-4 27 | Inkpen .......... tº ſº º ſº y º & C & E & © º º 36 42 38.821 || 5-19773428 || 157664.63 29.9 || + o-49 Butser ........................ IoI 20 58.887 5-41262566 || 258598-3o 49-o 18o o 6-4Io w Ditchling ..................... 62 8 32.926 5'24.999568 177826-17 | 33.7 : 28 Wrotham ......... tº º 'º - C & © tº tº tº tº 56 36 59.427 5-2251.7749 || 167949-og 31.8 || -I-II Tairlight ..................... 61 14 33-806 5-246.32215 || 176328.35 | 33-4 18o o 6. I59 Ditchling tº ſº tº tº tº º ſº º ſº º g º is ſº tº º ſº. C tº 32 25 23.862 4'993o O490 98.402-22 18.6 29 Fairlight tº º ſº º ſº tº º $ tº ſº tº º º i. C. C C C º 33 47 53-853 5.oob.98878 Io2091.31 I9'3 —o.86 Beachy Head.................. II3 46 44'447 5.225I 7749 I67949-03 31.8 I8o o 2. I62 Ditchling tº $ tº e º 'º º tº ſº tº t e º ſº tº ſº º tº e º ſº 3o 2 52.835 5-I48o 2983 140614:41 26.6 3o IButser ... • * * * * * * * * * * * * * * * * * * * * * * Io3 36 56-497 5-43605920 272934-98 5I-7 –2-49 : Dunnose............ * C tº t w tº tº º ſº ſº tº ſº 46 20 17-199 5-307828 II || 203155-28 || 38.5 18o o 6.531 Ditchling .................... • || 122 59 3708 5:5398.2975 || 339492-16 || 64.3 || 3I Dunnose........ tº ſº º tº ſº tº ſº dº e º 'º º tº t e tº I4. 36 40. I 77 5-oo89.8878 Io2091.31 I9'3 + 2.87 i Beachy Head.................. 42 24 21.613 5-43605920 272934.98 5 I-7 18o o 5.498 TRIANGLES. 477 TIGURE 16—continued. Di * sº of Names of Stations. Corrected Angles. Log. Distances. iStanceS in º of Feet. Miles. g i. O Af Af * Af Leith Tower .................. 38 57 30-167 4.9999 1518 9998o.47 | 18.9 32 Wrotham ..................... 53 56 18-495 5. Io995273 || 128544-27 | 24-3 || –o.7o Crowborough.................. 87 6 14.357 5-20088075 || 15881 I.O.5 30. I 18o o 3-ol 9 Leith Tower.............. tº º C tº 38 5I 3-484 || 4916o.4035 82421.47 | 15-6 33 | Ditchling ..................... 78 2 57.965 5. Io905273 || 128544-27 | 24.3 |supplementary. Crowborough.................. 63 6 o'773 5-od,883549 || II 71.75-14 22.2 I8o o 2.222 Ditchling ......... tº e º is c s sº e º is ſº º 45 46 38-698 || 5-og782678 || 125264. 14 23.7 34 Fairlight ..............------- 28 8 2. I 83 4-916ozłog5 82421.47 15-6 32 Crowborough.................. Iod 5 21:542 5-2251.7749 || 167949-og 31.8 I8o o 2.333 Seyerndroog .................. || 1 18 12 39-105 || 5: Ioro 5835 | 136199:71 23.9 35 | Chingford ................. tº Q º º 35 28 25.627 4.91965088 83 Io9'54 15-7 || –2-27 Banstead ............. tº $ tº º ſº tº º tº 26 18 56.362 4.8o268862 63487.56 I2-o 18o o I-og4 Severndroog .................. 66 29 18-456 4,8837 3766 || 76513-428 14.5 36 | St. Paul's ..................... 84. 53 36-254 || 4.91965o88 || 83109.539 I5.7 |supplementary. Banstead ..................... 28 37 6.000 || 4.60168807 || 39965-7.59 7.6 18o o o,716 Severndroog ............... ... || 14o 15 54.211 || 5-2066.6918 || 160941.92 || 30-5 37 Epping Poorhouse......... tº º 19 16 29.633 4.91965088 83 Io9'54 15.7 22 Banstead ..................... 26 27 37.256 4,94452493 || 88oo8-56 | 16.7 18o o I. Ioo Severndroog .................. 55 15 15.610 || 4:89028797 77676.20 14.7 38 | Banstead ...................... 63 12 14,903 || 4.92624594 || 84381.25 | 16.0 || – 1.54 Hanger Hill Tower ......... 61 32 30.842 4.91965o88 83 Io9'54 15.7 18o o I-355 Severndroog ................ tº º 61 12 15.907 || 5. Io92 I418 || 127796.84 24.2 39 || Leith Tower .................. 35 22 58-725 4.92624594 84381.25 | 16.0 || – 2.07 Hanger Hill Tower ....... tº º 83 24, 47.886 5-16066432 || I44765-25 || 27.4 18o o 2.518 * St. Paul's ..................... 74 5 41.232 4.89028797 || 77676-200 14.7 49 | Banstead ..................... 34 35 8.897 || 4-66131314 || 45847.234 8-7 |Supplementary. Hanger Hill Tower ......... 7I 19 Io.664 || 4.8837 3766 || 76513,428 I4.5 18o o o-793 | Leith Tower...... * @ tº º e º is tº C tº º ſº 63 30 32.97.I 5, 18494.765 . I 53090-29 29°o 4.I Wrotham. * * * * * * * * * * * * * * * * * * * * * 48 17 51.699 || 5.1062 1418 127766.84 24-2 || -o'71 Hanger Hill Tower ......... 68 II 4o. 200 5-20088075 || 15881 I.oG 30. I 18o o 4.270 478 PRINCIPAL TRIANGULATION. . FIGURE I6—continued. - Di - º No. of . Names of Stations. Corrected Angles. Log. Distances. iStanceS in Fº of A. Feet. Miles. º Leith Tower tº tº º ſº tº º ſº. tº º O C C C º e º 'º º 27 29 6442 4,8902 8797 77676.20 I4-7 w/ 42 Hanger Hill Tower ......... 21 52 17-943 || 4-797.25490 626.98.17 | 11.9 || –3.88 Banstead ....... & Q Q & & Q & ſº e º C & ... || 130 38 37-684 || 5. Io921418 || 1277O6.84 24.2 18o o o-869 Banstead ...... tº º º t e º 'º, º 'º a tº t e º & 77 37 58.94I 4'9447.5557 || 88055-31 || 16.7 43 | Leith Tower .................. 58 17 57.632 4.884781.49 76697.55 I4.5 || +4.32 St. Ann's ..................... 44 4 4.532 || 4-7972.5490 || 62.698-17 | II-9 18o o I. Ioff Severndroog .................. 36 24 45.324 || 4'9447.5557 88055-31 | 16.7 44 | Leith Tower.................. 86 II 56.315 5-1326,5942 || 135724.87 25.7 supplementary. St. Ann's ........ e Q tº e º 'º e º e º C tº tº 77 23 27.204 5-16066.432 || 144765-25 27.4 18o o 2-743 Severndroog ............. tº ſº tº 24 47 30.583 || 4,8382 IG99 68899.65 || 13-o 45 Hanger Hill Tower ...... ... || 124 18 30.117 | 5-13265942 I35724.87 25.7 33 St. Ann's ....... e e s e s e e o e º 'º e º is 36 54 o.429 || 4,92624594 || 84381.25 | 16-o 18o o I-129 Hanger IHill Tower ......... 25 3 54°oo9 4-5769.9033 377.56-378 7.2 46 St. Ann's ..................... 25 34. I-760 4.585036.96 38.462-452 7.3 +2.91 Hampton Poorhouse ......... 129 22 4-495 || 4-8382 1699 || 68899-646 || 13-o I8o o o-264 Hanger Hill Tower ......... 37 42 5.265 4.72243576 || 52775'914 Io-o 47 | Banstead ..................... 26 28 2.629 || 4.5850.3696 || 38.462.452 || 7-3 ||Supplementary. Hampton Poorhouse......... II5 49 52-536 4,89028797 || 77676-200 || 14-7 18o o o-430 Hanger Hill Tower ......... 79 44 45-ol.8 || 4,90386836 || 8oNA3.509 15.2 48 || Banstead ..................... 27 45 4'321 || 4-5789 og 99 || 37.923. II3 || 7-2 33 Ring's Arbour ............... 72 3o II.343 4,89028797 || 77676.200 14.7 I8o o o-682 Hanger Hill Tower ......... I6 58 45-743 4:53728700 || 34457.757 | 6.5 49 St. Ann's ..................... I8 44 5o. 548 4-5789 oggg 37.923. II3 7.2 33 Ring's Arbour ................ 144 16 23-888 || 4,8382 1699 || 68895,646 13-o 18o o o-179 º Hanger Hill Tower ......... 42 2 39:753 || 4:4378,5141 || 274O6.363 5-2 50 | Hampton Poorhouse......... 67 55 3 I-oj2 || 4-5789 og09 || 37923. II3 7.2 23 IXing's Arbour ..... * * * * * * * * * * 7o I 49.425 || 4.5850.3696 || 38.462.452 7.3 18o o o-230 Severndºgog................... 83 6 26-482 4.9418.4086 || 87466.320 | 16.6 5.I Epping Poorhouse * * * tº ſº ſº º ſº ºn e º 'º, 9 32 48-384 4.1647 1235 || 14612-og I 2.8 33 Greenwich Transit ......... 87 20 45.434 4.94.452493 || 88oo8-564 16.7 180 o o-3oo Severndroog tº tº it tº G & G * * * * * * * * * * * 61 3 II .377 || 4-7622 7507 || 57846.232 II.o 52 Chingford …...... . . . . . . . . . . . . 12 46 I3-449 4, 1647 I235 || 14612-ogi 2.8 39 Greenwich Transit ......... Io9 Io 35-365 4,80268862 || 63487.557 | 12.o 18o o o 191 TRIANGLES. 479 FIGURE 17. Distances in 4 *::: Names of Stations. Corrected Angles. Log. Distances. IFeet. Miles. Fº of O Af f/ Rippure........................ 36 23 Io:741 5.5498.6094 || 354699.8o 67.2 I Knockanaffrin ............... 9 9 25.023 4.97839889 || 95147-83 I8-o || – 1.02 | Ballycreen................. 134 27 29.901 || 5-6302 or 98 || 426777.96 80.8 18o o 5.665 + Knockanaffrin ...... tº dº º ſº tº ſº º 37 58 23:372 5-35055683 || 224159.34 || 42.5 2 | Ballycreen..................... 38 49 52.261 5.3587.6256 || 228434.96 || 43-3 || + 1.56 Forth........................... Io9 II 56.090 5.5498.6094 || 354699-8o 67.2 18o o 11.723 Forth......................----- I7 31 18.091 4.9375 of 91 86597.81 I6-4 3 Ballycreen • a s e s e s e e s s e s is a e º 'º - e > 33 4O 32-610 5' 202742 I4. I594.93. IQ 3o-2 —8. I6 Tara ..................“ I28 48 II.831 || 5'35055683 || 224159.34 || 42.5 18o o 2-532 Rippure........................ 78 I 59.597 || 5.69180902 || 491823-21 | 93. I 4 Snowdon ........ & e º is e º ºs e e s is e e 20 35 4.862 5.2473.5469 || 176748 of 33.5 || + Io:15 Tara ........... * * * * * * * * tº us e e º 'º º º 81 23 15.751 5-696.42725 || 49708I. Io 94' I 18o o 20.210 Kippure........................ 48 2 54.992 || 5.64174764 || 438275.95 83-o 5 Snowdon ................ tº ſº tº C 74 27 19:862 5-75418108 || 567781.29 Io?.5 || –o.31 Precelly.................... “. . 57 30 34.502 || 5-696.42725 || 497981. Io 94.1 I8o o 49-356 Snowdon ................. tº ſº º 63 38 6o-816 || 5.70085354 || 502173.21 | 95. 6 Precelly tº º ſº tº C º 'º º tº º tº ſº ºn tº ſº º ſº tº ſº tº . C. § tº 64 54 35-o'70 5-7054,534I 50752O-29 96. I supplementary. Ballycreen..................... 5I 27 Io. 984 5.64174764 438275.95 83.o - 18o o 46.870 Forth.............. tº e º 'º e º is º is tº dº sº º 79 I4. 23.858 5.6273,5616 || 423990.54 || 8o-3 7 | Tara ..... tº g º C & e º 'º º C & tº g º 'º - †. C. g º º 79 4. 28.934 5.6271 1621 || 423756-34 || 8o-3 || + o-20 Precelly........................ 2I 4I 22.825 5-202742I4 || 159493. I9 || 30-2 18o o 15.617 Reeper ........................ 53 20 43.282 5.4588 off31 || 2876 Io.88 || 54.5 8 Croghan............. tº º e º 'º - º º is lº 67 54 36-o21 5-521.39060 || 332193-09 || 62.9 |supplementary. Mount Leinster............... 58 44 59.903 5-4864-1948 || 306492.24 58.o 18o o 19.206 Knockanaffrin ............... 3I Ig 43.782 5-o80985o'7 || I2O499.45 22.8 9 | Torth........................... 68 23 I-926 5.33335974 || 215456-57 | 40.8 39 Mount Leinster.......... ſº & C. C. 8o 17 20:310 5.3587.6256 || 228434-95 43.3 18o o 6.018 Precelly........................ II 32 34.529 5. Io937 Io'7 || 128342.67 24.3 * | Tara ........................... || 127 4 58,619 5-7.0963518 || 51.1723.29 96.9 33 Mount Leinster............... 4I 22 37.664 || 5-627356T6 || 423990.53 | 8o-3 I8o o Io. 212 ICeeper “. . . . . . . . . . . . . tº ſº tº ſº ſº tº I6 52 3.242 5-15497676 || 142881.75 27. I II Mount Leinster............... 12o 42 47. III 5.62672955 || 423379-23 | 89.2 . 35 Ballycreen * * * * * * * * * * * * * * * * * * * * * 42. 25 I9'24.I 5-5213 9066 332 I.93-o9 62.9 I8o o 9:594 ! 48o PRINCIPAL TRIANGULATION. FIGURE 17—continued. No. of Names of Stations. Corrected Angles. Log. Distances. Distances in Error of A• Feet. Miles. A. O f Af W/ Snowdon ..................... 48 58 18-oj9 5-5712 95.08 || 372644.81 | 70.6 I2 | Precelly........................ 68 3o 39:949 || 5:6624.2412 || 459646.67 87.1 supplementary. Cradle ........................ 62 31 38-628 5.64174764 || 438275-95 || 83.0 | 180 o 35.736 Snowdon ....... tº tº gº º tº e º e º C. C. § ſº º 27 5 35.919 5:35027579 || 224014.32 42.4 I3 | Cradle ........................ 42 2 55.895 5:51.777889 || 329441-94 | 62.4 33 Longmount .......... ........ || 11o 51 45.303 || 5-6624.2412 || 459646.67 || 87.1 18o o 16.217 Precelly ............. tº º ſº tº e º 'º º 'º º 14 17 35-850 5.14527372 || 139660:54 26.5 14 | Snowdon ..................... 36 29 I7.341 5-5268,5968 || 336402.86 63.7 33 Cader Idris................ ..... || 139 13 15.368 5.64174764 || 4382.75.95 83-o I8o o 8.559 Cradle ........................ 47 23 2-olz 5-3783.5517 || 238976.49 || 45.3 I5 | Longmount .................. 89 o 9.496 || 5'51 I47454 || 324694.21 61.5 39 Cader Idris ............... 43 37 I-o'79 5'35027579 || 224OI4'32 42-4 18o o 12.587 Precelly...... ................. 28 33 59-798 || 5.3598.6096 || 229013.43 43.4 16 Snowdon ..................... 37 39 II:932 5:4662.3233 || 292571.71 55.4 33 Plynlimmon .................. I 13 47 2-688 5.64174764 || 438275.95 83-o 18o o 14.4.18 Cradle ........................ 52 52 21.599 || 5:31542799 || 206741-66 39.2 17 | Longmount .................. 67 22 19:829 5.37902352 || 239344-54 45.3 33 Plynlimmon .................. 59 45 28:625 5'35027579 || 224O14.32 42-4 18o o Io-o53 Snowdon ..................... 32 II 18.332 || 5.2853 odoo || 192888.35 | 36.5 i 18 || Longmount .......... tº º e s tº ſº tº dº 33 17 31.998 || 5-2983 Igg7 || 198755.87 37.6 || +2-14 Cyrn-y-Brain............ ;..... 114 31 17:872 5:51.777889 || 32944I-94 || 62.4 I8o o 8.202 Longmount .................. 55 8 5.923 || 5°32875363 || 213183.52 | 40.4 19 Cyrn-y-Brain.................. 76 55 55.640 5:4232.8240 || 253094.32 47.9 || +o.17 Mowcopt ..................... 47 56 7.855 5.28530600 || 193888.35 | 36.5 18o o 9-418 Longmount .................. 59 II 13-ol 9 || 5:44.438327 || 278216.75 52.7 20 Cyrn-y-Brain.................. 84 16 19:264 5:53829985 || 322329-35 | 61-0 || +6.67 Axedge ........ tº e º e s tº e º s e s a e s e e 36 32 40.272 5.28530600 || 192888.35 | 36.5 I8o o 12:555 Whittle ........................ Ioz I 58.344 5:52679449 || 336352.37 63.7 21 Holme Moss .................. 6I 52 7.841 5-48.184452 || 30328o.52 57.4 ||Sapplementary. Cyrn-y-Brain ........ 9 * * * * * * I6 6 o'466 || 4-97.94oz.I.9 95367.89 | 18. I 18o o 6.651 Cradle ........................ 57 I4 32-787 5-29868196 1989.21.61 37-7 22 || Longmount .................. 51 29 20-618 5.26738ozo || 185088.83 35.1 || –2.57 Malvern.............. * * * 0 e º c e s º 71 I6 I4-795 5-3.5oz 7579 224OI4'32 42°4. 18o o 8.2do TRIANGLES. 481 FIGURE 17—continued. s: of Names of Stations, Corrected Angles. Log. Distances. Distances in * Error of § Feet. Miles. A. O f f / f/ Longmount .......... • * * * * * * * 64 28 51.771 5.5oz.64454 || 318159:24 6o-3 i 23 Malyern:::::................ ... 81 Io 23-507 || 5-542O5398 || 34838o.62 | 66-o || +3.31 Bardon Hill .................. || 34 20 55-428 5.39868196 || 198521.61 | 37.7 I8o o 14.706 Axedge .................... tº ſº tº ſº 89 59 46.947 5.38966423 || 245281. 18 || 46.5 24 Mowcopt .................... ſº 72 54 18.808 || 5-3700394o || 234444.15 44.4 || –4:13 Bardon Hill .................. I7 5 59. I2O 4,85805603 72I2O.O.5 I3.7 I8o o 3-975 Cradle .................. g is tº dº ſº ſº I2 9 6-og8 5-od 81 oz.41 || II6977.52 22.2 25 Malvern tº g g g º º 'º º O ſº º ſº tº º º ſº ſº tº dº ſº tº C tº ſº I48 23 39.068 5.46425192 29I240-60 55-2 + o-75 Broadway Tower ........... º 19 27 17:503 || 5.26738020 || 185088.83 || 35.1 18o o 2.669 Malvern........................ 24 37 8:244 5-19936712 || 1582.58:53 || 30-o 26 Broadway Tower tº $ tº º ºs º ºs e e º 'º º I37 26 52-673 5-4097.8719 || 256913.66 || 48.7 || + o-38 Arbury Hill .................. I7 56 2-oz7 || 5.0681 oz.41 || 116977.52 22.2 18o o 2.944 Broadway Tower ............ 37 5I 52-743 5.2564II48 || 180472.68 || 34.2 27 | Arbury Hill ................., | 169 34 21:528 5,44254429 || 277641-16 || 53.5 || +2.11 Bardon Hill .................. 32 33 52-oš8 5-19936712 || 1582.58:53 || 30-o 18o o 6.329 Whittle Hill .................. 90 21 44.159 5.322O8677 || 209935-93 39.8 28 Holme Moss .............. tº tº tº º 62 37 15.688 5.27049915 || 186422.85 35-3 ||supplementary. Delamere, New......... * - C - C & 27 I 4.332 4.97.94oz 19 || 95367.89 | 18. I ſº I8o o 4. I79 -- Whittle Hill.................. 32 51 50.459 5:0446.0228 || 1108.15.95 21-0 29 || Mowcopt ....... tº t e º e º 'º e º is is e º º 65 54 19.862 5.27049915 || 1864.22.85 35-3 || + 6.85 | Delamere, New............... 8I 13 54'479 5:304984II 201829.25 38.2 18o o 4.8oo Holme Moss tº e º e º 'º e º e º 'º º ſº e º 'º tº tº 3I 46 25.88o 5-0446.0228 IIo815.95 2 I • O 3o Mowcopt tº ſº tº ſº tº e º 'º º 'º º º * * * > . C. e º 'º 94 o 48-4Io 5.32208677 209935-93 39.8 Supplementary. Delamere, New............... 54 I2 50. I.47 5.2322 8182 || 170718-99 || 32.3 I8o o 4:437 ¥owcopt ..................... 27 57 28.657 5. IoI96883 || 126464-56 23.9 31 Cyrn-y-Brain........ .......... || 24 15 21:157 || 5-O446 o228 || IIo815.95 2I-o || -o-o:7 Pelamere, New............... || 1274; 12.7% 3.33875362 || 2131833i | 40.4 18o o 2.604 3 P. 482. 12RINCIPAL TRIANGULATION. FIGURE 17—continued. No. of $ iº Distances in Error of Å Names of Stations. Corrected Angles. Log. Distances. Feet. Miles. A. . Delamere ............. tº a ſº tº C tº 43 7 32-762 4.98889949 || 97.476.40 | 18.5 32 Cyrn-y-Brain...... tº ſº º ºs e º 'º º º 'º º º 74 23 22.274 5-1377 7510 || 137333-06 || 26-o supplementary. Garreg ................... tº Q tº tº º 62 29 7.755 5. IoI96883 || 126464-56 || 24-o 18o o 2,791 Cyrn-y-Brain........ tº e s a e g º e s a 69 54 3.057 5-2762.7147 || 188917-19. 35.8 33 || Snowdon ...... tº e º is is º is ſº tº dº tº sº tº G & 28 58 6o. 169 || 4.98889949 || 97.476-40 | 18.5 55 Garreg ......... * c e º 's e º e º ſº º sº e a 81 6 61.052 5.2983 1997 || 198755.87 37.6 18o o 4.278 Cyrn-y-Brain............. { } { } e º ſº 92 33 29.577 5.22743148 || 168822.95 || 32°o 34. || Garreg ............. tº º tº e º e º 'º tº tº tº 52 12 56.343 5.12566706 || I33557. I2 25'3 33 Arrenig ........... tº dº º Q & © tº tº tº e s tº º 35 13 37: 137 || 4.98889949 97.476-40 | 18.5 I8o o 3-057 r Cyrn-y-Brain.................. || 52 2I I2.727 5-og2472.34 || 123729-24. 23°4 35 | Arrenig .................... ..., | 68 55 20,490 5.16378617 || 145809.62 27-6 53 Llanelian ..................... 58 43 30.408 || 5.12566706 || 133557. I2 25.3 I8o o 3.625 Cyrn-y-Brain.................. 4o I2 16.850 4,97836909 95141-30 | 18-o 36. Garreg ...... tº º ºſ e º e º 'º e º 'º e º 'º e º 'º º 98 23 3I. I64 || 5, 1637,8617 || I458og-62 27.6 32 Llanelian ..................... 4I 24 I4. I44 4'98889949 97.476-40 | 18.5 - 18o o 2.158 Cyrn-y-Brain.................. 7 56 63.398 || 4:54II4933 || 34765-568 || 6-6 37 | Llanelian .................... º 27 3o 35-233 || 5-off.479815 || II6090-893 22°o 33 Moelfre Issa .................. || 144 32° 21.920 5-1637,8617 || 145809.617 | 27.6 18o o or 551 Garreg ........ tº e s is º g º 'º $ & ſº ſº º & 8 º' 34 18 40-628 4,88724329 || 77.133-545 || I4-6 38 || Llanelian ......... º, º e º is ſº tº C tº tº tº º 9 44 20-244 || 4:36449953 || 23147'257 || 44 39 Gwaunysgaer........... º 'º º is º & 135 56 59.420 4.97836909 || 95141°303 | 18-o 18o o o.292 Garreg ........................ 15 12 25.532 || 4:5897.9975 || 38886.581 7.4 39 Llanelian ........'............. 12.4 52 8-534 5'o6504729 || 121631.844 23°o 33 Great Ormes Head ......... 39 55 26.648 4.97.836909 || 95141.303 18-o 18o o ... o. 714. * * r *. Llanelian .................. ... || II5 7 48.290 5-ooozoz6o || Iooo.46-661 18.9 4o Gwaunysgaer.......... ſº tº C C C º is º 20 36 II.762 4,5897.9975 || 38886.581 7.4 33 . Great Ormes Head ......... 44 I.G. o. 586 4,88724329 || 77.133'545 I4.6 18o o o-638 - Great Ormes Head ......... 24 51 15.776 4.67559345 || 47379.825 9-o 41 Gwaunyśgner.................. 37 42 33.4%o 4,8385326o || 68949-735 | 13-1 33 Moclfre Issa ........ * * * * * * * * g e 1.17 26 S.506 5-ooozozóo || Jooo.46,661 | 18.9 I8o o ...o.682. . . . . ! Moelfre Issa ........ º s º ºs e º ºs º gº º 25 50.834 || 4-7833 o866 || 60716.771 II.5 42 Great Ormes Head ........“. ... ; : 46.884 || 4:24:56.2642 || 17604-6 Io 3-3 JJ West End of Base............ IIo 45 22:516 || 4,8385326o || 68949-735 | 13. I 18o o o-234 *- TRLANGLES, 483 ** FIGURE I7—continued. No. of Distances in A Names of Stations. Corrected Angles. Log. Distances. F Mil Fº of tº €et. 110S, wº Moelfre Issa ........... * † º C is º º 63 & 18,672 4.624.19845 42091.892 | 8.o f/ 43 Gwaunysgaer.................. 21 4o 21.724 4.24562642 || I76O4.6Lo 3-3 || +6.60 West End of Base............ 96 19 19.777 || 4,67559345 || 47379.825 9-o g: 18o o o-173 -- Moelfre Issa ......... ......... 119 28 3:545 || 4:9300.4003 || 85121.649 | 16.1 44 Great Ormes Head ......... I5 41 4-695 4,4221 1757 || 26431-242 5-o supplementary. East End of Base ............ 44 5o 52.133 || 4,8385326o | 68949-735 | 13. I 18o o 'o. 373 Gwaunysgaer.................. | 24 I3 54.614 4.38947788 . 24517-596 || 4-6 45. West End of Base.......... tº ſº. 20 34 3.366 || 4:32 19323 I | 20986. I28 || 4-o || + o-o2 East End of Base........... ... || 135 12 2-105 || 4-624.19845 # 42091-892 | 8-o 18o o o-o85 FIGURE 18. Fairlight ..................... 47 53 2-952 5-12162477 || I32319.78 25. I I Wrotham, ..................... 46 37 57.496 || 5-II 285752 || 129675-38 24.6 || -o-94 Frittenfield .............. ſº tº ſº º 85 29 3.576 5.2499.9568 || 177826. I? | 33-7 18o To 4,024 || ". Fairlight ..... ſº tº º a tº a tº ſº tº G & © C & tº . 31 34 5.384 || 4,888274I6 77.316.85 14.6 || : 2 : Frittenfield .................. 87 I 37.3.II 5-16876.477 || I47490-74 27.9 || -2.64 Paddlesworth...... tº dº º ſº tº tº º & C & G º 6I 24, 19.660 5-II 285752 || 129675-38 24.6 i I8o o 2.355 Beachy Head...... tº C tº g º m ſº ſº tº ſº tº º 79 54 17.969 5:44218593 || 276812-65 || 52-4 3 | Leith Hill........ tº e º 'º C tº º tº º ſº tº e º 'º 5o 20 48.036 5.3354.0257 || 216472.42 || 41.9 || -291 Frittenfield .................. 49 45 4,759 || 5.33:162235 || 214596:37 40.6 180 o Io. 758 Wrotham .................... * 8 6.576 5-olog 93.76 || Ioz422. I2 I9. 38 43 56-57 3937 9°4. 4 Epping Cupola ............... 77 57 47.111 || 5.294386.29 || 169098:14 || 30-3 || +o,70 Danbury Spire tº tº º ſº tº º º ſº tº dº e º ſº º 63 I8 I9'759 5-1650.937.2 146249.28 27.7 I8o o 3-446 - Wrotham...................... 83 28 21.903 || 5-2917.3176 || 1957.63.52 37. I - 5. Danbury Spire tº º º is © tº $ 8 º' tº s º is C & 42 II 9.834 5. I2I 62477 * | * 132319.78 25. I + I-97 Frittenfield .................. 54 20 33.214 5-204386.29 || 16oog8-14 || 30-3 -º- I8o o 4.951 * , Danbury Spire ............... 8 Ro 5 5. 5-16371982 || 145787.34 27.6 6 | Frittenfield .................. § : §: 5.36369922 231046-4I 43.8 || +5.53 St. Peter's Tower............ 57 22 58-570 5.29.173176 ||. I95763.52 37. I 18o o 6.673 Danbury Spire – 84.580.76 ,-lº - “............ 52 7 22.869 5.2662 o'760 I84589.7 35°o 7 #. Tower tº dº tº dº e º is º e º 'º e 46 46 I9-605 5°231.45795 I7O395-43 32°3 —8.58 alton Lower ............... 81 6 24.835 5.36369922 || 23 Io.16-4T 43.8 I8o o 7.309 | . . 3 P 2. 484 PRINCIPAL TRIANGULATION. FIGURE 18—continued. No. of Names of Stations. Corrected Angles. Log. Distances. Distances in Error of A. * Feet. Miles. A. Danbury Spire .......... { i e C & 93 58 18862 5,4178 og56 || 261703.52 || 49.6 f / 8 | Frittenfield ................. iº 49 37 5'998 || 5.231.45795 || 170395.43 || 32.3 ||supplementary. Walton Tower .......... tº g º 'º º 48 24 42.985 5.29.173176 || 195763.52 37.1 18o o 7.845 Frittenfield ........... tº º C tº e º tº 92 31 39-901 5'4411 2305 || 276136 or 52.3 9 || Walton Tower .............. tº 16 14 38,849 4,88827416 || 773.16.85 14.6 33 Paddlesworth................. º 7I I3 46-oo.4 5-4178 og 57 || 261703.52 49.6 º I8o o 4,754 * Walton Tower ............... 39 29 47.507 5.0974.56Io || 1251.57-28 || 23.7 Io Danbury Spire ............... 8o 3o 60-516 || 5.288oo512 || 194090-88. 36.8 || - 2, Norwood ..................... 59 59 I6.925 | 5.231.45795 || 170395-43 || 32-3 I8o o 4.948 Norwood ..................... 65 2.5 3.61 I 5-2662 of 60 || 184589.76 || 35°o II | Walton Tower ............... 4I 36 37.329 || 5-1296,7533 || 134795-48 || 25.5 }} St. Peter's Church ......... 72 58 24-656 5.288oo512 || 194090.88 || 36.8 18o o 5-596 Danbury Spire ..... & G & º e º 'º e º 'º 52 38 28-180 || 5 II.494.225 || 130299-35 24-7 12 Wrotham .......... * * * * * * * * * * * 49 46 20. I59 5-og7456Io || 1251.57-28 || 23.7 || -2.55 Norwood ..................... 77 35 I5'407 5-204386.29 || 16oog8-14 || 30-3 18o o 3-746 Epping Cupola tº º 0 & 0 e º e º sº e º 'º e 56 I6 59°534 5.off35 I464 II.3.II3'55 2I-4 * : 13 Danbury Spire ........... tº º ſº º 74 51 5-980 || 5-11814186 || 131262.86 24.9 || -2.06 Gads Hill ..................... 48 51 57. II6 || 5'orog 9376 || Io2422. I2 | 19.4 : |T86 o 2-630 + Danbury Spire ............... || 41 5 41.960 || 4.92.626915 || 84385-76 | 16.o 14 | Gads Hill .................... ſº 77 7 58-594 5-og7456Io || 1251.57-28 || 23.7 || + I'o6 Norwood ..................... 61 46 21.635 | 5'o635 I464 || II31. I3’55 2I-4 º 18o o 2-189 Danbury Spire ........ ſº tº º ºs e º 'º 39 21 54,991 || 4:9734.2235 || 94O63-76 17.8 I5 Gads Hill ....... • ** - - - - - - - - - - - 90 55 53-697 5. I7Io9837 I48285-39 28. I |Supplementary. Severndroog ..... tº e º 'º C & Q & 8 & 6 s g 49 42 13.815 5-0535 I464 || II3113-55 2 I-4 18o o 2-503 Danbury Spire ..... tº º ſº ſº tº tº º ſº 35 29 Io:989 || 4:94452493 88oo8.56 16.7 16 | Severndroog .................. 42 29 57.547 || 5'olo29376 || Io2422. I2 | 19.4 9) Dpping Cupola ....... tº C tº e º O C & Ioz o 53.538 5' 17109837 || 148285-39 28.1 18o o 2-o/4 Severndºog .................. 35 Io 46-416 || 4-7342 obº) || 54.226. Io | Io-3 17 Gads Hill ............. º, º 'º º ſº ſº º º 52 5o 39.875 4,87513762 75oI3. I9 I4-2 jp Wrotham ............. tº Q & Q & Q º º 9I 58 34.665 4,97342,235 || 94.063-76 17.8 18o o o-'956 Epping Qupola tº º ſº tº e º ºs º g c s s º º g 72 16 7.329 5'12447598 || 133191.34 25.2 I8 Gads Hill ................... & C 37 53 48.908 4'9339.5I 5o 85891.76 I6.3 33 St. Paul's tº G tº º O ſº º C G D 0 || 0 || C C C C º 0 tº 69 5o 6.289 5. I 1814,186 131262.86 24-9 | 18o o 2.526 TRIANGLES. 485 FIGURE 18—continued. No. of Names of Stations. Corrected Angles. Log. Distances. Distances in Error of A. * Feet. Miles. A. - . . O / / / W.W Fairlight ..................... 8o 59 34.574 5-21903782 || 165591.42 || 31. I9 Frittenfield * * * * * * * * * g e ū ºl e º 'º wº 48 2O 35.85 I 5.og782678 125264. I5 23.7 |Supplementary. Crowborough....... tº $ tº a gº tº tº C tº º • || 5o 39 53.349 || 5 II 285752 || 129675-38 24.6 I8o o 3.774 Fairlight .............. tº ſº tº a g º º II2 33 39.958 5.3564. I398 || 2:27.202.96 || 43-o 20 | Paddlesworth.................. 3o 36 24.955 5-09782678, I25264. I5 23.7 53 Crowborough................ tº ſº 36 49 59. Ioo 5: 16876.477 || I47490.74 || 27.9 18o o 4.org Erittenfield .......... tº gº tº G & º & º 37 8. 27.725 4.9999 I518 || 9998o-472 | 18.9 2I. Wrotham ..................... 89 49 5-408 || 5-2 1903782 || IG5591-416 || 31.4 33 Crowborough................ tº 53 2 29.979 || 5. I2I62477 || I32319.78o 25. I 180 o 3-112 Frittenfield .................. 49 22 33-790 5-O-493.8793 || II2O43-83 21.2 22 | St. Peter's Church ........ § 3I 35 *::::: 4.8882 7416 773.16.85 I4.6 || + o-3o Paddlesworth.................. 99 2 23.999 || 5-1637 1982 || 145787.34 27.6 18o o 2-or 2 £riºnfield.................., | 66 25 3.352 5-12967533 || 134795-48 || 25.5 23 St. Peter's Church ......... 31 16 53.520 4,88166881 76149-8I I4.4 || +4.12 Norwood .......... tº º º dº º 'º e s ∈ tº c 82 24 5,521 || 5-1637 1982 || 145787.34 27.6 I8o o 2.393 FIGURE 19. Dunstable ................. Q & C. C. 47 34 45-525 5-o/797421 || II9666.95 22.7 I Epping Cupola ............... 51 8 17.359 5. IoII.4.199 || I26224 or 23.9 || +3.81 Tharfield ..................... || 81 16 60.628 5.20474992 || 1602.32-25 || 30-3 18o o 3.512 * Dpping Cupola ........... ſº tº ſº º 45 4I I5'573 4.944.29699 87962.38 | 16.7 2 | Tharfield. ..................... 57 32 47.274 || 5 or 59 I555 || Io9732.67 | 19.6 || –o.66 | Thaxted Spire ............... 76 45 59.242 5-o/797421 || II9666.95 22.7 18o o 2.089 Dunstable .................... ſº 49 13 30.774 4,9884.1660 || 97,368.08 18.4 3 Tharfield .......... tº ſº tº º tº e º 'º - e. e. 5I 45 4:2O4. 5-oo.42 Io'72 || Ioog'74-27 | IQ. I ||Supplementary. Berkhampstead....... * tº C tº tº º tº 79 I 27.292 || 5. Iol I4199 || I26224 or 23.9 18o o 2.270 Thaxted Spire tº . C C C C C C º º ſº tº º ſº tº 49 3 I 4-667 4.9884.1660 97.368.08 18-4 4 Tharfield .............. tº º ſº º 'º º º 87 4 43.698 || 5. Io96.9127 | 127847.21 | 24.2 23 Berkhampstead............... 43 24 13.647 || 4:944.29698 87962-38 | 16.7 18o o 2-or 2 Epping Cupola ............ tº º º 8 56 47.503 i 5-ooozoool || IoI437-84 19.2 5 | Thººted Spire ............. tº º 3. : #: 3.01.039376 || 102432-13 | 19.4 || -o-66 Danbury Spire .......... § {} º 'º º 61 Io 17.377 5-or 59 I555 Io9732-67 19.6 I8o b 2.141 486 PRINCIPAL TRIANGULATION, JFIGURE 19–continued. No. of Names of Stations. Corrected Angles. Log. Distances. Distances in Error of A. Feet. Miles. A. Danbury Spire tº º tº º ºs º a º C G e º 'º a º 66 43 4%863 5.ogSI 71.57 || 1245oo.64 23.6 f / 6 Thaxted Spire tº tº ſº e º 'º º ſº, ſº tº g º º dº ſº 64 5o II-635 5-08877.019 122678-99 23.2 Supplementary. Stoke Tower .................. 48.27 3.199 || 5-ooºzoool || 101.437.84 19-2 | 18o o 2-688 Danbury Spire ...... tº e º 'º º ſº ſº tº ſº 35 39 6:305 || 5'ooz43148 || 190561.44 19-o 7 | Stoke Tower .................. 99 I 43. I39 5°23.145795 || 179395:43 32.3 || + 3-02 Walton Tower ..... tº g º O C C º º ſº it 45 19 13.422 5-oS877OI9 || 122678-99 || 23-2 I8o o 2.866 Walton Tower ...... ......... 54 28 28.535 | 4,9737,0309 || 94124.59 || 17-8 8 Stoke Tower.................. 65 7 25-35o 5-0208.6658 || IoA922-oo | Ig:9 || +2.02 Otley Tower .................. 6d 24 8. I55 5-oo.243148 || Iooj6I-44 || 19-o I8o o 2-ozo Walton Tower ............... 32 41 53-678 4:79746879 -- 62729.06 II-9 9 || Otley Tower .................. 82 40 I3-844 5-off 134083 || II517o-39 || 2 I-8 || – I-2I Naughton Tower ............ 64 37 54'OI3 | 5.0208.6658 IO4922-ol I9.9 | 180 o 1,535 Thaxted Spire • . . . . . . . . . . . . . . 34 29 3.462 4.85277.347 ºr 71248. I3 I3'5 Io | Stoke Tower......... tº º ºs e º 'º e º 'º 63 53 4.716 5-oš30526o || II2993-28 || 21-4 supplementary. Lawshall Tower............... 8I 37 53-695 5-og SI 71.57 I245oo-64 23.6 18o o 1,873 Stoke Tower.................. 5o 7 45-635 4.73829I43 54738.316 IO-4 II Lawshall Tower............... 37 I6 54-184 4,63549885 432OI-502 8.2 -4:35 Naughton Tower ............ 92 35 20.737 4.85277347 7I248. I3o I3-5 I8o o o-556: g * * * * * , # , "a tº * * * Thaxted Spire ..... tº ſº tº C. § C & © º º 9 37.427 | 4:96099533 9I4IO-34 I7-3 I2. Lawshall Tower............... ; # 7'452 4-81651580 - 65541-41 I2-4. + o-31 Balsham Tower............... 90 33 I6.53o 5'o630.526o. - II2993-28 2I-4 # 18o o 1,409 || Tharfield ..................... 43 I2 24-909 4,816.5 I58o 65541-41 13.4 13 || Thaxted Spire ............... 7o 2 Io-972 4'954I4333 || 89979-45 I7'o +o.65 Balsham Tower............... 66 45 25-393 || 4:9442 9698 || 87962-38 16.7 180 o 1,274 Tharfield ..................... 36 21 30.859 4.999.07870 – 97741-43 | 18.5 14 | Balsham Tower....... “...... || Tio 33 55-795 5-18854762. || 154364.57 29.2 || —4:51 Ely Minster ............. tº ſº dº º º 33 4 35:283 4'954I4333 89979.45 I7.o 18o o 1.937 Danbury Spire ............... 4o II 35.458 5'o6134083 II517o-39 21.8 -- I5 Walton Tower ............... 67 5 48.28o 5.2.1.58 73 Io I64389-13 31. I — I-48 Naughton Tower ............ 72 42 4O'5I4. 5' 231.45795 I7O395-43 32°3 I8o o 4.252 Danbury Spire tº ſº e º ſº tº $ tº t e º tº e º 'º 62 Io 18.71o 5-1686.7489 || 147460-22 || 27.9 16 || Naughton Tower ............ 37 28 12.538 5-oodzoool || IoI437-84 || 19.2 |supplementary. Thaxted Spire ............ 8o 21 32.220 5:21.5873Io-|| 164389-13 31.1 18o o 3,468 sº TRIANGLES. 487 **** - ". ... *- ºn FIGURE 19–continued. : - - Distances in : sº Names of Stations. Corrected Angles. Log. Distances. # all CeS 1 Miles. Fº º Danbury Spire ............... 13 12 4£754 4,73829I43 || 54738-31 | Io.4 &/ 17 | Naughton Tower ............ 79 35 43.054 5.21382.252 || IG3614.78 || 31°o |supplementary. Lawshall Tower ............ 81 II 37.273 5.21587310 || 164389-13. 31. I I8o o 2-o&l Balsham Tower............. ... || 61 9 Io:504 || 5.25565212 || 18O157:40 || 34’ I 18 Lawshall Tower............... 92 27 39.775 5.31279324 || 205491-2I | 38.9 35 * Swaffham Spire............... 26 23 I3.590 || 4:96099533 9I4IO-34 I7'3 18o o 3.869 º Lawshall Tower............... 37 4 43-oz I 5-oš944oz8 || II4667-48 || 21.7 I9 || Swaffham Spire............... 34 13 40-684 5-oz929982 || 196979-32 | 20-3 || –4.64 South Lopham Tower ...... Io8 41 39-oz8 5.25565212 || 18O157:4o 34. I * .. 18o o 2.733 g Lawshall Tower........... ... || 48 45 58.349 || 4,9239,0084 || 83926.83 I5'9 || : 20 | South Lopham Tower ...... 57 46 52-628 4.97504827 94416.58 I7.9 || + o-35 Brandon.................... ..., | 73 27 10.810 5:02929982 || 106979-32 ) 20:3 18o o 1,787 Brandon........................ 82 33 23.173 || 5-oš944O28 || II4667-48 || 21-7 21 | South Lopham Tower ...... 5o 54 #: 4.953o 8184 || 89759-79 || I7-o || +o. 18 Swaffham Spire............... 46 31 52.184 || 4.9239 oo84 || 83926.83 I5'9 18o o I-757 Brandon................. © º 'º º q Q tº Ior 33 15.645 5.11948.288 || 131668.8o 24.9 22 | Swaffham Spire............... 36 32 ; 4.903.18.158 || 8ooI6.87 15-2 || –2.81 Ely Minster .................. 4I 54 17.731 || 4:953o 8184 || 89759-79 I7'o 18o o 1,655 | Tharfield ..................... 20 17 o'972 4903.18.158 8ool 6.87 | 15.2 23 Ely Minster ........ tº ſº tº º º ſº º ſº tº ſº. 117 44 42.617 | 5-3132.3174 || 204282-77 38.7 || -4-51 Brandon........................ 41 #8 i9.58% 5, 18854762 || 154364.57 29.2 18o o 2.571 Lawshall Tower:tº ſº º tº º t t e º is e ſº 42 2 30.025 || 4-86177302 72739.95 || 13.8 24 | South Lopham Tower ...... 57 55 54'994 4.964Oo379 92.047°o3 I7-4 || –4.05 Mickfield Tower tº ſº tº ſº tº tº ſº e º 'º º 8o I 36-532 5-O292.99.82 Ioff079-32 20.3 I8o o 1.551 Lawshall Tower....... tº Q tº C tº ſº º ſº 34 3 11.847 || 4-7470.7502 || 55856.67 Io.6 25 | Mickfield Tower ............ 33 16 53.244 4.73829I43 || 54738-31 || Io.4 || + o-o4 - Naughton Tower ............ II 2 39 55-573 49640 oo?9 || 92.047°o3 17.4 ** I8o o o-664 Lawshall Tower............... 76 5 41.873 5-og272163 ||. Io?825-54 20:4 26- . South Lopham Tower ...... 29 31 24.778 || 4-73829I43 54738-31 || Io.4 Supplementary. Naughton Tower ............ 74 22 54.686 5-oz929982 || Io9979-32 20.3 18o o I-337 - Naughton Tower ............ o 22 46.8 4.5022.5966 || 31787.74I | 6′o 27 | Mickfield Tower ............ § : § 4.79746879 || 62729,062 II-9 +6.16 Otley Tower .................. 62. 45 34.2%; 4,74767532, 55856-667 | 10:6 18o O O-4I? #. * 488 PRINCIPAL TRIANGULATION. FIGURE 19–continued. No. of Names of Stations. Corrected Angles. Log. Distances. Distances in Error of A. Feet. Miles. A. O Af f / Ely Minster ................. ſº 36 31 35-533 4-76489.460 58196. I9 II • O & M 28 || Balsham Tower............ tº tº º 5I 55 48-690 4,88635394 76975-75 14-6 ||Supplementary, Cambridge Obs' Dome...... 9I 32 36.830 4.99067876 || 97741.43 | 18.5 I8o o I'o63 Ely Minster ............... ... || 12I II 42-267 5.1360 1911 || 136778.90 25.9 29 | Brandon....:::::::::: tº ſº ſº º tº ſº º C & 28 46 37.951 || 4,88635394 76975-75 14.6 35 Cambridge Obs' Dome...... 3o I 41.02I 4,903.I 81.58 || 8ool 6.87 | 15.2 18o o 1,239 FIGURE 20. Walton Tower ............... 41 24 14-662 4,861 I 1526 || 72629.87 | 13.8 sº I | Otley Tower............ º ſº tº $ tº dº 65 46 12.132 5-oooo 226o || Ioor 43.46 19-o || +2-62 | Orford Castle................. || 72 49 34:840 || 5 ozo&6658 || 104922 or | 19.9 : 18o o I-634 Orford Castle......... tº ſº tº º ſº º tº ſº º 48 4 45-204 || 4-8II9 II 26 64850. I9 I2.3 2 | Otley Tower............ tº tº e º 'º º 75 28 43.276 4.92.61 9812 84371.96 | 16.0 || – I-60 Laxfield Tower............... 56 26 32-592 || 4,861 I 1526 72629.87 13.8 i 18o o 1,072 | Orford Castle.................. 47 o 50.713 || 4,848.28369 70515°35 | I3-4 3 Laxfield Tower......... tº ſº tº º ſº tº 7I 54 34.442 4.962o.4025 91630.54 I7.4 || +3.49 Southwold Tower............ 61 4 36. I75 || 4.926I 9812 8437 I-95 || 16.o 18o o 1,330 Southwold Tower............ 77 19 31.894 || 4:93547002 861.92.61 | 16.3 4 || Laxfield Tower............... || 49 43 5-599 || 4-8286.3613 67396-31 || 12.8 || –4.6o Tofts Tower .................. 52 57 23.607 || 484828369 70515-35 | I3-4 18o o 1.091 Laxfield Tower........... ſº ſº º º 69 4o 51.417 4'9955.4995 9898o. 57 | 18.7 5 || Tofts Tower .................. 55 34 19-oo.5 4'9398 Igó3 87060.19 I6.5 || -o-o8 Bunwell Tower .......... it tº e G 54 44 51°233 4°93547Ooz 861.92.61 I6.3 18o o 1.655 Laxfield Tower............... || 39 Io 37,852 4,8867.4290 77O44-72 I4.6 6 || Tofts Tower .................. 95 51 I4-336 5-oS39.4854 || 121324:51 23-o || +o.87 Norwich Spire ............... 44 58 9.366 4.93547002 861.92.61 | 16.3 I8o o I-554 Laxfield Tower............... 3o 3o 13.565 4.80627646 64O14.22 | 12.1 7 | Norwich Spire ..... tº º º º ſº. C C tº C tº 43 39 23.907 || 4:93981963 87O60-19 | 16.5 || – 1:32 Bunwell Tower............... Io.5 50 23.789 5'o639.4854 || 121324.5i 23.6 I8o o I.261 Laxfield Tower............... 3o I 59:473 || 4,66092.175 45805-934 8.7 8 Iłunwell Tower:::::: tº g tº º dº º ſº tº 77 55 40.856 4'95180537 89496.359 I6.9 +o. 18 South Lopham Tower ...... 72 2 20:588 4,9398 I963 || 87O60,194 | 16.5 18o o oxg17 TRIANGLES. 489 I'442 FIGURE 20—continued. - Distances in º sº Names of Stations. Corrected Angles. Log. Distances. JFeet. Miles. Fº of O f & f/ South Lopham Tower ...... 42. 59 5*47 4-66.154706 || 4587 I-935 | 8.7 9 | Bunwell Tower............... 94 4 54.950 4,82668126 || 67.993.625 | 12.7 || + 1.16 Hingham Tower ............ 42 55 14,496 || 4-66092.175 || 45805.935 | 8.7 I8o o o-493 South Lopham Tower ...... 44 36 57.653 4,80279878 || 63503.66 I2-o Io Mickfield Tower ............ 81 49 18.416 4.95180537 || 89496.36 | 16.9 || + 6.85 Laxfield Tower............... 53 33 45-ood 4,86177302 || 72739.95 || 13.8 - 18o o 1-075 H Norwich Spire ............... 38 11 55.911 || 4-66.154706 || 45871-935 | 8.7 II Bunwell Tower............... 82 9 o.406 || 4.8661 9434 || 73484.263 || 13.9 || + o-26 Hingham Tower ............ 59 39 4,367 4.80627646 || 64oD4:220 | 12:1 18o o o-684. Norwich Spire tº ſº º 'º º ſº tº $ tº ſº º º º 86 33 59.266 5-O759 2535 II9Io9-73 22.6 I2. Hingham Tower ......... tº ſº º 55 25 7.429 4:99227458 98236.88 18.6 +3.84 Baconsthorpe Tower......... 38 o 55-ooo 4.86619434 73484.26 || 13.9 18o o 1.695 Baconsthorpe Tower......... 3o 48 34,891 4.842.96670 || 69657-31 || 13-2 I3 Hingham Tower ........... O 88 3 ió.557 5-13328924 || 13592 I-84 25-7 || +3.48 Swaffham Spire......... tº dº ſº tº tº º 61 8 7.562 5-o/592535 | I 19103.73 22.6 I8o o I-950 Baconsthorpe Tower......... 6 9 36.622 4'93947357 86990.85 16.5 I4 | Norwich Spire ............... : 7 ; 4-928.73302 || 84865-86 16.1 || +3.95 Happisburgh Tower ......... 69 42 51.257 4.99227458 98.236.88 | 18.6 I8o o 1,629 Happisburgh Tower......... 61 27 4-117 || 4-98334618 96oi6.57 | 18.2 I5 | Norwich Spire ............... 65 48 53.416 499875162 99712.96 | 18.9 || -8.34 Gorleston Tower ............ 52 44 4.265 4'93947357 86990.85 | 16.5 * 180 o I-792 Happisburgh Tower......... 40 26 9-157 || 4,8867.4290 77044.71 14.6 I6 | Norwich Spire ............... 92 28 57.836 5-o/43617o || 118675-67 22.5 || -7.38 Tofts Tower .................. 47 4 54.618 4'93947357 86990-85 | 16.5 I8o o I-575 Southwold Tower...... tº ſº tº c º º 26 43 35.598 || 4.64320396 || 43974.809 || 8:3 17 | Tofts Tower .................. Io9 43 5,896 || 496405257 || 92056. Ioo 17.4 || -I-58 Gorleston Tower ............ 43 34 19.162 4,8286.3613 || 67396.312 12.8 * 18o o o-656. Swaffham Spire............... 66 33 10.847 5:21825628 || IG5293-69 31-3 18 Lawshall Tower ............ 22 44 40-o/3 || 4.842.96670 69657.31 13.2 |supplementary. Hingham Tower ............ 90 42 11.788 5.25565212 || 18O157:4o 34. I 18o o 2.708. i. Swaffham Spire............... 78 51 22:347 5-oro43112 || Ioz430.93 19.4 I9 Pandon........................ 4I 5I IO-627 4.842.96670 69657.31 I3-2 — O-49 Hingham Tower ............ 59 I'7 28.468 4:953o 8184. 89759-79 |. I7. I8o o 3 Q 496 PRINCIPAL TRLANGULATION. FIGURE 20–continued. No. of Names of Stations. Corrected Angl Log. Distances Distances in | Error of A. Angel ºf unuses. Feet. Miles. ||_A. Brandon...... : “... . . . . . . . . . . . . 6. 35 37,694 5-054I 7261 || II3285-05 || 2 I-5 Af 20 | Swaffham Spire............... 69 42 19:639 5-ofoS 1280 || 117628.57 22.3 supplementary. Bunwell Tower............... 45 42 4.91o 4'953o 8184 || 89759-79 || 17-o 18o o 2-243 South Lopham Tower ...... 76 43 7.737 5-o54I 7261 || II.3285-oš3 21.5 21 | Swaffham Spire............... 23 lo 27:455 || 4-66092.175 || 45805'934 || 8.7 35 Bunwell Tower............... 8o 6 26-oro 5-oš944O28 || II.4667.483 21.7 18o o I-202 Swaffham Spire............... 7o 17 Io-2Io 5.16028047 || 144637.36 27.4 22 | Bunwell Tower............... 62 I2 36.729 5-13328924 || I3592 I-84 25.7 33 Baconsthorpe Tower......... 47 3o 16:470 5-oš417261 || II3285-off 2I-5 I8o o 3-409 - Bunwell Tower............... 38 16 34,027 4,80279878 || 63503.66 | 12-o 23 Laxfield Tower............... 83 35 44'479 5.oobo 7356 IoI876-39 I9.3 + I-16 Mickfield Tower ............ 58 7 42.786 || 4,93981963 87060-19 | 16.5 {} 18o o 1.292 | FIGURE 21. Great Whernside ............ 44 55 II.738 5-2Ioo 2890 || 16219 I-80 || 30-7 I Botton Head.................. 65 58 43.267 5.3218 I28o || 2098o3.53 39.7 || -2.73 York Minster.................. 69 6 12.468 5-33160691 || 214588.73 40.6 18o o 7,473 | . . . Botton Head.................. 26 II I4.503 || 4,8547.8165 || 71578.34 || 13-6 2 York Minster.................. 63 2d 47.386 5-16124532 || 144959-oA 27.5 || + 5°99 Acklam Wold ...... tº ſº tº ſº tº it is tº 90 28 6.55o 5-2Ioo.2890 || 162191.8o || 30-7 18o o 2.439 || Great Whernside ............ 33 21 18.282 || 5 16124532 || 144959-oA. | 27.5 3 | Botton Head.................. 92 9 57.779 5-4207 1759 || 263461.76 49.9 |supplementary. Acklam Wold ............... 34 28 51.256 5:33:160691 || 214588.73 40-6 18o o 7.308 • gº, Great Whernside ............ 36 35 59.612 5:27097898 || 186628.93 35.3 4 York Minster.................. IöI 18 56.589 5.4879.5434 || 306940-61 58. I 35 Clifton Beacon ............... 42 5 12.826 5:3218 128o 2098o3.53 39.7 18o o 9-oz7 Great Whernside ............ 48 9 53.068 5.37310914 || 236107.15 44.7 5 | Clifton Beacon ............... 56 I4. 27.573 5'42O7I759 || 263461.76 49-9 22 Acklam Wold ............... 75 35 53.523 5:48705434 || 306940.61 58.1 I8o o I4. I64. Great Whernside ............ 37 548.307 || 520353963 || 159786.33 30.3 6 || Acklam, Wold ..... tº ſº tº tº C. § 3 tº º 46 53 37.832 5.2864.8277 || 1934.11.71 || 36.6 ?? Garforth Cliff ............... 96 o 4I-o87 5-4207 I’759 || 26346I-76 49-9 18o o 7.226 TRIANGLES. 491 FIGURE 21—continued. No. of -- tº * Distances in Error of A. Names of Stations. Corrected Angles. Log. Diane. Feet. Miles. A. Great Whernside ............ 27 15 26%68 5-1684.5706 || 147386-28 || 27.9 # / 7 Clifton Beacon * * * * * * * * g º º º a ſº º 45 I5 Io'o64 5-3.590 of 53 228560-69. 43°3 |Supplementary. Holme Moss .................. Io? 29 31.232 5.48705434 || 306940.61 58. I I8o o 7.554 Great Whernside ............ 38 19 31.029 || 5-1536 I486 || 142434.39 27.o 8 Holme Moss .................. 57 21 30.977 5.28648277 || 1934II-7I 36.6 J } Garforth Cliff ............... 84 18 64,439 5.3590 or 53 || 228,560-69 || 43.3 I8o o 6.445 Great Whernside ............ 25 31 54.851 || 4:9567.4278 90519-63 17. I 9 York Minster ............... 67 3 44-191 5.28648.277 1934II:7; 36.6 33 Garforth Cliff ............... 87.24 25-ozo 5.3218.1280 || 2098o3.53 39.7 I8o o 4-112 Clifton Beacon ............... 33 26 44.606 5-2067.6564 || 160977.67 30.5 w Io | Acklam Wold ............... 29 29 28.839 5-oog64557 || Ioz.245-82 | 19.4 || -4.95 Crowle ........................ I26 3 49.683 5:373 Io914 2361oz. I5 44-7 18o o 3-128 Acklam Wold ....... tº ſº tº C ºn tº ſº º 49 II 44°530 5: I.255.472 I || I33520-27 || 25-3 II | Crowle ........................ 64 56 16-61 I 5-20353963 || 159786.33 || 30-3 || –4.54 Garforth Cliff ............... 65 52 3.436 5-2067.6564 || 160977.67 30.5 I8o o 4.577 Holme Moss .................. 48 19 5.713 || 4.9323 ogg2 || 85567.71 | 16.2 12 || Axedge ........................ 3I 2.2 19.947 || 4-77557631 5964.5-31 || II 3 ||supplementary, Back Tor ............ tº ſº dº ſº tº º ſº, º gº Ioo 18 35-521 5-oš200814 || II2721.86 21.3 I8o o 1, 181 - Bardon Hill .................. 17 52 13.991 || 4.93.230993 || 85567-71 I6-2 13 | Axedge ........................ IoA. 54 36.554 || 5-43649548 || 26.9460-73 || 51-o 33 Back Tor ..................... 57 I3 I4-ol 3 5-37003940 || 234444. I5 44'4 I8o o 4.558 - - Holme Moss .................. 37 41 1.543 5.02780527 || Io961 I-8o 20:2 14 | Clifton Beacon ............... 19 59 56.027 || 4-77557631 || 5964.5-31 || II-3 33 Back Tor ..................... 122 18 63-694 5.1684.5706 || 147386.28 27.9 18o o I-264 | Bardon Hill .................. 77 58 23.981 5.49065668 || 309497-17 | 58-6 I5 Axedge ........................ 54 i3 25.153 5:40947466 || 256728.84 48-6 || +5.48 Lincoln Minster ............ 47 48 24.707 5-3700394o || 234444. I5 44'4 agº. I8o o 13.841 Bardon Hill .................. 6o 6 9-990 || 5:42 II5715 || 263728-55 49-9 16 || Back Tor ..................... 57 33 26.361 5:40947466 || 256728.84 || 48-6 sunknºwn. Lincoln Minster ...... tº . . . . . . . 62 20 43,810 5-4304.9548 269.460.73 5I-o I8o o 14. IoI - Crowle * * * * * * * * * e s e e s e º e s e s e s e e . 6 •42II 57I5 263728-55 49-9 17 Back Tor . . . . . . . . . . . . . . . . . . . . . ; ; ; #; 2460' - 151260.18 28.6 y? Lincoln Minster ............ 5ö 23 36.73% 5.30938.462 || 203884-69 38.6 I8o o .. 7.226 3 Q 2 492 PRINCIPAL TRIANGULATION. FIGURE 21—continued. - Distances i i sº Names of Stations. Corrected Angles. Log. Distances. #. In CeS IIl Miles. Fº of - Clifton Beacon ............... 6í 34 33% I6 5. I797 2459 151260.18 28.6 & f I8 Crowle ::::.................... 8I 56 61.227 5-2312 1621 || 1703oo.61 32.2 || + o-28 Lincoln Minster ............ 36 28 30.257 5-oo964557 || Ioz245-82 | 19.4 18o o 3-600 Bardon Hill .................. 24 47 23:58o 4'9039.2124 || 8or 53-27 | 15.2 I9 Arbury Hill ........... tº e º 'º tº $ tº | 45 57 24.374 5. I38o3435 || 13741 I-90 26-o || – 7.17 Naseby Tower ............... | Io9 15 14,491 5.2564II48 || 180472.68 34.2 18o o 2.445 Arbury Hill .................. 92 23 41.831 5:34.135081 || 21.9457-69 || 41-6 20 | Dunstable ..................... 21 24 9-599 || 4,9039.2124 || 8or 53.27 15.2 supplementary. Naseby Tower ............... 66 12 12-355 5:30314247 || 200975-20 38. I 18o o 3.785 Arbury Hill .................. 76 57 40.328 5.0406.2719 || Io9806-28 || 29.8 2I | Naseby Tower ............... 57 42 43’557 4'9790 IQ99 95284-oo | 18.0 33 Elanslope Spire tº e º 'º tº ſº tº ſº tº º is tº tº º is 45 I9 37.865. 4'90392. I24. 8or 53-27 I5-2 I8o o 1,750 Arbury IIill .................. I5 26 I'503 5.o.493518.5 II2O34-5 I 2 I • 2. 22 Dunstable ..................... I3 4 53. I27 4'9790 IQ99 952.84.oo | 18-o 33 Hanslope Spire............... I5I 29 6.568 5:30314247 || 200975-20 38. I 18o o 1,198 Dunstable ..................... 99 I5 3.892 || 5.25946006 || 181743.98 || 34.4 23 Tharfield ...................... 37 28 33-397 ||5-0493518.5 || II2O34:51 21.2 | . , Hanslope Spire............... 43 IC 25.994 || 5. IoII.4.199 || 126224.02 || 23.9 18o o 3.283 Dunstable ..................... 53 45 36.563 || 5-oS8494.18 || I226or-oA 23.2 24 | Tharfield ..................... 7o 6 9-565 5-1551.3234 || 142932-94 | 27. I | +2.27 Keysoe Spire.................. 56 8 I7-295 5. IoII.4.199 || 126224.02 23.9 I8o o 3-423 Naseby Tower ............... 39 17 9-268 || 5 IS5I 3234 || 142932-94 27. I 25 | Dunstable ..................... 37 10 16.858 5-1347.6222 || 136383-62 25-8 supplementary. Keysoe Spire.................. 103 32 44-331 || 5:34.135081 || 21.9457-69 || 41-6 18o o 4:457 Dunstable ..................... - 45 29 27.330 5-or 12 1272 || ro2615:43 | 19.4 26 || Keysoe Spire.................. 51 7 56.573 5-oag351.85 || II2O34°51 21.2 33 Hanslope Spire............... 83 22 38.783 || 5-1551.3234 || 142932-94 27. I 18o o 2.686 Tharfield ...................... 32 37 36.168 5-of-12 I272 || Io.2615-43 | 19.4 27 | Hanslope Spire tº tº dº ſº tº º 'º º & g º º e º 'º 4o 6 ia.789 || 5-oS8494.18 || 1226oi.o.A. | 23.2 33 Reysoe Spire.................. Io? I6 13.868 || 5-25946.006 || 181743.98 || 34.4 | 180 o 2.825 Tharfield º, º ſº tº tº £ tº ſº tº º ſº tº ſº tº º º ſº º tº º' 7I 30 6.766 5.2.1447396 163860.38 3I.O 28 Ely Minster .................. | 45 II 54.178 || 5-oS8494.18 || 1226or-o4 || 23.2 || +5.73 - Reysoe Spire.................. 63 18 3.277 5-18854762 || 154364.57 29.2 | 18o o 4.221 TRIANGLES. 493 I8o O 3'934. FIGURE 21—continued. Distances in sº Names of Stations. Corrected Angles. Log. Distances. Feet. Miles. Fº of Balsham Tower............... 68 7 2.809 5.2.1447396 || I63860.38 31.o ſ/ 29 | Ely Minster ............ ..... 78 16 29.461 5-237791.99 || 172898-8I 32.7 |supplementary. Keysoe Spire.................. 33 36 31.418 4.990o 7870 97741-43 | 18.5 18o o 3.688 Ely Minster .................. 45 39 33-226 5-I4656688 || I4O14I'53 26.5 30 | Keysoe Spire.................. 77 35 49.577 5-281.88890 || 191376.63 36.2 || – II. I.4 Easton Tower ............... 56 44 42,471 5:21447396 163860.38 31.0 I8o o 5.274 Naseby Tower ............... 6I 39 20.814 5.14656688 || I4ol4I-53 26.5 31 | Keysoe Spire.................. 59 25 5-519 || 5-13698375 || 137983-94 26-o || –4.23 IEaston Tower ............... 58 55 37-536 5-1347.6222 || 136383-62. 25.8 18o o 3.869 Easton Tower ............... IoI 14 18:513 5.24153707 || 174396-22 || 33-o 32 | Keysoe Spire.................. 26 44 48.893 || 4.903.20291 || 8oozo.8o I5-2 || +3.65 Tilton........................... 52 o 55-181 5.14656688 || I4OI4I'53 26.5 18o o 2.587 Naseby Tower ............... 96 18 59:468 5.24153707 || 174396-22 || 33-o 33 Keysoe Spire.................. 32 4o 16.627 4.97642,582 94716.54 I7-9 || -4.95 Tilton........................... 51 o 46.925 5-1347.6222 || 136383-62 25.8 18o o 3.020 Bardon Hill .................. 43 31 25-417 | 4,97642,582 || 94716:54 || 17-9 34 | Naseby Tower ............... 48 56 24.418 5-or 58.0934 || Io9707-3o 19-6 || + 2.19 Tilton .......................... 87 32 12-473 || 5-138o 2435 || 1374II-90 26-o || 180 o 2.308 - Bardon Hill .................. 26 36 13.864 || 4-8275.528o 67228-40 | 12.7 35 | Tilton........................... Io9 42 8.523 5:1502,5296 I41336-oš 26.8 ||supplementary. Buckminster Spire ........ º 43 41 39.156 5-org&og34 || Io3707-30 || 19.6 I8o o 1.543 - Bardon Hill .................. 35 15 36.233 5.21267626 I63183.5I 30.9 36 Lincoln Minster ............ 36 o o.226 5-1502,5297 || I4]336-25 | 26.8 33 Buckminster Spire ......... || 1:14. 44 28.472 5:40947466 || 256728.84 || 48-6 I8o o 4.925 Lincoln Minster ............ 63 3 55.211 5.21044044 || 162345.56 || 30-7 37 | Buckminster Spire ......... 53 16 57.852 5-16426204 || 145939:47 27.6 33 Boston Tower ............... 63 39 ii.93o 5.21267626 || 163183:51 30.9 * 18o o 4.993 º Buckminster Spire ......... 2 41.836 5.219558oo || 165789.87 31.4 38 Boston Tower ............... ſ: s: : 4,870I 7548 74I60-98 || 14-o 33 Paston Tower ............... 74. 2 I 30.809 5-21 O44O44 62345-56 30-7 18o o 2,784 Boston Tower ............... 1 22 34.564 5-22003868 || 165973.47 31.4 39 Fººton Tower * & tº e s e e s tº t e º 'º e º § 26 *::::: 5-O272 off?.9 Ioé464.74 || 20-2 +3-ol Walpole, St. Peter's......... 71 II 20.772 5.219558oo 165789.87 3I-4 494 PRINCIPAL TRLANGULATION. FIGURE 21—continued. Di * s: of Names of Stations. Corrected Angles. Log. Distances. F = *H Bº of * - €0 IIeS. --__ Easton Tower ............... Il 38 4: 28.098 5-o&I 9897o || 120778.52 22.9 & f 4o | Ely Minster .................. 59 12 30.837 5:22Oo3868 || 165973.47 || 31.4 || +2.96 Walpole, St. Peter's......... 82 6 5.735 5:28.188890 || 191376.63 || 36.2 18o o 4-670 - Ely Minster .................. 5o 17 2-ol.2 5-o:322.4369 || Io'77O6-94 20-4 4I | Swaffham Spire............... 59 36 24,346 5-oSI98979 || I2O778-52 22.9 || –o.5o Walpole, St. Peter's......... 70 6 36-519 5-11948.288 || 131668.8o 24.9 18o o 2.877 Boston Tower ............... 21 49 58:533 5.03.22.4369 || Io?706.94 | 20:4 42 Walpole, St. Peter's......... 136 35 56.974 5-29883936 || 198993.71 37.7 || + 1.47 Swaffham Spire............... 21 34 6.345 5-0272 off?9 || Io9464.74 20:2 18o o I-852 Ely Minster .................. I7 24 I3’ I 5o 4,6013 I725 3993 I-649 7.6 43 Walpole, St. Peter's......... 97 49 5-140 5-12144542 || 132265. I47 || 25.1 || -2.69 Ilynn Tower.................. 64 46 42.834 5-o819897o I2O778.519 22.9 I8o o 1,124 Boston Tower ;............. - I7 33 34. I83 4-6013 I725 wºr 3993 I-649 7.6 44 Walpole, St. Peter's......... Io8 53 28.353 5-o977 og2O I25228.506 23.7 | + 2. I2 Lynn Tower .................. 53 3, 58.3 5-oz720579 || roG464,738 20.2 18o o o-946 Walpole, St. Peter's......... 27 42 28.621 || 4-8733 1191 || 74698.505 || 14-1 45 | Swaffham Spire............... 14 23 31.722 || 4-6013 I725 || 39931.649 || 7-6 || -2.23 Lynn Tower................. || 137 53 60.127 5-og22.4369 || Io?706.941 20:4 18o o O-470 Boston Tower ............... 47 57 6.336 5-o3597.279 || Io9635.75 20.6 46 Walpole, St. Peter's......... 85 21 5.834 5-16379957 || 145814. II 27-6 || -5-85 Docking Tower............... 46 41 50.541 5'oz72 o'S79 || Io9464.74 20:2 18o o 2.7 II Walpole, St. Peter's tº ſº tº ſº tº º 5I I4 51. I4I 4-97 II og85. 93562-94 17.7 47 Swaffham Spire tº e g º 'º º ſº º dº º $ tº e º 'º 64 53 21.776 5°o3597.279 Io8635-75 20-6 ||Supplementary. Docking Tower............... 63 5I 49'229 5'o622.4369 Io'77O6-94 2O'4. 18o o 2-146 Swaffham Spire............... 8 58 15.751 5.07488551 || 118818-89 22.5 48 Baconsthºrpe Tower......... i. ; § 4-97 II og85 93562-94 | 17-7 33 Docking Tower........... tº s is ſº 78 35 37-423 5-13328924 || I3592I-84 || 25-7 18o o 2.563 | Lynn Tower........... tº $ tº ſº º ſº º 8 727.454 || 4.97+12385 || 93562.94 | 17-7 49 | Swaffham Spire............... º: & § 4.86788852 73771-48 || 14-o || >, Docking Tower....... * * * 0 ºr e º º 51 22 43°759 4,8733 I 191 74698.5o I4. I 18o o I. 268 Boston Tower ............... 3o 23 32-154 4.867888.51 73771-48 || 14-0 5o Lynn Tower.................. 90 25 34-Oo3 5. I6379957 I45814. II 27.6 — I-47 Docking Tower............... 59 Io 56-oro 5-0977 og20 125228.5o 23.7 - 18o o 2. 172 TRIANGLES. 495 FIGURE 21—continued. - Di º s: of Names of Stations. Corrected Angles. Log. Distances. iStanceS in B. of ſº - - i Feet. Miles. i. Crowle Beacon ............... 3. 5: 17498 4.9977 8388 99.491-02 | 18.8 & f 51 | Lincoln Minster ............ 25 28 23-o'ſ 3 || 4-8743235o 74872-70 I4-2 ||Supplementary. Gringley Beacon ............ || 119 4o 26.951 5, 1797 2459 || 151260-17 | 28.6 18o o 1.522 - Crowle Beacon ............... 47 5 43-729 4.8755 I675 75078.70 || 14-2 52 Qlifton Beacon ............... 46 55 35-760 4-8743235o 74872.70 || 14-2 || -2.55 Gringley Beacon ............ 85 58 41.829 5-oog64557 || Ioz245.82 | 19.4 18o o 1.318 Clifton Beacon ............... 34 44 43.693 || 4:34684011 || 44344'535 8.4 53 Gringley Beacon ............ 7o 28 19.615 4-86528943 73331-3o& I3-9 + 9.25 | North End of Base ......... 74 46 57.43o 4.87551675 || 75978-701 || 14-2 .# ... + 18o o o-738 - - - Clifton Beacon ............... 20 47 13-4Io 4:42O67955 || 26343.869 5-o 54 | North End of Base ......... 6o 17 18.138 4.80936456 || 64471.023 12.2 || +5.49 South End.............. e e g º º º º 98 55 28.847 || 4-86528943 73331-308 13.9 18o o o-395 * | Gringley Beacon ............ 19 17 21:488 || 4-42067.955 || 26343.869 5'o || 55 | North End of Base ......... I4 29 39-293 || 4:300I 5176 || 19959:597 || 3.8 || +o'90 | South End..................... || 146 12 59-288 || 4,6468.4011 || 44344'535 | 84 r − = P + = 18o o o-oé9 The triangles for the connection of special points with the general triangulation will be found in the divisions or Figures into which they naturally fall. Thus, the triangles for the connection of the extremities of the Misterton Carr Base are given at the end of Figure 21. DETERMINATION OF THE MERIDIONAL DISTANCES OF HENSBARROW AND BEN HUTIG, DUNNOSE AND SAXAVORD. THE first of the following tables contains the calculation of the successive distances Hensbarrow—Precelly, Precelly — South Lomond—Ben Wyvis. Berule, South Berule — Ben Lomond, Ben The second contains the calculation of the successive distances Dunnose—Arbury, Arbury—Clifton, and Clifton—Burleigh Moor. HENSBARROW TO BEN WYWIS. Logarithmic Sines -- Names of Stations. Spherical Angles. of Log. Distances. Distances in Feet, References. Reduced Angles. IHENSBARRow TO PRECELLY. Precelly .......... tº C. § 44' 35.498 9-oooz766o 5.4594o875 288oro.79 || A 7, page 461 Lundy Island ...... I68 34 9-147 | 9:297.08.219 || 5,7562 I434 570445.74 Hensbarrow......... 5 41 19-185 8.996.1468o 5:4552 7895 285285-or A 2 s, 460 18o o 3,830 | Pregelly.............. 22 7 14:034 9:5757,8754 5.338o3015 217811-17 | A 7 s. 461 High Wilhays...... 99 33 57.294 9.993.92.173 || 5-7.562 I434 570445-74 Hensbarrow......... 58 19 13.545 9-9299.1798 || 5-6922 IoS9 || 492278-19 | A 9 × 461 18o o 24,873 FRECELLY To SouTII BERULE. | South Berule ...... 44 27 23.532 9.84527835 5-75418108 || 567781.29 A 5, page 479 Kippure ............ 96 57 34,964 9.9967.9384 || 5'90569657 804815.95 Precelly ............ 38 36 8.536 9-7950.6436 5'70396709 || 505786.34 A 1 » 433 18o o 67.032 South Berule ...... 20 o I-984 9:534o II34 5.64174764 || 438275.95 | A 5 . , 479 Snowdon ............ I4I 5 58.925 9:79796927 5'90569657 804815.95 * Precelly ....... ſº tº tº º ſº 1854. 25.964 9'51053887 5-61827517 || 415217.05 || A II , 434 18o o 26.873 MERIDIONAL DISTANCES. 497 HENSBARROW TO BEN Wyvis—continued. Logarithmic Sines Names of Stations. Spherical Angles. O Iog. Distances. Distances in Feet. References. Reduced Angles. {-mº- | w | SouTII BERULE TO BEN LOMOND. Merrick ....... tº $ tº º 0. 1.1% 114715 9.9498o019 5-7.002.79 II 5O1509-43 Ben Lomond ...... I9 46. 33.247 9:52932612 5.27979904 || 190457-92 | A 33, page 440 Criffel ....... tº e º 'º is tº º º 43 I2 27.406 || 9-835.45330 5'5859.262 I | 3854.12.87 A 16 , 457 18o o 15.368 Criffel ............... II8 6 Io.698 9.945.53320 | 5-87.241318 7454.40.84 Ben Lomond ...... 25 30 I-296 9:63393441 5:56081440 || 363759-55 A 16 s, 435 South Berule ...... 36 24 25.830 9.773399.12 5-7.002 7911 501509-43 18o o 37.824 Ben Lomond ...... 5 43 28-o49 8-99.8841.83 5.56Io8339 363984.92 | A Io 3, 434 South Berule ...... 6 3 45-541 9-o2368465 5:58592621 || 3854.12.87 | A 16 s, 457 Merrick ............ 168 12 53.144 9.31ó17163 5,8734 1318 743440.84 18o o 6.734 - | Merrick ............ 85 13 5.470 9.99848388 5-69804595 || 498937.26 * Knocklayd ......... 46 38 II.740 || 9,86152132 5.56Io8339 363984'92 | A Io 2, 434 South Berule ..... • | 48 9 I4.586 9.872 I ozog 5'571664Io 37.296 I-58 A Io 3, 456 18o o 31.796 Knocklayd ......... 96 I2 22:447 | 9.997.45167 5-8724. I318 7454.40.84 Ben Lomond ...... 4I 43 7.098 || 9,823O8444 || 5-69804595 || 498937.26 * South Berule ...... 42 5 29.044 9.82623358 5,76119565 562.568.30 | A 36 , 458 18o o 58-589 BEN LOMOND TO BEN WYVIS. Ben Nevis .......... 92 16 56.552 9.99965577 5:57469157 375570-59 Ben Macdui......... 38 29 26-235 | 9.7940.4638 5.3690.8218 233927-98 || A 17, page 457 en Lomond ...... 49 13 52.846 9.8792.8856 5.4543.2436 284658-63 A 3 s, 45o 18o o 15.633 - Rºn Lomond ...... 29 36 23:309 9-69373293 5-45614422 285853.96 | A 9 × 450 Ben Macdui......... Io9 55 39'585 9.97319102 5.7356 oz.31 544004:27 Ben Wyvis ........ {} 4o 28 20.817 | 9.81228028 5'57469157 375570-59 18o o 23.711 Ben Nevis ......... I46 43 59-963 9:7392 I637 5-7356 oz31 || 544004:27 Ben Wyvis ......... I3 38 40-542 9.37269624 5.36908218 233927-98 || A 17 2, 457 Ben Lomond * * tº e s e _19 37 29-536 9:5261.39.13 5.5225 2507 33306 I'99 A IO 3, 450 18o o Io-o41 + # * 3 IR 498 PRINCIPAL TRIANGULATION. DUNNOSE TO BURLEIGH MooR. Logarithmic Sines Names of Stations. Spherical Angles. O Log. Distances. Distances in Feet. References. Reduced Angles. | | l |- DUNNoSE To GREENWICH. * Leith Hill ......... 10 56'46.254 9:2745,5398 || 4-76227567 57846.23 A 52, page 478 Chingford............ 26 5o 3.477 9-6545713o 5-I42.293.29 I38769-27 | Greenwich Transit I42 1.9 II.423 9.7862 2207 5.27394406 || 1879.07-48 15 s, 475 I8o o I. I54 Leith Hill ......... 19 24 2-634 9:52 I35779 5. I48o 2983 || I4O614:41 I5 s, 469 Butser ............... 138 44 o'368 9.81925928 5:44593140 2792 Io:28 Dunnose ............ 21 52 o'498 || 9:57 Io 6216 5, 19773428 I57664.63 26 × 476 I8o o 3-446 Dunnose ............ 2 I 15.449 8:5473.2536 5-1422.9329 138769-27 | Leith Hill ......... 173 54 38.028 9.92564294 5-6206 Io97 || 417456-16 Greenwich ......... 4 4 7.490 8.85096347 5:44593I40 2792 Io:28 18o o o-'967 -- Leith Hill ......... Ioo 16 40.258 9-99297,571 5:44.02 1939 27.5562-oA. Beachy Head ...... 29 42 13.726 9-6950.496 I 5. I422.9329 || 138769-27 Greenwich ......... 5o I 12.909 || 9.88437867 5-33162235 214596.36 3 * 483 18o o 6,893 Dunnose ............ 41 6 12.327 | 9.81782547 5:44.02 1939 27.5562 of Beachy Head ...... 84 48 49.191 9.998.2 1695 5-6206 Io97 4174.56-16 Greenwich ......... 54 5 20-399 9.90843583 5:53082975 339492-16 31 , 476 18o o 21.917 DUNNOSE TO ARBURY. * * Leith Hill ........ & 35 1944,621 | 97621 1397 5:3984oool 250264.94 5, page 474 . Whitehorse Hill ... 98 59 53.238 9.994.62418 5-6309 Ioz3 427474.52 Arbury ............ 45 4o 4o. 142 9,8545.5oE.2 5.490.83617 | 309625. Io 7 2; 474 18o o 18.ool ... : * Arbury............... 18 45 59.399 || 9:5074.4165 5'1422.9329 138769-27 Leith Hill ......... 63 31 41.888 9.95189371 5-58674535 386.140.5o Greenwich Transit 97 42 31.203 9.9960.5859 : 5-6309 Ioz3 427474.52 I8o o 12.490 : | Arbury ............ 26, 3o 47.694 | 9-6496.9176 5:44593140 2792 Io. 28 Leith Hill ......... 11o 22 56-139 9-97.192712 5:768.16675 586.363-25 Dunnose ............ 43 6 42.485 9.83467659 5-6309 IO23 42.7474-52 18o o 26.318 g Dunnose ........... 4, 5 27-936 98.1770332 5:58674535 386.140.5o Greenwich ......... 93 38 23-712 9.999.I 2472 5-7681 6675 586.363.25 Arbury ............ 45 10 47,093 9.85156883 5-62061087 || 417456.16 I8o o 37.84I - * MERIDIONAL DISTANCEs. 499 DUNNOSE TO BURLEIGH MooR—continued. Logarithmic Sines * Names of Stations. Spherical Angles. O Dog. Distances. Distances in Feet. References. Reduced Angles. * * | ARBURY TO CLIFTON. Bardon............... 133 to 33 ogó 9.883.I. 2623 5.5996.8937 397822.53 Arbury............... 29 32 36.796 9-6929 II5I 5-40947466 || 256728.84 A 15, page 491 Lincoln Minster ... 20 16 52-433 9:53984834 5-256.41 148 180472.68 A 19 × 492 18o o 8.325 Lincoln Minster ... 76 15 50.254 9.9873.9636 5-43504841 272300-48 Bardon.......... tº gº º ſº º 37 24 42.065 9-7835.6417 | 5-2312 1621 I70300-61 | A 18 . 492 Clifton............... 66 19 37.667 || 9.96.182261 5-40947466 256728.84 || A 16 . , 491 18o o 9.986 Lincoln Minster ... 96 32 42.687 9.9971 6139 5-65343405 || 450229.61 Arbury......... tº C tº dº ſº tº 22 4 28-287 9:57494355 5-2312 1621 170300-61 | A 18 × 492 Clifton ............... 6I 22 64.852 9-94341671 5.5996.8937 397822.53 - 18o o 15.826 Arbury............... 7 28 8.509 9-11389756 5.43504841 272300-48 Clifton............... 4 56 32,815 8.9352.6062 5.2564 1148 180472.68 A 19 × 492 Bardon............... 167 35 21:16o 9:3322 8320 5-65343405 450229.61 I8o o 2-484 CLIFTON TO BURLEIGH Moor: AND EASINGTON. Easington............ 7o 41 35-oS2 9-97.485951 5.445987 Io 279246.09 Wordeslow ......... 76 17 2-4II | 9.98743342 5-45856Io2 287449-15 Great Whernside... 33 I 32.790 9.7363.9836 5.2075.2595 | 161259.74 A 43, page 441 dº | 180 o Io.283 - Great Whernside... 87 48 64. Ioz 9.99968438 5.61537072 41.2449-44 Clifton............... 44 8 34-230 9.8428.7468 5.45856Io2 287449. I5 Easington............ 48 242,394 9.871368or 5.48705434 306940-61 | A 4 - 490 18o o 20.726 Basington............ 81 36 50,869 9.99533125 5-6 III 1831 | 408430.64 Qlifton:::::.. tº Q is is tº º tº ſº 5 52 41-438 9-olog 3028 || 4-6261 1735 42278-28 || A 4o , 440 Burleigh Moor...... 92 30 31-748 9.99958365 5.61537072 412449-44 I8o o 4,055 The distance of Easington and Saxavord, which are very nearly on the same meridian, is obtained in the following manner:— Through Easington draw a meridian line extending to Saxavord. The direction of this line is determined by the azimuthal observations at Easington, from which we have the angle between Cheviot and the north meridian line, 38° 48' 58”.68 approximately (this was the angle actually assumed in the calculations). On this meridian line take a point, A (see Figure 1, plate xviii.), whose distance from Easington is equal to the side Easington — Cheviot. Join the point A with Cheviot and Mount Battock, - 3 R 2 5CO PRINCIPAL TRIANGULATION. and it is evident that we can determine the distance of A from Mount Battock, and Next take the point, D, in the meridian line whose distance from A is equal to the side A — Mount also the angle at A between Mount Battock and the north meridian. Battock. Join D with Mount Battock and Scarabin, then we can determine the side D– Scarabin, and its inclination to the north meridian at D. Next take a point, G, in the meridian line whose distance from D is equal to the side D–Scarabin, and join G with Next take a point, H, in the meridian line whose distance from G is equal to the side G–Eoula, and join H with Foula, Yell, and Saxavord. From Saxavord drop a perpendicular upon the meridian line, meeting it in S, then we can obtain HS, or the distance from Easington to S, and the perpendicular just mentioned, which is only about two hundred feet. The following table contains the calculation :- Scarabin, Titty, and Foula. Logarithmic Sines Names of Stations. Spherical Angles. of Log. Distances. |Distances in Feet. References. IReduced Angles. f f ºf Hart Fell tº e º 'º e º 'º e º & tº ſº 98’ 36 51.175 9.995o 7489 || 5.625394.55 || 422O79-79 - Cheviot ............ 43 31 13:533 9.837962.27 5:46828 172 293955-59 A 27, page 458 Ben Cleugh ......... 37 52 13-190 9-7880.6486 || 5:41838.451 262050:21 | A 4 , 437 18o o 17.898 - Dunrich ............ 126 3o 44-697 | 9.905I 1451 5.625394.55 42.2079-79 Cheviot ............ 28 56 46.871 9-684.82354 5-405 Io957 254I57.88 || A 3.0 , 458 Ben Cleugh ........ • 24, 32 38.903 9-6184.4427 5.33872431 218134-48 || A 27 s. 439 ; I8o o Io.47 I Sayrs Law tº ſº tº g º ſº tº tº & I42 58 33’534 9.7797 J369 5-74 Io 2635 55084I. I2 Cheviot ............ 26 3:492 9:6439 oš89 5-6052.2155 | 402922.52 A 21 × 457 Mount Battock ... Io 53 32.828 9-27634792 5:23766o58 172846.5o A 24 , 439 I8o o 9.854 * Den Cleugh º, º e º ſº tº º tº tº 90 53 22.560 | 9.999948oz 5-74.102635 | 550841-12 Cheviot ........ ... 39 - 6 25.168 9:7998.4162 5'5409 1993 || 347472. Io | A 32 x 458 Mount Battock ... 50 o 46.728 9.8843 1622 5:625394.55 42.2079.79 * * 34.4% Ben Macdui......... IoI 2 23.384 || 9.99.189031 || 5-69327789 493489.46 Scarabin ............ 22 12 39.972 9:57748334 5-37887ogI 1900.51.33 A 1 » 452 Mount Battock ... 56 45 15-669 9-92236723 5-62375481 420489.17 | A 20 , 45I - I8o o 18.425 Mount Battock ... 49 31 61.184 9.88124869 5.5774o?24 |3 77926.41 A 29 3, 452 Scarabin ............. 33 53 44.316 9:74617270 5:44233125 || 276905-29 | a 3 . 453 Mormonth ..... tº g º º 96 35 39:or9 9.9971 1934 5.69327783 493489:46 18o o 24,419 Ben Hutig ......... 77 51 53'492 9-990I 82.49 5-60784oo5 || 4o • 2 I Fitty Hill ........ . 31 6 28-o.41 9.71317378 5:33O83134 ::::::::: A 3 × 444 Scarabin ............ 7* * 57-75° 9.9757,5970 5'59346827 3921.16.33 a 19 . 4.46 18o o 19:283 Bon Clibrig tº dº º ſº ſº tº º q & 57 22 6-128 9.925.38537 5-6078.4005 405359.2 I Fitty Hill ºn tº g º 0 tº º ſº tº I9 Io 39'581 9'51650375 5, 19895844 I58 Io9'67 A 9 × 445 Scarabin ............ Io9 27 38-929 9,9879 Ioz2 5:67036496 || 468.128-30 | A 19 , 446 18o o 14.638 MERIDIONAL DISTANCES. 5oi Names of Stations. Logarithmic Sines Log. Distances. Distances in Feet. References. Easington....... tº e º 'º º Cheviot A. i.e. º 'º º Cheviot Mount Battock ... D ............. © e º 'º e s tº tº Mount Battock...... Scarabin Scarabin tº º ſº º 6 * * * * * * - G. & J C is ſº tº ſº tº tº tº ſº © º 'º º º 'º º ſº tº º Scarabin ............ Fitty Hill s & © tº e º g º º & © e º 'º e º 'º º 'º º & º 'º - tº º tº 0 ºn tº g º & © tº º is ºn e e is sº tº tº º tº 9 tº e º e º 'º e º 'º º g º º | Yell * * * * * * * * * * * * * * * * * c s e e H ..................... e e s e e s e º 'º e º 'º e s e . Spherical Angles. O Iteduced Angles. O Z Af 38 48 58.68o 9.797I 2273 7o 35 44.371 9.974,59586 7o 35 44.371 9-97.459586 I8o o 27.422 82 o 12.5I2 9.9957.5285 29 3 54.253 || 9.6864 1343 68 56 29.986 9.96997181 18o o 36.751 4o 27 45-643 9-812I 7on I 69 46 33-223 9.97235031 69 46 33-223 9.97235031 18o o 52-o89 87 33 57.72 I 9.99960062 4o 17 59'898 || 9.81.07 24.15 52 849:197 9.8973.7484 18o o 46.816 6o 58 20.096 || 9.94167231 58 4 37-540 9.92875IIo 6o 58 20-og5 9-94.167231 18o o 77.731 41 44 38. I59 || 9-8233 1466 42 51 2 I-675 9-83.258o37 95 24 39-4Io 9.998o0305 I8o o 39:244 73 I 48.585 9.98065909 47 28 7.794 | 9.8673.9308 59 30 36.553 9.935352 Io 18o o 32.932 29 48 53.953 9.6965 or 72 75 5 45.354 9.985I 3336 75 5 45-354 9.9851 3336 18o o 24.66I 23 35 5-47.o 9-602I 6749 77 29 53. I62 9.9895775I 78 55 6.593 || 9.99.182532 18o o 5.225 129 7 46-789 9.8897.9599 23 23 49.939 9.59890or 2 27 28 25-238 9.664o 1945 18o o 1,966 o 4 3.755 || 7-072522I– 89 55 56.255 9.99999970 89 59 6o-ooo I8o o o-oro 5.45746797 5-63494IIo 5-63494 IIo 5-7668o739 5.45746797 5-74 Io 2635 5-60662719 5-7668oz39 5-7668 of 39 5-7955og66 5-60662719 5-69327789 57955og66 5-782.588.44 57955og66 5-60784oo5 5.617 Io976 5.782.588.44 5-6624 1275 5:549,14673 5.617 Io976 5.37378112 5-6624 1275 5:6624 1275 4.984I 2328 5'37 I53330 5-37378II2 5.27492916 4.984I 2328 5-O492.4262 2:34745.125 5.2749.2886 5,27492916 286726.59 43.1460-56 43.1460-56 584530.79 286726.59 550841-12 4O4228.74 584530.79 584,530.79 624467.25 4O4228.74 493489:46 624467:25 606161.63 624467.25 405359-2I 4I4IOO-5I 606161.63 459634-64 3541 I6.96 4I4 loo'5I 236472-76 459634-64 459634-64 964Io.26 23.525I-99 236472-76 I88334, 19 964 Io-26 II2OO6-34 222-56 188334,05 I88334, IQ A 8, page 437 A 26 s: A 5 3, 443 A Io 33 443 5O2 PRINCIPAL TRLANGULATION. In order that no doubt might rest upon this determination, another calculation was made, using a different series of points (see Figure 2, plate xviii.) The distance Easington–Hartfell was first obtained, and the angle Hartfell—Easington–Cheviot. Take a point, K, in the meridian line (the same as previously used) passing through Easington, so that the distance Easington to K may be equal to the distance Easington— Hartfell, and join K with Hartfell and Ben Macdui. Take L in the same meridian line at a distance from K equal to the distance K–Ben Macdui, and join L with Ben Macdui, Ben Clibrig, and Fitty Hill. Next take a point, M, in the meridian line, so that LM shall be equal to the line L–Fitty Hill, and join M with Fitty Hill, Ronas, and Saxavord. The right-angled triangle Saxavord—M–S will give MS, or with it the distance Easington, to Saxavord, and the perpendicular from Saxavord upon the assumed meridional line through Easington. * The calculation is shown in the following table:— Logarithmic Sines Names of Stations. Spherical Angles. - of Log. Distances. Distances in Feet. References. Reduced Angles. O f - & W Cheviot ............ 124 46 24'416 9-91.457252 5-79264717 | 619568.36 - Dasington ......... 20 20 3'494 9:54O9 og87 5:418384.51 262050.21 || A 2, page 437 IHart Fell ......... 34 53 53.918 9:75746645 5-634941io || 431460-56 a 8 , 437 I8o o 21.828 - Cheviot ..... ....... 54 12 16:974 9.99926864 5-54678995 || 3522Oo.49 | Easington ......... 42 I6 33.386 9-8278o409 || 5.4655.2539 29.2095,85 A 5 , 437 Cross Fell ......... 83 31 33.665 9.9972 1979 5-6349.41 ſo 431460-56 A 8 , 437 I8o o 24-oz 5 Cross Fell ......... I33 51 44:455 9-857952.18 5-792647.17 | 619508.36 - Sasington ......... 2I 56 29-893 9:5724.4548 5.5oG54.047 32io26-19 A 3 s, 437 IHart Fell........... 24 12 4.815 9-61269496 || 5-54678995 || 352200-49 s 18o o 19. 163 Ben Lawers......... I27 56 2I. I58 9.8969 or 81 5-7851 2472 60971 I-97 Hart Fell............ I6 39 18. I39 9.4572.4638 5'34546930 22.1548.75 A 3 × 450 13en Macdui......... 35 24 39-og3 9-762987.06 5-6512 ogg7 447929-82 | A 19 , 457 18o o 18.390 - * * * * * * * * * * = Sayrs Law ......... II2 29 42. I45 9.96563773 || 5-7851 2472 60971 I-97 | Ben Macdui......... 19 30 16.791 9.52354806 5:34393505 220310.43 | A 24 , 439 IIart Fell............ 48 o 24.61 I 9.87 II off 29 5-69059.228 490447-23 A 21 × 457 I8o o 23-457 Foula …............ 169 34 57.385 9:25725165 5,73084564 538078.50 Titty Hill............ 3 35 9334 8-79586.133 5-26945531 1859.75-32 a 5 , 443 Ronas .......... ſº tº º O ſº 6 5o 5-o/7 || 9 of 555274 5'54914673 354116.96 . A 26, , 446 18o o 2.796 º -- Fair Isle & Q & Q Q & Q tº º º is tº II5 7. 20.954 9.9568.4847 || 5,73084564 538078.5o Fitty Hill............ 37 39 54.82, 978556389 5:55956 ioë 3627.11.28 a 3 , 443 Ronas ............... 27 I6 5.218 9-66098383 || 5.4349810o 27.2258.22 A 26 s, 446 I8o o 20.993 MERIDIONAL DISTANCES. 503 Logarithmic Sincs Names of Stations. ‘Spherical Angles. O Log. Distances. |Distances in Feet. References. Reduced Angles. Easington s ſº tº º º ſº º ſº ſº dº º º 59 9 2. I74 9-9337 I7or 5.78637541 6II470-37 Hart Fell............ 6o 26 7.627 9-93938877 5.792.04717 619508.36 K..................... 6o 26 7.627 9.93938877 5.792.04717 | 619508.36 I8o o 77.428 * Hart Fell............ 63 19 39-298 || 9.95II og53 5.80684175 640975-98 Ben Macdui......... 58 28 51.122 9-93064319 5.78637541 || 6 II.470-37 K..................... 58 I2 47.855 9-9293.925o 5-7851 2472 | 6097 II-97 18o o 78-275 * * Ben Macdui......... 59 20 Io-o88 9-93455 III | 5-8o0.84175 640975-98 | K..................... 61 21 4.519 || 9-9432.5196 || 5-8:155426o 653947.oğ L ...................” 59 20 Io-o88 9-934551 II 5.80684I75 640975-98 18o o 84-695 || Ben Macdui......... 75 29 30-444 9.9859 1334 5.84174859 || 694622.09 L .........:----------. 38 49 I7-535 | 9:797I 3766 5-65297.290 44975 I-79 A 21, page 451 Ben Clibrig ......... 65 42 18:901 .9-9597 of 36 5-8155426o 653947.oS 18o o 66.88o Ben Clibrig ........ 6o 52 53:226 9.94129387 5.7927.9421 620574.90 J. ::::::: : “.......... 41 I3 38.707 || 9.8.1886.456 5-67036490 468.128-30 | A 19 , 446 Fitty Hill ......... 77 54 34,779 9-9902.4825 5.84174859 694622.09 18o o 66,712 [.....:º:------------ 4o 36 53-670 9-8135.1397 5-634I 7002 || 430695-19 Fitty Hill............ 69 42 2.597 9.972 I 3815 5-7927.942 I | 620574.90 M..................... 69 42 2.597 9.972 I 3815 5’7927.9421 620574.90 *. 18o o 58.864 - w - Fitty Hill.......... ū 36 25 29.867 9-77358717 | 5-5044,4385 || 31948o. 13. Ronas ............... 53 Io 20-676 9.9033 1334 5-634.17ooz 439695. I9 M..................... 90 24, 41-763 9.99998896 5.73O84564 538o?8.5o 18o o 32.306 - - Ronas ............... 114 35 40.908 9.95869842 5-60998713 407368.21 M..................... I9 55 8.oz.5 9.53233876 5-18362746 I52625-63 | A 8 × 443 Saxavord ............ 45 29 21:476 9.85315515 5'50444385 || 31948o. I3. 18o o Io-409 - - M....... tº e º ºs º ºs e º e º e º ſº tº o I 52.385 6.7362569- 2.3462.4405 22 I-94. Saxavord........... . 89 58 7.636 9.99999994 || 5-609.987c6 4O7368. I4 * * * * * * * * • . . . . . . . . . . . . . 9o O O"OOO 5-609.987 I3 | 407368-2I I8o o o-o2I r ... If s be the distance of two points, A B, whose reciprocal azimuths are & a measured from the north, and if the line be very nearly in the direction of the meridian, the distance of the parallels of the two points will be S = s sin #(a tºmº c.) sin ;(a + 3) 504 PRINCIPAL TRIANGULATION. When the azimuth is given at only one extremity, A,” S = s — 2 v ºn 4 sin & cos(x + 6) 2. where v is the normal at A, whose latitude is A, and 6 results from the equation s = v 0. The reciprocal azimuth o' is given by the equation sin &’ cos x sin & cos(x+6) with sufficient exactness for the purposes required at present. Distance of Parallels of Hemsbarrow and Ben Hutig. At Precelly, Lundy reads 33 Snowdon reads . . ..'. Angle Snowdon—Precelly—Lundy ,, Snowdon—Precelly—South Berule . . , Lundy—Precelly—Hensbarrow . . . ..". Angle Hensbarrow—Precelly—South Berule . At South Berule, Snowdon reads 33 Merrick , , , ..'. Angle Merrick—South Berule—Snowdon , Snowdon—South Berule—Precelly , Merrick—South Berule—Ben Lomond . ... Angle Precelly—South Berule—Ben Lomond At Ben Lomond, Ben Nevis reads . . 35 IGnocklayd , . . . ..'. Angle Ben Nevis—Ben Lomond—ICnocklayd , IKnocklayd—Ben Lomond—Merrick , Ben Nevis—Ben Lomond—Merrick , Merrick—Ben Lomond—South Berule , Ben Nevis—Ben Lomond—Ben Wyvis . ..'. Angle Ben Wyvis—Ben Lomond—South Berule g * If 90° – A – 0 + æ be the third side of a spherical triangle of which the other sides, 90° – A, and 6, include the small angle a, then sin(* + 3 − 4) = cos ? sin x + cos & sin 6 (1 – 2 sin” a), therefore, neglecting the square of a, coS X sin 6 . l = Hºmºmºmºmºmºmºmºr 2 2 cos(A + 6) Sin”: a 355 I? 2Oo 30 #/ 53.498 38.68o I54 47 18 54 5 44 14.818 25-964 35.498 179 26 34-I 4I 186 38 I6.28o 50°434 I9.850 I55 3 2O 30.584 I-984 45'54I O 6 3 7 181 I6I 42 28 I9 18. Io9 57-615 7.078 II9 9 47 26 I93 23 5 43 I9 37 50-537 35. I46 34.317 28.049 29-537 I79 29 32.829 MERIDIONAL DISTANCES. 505 O / At Ben Wyvis, Ben Hutig reads . . . 182 16 1 345 5 33 Ben Nevis , . . . I4 47 44-235 Angle Ben Hutig—Ben Wyvis—Ben Nevis . . 192 31 30.78o 3, Ben Nevis —Ben Wyvis—Ben Lomond . 13 38 40-542 ... Angle Ben Hutig—Ben Wyvis—Ben Lomond 178 52 50.238 If to the reading of Lundy at Precelly we add the angle Lundy—Precelly—Hens barrow, we get 1° 2'28".996 for the reading of Hensbarrow at Precelly. Now the true azimuth of the referring-object at Precelly was 211° 58' 46". 38, whereas in the list of bearings (page 144) it is given as 2 II* 58' 30".og; therefore all readings at Precelly have to be corrected by the quantity + 16"-29, so that the true azimuth, measured from the north, of Hensbarrow at Precelly is 178°57' I4".714. The angle Lundy—Hensbarrow —Precelly, 5° 41' 19". I85, when applied to the reading of Lundy at Hensbarrow gives 181° o' 43”. 591 for the reading of Precelly at Hensbarrow. The correction to reduce the readings at Hensbarrow to the true meridian is — 5". I9 (see pages 118, 197). Therefore the azimuth, measured from the north, of Precelly at Hensbarrow is 1° o' 38".761. The calculation” of the successive distances of parallels from Hensbarrow to Ben Hutig is as follows:— HENSBAIRIRO W TO PRECELLI. & = 1° o' 39” a’ = 178° 57' 15" a' — a = 177° 56' 36” Log sin (88° 58' 18") . , 9.99993004 a’ + cz = 179° 57' 54" – Log sin (89° 58' 57") . . o. 2. Log Distance . . . . . 5-7.5621434 ºmºmº-º-º: Distance of parallels = 570353.88 . . . . 5-7561444o PIRECELLF. To Sova II BERULE. a = 1° 36' 29” Log Distance . . . 5-905697 — Log v sin I" . . . . 7.992886 Log Sin & . . . 8.584029 Log ( = 791.7") • - 3.898583 v . . . . 7.321539 33 Cos A. . . . 9.789864 * * * * * * ºn tº $ tº 9.789864 , Sec (x + 3) . o.232301 . . . . . . . . . . o.232301 , Sin *; c. . . . 6.294268 Sin & . . . 8.44812I # Correction = 166.73 . . 2.222001 Sin 2' . . . 8.470286 a' = 175 18 28 181 7 18 359 25 46 * The approximate latitudes used in these calculations are— # & A O & ºf Procelly . . . . 51 56 46 Ben Lomond . . . 56 II 25 South Berule . . . 54 8 58 Ben Wyvis . . . 57 4o 45 3 S 506 PRINCIPAL TRIANGULATION. SouTII BERULE TO BEW Lolroy D. a = o' 34’ 14" Log Distance 5-872.413 – Log v sin I" * 7.992833 Log Sin 0 8.550706 Log ( = 7332") . . 3.865246 35 ° 7.32 I592 , Cos x . . . 9.767655 . 9.767655 , Sec (A + 3) . o.254537 . O-254537 , Sin ** a . 5:394286 Sin & . 7.9981.68 * Correction = 19.44 . 1.288776 Sin c.' . 8.020360 O f f/ a' = 179 23 58 I79 29 33 358 53 31 BEW Loiſowd To BEY WI"VIS. a = 1° 6' 29". Log Distance 5,735602 – Log v sin I” wº 7.992784. Log Sin 6 8.41388o Log (6 = 535o") . 3.728386 33 tº 7.321641 - , Cos x . 9:7454.16 . 9.7454I6 , Sec (A + 3) . o.271889 . o.271889 , Sin ** a . 5-970804 Sin & . 8.286412 # Correction = 52.92 . I-7236.30 Sin &’ . 8.303717 O f Af &’ = 178 50 49 I78 52 50 * 357 43 39 BEy WYWIS TO BEy HUTrø. cz = 2° 16' 2I’’ Log Distance 5.5og730 — Log v sin I” i. 7.992749 Log Sin & 8.182073 Log ( = 3137”) . 3496.479 3, 19 • • 7.321676 , Cos A 9-728.077 9.728o77 , Sec (x + 3) . o.282541 o:28254I , Sin ** a . 6:59.4646 Sin & . 8.598267 # Correction = 128.53 2. Io9013 Sin 2' . . . 8.608885 Azimuth of Ben Wyvis . 2' = 177° 40' 16" . at Ben Hutig. Summation. Hensbarrow to Precelly 570353-88 – ......... Precelly to South Berule ſº 804815.95 – 333.46 South Berule to Ben Lomond. 74544o.84 – 38.88 Ben Lomond to Ben Wyvis Ben Wyvis to Ben Hutig . 544oo.4:27 — Io5.84 318955.81 — 257.06 ... Distance of Parallels of Hensbarrow w * , and Ben Hutig . . . . } = 298.3570-75 — 735-24 = 298.2835. 51 MERIDIONAL DISTANCES. 507 Distance of the Parallels of Dunnose and Saa'avord. At 1) unnosc, Beachy Head bears . . . . . 26. 55 18383 By Azim. Obs, at Dunnose. Angle Beachy—Dunnose—Arbury . . . . . . . 82 II 39-363 * At Dunnose—Arbury bears . . . . . . . . 179 43 39.020 At Arbury, Dunstable bears . . . . . . . .310 37 52-253 By Azim. Obs, at Arbury. Angle Dunstable—Arbury—Whitehorse . . . . . 68 I4 58-794 , Whitehorse—Arbury—Leith . . . . . . . . 4.5 4o 40.142 , Leith—Arbury—Dunnose . . . . . . . 26 30 47.694 At Arbury, Dunnose bears . . . . . . . . .359 42 58-599 At Arbury, Bardon bears . . . . . . . . 172 16 46.048 By Azim. Obs, at Arbury. Angle Bardon—Arbury—Clifton . . . . . . . 7 28 8.5og At Arbury, Clifton bears . . . . . . . . . 17944 54,557 At Clifton, Lincoln Minster bears . . . . . 298 21 27.421 By Azim. Obs. at Clifton. Angle Lincoln—Clifton—Bardon . . . . . . . 66 19 37.667 , Bardon—Clifton—Arbury . . . . . . . 4 56 32.815 •. At Clifton, Arbury bears . 359 44 32'273 At Clifton, Great Whernside bears . . . . . 147 5 43.126 By Azim. Obs, at Clifton. Angle Great Whernside—Clifton—Easington . . . 44 8 34-230 tº At Clifton, Easington bears . . . . . . . 191 14 17.356 At Easington, Wordeslow bears . . . . . . 130 17 2-505 By Azim. Obs, at Easington, Angle Wordeslow—Easington—Whernside . . . . 7o 41 35-o82 , Whernside—Easington—Clifton . . . . . 48 2 42-394 ‘. At Easington—Clifton bears . . . . . . II 32 45-o29 \ JDUNA’OSE TO ARBURY. O J # / c. = o I6 2I 2' = I79 42 59 O / // Log Dist. 5-768.16675 a' + x = 179 59 20 . . . 89 59 4o . . . . Cosec. o'...... ..... a' — a = 179 26 38 . . . 89 43 19 . . . . Sine 9.99999489 Distance of parallels = 586356.36 Log • 5-768161.64 AIR BUIºr TO CLIFTON. C. E. & 13 § * a' = 179 44 32 'o a Log Dist. 5,65343405 a' + x = 179 59 37 . . . 89 59 48.5 . . . . Cosce. . . o............ tº a' – c. = 179 29 27 . . . 89 44 43.5 . . . . Sine . . 9.9999957.1 Distance of parallels = 450225-16 Log • 5,65342976 CLIFTOW TO EASINGTON. a = 1; 14 1% 2' = 168 27 15 O & ff Log Dist. , 5.61537072 * + 4 = 179 41 32 . . . 89 50 46 . . . . Cosec. . o......... I57 * - 2 = 157 12 58 . . . 78 36 29 . . . . Sine . . 9...991.35854 Distance of parallels = 404325-22 Log . . 5-60673O83 3 S 2 508 Pl{INCIPAL TRLANGULATION. JEASINGTON TO BURLEIGII Moor. O / / / c. = 86 5o 24' lo Log Dist. . . 4.6261173 (Dist.)” . . . 9.25223 Cos & . . . 8.7413405 Sin *c. . . . 9.99868 2330°55 ' ' - 3.3674578 Tan X • , . o. 14787 (2 v) " " . . 2.37736 –59-72 - . . . . © C s e e s º I-77614 2270.83 = Distance of parallels. - Summation. Dunnose to Arbury . . . . . . . . . 586356.36 Arbury to Clifton . . . . . . . . . 450225. I6 Clifton to Easington . . . . . . . . 404325-22 Lasington to Burleigh Moor . . . . . . 2270.83 Distance of parallels of JDunmose and Burleigh Moor = I443177. 57 Dunnose and Easington = I44O906-74 * For the distance of the parallels of Easington and Saxavord, we have— By first Calculation, pages 500, 50l. By second Calculation, pages 502, 503. Dasington to A. . . . 43.1460-56 Easington to K . . . 619508.36 A to D . . . 584530.79 IC to L. . . . 640975-98 D to G. . . . 624.467.25 L to M . . . 620574.90 G to H. . . . 459634-64 M to S . . . 407368-14 II to S . . . I88334-05 Dasington to S . . . 22884.27-29 Easington to S . . . 2288427.38 Distance of parallels of {;" and Saaavord = 2288427.33 Dunnose and Saaavord = 3729334. O7 By the first calculation of the connection of Easington and Saxavord, the bearing of the latter is o' o' 20". 130 east of the assumed meridian line at Easington. By the second calculation it is o” o' 20".o44, which differ by a tenth of a second only. The mean is o° o' 20".o87; so that the Angle : Cheviot—Easington—Saxavord = 38 49 18767 By the first calculation the distance of Saxavord from the assumed meridian at Easington is 222-56; by the second calculation the same distance is found to be 22 I ‘94. SECTION IX. 0 BSE RW EI) Z E NITH DIST AN CES AND AL TITUI) E S. As the position of a point in space is determined by three co-ordinates, so the position of a point on the carth's physical surface is incompletely given without its three co-ordinates of latitude, longitude, and altitude; the latter co-ordinate being the distance of the point in question from the mean surface of the earth, or rather from the mean surface of the sea. * * Regarded as a part of the principal triangulation, the accurate determination of the heights of the trigonometrical stations by vertical angles has been considered a matter of secondary importance, inasmuch as it belongs more properly to subsequent operations. The co-efficient of refraction is a quantity so variable, that at great distances the average of any number of observations, however large, cannot be entirely relied upon. When the determination of altitudes becomes a matter of primary importance, the stations must be within a short distance of each other, or no very consistent or accurate results can be obtained; for the uncertainty of refraction being as the distance, the uncer- tainty of difference of height is as the square of the distance. If we suppose, for instance, an object at fourteen miles' distance to be observed, and that in the calculation of the difference of height between this point and the point of observation an error of .oz is made in the assumption of the co-efficient of refraction that ought to be used—as is quite possible if the number of observations be small, and taken under similar circumstances—then the error in the assumed zenith distance will be .oz sin 12' and the error in height o2 sin “Iz' multiplied by the radius of the earth, or 5. I feet, whereas had the distance been about seventy miles, or one degree, the error in the assumption of the true zenith distance would have been .oz sin 1°, and the resulting error in the computed difference of height .oz sin “I” multiplied by the radius of the earth, or 127.4 feet. But if the observations had been so numerous that the mean refraction, due to them all, approximated to a mean refraction derived from a combination of a great many zenith distances, then the errors would probably be much smaller than those exhibited above, which are only possible errors. - The precision of the results is very much increased by simultaneous and reciprocal zenith distances. This case, however, does not exist in the Ordnance Survey, for the observations, though generally reciprocal, are not simultaneous. The vertical observations with the larger theodolites are generally numerous (at least in the more modern observations), and taken under all circumstances. In the vertical circles of the two 3-ft. theodolites one division of the micrometer is equivalent to 3"; in the 2-ft. theodolite one division of the micrometer is equivalent to 2". In the 18-inch 5 IO g PRINCIPAL TRIANGULATION. theodolite the vertical circle is read by verniers to Io". The practice has been to record in each observation the vertical reading of the object after the horizontal reading: this applies more especially to those stations visited since 1839, the older observations not being SO Inllmer OllS. + In some cases the vertical observation is taken to the top of the pile, sometimes the base of the pile or surface of the ground, and sometimes to a heliostat. The observations to a heliostat are generally more regular than the observations to the ground at the same point, the former being a better object for bisection. In some cases the height of the observing telescope above the ground has been omitted to be recorded, and consequently a mean height of 5.5 feet has been assumed. -- * # Let h h' be the heights of two points AB above the surface of a sphere whose radius is r, and let the distance of their projections on the sphere bes, this arc subtending an angle v at the centre C. Let 2 + A 2 be the true zenith-distance of the point B at the point A, and 2' + A 2' the true zenith-distance of A at B, then the angles of the triangle ABC are 180° — (2 + A 2), 180° – (2' + A 2') and v, and the two sides including the angle v, are r + h and r + h’; hence we obtain immediately, - z' + 2 + A z' + A z = 180 + v h' — h - a; TFT = tan + (2 – 2 + A 2'- A 2) tan 4 v h' + h + S? ). ſº ’ — i-º-º: ..l. (2' — ’ — I ... h. h = stan + (z z -- A z A :) ( -- 27° I 27” If we here take 2 and 2' to be the observed zenith-distances, then A 2 and A 2' are the refractions at A and B respectively. The usual assumption is, that A z = A 2', which, however, is not true, except in particular cases that may occur. If k be the co-efficient of refraction, then A z = A 2' = k v, and the above equation gives the two following:— h' — h = scot (2– I =#9) (1 + * + 2 + S” )] ºf 27. I2 r? J.A , , f : . . . . . (I) I — 2k h' + h S - h — h’ = scot (2– w) (1 + r) + ..) - 2. 27° I 27- or, if the reciprocal observations be used, h' + h S? ’ — {-} I ~' — 2: ) L -H - - - - ) . . . . . . . . . 2 h h = stan + (z ) (1 + 27' +- #) (2) In general, when 2' and 2 are given and not simultaneous, it will be more advantageous to obtain the two independent values of h' – h by means of a co-efficient of mean refraction, and to combine them with reference to their weights; so that if 2 observed n times gives h' – h = e, and 2' observed n' times gives h' — h = e, then 7te + n'eſ h' — h = − . . . . . . . . . . . . . . . . . . Q’ - ſº n + n’ (3) The co-efficient of refraction (which is sometimes and perhaps more properly referred to the whole ray, and then expresses the ratio of A z + A 2' to v) may be obtained from OBSERVED ZENITH DISTANCES AND ALTITUDES. 5II the reciprocal observed zenith distances 2 and 2' of two points; for 2 + z' + A z + A z’ = I8o + v P jº O ... – ak = +=* . . . . . . . . . . . . . . . (4) 7) It may also be obtained by means of the observed mean zenith distances of two points whose heights have been previously ascertained by some more precise operation, as levelling; for if H H be the heights of the points, Z Z the true reciprocal zenith distances, and h the mean of H' and H, 4. (Z + Z) = 90° + 4 v A — , / H’ — H J. S2 - N ? • * * * * * (5) 3 (2 – z) = tan- (*—H {: – ; – #3) and if 2' and 2 be the observed zenith distances, then Z — Z7 – 2' k = #, and k = −. . . . . . . . . . . . . . . . . . (6) Q) Q} The above equations have been deduced on the supposition of the earth being a sphere; but it is easily proved, that if the normal for the mean latitude of the two points be used as the radius of the sphere, the remaining errors due to the eccentricity are quite inappreciable. The path of a ray of light joining two given points, inasmuch as it depends upon the refractive power of the atmosphere at every point through which it passes, is necessarily very variable. It is not, however, without some obvious laws; for refraction by night, for instance, is well known to be greater than by day. When observations are recorded as having been taken at some early hour in the morning, as 5 A.M., and from that time until 8 A.M., they almost invariably show a smaller zenith distance than during any other part of the day; sometimes the difference is very considerable, and shows that no vertical observations should be taken early in the morning. Towards the middle of the day the zenith distances seem to diminish, and again increase towards evening. These rules, however, are not invariable, for at the station on Hart Fell, at which the 2-foot theodolite was used, a remark- able case of refraction is shown, when from 1 P.M. till 3 P.M. the refraction was double its mean amount. This was in the month of September.” * A series of observations for determining the daily variations of refraction were carried out by M. Hossard, at Angoulême, during the months of May and June 1844. The observations were made half-hourly, from daybreak till twilight; and the object observed was at a distance of about 13 miles. To exhibit more clearly the laws of the variation of refraction, daily curves were constructed from the observations, having the time as abscissa, and the corresponding ordinate being the refraction. The consideration of these curves, which were very consistent with one another, lead to the following conclusions:—The refraction is greatest about daybreak; from 5 or 6 A.M. until 8 A.M. it diminishes very rapidly; from 8 A.M. until Io A.M. the diminution is slow ; from to A.M to 4 P.M. the curve remains nearly parallel to the axis of abscissas, or the refraction is nearly constant from 4 P.M. the refraction commences to increase. The comparison of the curves with one another shows that the maximum refraction about daybreak is very variable, both in magnitude and as to position or time; during the daytime, however, from 10 A.M. until 4 P.M., the variations from day to day are very small, notwith- standing any changes in the thermometer and barometer, upon which the variations do not depend so much as on the rapidity of the diminution of temperature. *= 512 PRINCIPAL TRIANGULATION. The co-efficient of refraction has been observed of all magnitudes from .50 to , oo, and even negative refraction has been observed in a few instances. The smaller the altitude the larger, generally, will be the mean co-efficient of refraction. The large co-efficients exhibited in the operations at the Lough Foyle base are due to the smallness of the altitude of some of the stations. Delambre determined the mean co-efficient of refraction at .oz86, which is probably larger than it ought to be, as his instrument gave zenith distances too small. The determination of Bessel, from his operations in Prussia, is oô85. Gauss, from his observations, obtained 'o653; Coraboeuf, o642 ; Struve, 'o618; and the mean co-efficient derived from the operations in France is 'o665. º M. Struve has given the following formula for the co-efficient of “normal refraction,” that which exists previous to and just after mid-day, • 1298 ) IB (20 — T) A. 736-586 k = (oy238 -- I.of 1838 in which A is the mean height of the ray above the ground, expressed in metres; B the height of the barometer in millimetres, and reduced to the freezing point; and T the temperature of the air in centesimal degrees. When a number of points, connected in a network of triangulation, afford by the vertical observations the means of ascertaining their relative altitudes, these observations should be so combined as to furnish the best and most probable results. The first operation is the ascertaining the value of the co-efficient of refraction: this, as before stated, may be determined either by reciprocal zenith distances, or by the com- parison of observed zenith distances with the corresponding true zenith distances, calculated from known heights of mutually visible points. Each pair of reciprocal mean zenith distances will afford a value of k, the co-efficient of refraction, and all values of k thus obtained must be combined with regard to their weights in obtaining the mean value of k. Now the value of k in each case will depend on the number of observations at each end: if one zenith distance be observed a times, and the other b times, then, so far as the number of observations goes, the weight is the product divided by the sum of those quantities. But each value of k is affected both by variability in k itself, and by errors of observation. If we suppose, first, k constant, and ascribe the different values of k to errors of observation, and, secondly, suppose k to have slightly different values, or to be variable within small limits, and suppose no errors of observation, then the weight in these separate cases would be - abs and ab a + b a + b Now, neither of these suppositions is true, but the truth probably lies between ; we shall therefore assume for the weight of each value of k, as M. Bessel has done, abw/s CD E a + b OBSERVED ZENITH DISTANCES AND ALTITUDES. 5I 3 the mean value will then be * = **t k, w, + k, w, + . . . . . w; + w, + wa + . . . . When a value of k is derived by means of a zenith distance taken a times, and compared with its true value calculated from the known heights of the two points, then its weight is a Vs ; but such values should be combined with similar, and kept separate from the determinations arising from reciprocal azimuths. * The mean coefficient of refraction being determined, each zenith distance will give a difference of height: If v, w, w, . . . . .wn be the heights of the various points, the observed zenith distances will give, each, an equation of the form & a; - a, + q = o Should the points a, w, mutually observe one another, there will be two equations in w; and 4, at - a, + q = o — a + æ, + q = o - All equations being formed, they must be solved by the method of least squares, regard being had to the weight of each, which will be as the number of observations and inversely as the distance, or, in other words, the quantity > (a (a – a '+ r.)') must be made a minimum. If, however, the points are very numerous, the solution of the above equations will become unmanageable, from the number of eliminations required, and in this case a small number of points must be taken at a time and determined as above. These results must then be used for the determination of others by the same method. The following pages contain the Mean Observed Zenith Distances, showing in each case the number of observations on which the mean depends. When the fourth column is blank, the object observed is the surface of the ground; though there are, indeed, a few cases in which there is no record by the observer as to whether the observation was to the surface of the ground or the top of the pile. Those observations in which the object was a heliostat, are distinguished by the letter H. 3 T 514 PRINCIPAL TRIANGULATION. OBSERVED ZENITH DISTANCES. Object * - - • . . ' Object Stations observed. Mººn §: °. d Reduction. Stations observed. * 3. º Reduction. - Surface. º | -- Surface. SaxAvond. Telescope above surface 5' 5 feet. RONAS. Telescope above surface 5' 5 feet. O Jº f/ ** * Brassa . 90 20 48' 5 2 º, ºn – 4° 4 || Saxavord 96 22' 55's 2 Eºmº 7'4' Yell . . . 90 16 3' 5 2 tº º — Io I | Fetlar 90 37 45 ‘o 2. . – Io'4. IRonas . . 89 58 45' 5 2 tº º — 7' 4 || Yell . . 90 47 28-7 3 ... — 17' 6 Balta . 9I 34 59' 5 2. º, –38° 4 || Brassa . . 90 27 o'o 3 ... – 7° Fetlar , 90 24 I4' 5 2 ... I — I4' 9 || Foula 90 I4. 53 'O I ... I — 6' I With a 7-in. Theodolite. Telescope 5'o feet. BRASSA. Telescope above surface 5' 5 feet. Gerth of Scaw . 93 48 6’ 3 Io –78-7 || Fair Isle 90 16 37' 3 7 ... – 4:8. Nivo Hill . 91 29 I5'8 || 23 —63.3 || Foula 90 o 36-8 5 ... I — 6' 2 * ſº Ronas 89 55 25°3 6 tº — 7' I - Yell . 90 II 51 7 6 ... - 7' 5 GERTII of ScAw. 7-in. Theodolite. Telescope above Saxavord . 90 I5 21 °o 2 . . . . *- 4 * 4. surface 5 'o feet. Fetlar . . . . . 9o 16 45' 8 6 — 6'2 IBalta . . 85 5i 21.7 I 2 ... - 4.3 °o 4 * º Niyo Hill 87 Io 53°8 Io ... - II.4 ° 3 Foul A. Telescope above surface 5' 5 feet. Saxavord wº º 86 I4. IO "O IO tº-gº 78-7 º f Ji f/ * , - Ronas . 90 Io 39°o 2. ' tº — 6' I Yell . . . 90 26 11 °o I tº ſº — 4-8 BALTA. Telescope above surface 5' 5 feet. Brassà, . . 90 24 6' 3 3 — 6' 2 - - Pair Isle . . . 9o 25 28' 5 2. – 4: 9 O / / / Aſ ºf Fitty Hill 90 32 II 'o I – 3:2 Fetlar . . . . 89 37 34’ o I —22 7 *- Yell . . . . 89 46.48°o 2 — 12 3 Saxavord 88 30 6 o I –38° 4 FAIR ISLE. Telescope above surface 5' 5 feet. With a 7-in. Theodolite. Telescope 5 'o feet. Gerth of Scaw . Nive Hill . . . 90 12 28-6 88 35 7'o I5 I6 IFoula Brassa . * Stronsay . . Fitty Hill Ronas . . . 96. 6 16.5 90 I5 38°o 90 24 16 o 90 20 31 '5 90. I? 34’ o i i : FETLAR. Telescope above surface 5' 5 feet. FITTY HILL. Telescope above surface 5' 5 feet. 9o 8 3o' 5 | Brassa. . . . 96 8' 26" 5 2. ... – 6.2 | Wart Hill IIoy. 85 48 12" o 4. e e I - 7°3 Yell . . . . . 89 52 53° 3 2 ... —23' 4 || Foula . . . . . 9o 16 25' 5 2. ... - 3" 2 Ronas . | 89 37 29' 5 2 . – 16' 4 || Fair Isle . . . 9o 16 37' o 3 • . . ; - 4 ° 2 Saxavord . 89 46 28’ o I – 14:9 || Stronsay 90 20 5'8 5 • - I O 2 IBalta 90 29 44' o I –22 7 || Deerness . . 9o 16 8' 3 3 ... I — 8-6 North Ronaldshay Lighthouse 90 23 31 °o I – 9: 2 YELL. Telescope above surface 5' 5 feet. O / / / • iſ f STRONSAY. Telescope abo º tº º Foula . . . 9o 5 IQ 7 3 . — 4-8 C p We surface 5' 5 feet Ronas . 89 2 I 17" 7 3. . — 17:6 C & N M fy Saxavord . . . 89 59 14°o 4. . . -Io' I | Deerness . . . 89 57 44' o 6 tº —I 7' 5 IBalta. . . . . 9o 25 45' 7 3 . |*-12'3 || Wart Hill Hoy. 89 41 33 o 2 tº ſº – 6:8 Fetlar . . . . 9o I3 48°3 3 E. g. —23.4 | Fitty Hill 89 55 2 I 5 6 — IO " 2 Brassa . . . . 9o 8 25°o 4. . — 7° 5 || Fair Isle 2 ... – 4'8 *# , º, º * OBSERVED ZENITH DISTANCES. 515 º Object º Object Stations observed. | *...* §: º Reduction. I Stations observed. Mºl 3. º: d Reduction. Surface. Surface. DEERNESS. Telescope above surface 5' 5 feet. . FASTIVEN. Telescope above surface 5' 5 feet O ş J. f/ Monach . º 96 27 57°o 2 º 41 SouthRonaldshay 90 o 9°o I . — 15.8 Cnocghuibhais . 91 42 Io'o 5 —63.3 Wart Hill Hoy. 89 28 36: o 2 — 16: o || Ben Hutig . 90 I2 34° 5 5 – 15' 3 §. Hill . . . 9o 2 6'o || 2 | ... — 8-6 Hººhºº. l 89 33 6'7 || 7 — 7' 5 ronsay o, I I 37 °o . . , || -- I'7° flSll U:ll'Il:lº Il 9 37 3 7' 5 Tide station. º - - Hºg. 92 56 5o 9 ; 7°2 + I 3 '9 - - º ºr * º Lower Cross || 92 57 37'8 2 2 | —27 7 WART IIILL Hoy. Telescope above surface 5' 5 feet. Rispond Tide , a f/ Station :- 6 Ben Clibrig 96 3 33° 3 3 — 3' 6 Upper Cross || 91 46 37' 6 3 20°o +63-8 Fitty Irillº 90 32 36' 5 2. — 7° 3 H. C. 91 48 £g 6 : -24.3 Stronsay 90 4o 34° o 2 — 6'8 ower Uross || 91 47 I3 3 || 15 “o +41 '8 Deerness . . . 9o 46 39°7 3 - IO "O - South Ronaldshay 9o 52 32°3 3 T*3' || || BEN HUTIG. Telescope above surface 5' 5 feet. Ben Cheilt . . . 9o 24, 33'5 2 - 5'4. Fashven, * 85 58 8.8 5 tº tº tº —15°3 SouTII RONALDSHAY. Telescope above surface. º: . : # º : . -: 5' 5 feet. SouthRonaldshay 9o 31 51 5 I — 3 7 Dunnet Head 90 29 35' 2 — 5 “I º § 24. tº Ben Cheilt . O 22 23°4. 4. * – 4'9 IBen Cheilt . 90 2 3b o 2. — 6 o •ok;" | 9 3. º Dunnet Head 90 5 I ‘o I – 12 '4 iºd. º ; ;: #: ; . – §§ Ben Hutig . . . 9o Io 48' o I T_37 Roan island Tide * | Wart Hill Hoy. 89 19 3' 3 || 6 -13. Šaj. . Deerness . 90 9 47° 3 | ... 3 — 15.8 Upper Cross 91 56 or 6 || 10 | 18-o +78-9 Lower Cross || 91 56 39° 7 || 14 | 13°o +47:3 * - Base ... 91 58 I 3 '4 4. ... -34 °7 DUNNET HEAD. Telescope above surface 5' 5 feet. Rispond Tide - *E*--— i. Station?— * o J/ f/ Upper Cross || 92 39 5 I ‘9 9 2O’o |+ Io9' 5 Scarabin . . 89 38 42 °o I — 6-7 #. Cross || 92 4o 36°9 || 9 || I5°o |+ 7I '8 Ben Clibrig 89 4o 42° 5 2 ... - 4° 5 Dase 92 42 22 °3 5 4. I' 5 Ben Hutig . . . 9o I ro'o 2 - ... - 5 ' I - Fashven . . . . 9o 7 52 'o I ... - 3 ° 9 - - - Wart Hill Hoy. 89 19 23 o 4 is g – I 3 '4 BEN CHEILT. Telescope above surface 5' 5 feet. SouthRonaldshay 9o 7 50' 3 6 ... - I2 °4. © iſ ſº J/ Ben Cheilt ... . . 89 54 52°o 2 ... - 8:9 || Scarabin 88 54 18°o I –20' 6 º Tide, Sta- Ben Clibrig 89 36 II o 3 — 5' 6 lon-:— . . . Ben Hutig .. 90 Io 9' 5 2 – 4'9 Upper Cross 92 3 12 3 8 || II.'8 |+|145° 2 | Wart. Hiſ Hoy 90 4 23°o 3 – 5 °4. Lower Cross 92 5 9 I 8 6-8 |+ 30°6 South Ronaldsha 90 23 38°3 3 — 6' o Base .. 92 7 48' 5 8 ... I-126'. I | Knock . . . . 90 14 39° 7 3 — 3 ° 9 * = - - -- Corryhabbie 90 9 5 'o 2 ... - 3" 2 CNocGIIIUBILAIs. Telescope above surface 5' 5 feet. MoNACII. Telescope above surface 5' 5 feet. | N. Rona Island 93 25 4éo 2 • * = | " 4" 5 Cleisham . . 85 36' 20" I9 • I - 646 Ben Hutig 89 52 46' 9 || 5 ... – 12-5 | N. Rona Island 96 25 43°3 7 ... - : 3: 9 Fashven 88 22 35.7 6 –63 - 3 || Cnocghuibhais . . 9o I6 5' 3 I ... - 4 ° 2 Monach º * - 90 20 20 '8 4. – 4" 2 - Fashven º 90 IO 57.6 I I º sms 4. "I Clash . Carnagh * Ben Clibrig. 90 3 27' 5 8 – 3: Tide Station: Scournalapich . . 9o 6 22 '7 2 —. 2' 6 Upper 9.9ss 93 41 38.2 | 9 || 7-2 || +29-7 || Rū Rea. 90 12 44' 5 || 8 — 5-2 Lower Cross 93 43 6.8 || 3 || 4-2 || || 33-3 || Stor; go 4 33-3 || 9 |_....|- 3°. 3 T 2 516 PRINCIPAL TRIANGULATION. Zenith | N º * Object Stations observed. Mº. l ô. O . d IReduction. Stations observed. Mºl à. º Reduction. Surface. Surface. Wisp. Telescope above surface 5' 5 feet. CLEISTIAM. Telescope above surface 5' 5 feet. Hart Fell . . 83 43 43.7 3 ... — 11:2 || Ben More, S. Uist 93 26 3*o 4. * * * 4°1 | Criffel . . . . 9d I4. 25' 7 || 3 – 3: ||Nº|alianº º # 93.3 || 3 T 3.3 Dunrich . . . 89 53 43°o s--s fº * onach ..., , . . . . 9o 48 8-7 || 1 – h * Cheviot . . . § # #: : * 3.3 Cnocghiubhais . . 9o 42 20-7 3 * — 2 7 Cross Foll o 2 31 °o I — 4.8 hºlyen. . . . 99 38 36.3 || 4 — 2 7 • 9 tº . Itu Ikea . . . 90 4 I 49' 5 3 – 5 °4. Scournalapich . . 9o 18 Io' 5 3 — 2 8 CALTON HILL. Telescope above surface 5' 5 feet. * ; : ; ; #: º – § C. J. W. S.W. corner Sir Ben Lomond . 89 49 16.7 3 , , , - 3°7 | Fred. John- Ben Cleugh . 89 22 26-5 2 . – 7.8 stone's cottage, Ben Lawers . 89 38 12'o 1 – 3.8 near Tide Pole | East Lomond . 89 3o 26°5 2 — 16-8 || Loch Seaforth, Kellic Law . . . 9o 2 4o'o 2 — 8-4 | Is" of Lewis: Ground 97 22 I5'4. 8 o'o —56' 3 - - - Eayes of roof, . 97 22 21.8 8 II: 2 | +58-9 BEN CLIBRIG. Telescope above surface 5' 5 feet. Chimney band . 97 18 53°o 8 19°4 |+ 142 5 Ben Wyvis . . . 93 9 544 20 – 5"; IRU REA. Telescope above surface 8' I feet. Scournalapich . . 9o 17 36' 4 || II – 3:3 O / fi Storr . . . . 9o 36 37' 9 - 2' 6 || Storr . . . . 89 37 23.9 29 tº tº º – “s Monach . . . . 9o 47 29.8 || Io - 3’ I | Cleisham . . . 89 47 7.2 21 ... I — 8 o | Fashyen. . . . 90 48 14-2 || 17. - 7' 5 || Monach . . . . 9o 17 15: 7 || 11 – 7: 7 #. # tº ſº. % s .# 33 - 9’ 7 || Cnocghiubhais . . 9o 21 36' 3 || 8 – 5' 3 *1tty 11111 . . . 35' 3 – 2 °4. Wart Hill Hoy. 9o 39 19 'o 4. — 3' 6 - - Dunnet Head . . 9o 54 54°3 4. – 4' 5 CowHYTHE. Telescope above surface 8.8 feet. South Ronaldshay 9o 51 44' I 2 ... - 3' 3 Ben Cheilt . . . 9o 52 7'o II ... | – 5' 6 * 9 ... ." * º Scarabin . . . 9o 35 Io' 7 || 32 — 7-2 §: ... . . . 88 30 4.2 4. 2.5 +47.7 + e * i. orryhabbie . 89 22 5' 9 22 || 13 o | + I4°o Corryhabbie . . 9o 33 7.4 6 ... - 2'8 || Sarāb; 8 ſº º i. Ben Macdui . . 9o 22 48-6 4. tº {} – 2 - 5 carapin... . *f 9 54. 43.5 24 11.5 -- 2. Roan Island Tide Ben Cheilt . *H 9o 9 52 “o 19 I o | – 6' o Station . . . 91 32 57' I 7 — 9'6 - - BEN WYvIs. Telescope above surface 5' 5 feet. SCARABIN. Telescope above surface 6 o feet. Ben Nevis . . . 96 12 15°o 2. , , I - 3. 4. © ºf f/ ...T. Mamsuil . . . . . 9o 4 'o I . – 6' Ben Macdui . 96 11 9-3 I tº º – 2 9 Scournalapich . . 9o f : 2 i. ºmº }.} Ben Wyvis . . . 9o 2 17-7 || 4 tº º — 4.5 || Ben Hutig . . . 9o 44 29'5 2 . — 3' 6 Ben Clibrig. . . 89 47 28' 2 | 12 ... – 7.8 || Ben Clibrig. . . 9o 18 31 7 3 . – 5' 5 Ben Hutig . . . 9o 26 54° 5 || Io ... — 5-8 Scarabin . . . . . 9o 35 51 "o 2 . – 4 I ... (4) 94 4o 54°8. 8 o'o —53.8 || Corryhabbie . . 9o 32 12'o I ... – 3' 8 Berridale J E (3)| 94 39 47° 3 8 8-o +17-9 || Ben Macdui . . 9o 8 26 o 3 . – 4°o Tower #3 ; ; ; ; || 3 ||3: I 2 3 * tº ſº Wart Hill Hoy. ; : 4. à º : sº tº: MoRMONTII. Telescope above surface 6-2 feet. Dunnet Head . . 9o 45 13-8 ; 13 . — 7° 3 O f f/ SouthRonaldshay 90 4o 45 ° 2 6 tº — 5 ° 2 Dudwick . . . 9o I4. I 3 'o 2 I IO* O. +13.6 Ben Cheilt . . . . 91 13 44' 7 || 13 ... —22 - 5 || Blue Hill . . . 9o 18 II •o Io 9°o + 3' I Mormonth . *H | 90 37 38' I 3 2 °o – 2 2 | Brimmond . . . . 9o 8 47-3 || 15 8’o + 2 + 3 Cowhythe . . . 9o 4I 23 9 4. ... – 4-6 || Mount Battock H | 89 56 49.7 21 I 2 — 3 7 ICnock . . . . . 9o 27 32 °4 4. – 4:4 || Corryhabbie H | 89 52 9.2 25 2 * 3 || – 2 * - bbi tº i. * 3 3 * 3 Corryhabbie . . 9o 17 44°o 4 – 3' 8 || Knock . . . . 89 54 29° 5 || 13 | 12:5 + 9' 1 * H signifies that the object observed was a heliostat. OBSERVED ZENITII DISTANCES. 517 Zeni Object - tº T Object - Stations observed. *.th §: º Reduction. I Stations observed. Mºh 3. º Reduction. Surface. Surface. MORMONTII—continued. LAYTON. Telescope above surface 5' 5 feet. Scarabin . H 93 14 2.6 I9 3° 3 || – *6 O / / / Af Ben Cheilt . , H | 9o 23 58' 0 | 19 o' 2 – 3 3 || Blue Hill . 89 48 9'8 5 — 16 o Peterhead, Old - Tarbathy . 89 55 16: 12| 8 —42 '8 Windmill . 90 42 22 °o || 4 || 27°o || + 74°9 || Brimmond . . . 89 19 24. 4. 5 — 19: 7 Reform Monument 9o 32 26°o | Io Top. —20.8 . Over Hill . . . 88 59 35.2 5 –61 : 5 Iittle Stirling 90 26 4' 5 || 21 Io'o + 1 I 6 | Dudwick 89 35 49' 7 6 –20-7 & * • 5 feet. +º, ICNocR. Telescope above surface 5' 5 fee GREAT STIRLING SECTOR STATION. Telescope above - O - # fº & f surface 5 °o feet. Ben Cheilt . 90 26 26°o 2. ... - 3 ° 9 Cowhythe 9I : 42 “o 3 4. -: - Mormonth go 20 15°o 2 — 7' Little Stirling 83 24 5*o II –21% Dudwick . . 9o 29 47 'o 2 T 7.3 | Reform Monument 96 9 6'o 11 ºmº §4 Mount Battock . . 9o o o 'o I T + 9 || Peterhead Old - Windmill . 90 32 8° 5 II 27°o +255'4 LITTLE STIRLING. Telescope above surface 5' 5 feet. IBlue Hill 93 6 2.3% o 2. • , , . " #7 STORR. Telescope above surface 6' I feet. Dudwick . . . 89 44, 29° 7 3 –24° 9 Mormonth 89 42 52 '6 5 — 16: 7 * + O M M f MA - Ben Heynish II 9o 41 17 'o 4. 5'8 — o' 2 Den More, S.U. . . 9o 20 32: 5 9 ... – 5'3 With a 7-inch Theodolite. Telescope above surface 5 feet. Ben More, S.U. H 9o 20 38°3 13 5 o – o 9 Cleisham . . . 9o 9 47-3 | 16 ... I — 6' I - .. * * * * Cleisham. . H 9o 9 53°o 17 2 3 || – 3 7 *. . . . 89 42 o'o 6 T*5'' | Monach . . H go 38 iſ 1 || 23 “I 3 ; – 3 ‘2’ “tº hºld Old ſº Cnocghiubhais. H | 9o 41 46' 5 | 12 2 : o — I '8 Windmill . 90 37 23° 3 6 27°o |+229°4 Ru Rea. . . . . 9o 42 45°6 I5 . — 8-7, Reform Monument 90 2 I 33 I 8 - –83-6 Ru Rea . . H | 9o 42 47°4 4. I 5 || – 6' 5 | Sector Station 90 37 58' 8 4. T**7° 7 || Ben Clibrig . II go 23 27-3 17 2 °o — I 9 *- - - Mamsuil. . 89 52 I9' 5 8 ... – 5’ 6 IPETERHEAD OLD WINDMILL 7-inch Theodolite. Tele- łºś. º H : 5 : : ; : º – 3.3 scope above surface 32' 6 feet. Ben Nevis H | 9o 3 45' 7 || 2 I I 5 – 2 7 w O / / / , Ben More, Mull . . 9o 1942 I 5 ... - 3" 2 Little Stirling 89 24 47' 5 8 ... —333°7 || Ben More, Mull. H| 90' 19 46' 3 || Io o' 6 || – 2 9 Mormonth 89 2 5 27' 5 8 ... – II 5" I •, Sector Station 89 3o 5’ O 8 – 371 ° 5 Reform Monument 88 59 4o'o | 8 -**| ScounsALAricii. Telescope above surface 7.5 feet. DUDwick. Telescope above surface 5' 5 feet. Mamsuil. . . . 855: 8.7 11 26-8 |+|114 O J M iſ & A Ben More, S.U. II | 9o 44, 18 o 22 5 °o — I 2 Tarbathy 90 22 35'8 4. – 14' I | Cleisham . II 9o 37 55' I 15 ... – 3' 8 Blue Hill 90 II 24' o 4. – 9: I | Monach . . II 9o 53 51 2 II 2 - 3 || – 2 '5 Qver Hill 90 Io 26.7 3 — 17° 3 || Ben Clibrig . . . 9o 29 59' 5 9 12 o + 2 7 Brimmond • | 89 56 56' 5 2 – 11 : 1 || Ben Wyvis . . . go 18 22:2 |, 22 | 12'o + 6.3 Mount Battock . . 83 45 6-3 3 — 5: I | Corryhabbie. H | 90 37 23°o 26 o' 9 || – 3 ‘7 Corryhabbie 89 45 5o' 5 2 ... – 4: 9 || Corryhabbie . . 9o 37 o'8 3 | 16.8 || + 5.2 Knock...; . . . 89 #2 34-7 || 6 | ... – 7-3 || Ben Novis . . . go "4 6-2 26 || 8°o + 2.5 Mormonth. . 89 55 7'o 2 ... — 18 I | Ben Nevis . H | 90 4 24 'o 7 | 1.5 – 5.9 Little Stirling 90 22 7.5 2. –24 9 || Ben Macdui. II go I 5 3’ o 17 I •o - #3 Layton 99 3 I 47' 5 4 —23.7 | Bon Macdui. . go 14 26-4 || 12 20°o | * * 7 518 PRINCIPAL TRIANGULATION. Stations observed. Mean Zenith Distance. No. Obs. Object observed above Surface. Reduction. Stations observed. Mean Zenith Distance. No. Obs. Object observed above Reduction. Surface. BBIE. Telescope above surface 7' 2 feet. * - Cority IIABB p 7 BRIMMOND. Telescope above surface 5' 5 feet. Glashmeal 89 53 59' 9 || 16 | ... – 8' 5 © f f/ # It Ben Macdui. 89 26 16-8 24 ... — Io. 8 || Mount Battock . . 89 23 35' 5 2. tº º – 8:8 Ben Nevis 90 I2 I5' 3 I9 | . . . — 3-6 || Knock 90 I I5' 5 2 tº º — 6'2 Mamsuil . . . . 9o I3 58' 2 | 20 . – 3.9 || Mormonth 90 II 32 °o 2 — 7'o Scournalapich . . 9o I3 32 °4 23 . — 4-0 | Dudwick, 90 I5 36 o 2 -- I I " I Ben Wyvis . . . 9o Io 15' 7 || 27 . – 5 'o Over Hill 90 38 35 'o 2. –28°4 Ben Clibrig . H. 90 22 41 6 || 31 . — 3’ 7 || Layton . 90 48 41 ° 5 2 — 19:7 Scarabin . H 90 28 Io' 5 || 35 I'o – 3’9 || Tarbathy 91 - 8 41 ° 3 3 –3 I 2 Ben Cheilt . H 9o 4o 8' 2 28 1.5 | – 3-3 | Blue Hill 90 4 I 2 °5 2 –31 : 5 Den Cheilt . . . 9o 4o 2 I 3 4. . – 4 ° 2 |_ - - Cowhythe H 91 o 23 I 32 I o – 7 9 * * Fººd . H ; # #: i. | Tºy || – '...} Blue Hill. Telescope above surface 5.5 feet. Dudwick. . . 9o 45 48' 3 || 24 ... – 6'4 O & // # / Mount Battock . . 9o 12 18- 9 || 49 ... I - 8 7 || Mount Battock . 89 I5 48' 5 2 . — 8' 5 --- Dudwick ... 9o 6 23:3 4. – 9: I Little Stirling . . 9o 13 39°o I 7.7 MAMsuIL. Telescope abovo surface I4'o feet. - • Ben More, Mull. 9o 32 Io'o 9 ... I — 8 o DEN MACDUI. aco '8" * > IBenlyſore, S.U. H. 9o 44, 34-8 I5 I ‘5 - 6°o scout Telescope above surface:8 2 feet | Ben More, S.U. . . 9o 44, 25' 5 || 4 | ... – 6'7 * * * C f f/ * d iſ Storr. . . 9o 38 54'4 32 ... - 12 ‘8 || Ben Cleugh . H 9o 43 25°3 || 19. 1 - 3 | – 4:4 | Cleisham 90 39 IQ 9 I 3 ... – 7°o || Ben Lawers . . . 9o 20 30°4 8 ... – 7:6 Scournalapich 90 I2 4o 5 43 ... —83°o || Ben Lawers. H 9o 20 39'2 34 2 5 || – 5:3 Ben Wyvis . . . 9o 2 I 5 4 || 34 ... – 16°o || Ben Nevis . . . 9o 18 16.6 8 ' ' ... – 676 | Corryhabbie. H | 9o 38 36' 5 27 o°9 || - 7 I | Ben Nevis , II 9o 18 37°4 31 || 1 : 5 – 4: 9 Ben Macdui . 90 16 5' 2 | 12 ... - 9° 7 || Mamsuil . . H 9o 25 54' 5 7 4 o – 2 ° 9 Glashmeal . . . 9o 3o 2 'o 3 ... – 7' 6 || Scournalapich H go 26, 59.5 28 || 3: o – 3-6 | Ben Lawers . H 90,21,38-6 21 I ‘5 – 8°o || Ben Wyvis . H | 9o 30 26:9 Io I o – 5 - 2 Den Nevis 90 2 14-2 || 23 ' '... — 16' 2 | Ben Clibrig . H 9o 4o 7.2 | Io || 2 | 8 || – 2:5 Scarabin . . H | 9o 48 I 6 17 3 o – 2 6 - Ben Cheilt . FI | 9o 57 24 o 18 2 : o — 2-8 Over IIILL. Telescope above surface 5' 5 feet. Corryhabbie . . . 9o 53 22 9 || 2 I ... - 12 3 - - Dudwick . H 91 1 32 °o 13 I ‘7 — 3 9 tº O M MA u , || MountDattock. II 9o 45 9' 3 || 39 I o — 7-8 | Brimmond . . . . 89 27 25' 5 2 . -28’4 || Glashmeal 90 35 58°6 22 ... I — 18' I Möunt Battock . . 89 28 50: o 3 . - 3.7 | Sayrs Law . H go 52 I 2 8 || 2 | 5 || – 2 '4 | Mormonth 90 I o'7 3 ... – 8 9 - - * | Dudwick. 89 58 46 o' 4. ... I — I 7° 3 Little Stirling 90 II 18' 5 2. ... - I2 "O * # Layton 9I 4 7° 7 3 ... —61 : 5 || BEN MoRE, SouTH Uist. Telescope above surface 5.4 feet. Tarbăthy . 90 57 I4 ° 3 3 ... —64-7 Blue Hill . 90 3 35' 5 2 º, º 0. ”* | Cleisham . 93 1: 464 8 ... – 4:1 Cleisham . H. 9o II 14' 5 || 34 3 °o — I '8 TARDATINY. Telescope above surface 5' 5 feet. š. tº . . . 9o II 44 ° 5 9 ... - 4 - 7 OTI . ; H 9o II 32 7 || 37 6-8 + 1 .. 2 O ş Aſ , Scournalapich H | 9o 17 4-3 || 25 o' 8 || – 2 - 2 Blue Hill . | 89 4o 35°8 4 | . . . –25°6 || Mamsuil: , H | 9o 14 31°7 | 19 || 14 o + 4-1 Mount Battock . . 89 2 I 43°o I . – 6-9 || Ben Nevis : H | 9o 16 36-8 15 | i. 5 || – 1.7 Brimmond 88 57 17'o 3 . – 31 2 | BenMore,Mull. H | 9o 17 29'o 27 || o'o – 2.8 Ovor Hill 89 6 23°o 3 . -64' 7 || Jura. . . . . . H | 9o 34 i 7 || 13 || 2 | 1 || – 1-2 Dudwick . 89 49 o'o 2 . – 14° 1 || Ben Heynish H | 9o 38 42.5 39 ... - 3 ‘7 Layton . . . . . 9o 9 27°7 3 ... —42 8 || Callernish Tide º Little Stirling . . 9o 2 o'o 2 . I — Io' 9 Station . 98 23 31 3 || 14 | ... —82 - 5 OBSERVED ZENITH DISTANCES. 519 Mean Zenitl N Object S. Object º Mean Zenith No. observed * º Mean Zenith No. lobserved tº. Stations observed. - Distance. Obs. above Reduction. Stations observed. j Obs, . Reduction. Surface. Surface. MoUNT IBATTock. Telescope above surface 5'8 feet. ' Glashmeal... . 85 4. 24. 28 || 14-0 || 1 #7 Rellie Law . H 90 ; §§ 8 3. isºmº §§ East Lomond ... 9o 32 34°5 | 13 11-6 || -- 3: 9 Ben Cleugh . H go 26 7-6 || 1; I ‘o | – 2 '8 Ben Macdui . . . 89 41 49' 5 || 11 8 o + 2 - 4 Ben Macdui. II | 89 41 56.9 15 | 1.8 – 4:3 Ben Macdui. 89 42 2 o 6 ... — 6' 2 Corryhabbie 90 1 1 38-1 || 24 16'8" | + 13 '4 Knock . . . 9o 33 8*6 13 |. 12 5 + 6'o Mormonth .-----|-90-41 48-1 |- 15 | ... -- 4:3 Dudwick . 90 45 56° 5 || 7 Io “o + .3° 9 Over Hill ' ' '. 90 54 33 °o 7 8°o + 2 8 Brimmond . go 53 53° 5 | 16 8’o + 3' 6 Blue Hill . 91 3 2-8 16 9°o + 5°o Lumsden H | 9o 43 23 9 || 17 I 7 || – 2 I Sayrs' Law . H 9o 34 52 2 I4 2 5 — I 7 *- BENNEvis. Telescope above surface 5' 5 feet. GLASHMEAL. Telescope above surface 5' 5 feet. Den Cleugh . Ben Lawers . Ben Macdui Corryhabbie Mount Battock . East Lomond . Hºmº--- O f Af f/ 90 34 3 “o 2 – 4 3 90 7 27°o 3 – 5 °4. 89 38 30°3 4. - I2 * I 9o 31 46' 3 || 3 — 6' 5 90 35 20° 5 4. — 8' 8 90 47 7' 5 2 – 4 9 *=- EAST LOMOND. Telescope above surface 5' 5 feet. | Dunrich iſ . Calton Hill . | Ben Cleugh . Ben Lomond Ben Lawers. Glashmeal Mount Battock. Rellie Law . Lumsden . Sayrs Law . 90 3 37 °o || 2 — 4' 6 90 44 46°o I —Io 8 89 41 49' 5 2. – IO "O 89 59 51 5 || 2 — 3 ° 9 89 39 16 o || 3 | . — 4. ‘9 89 46. 23 o 3 – 4 ° 9 90 5 48° 7 || 3 ſº — 4.' I 90 4o 19°o 2 — 12 7 90 26 44°o I . – 4. ‘7 90 7 28 ‘o 2 — 6'2 BEN CLEUGII. Telescope above surface 6-o feet. Merrick . Goat Fell Ben Lomond Ben Novis . II Ben Lawers. Ben Macdui Glashmeal . . . Mount Battock . East Lomond Sayrs Law . . . O f” WI * #! 90 24 31 7 I3 — 3 °o o 19 37° 3 || 8 - 3 5 9 55 55 °o 45 . . . . . — 7'o 90 2 I3 ° 9 27 I 5 – 2 8 89 36° 17' 4 || 37 ... — 7 7 90 I 46' 6 21 tº º — 3' 8 90 3 22 "o 20 * † — 4.' 7 90 22 o' 5 || Io — 3' 6 90 35 Io' 5 22 — Io: 9 90 25 46' 9 || 15 ... – 4'8 99 56 59' 5 7 Top. — 8' 5 90 16 25 'o 9 ... – 4 ° 9 90 I6 22-8 8 . – 4 ° 2 90 Calton Hill Obsy Dunrich . . . Hart. Foll - * *-*** ** gº tºº º is * ~ * ºr ºn ** * * * * * * • , t < * * * *** - *** * 25 39° - sº * O & J/ f/ Jura . . . II 9o 43 o' 2 9 I 5 – 2 “I Ben More, Mull. 9o 34 15-7 || 14 ... — 4-6 BenMore,Mull. H | 9o 34 20° 3 | 1.4 I ‘8 || – 3 2 Ben Heynish H 91 1 17:7 23 I 3 || – 2 2 Ben More, S.U. H | 9o 49 57.8 13 5 * 3 — O' I Storr . . . . .90 44 13 6 7 ... - 3' 3 Storr . II | 9o 44, 18 °o 7 I 3 — 2 5 || Maimsuil. . . 9o 23 I 3 '7 8 . – 6'4. | Scournalapich. II 9o 25 9°4 24 I “o — 4. '4 Scournalapich . . . 9o 24, 5o I 23 . . . . - 5 "4 Ben Wyvis . H | 9o 32 7.8 15 | 1.5 | – 2:5 Ben Wyvis . . . . 9o 32 41 ‘8 27 . . ... – 3-4 Corryhabbie H | 9o 44, 51 °o 14 2 * 3 || – I 6 Ben Macdui. H | 9o 21 52'8 13 2 * 5 || — 2 °2 IBen Macdui. 90 21 6 1 || 21 ... - 4. ‘o IBen Lawers . . . 9o 20 52 5 || 26 ... — 6' 2 | Ben-Cleugh . H go 44, 37°2 14 I 5 – 2 °4. Ben Lomond . go 34 Io' 3 9 ... - 4.” 9 Ben Lomond H 9o 32 50°o | Io 4' 6 — or 8 BEN LAWERS. Telescope above surface 6'o feet. Merrick . . . H 96 44 29°8 || 16 • I - 24 Goat Fell ... H 9o 37 29.8 5 , | I o | – 2 6 Goat Fell ... 90 37 29' 3 5 . . . . . - 3 °2 Don Lomond . . 9o 28 4o 9 || 15 . . ... — 8 o Ben Lomond H | 9o 28 4o" 2 7 I 2 – 6'4 Jura. . . . . H | 9o 4I 27°8 19 I 6 || – 2: I Den More, Mull. H | 9o 33 9°4 || 14 || 8° 5 || + I 4 Ben More, Mull. 90 33 17°8 5 § tº º – 3° 4. Ben Nevis . H | 9o 5 I 5 20 I 2 – 5 °4. Ben Nevis . . . 9o 4 59' 3 7 ... – 6'7 Mamsuil . . [I 9o 24 II 3 2O I 5 — 2 8 Ben Macdui. H 90 to 57° 4 || 33 . • 2 – 4' 5 Glashmeal . H | 9o 22 50°2 35 I 2 | – 4'7 East Lomond . . 9o 53 49°6 | II . . ... – 5' 3 Sayrs Law. ... H | 9o 47 27°5 I4 - || 1 | 3 || – 2:4 Ben Cleugh . H. 90 46 21 "3 27 | I 2 || – 6'2 Hart Fell . H 9o 41 44' 6 12 o' 7 || – 2 '4 sº IBEN MoRE, MULL. Telescope above surface 5-5 feet Jura. . . . . . 9o 24, 14' 3 7 ... – 5 ° 9 IBon Tartovil 90 49 40°3 4. . — 4 ° 2 Ben Heynish . 91 3 39°o 2. — 6' 2. Den More, S.Uist 90 37 35 'o 2 – 2:9 Storr . . . 9o 34 58'5 2. — 2 ° 9 Ron Novis 89 59 58: o 4. - 4:6 Den Lawers. 90 18 21 'o 2 – 3: Ben Lomond. 90 20 28°3 3 – 3.9 Goat Fell O I — 3 °4. 52O PRINCIPAL TRLANGULATION. Stations observed. Mean Zenith Distance. No. Obs. observed above Surface. Object Reduction. Stations observed. Mean Zenith Distance. No. Obs. Object observed above Surface. Reduction. T}EN HEYNISII. Telescope above surface 5' 5 feet. MoRDINGTON. Telescope above surface 6' I feet. Ben More, S. Uist Ben Nevis . . Ben More, Mull. | Jura . º J 93 3 3. 89 55 39° 89 22 21 89 52 45° 5 O O 3 * I I 4. 2. f : : I}URNSWARK. Telescope above surface 5' 6 feet. Cheviot . Cheviot . Wisp . II Dunrich . H Sayrs Law . I}lackheddon . It 85 I I I I 9 89 I I I I ‘o 90 I 54° 7 89 52 14-6 89 38 16. I 90 4 36' I II 3o I 2 2 I I5 I I º: i !! IO " — Io 3 tºº I º 3" 2 – I O "I — 18' 3 MERRICK. Telescope above surface 6' 3 feet. - O Af J/ J/ O J. f} ** Criffel . . . . . 89 31 55°o | I2 º C & ~ 12' 4 || Burnswark . o 42 6'6 2. ... - 5 '2 Merrick . . II | 89 52 o' 5 22 I 6 || – 3 3 || Jura . . . H ; # 31 7 || 17 I 5 || – 2 3 Hart Fell . . . 89 1744-8 15 ... - 9:8 || S. Donard . H go 31 39.7 || 23 I 6 – 2 - 1 | Wisp . . . . 89 29 59° 5 || Io -** * | Ben More,Mull.II | 9o 36 26.3 | 12 || 1 7 || – I'7 Cross Fell . II | 89 44 6'7 16 * 9 || - 4.3 || Goat Fell . H go 14 53° 0 || 13 I “o — 4.' 7 Sca Fell . . H | 89 42 42 I | II |-3.4 7, 9 Wisp . . [I 9o 31 9 9 || 15 I 3 – 3 3 Hart Fell . H 9o 18 50' 6 28 I 4 || – 4 I Sca Fell . . II 9o 21 17:7 || 32 ... – 3 6 DEN LOMOND. Telescope above surface 5' 5 feet. Criſfel . . . . 9o 29 41 °6 20 tº ſº tº — 6'8 IXnocklayd . II 9o 35 20°o 26 Io 5 | + 2 + 3 r o / // m , | Blackcomb . FI 9o 34 46' 4 || 35 ... - 3 °2 Goat Fell . 90 2 I 24' o I . – 4 8 || Divis . . 9o 36 51 6 6 ... - 3 °4. ICnocklayd . 90 45 20 ‘o I tº º º – 2 3 || Divis . H 9o 37 26' 3 5 I 5 || – 2 6 Jura . . . . . . 9o 28 26°o I . | – 3' 8 || Ben Lomond H | 90 22 51.5 29 . - 3 '4 Den More, Mull . . 9o 2 I I I 2 ... – 3 9 || Ben Lawers II 9o 27 28' 5 | 16 I "O || - 2 " I I, Ben Nevis . . . 89 59 5' 7 3 . – 4' 9 || South Berule II 9o 36 19° 5 35 &. - 3' 6 i Ben Lawers. 89 53 53° 3 3 ... – 7' 4 || Trostan . . H 9o 33 26' 6 31 f 5 || – 2.8 Last Lomond . . 9o 4 I I o 3 ... - 3’9 || Ben Cleugh . H 9o 31 5 I I Io I 2 | – 2 6 Ben Cleugh . 90 29 6' 5 4. ... – 6'5 | Cross Fell . II 90 29 52°8 Io I 6 – 2 - 2 Dunrich . . . 9o 33 IQ'o 2 — 3 ‘o Hart Fell . . . 9o 31 39°o I — 3 ‘o IIART FELL. Telescope above surface 5' 6 feet. BEN LOMOND. Telescope above surface 6'2 feet. (1855.) | Dunrich . . II 93 14 56°o 23 3° 5 || – 5" 7 º ºgh . H | 9o 23 13 8 || 13 I 6 || – 2 8 O f ºf f/ Terrick . . H | qo 14. 4.1 ‘8 I O " – A * Ben Cleugh . 90 28 54' 5 I “ | T 7.3 || Cross Fell . II ; # #: § .# º ;: Jura . . . 90 27 2 I o I ... - 4 3 || Criſſel . . . 9o 27 12 5 16 — 6' 5 Ben Nevis 89 58 3' 8 2. * … º. ~ ā’5 | Sca Fell II O I • 6 º: - fºl" ºrs. . . ; ; ; 9 || 4 | ..., | – $3|R." . . . . . . . . . . .” I,...; Goat Fell . 9° 4° 39'5 || 4 || “ 5'4 Cheviot . . If | 66 & #7-3 || 2 || 3:5 — 2. §" . H | 9o 29 6' 6 || Io 4."O | – I 5 & Oat l'e º º - ? " ICELLIE LAw. Telescope above surface 5'8 feet. I}cn Lomond H ; : i. 1. 1. 3 || – 3. - Den Lawers. II 9o 20 26:6 15 o' 5 – 2 3 Sayrs Law Ç 85 43 33.5 I5 ... mº 8:1 T}urnswark {} º 90 58 7. 9 I I Q & © Hºmº 9'8 . Sayrs º . H | 89 43 26' 9 || 14 2' 6 — 4' 5 y º t = X -* º Łºſi º ; ; £: º Tºp ſº Eğ JURA. Telescope above surface 6: o feet. Last Lomond II | 89 33 2 °o 14 I 2 — to 7 + O M M & | Glashmeal 89 38 29 2 4. º tº º - 4' 7 || Ben Tartevil . 91 3 49.7 12 I5 °o +167 Glashmeal . H | 89 38 50' 5 I3 I 3 || - 3-6 || Ben More, Mull. go 2 3-1 I6 || 20°o +15° I Mountlattock.II | 89 51 23'3 2 O I 2 | – 3-8 || Ben More,Mull. H go I 59' 3 4. - - - — 6' 5 Lumsden . . 9o 8 54°2 I 2 º, º º — 7'o | Inocklayd . 90 30 2 I 3 9 Io'o + 3 'o Lumsden . H | 9o 8 55' 3 | 18 I I - 5' 7 || Goat Fell . . . 9o 8 Io'o 13 | 16 o 4-16-6 OBSERVED ZENITH DISTANCEs. 52 I º;: Mean Zenith N . ſ N Object * learl Zelll O. ODSerye * g Mean Zenith o. lobserved * Stations observed. Distance. 6. "..." Reduction| Stations observed. Distance. ð... "." Reduction. Surface. Surface. JURA—continued. SAYRS LAw. Telescope above surface 5' 5 feet. Ben Lomond . 93 I 3 23.9 6 I9'o + 9°o Wisp . . . & 11 53.1 6 – 24 Ben Lomond H 90 13 40-9 5 o:8 – 3' 6 #Fal * - ; O #: 3 , , ; - ;: Ben Heynish II 9o 45 21:5 26 I 0 || - 3 7 | Dunrich . . . 89 54 2 I I 6 tº º – 7:8 º S.U.H. 9° 4: 13. ... 8 * 5.2 – 3.4 Lumsden . . . 9o 42 41 6 13 . . . —II 6 errick . . II | 90 28 1.6 14 I '9 * 9 | Ben Lomond 90 I5 52 “o I – 2 * S. Snaght . H go 31 299 || 15 3'8 - I 2 | Ben Clough . 90 9 £1.5 6 " | – £4 Ben Nevis . H | 9o Io 4-6 | 16 o' 8 || – 2 8 || Ben favºrs. II | 9o 5 55' 7 8 3.5 - I "O Ben Nevis . . go 9 25°o | 12 21 °5 + 8° 3 | East Lomond . 90 I7 55 ° o 8 — 6'2 | Ben Lawers. H | 9o 18 2 2 21 3.9 4 || Ben Macdui . . go 15 41 -o 2 ... I – 2 * 3 Trostan . . H | 9o 3o 2 I 3 || 12 .5 3.2 Glashmeal . H go 13 ió-o 9 I 5 — 2 I Mount Sandy H go 49 20' 6 Io * 3 | T 3° Mount Battock H go 2: 3'o 3 I 7 | – 2 'o Kellie Law . H | 9o 36 49-7 7 I o – 6' 3 Blackheddon. . . 9o 34 14-2 8 . – 6-7 GoATFELL. Telescope above surface 7 feet. §: * † fi : 53 47' 2 8 ... I — 6’ 6 neviot . . II | 89 53 5o 9 3 2 : o – 4 2 Mordington . . . 9o 39 27°6 Io ... – 9-2 O ! ſi f iſ b Jura. . . . . . . 9o 19 4'4 5 — 7' 4 Merrick . . . . . 9o 17 49' 3 6 - – 6-2 Ben Lomond . 90 II 55' I 8 ... – 6: I f Knocklayd . . . 90 33 48’4 6 ... – 5 ° 2 DUNRICII. Telescope above surface 7-7 feet. Ben Cleugh . H 9o 29 50' 3 6 I 2 | – 3 °4 Slieve Donard . . 9o 38 24.8 4. ... — 2' 6 Mordi * . . . .". WA Hart Fell . II go 28 18.7 || 6 | 1.4 — 3 o . H|924; 2.5 | | | | 3 || – 5.4 Trostam . . H | 90 33 Io'o 4. I 5 – 3 9 #. ºn º É. I8 46.8 5 | ... - 4.3 IBen More, Mull H | 9o 20 39°3 4 | I 7 | – 3 3 gº i. . . . 89 # 33.9 3 - 2 I " 2 Divis . . II | 9o 39 23 o' | 4 I 5 – 2 '8 i.e. . . . 90 º: 38.2 2. — Io' 9 South Berule H | 90 46 II 3 6 ... I — 2' 6 #. ºleugh . . . 9o I 45.8 4 — 6’ 3 Criffel . . H 90 37 9°o 6 I 5 || – 2 - 8 É. H 90 3o #: 4. * - º 6'5. Slieve Snaght . . 9o 38 45°o 5 ... - 3 ‘I ackheddon . . 9o 41 3 .5 2 * mºs 6: Ben Lawers. H 9o 17 27' 5 8 I o — 3 2 Wisp... . . . . . 9o 22 44°o 3 — I 3 '9 Cheviot . . . . 9o II 4'o 4. ... - 7° 3 Criſfel . . H 9o 25 29'8 8 I 3 || – 5' 3 LUMSDEN. Telescópe above surface 7 fect. O / ſſ f/ CHEVIOT. Telescope above surface 8.9 feet. Sayrs Law . . . 89 31 23' 4 || I2 ... I — I4'8 fºnd tº ; 3. .. 4. tº º º — 6' o O / f/ f/ Kellie Law . II | 9o 14 53°6 | 1.4 1. o – 7-2 || Lumsden. . . . 9o 53 16.2 II ... – II '7 Glashmeal . H | 9o 6 8°o 6 1.5 – 27 | Blackheddon . 91 39 27°6 21 ... - 25 °o Mount Battock II go Io 46' 5 6 1.7 – 2.8 | Sayrs Law . . . 9o 30 23-2 | 12 ... I — Io'6 Blackheddon . go Io 43°4 8 ...' | – 12.7 Sayrs Law . H 9o 39 25'5 2. 4°o – 5'9 Cheviot . , H | 89 28 35-6 || 25 || 2:o – 6-6 || Wisp . . . . . . 90 26 15°o 13 || ... – 9-9 Collier Law . H 9o 31 22 1 || 17 I 5 || – 5' 9 a-ºm- Sca Fell . . II 9o 25 49.8 11 o “5 — 4°o - - Cross Fell . H 9o 17 39-9 I2 I 5 || – 5' 2 BLACKHEDDON. Telescope above surface 5'8 feet. Cross Fell . . . 9o 17 15: 7 5 ... – 6'3 *: Easington . II 90 46 7°2 | 12 2 ‘8 — 3 °o Botton Head. H | qo 4o 41 ° o I ... } – 4. ‘I Cheviot . . . . 8á 3i 46 I8 - - - —16°3 Dunrich . . H ; § #: : o “8 || – #: Dunrich . . . . 89 54 52. I 5 ... — 4-6 | Dunrich '. . . 9o 19 2'o || 4 | ... – 8:4 Sayrs Law . . . 89 49 $8.1 22 ... — 7-1 || Wordeslow . II 9o 44; 46: 7 || 20 1. 3 || – 5'8 Lumsden . . . 9o 5 39.8 18 ... – 10-6 || Hart Fell . H | 9o 18 36-8 || 13 2- 5 – 5' I Mordington . . . 9o 5 54-6 6 ... – 17-6 || Hart Fell . . . 9o 18 5o'o 4 ... – 7'o Mordington . H 9o 5 39.7 7 || 1:2 —13. 9 || Mordington . H 91 5 52'2 | 18 || 3 | 7 || - 8'9 3 U. 522 PRINCIPAL TRLANGULATION. Stations observed. Object Mean Zenith No. lobserved Distance. . Obs. above Surface. Reduction. Stations observed. Mean Zenith Distance. No. Obs. Object observed above Surface. Reduction. BEN TARTEVIL. Telescope above surface 5' 5 feet. SouTH END OF BASE. Telescope above surface 5 'o feet. Slieve Snaght 93 3 33°o 4. ... I - 42 N. End of Base . -- - 3. § 24's 8 - - –24's Jura -. . . . . 89 II 48° 5 | 12 | ... . . -Io 2 | Slieve Snaght § 5I Q' 5 3 | . — II '7 Knocklayd r..m 89 59 24-9 9 ... – 5 °4 || Mount Sandy 90 5 26-8 8 ... - Ig 4. Ben More, Mull. 89 48 8-6 4. ... | - 4 2 | Cundtham 8o 23 2d * 3. Trostan 6. # P ... ..., | 89 23 29°o Io I & "O Ben Heynish º ; : ... ; ~ | – †: Do. Top of Staff 89 22 34°o 2 | 16.7 | +42. I t .. TRostAN. Telescope above surface 5 'o feet. DRUNG PoſNT. Telescope above surface 5' o feet. f JJ A. f O f J/ f/ Divis” . 96 1642 - 5 8 – 6. 4. Mount Sandy, Top Knocklayd 90 I2 53° 5 7 –21.5 of Staff. E. 90 2 28°3 6 || 14° 5 | +42' I T}en Tartevil: 90 3 I 4o ‘o 2 * — 4-3 || N. End of Bºse, Slieve Donard 90 II 35°o 3 T 3...? | S *::::"... 90 3 59° 7 6 || 14°o +44'2 Jura . . . o I3 35 °4. I = 2 * ...lºnd 9t, lºse, . . . . . . . . . . . . . . . . . . . Goat Fell . ; 7 #: I ºmº ; : Top of Staff . , 90 1 o'o 6 14° 5 || +39.' I Sawel . . . . . . 9o 7 3°5 2 – 5' I - - sº Knockºxyp. Telescope above surface 5.o feet. NonTII End of BASE. Telescope above surface 4.5 feet. Slieve Snaght . 93 : 36.8 || 3 | ... – #6 |*.*.*.*, * * 168 || 8 | ... —803 | Divis . . . . 9o 16 37' 5 || 8 - 5.9 || Top of Polo 89 56 21-0 || 4 || 14-5 | +49. Sawel 90 5 24' 6 8 ... – 5 'o p 9 ſº +49.5 Trostan . . . . . 89 54 24'8 || 13 || ... —21 9 Cundtham 88 57 13-7 6 ... 23 ° 9 SLIEVE SNAGHT. Telescope above surface 5 'o feet. Stoke Hill. Telescope above surface iſ 5 feet. Sawel . . . 96 5 36:1. s – 6'8 wingreen . º 96. # 34.4 24 ... - 23.6 Šlieve League . . . 9o 24, 45°o I – 2 9 || Westbury Down | 89 58 47.7 3o ... . . . [- 125 3 Cuilcagh. 90 24 39°o I - 2 7 || Westbury Down | 89 57 53'2 13 || 14 o |+ 27.2 . . . . . . - Milk Hill . H | 89 51 49.2 23 I 5 – 33° 5 ** * * * * - - - - - º - - -- - *** * #. Hill . H 9o 3 48° 5 25 . . I 5 - I4° 7 : MoUNT SANDY. Telescope above surface 5 'o foct. º # ; º *::: - : ; : – #: - ! o odge . H | 9o I3 I5' I 4 | I 5 – 19°2 Slieve Snaght . 88 46 12.0 4. ... • —12°3 Qld Lodge . . . . . 9o 12° 15' 3 6 || 27-3 |+ 3o" 2 Cundtham . . . . 89 2 o' 7 || 6 || 16. 7 || +59' 6 Old Sarum Cas. H | 9o 19 7.5 11 2-8 – 20° 3 . End of B ~~~ ºr if ſº - i. Four Mile Stone 9o I5 49' o 26 . . ... – 32 S. End of Base . 90 1 22.2 5 14° 5 || 4-36-8 9 9 - 32°4. Drung Point . 9o 3 32° 5 3 | . . . –22 I N. End of Base . . 9o 13 24'o 4 . . . –89'2 Do. Top of Staff 90 12 15' 3 6 5' 3 | + 5°2 --- - - Upcot Down. Telescope above surface Io. 9 feet. CUNDTHAM. Telescope above surface 5 'o feet. | Milk Hill. . . 85 54 28°3 21 || 25'4 +7% -: * ~ * - * | Stoke.Hill . 90 I2 46'7 14 ... —23 6 * * } O M MA ...T. Westbury Down 90 12 11. I4 | ... I —26. Mount Sandy . 91 I 30°o 4 I4°5 +48° 5 || Mendip y ... H #: I2 ; ; 3'o -ºš : N. End of Base . 91 7 Io'o 4 I4°o +47:8 | White Horse Hill 9o 6 34-3 || 29 || ... —34-6 S. End of Base . 91 43 47°o 3 || I4°5 | + 34-2 || Inkpen 90 3 34° 2 I2 —24'8 * ** -º- ºr--" rº- * “rº- º ºs. wº .* * *r *...* + rºs. " < * *** * = ** * r. • * * * * * *** - OBSERVED ZENITH DISTANCES. 523, Mean Zenith Object ... Object Stations observed. #. §: º Reduction. Stations observed. Mºh §: º Reduction. * Surface. Surface. MILR HILL. Tele 1. ſº GoRLESTON ſ Telescope above surface 91 3 feet. MILI * till relescope above surface 21 7 feet. TOWER. 93 battlement . 3' 6 feet. wingſeon . . H 93 12 iſ 3 3 || Io'8 –4. 5 | Norwich Sp. Top 86 sé 36. 8 •- Jº" ..., T.I:ll . Top | 89 59 30 307 °o tº Stoke Hill 90 18 17.3 4. . . ... -72 5 tº; 9 30 '9 Westbury Down . 90 15 13:5 4 || 14’o -20'3 || Tower . ,” 9o 5, 19°o 13 |111 3 |+ 41.4 Mendip . H | 9o II 59°o 9 3°o |-22°8 | Southwold Tower Upcot Down . 90 Io 59' 6 7 5*4 –86°4 || Pole . Top 9o 5 31 °o | I 118°o |-|- 59'9 Inkpen ... . . . . 9o 6 38' I 4. ... -5° 4 || Toft's Tower , 9o o 35°o 6 || 57°o |–16o'7 Beacon Hill . . H. 9o 19 37' 2 7 || 2 : o -53.2 -> # Dean Hill . H | 9o 21 27°6 6 I 5 – 31 °o º: Stone. [I 9o 23 3.3 9 I 5 —44 ° 3 Tol b f ld Lodge . H. 9o 2 I 32° 4 || 4 | 7 || -35 “I | . 3. elescope above surface 72°o feet. Öidsarumcastle.H 90 26 36 ‘o 5 2 - 5 || – 38' I TOFT's Tower.{ 33 to Wor I5 o feet. White Horse Hill 9o II 26' 5 2. ... -45 ° 9 º * Happisburgh O ºf f/ JJ Tower Top 9o 8 15' 5 9 |11 I-6 | +68-2 Four MILE Stone. Telescope above surface 6.4 feet. |Norwich SP. " | 89 5% +7 4 || 3 ||387.9 , : -- Gorleston Tr. , 9o 6 39°o Io 87° 7 | +73'5 O Southwold Tr. , 9o 6 41 ° 9 || I5 95°o +70° 4 Wingreen . H| 854; 14.3 2 1.3 — tºo Lºftºld Ch. * . . º Westbury Down. H | 89 55 44' 5 2 2 5 || – 9'6 nºr. • 35 ; : #: ; ;: #3 Westbury. Down. |89 55 29'5 I 14. o. + 18:8 Do. . 'H | 33 2 * 8 || 8o'o -- 16: Stoke Hill . . H | 89 54 25' 3 3 6°o — I I * . 90 3 4.2 ° 9 + Ib 7 Dean Hill . H | 90 4 29'6 4. 1 : 5 — 17.8 s NortWICII Seine. { Telescope above surface .. 305°o feet. OLD SARUM GUN. Telescope above surface 37' 5 feet. Vane above telescope zºo feet. - * C) * fº & A s C} 6 #. 6 -- ºn “ Beacon Hill . II | 89 25 53' 7 || 6 || 1 'o Hingham Tr., Top 9o .5 87.7 Old Lodge 89 33 51 ‘8 2 27° 3 #: ,, . 9o I 3 59 °o 4 77 Tower . , 9o 6 45°o 4 59' 5 Happisburgh T • 3 O I2 O * 2 |III " OLD SARUM CASTLE. Telescope above surface 37-8 feet. Lºch. , 9 4. 3 *- - Tower . , 9o IO I 5' 4 I 93-8 .. tº 9 . . .” - - - u || Toft's Tower 90 I2 45°4 2 57 "o Stoke Hill 89 54 *1 4 25 "I – 29° 9 r 32 † g Milk Hill 89 49 45'9 3 ... – 75 ' I Bunwell Tr. , ; 9o 7 49°4 7 75 'o Beacon Hill 89 41 56°o 2 6:3 –171 ‘o - —º §º 89 49 39°3 || 2 | 27'3 – 55' 7 * * r * Qān Hill 89 56 29' 3 2 ... [-186°6 | Baconsthompe ſº above surface 65 'o' feet. ToweR. 35 battlement 5' 5 feet. Hºan {Tº above surface . 116-6 feet. Happisburgh O / WW oweſt. 33 parapet . 5°3 feet. Tower Top 9o 12 Io. 5 || 8 |III 3 |+1 12"4: Norwich Sp. , 9o 64o'o 5 |307'o . . #6 * .. © f" ºf f Hingham Tr. o 8° 45' 5 g is º " — II.2 *** i., Tºp|93 & #3 || 7 |;oro || 4 |Šºš, ; ; ; § || 3 |ºsſº. T pe. . . | - is ſº Docking Tr. ,, . 9o 7 25°8 3 || "... " - frºz'8: 9Wºr , , , | 89 59 58' 5 || 4 || 59' 5 tº ſº tº • . . . . !. Gorleston Tr. * *|-96 8 47-3 || -4 $7.7 |... ... - — Tofts Tower , 9o 9 3.5 3 57°o. . . ... - - - - - * Heliostăţ Top.” ". . cº-- 3 U 2 524 PRINCIPAL TRIANGULATION. Zenith N 9. tº Object Stations observed. Mº. à. º: Reduction. Stations observed. * §: º IReduction. Surface. Surface. IDOCRING TOWER. HINGHAM Tower. | Walpole, St.Peter's C} f ºf A M 3 : ". Af Tower Top 9o I5 53° 2 5 i 81 o º § Top . 7 3.9 3 || 75.9 IBoston Tower 2, 9o II 59' 5 6 £º » 9o 4 34' 5 5 307 °o Baconsthorpe º i. º, Tower . • 35 90 9 5 °3 6 59' 5 sºn's 33 ; 7 :::: % 3.3 tº Lynn Tower . , 9o 16 56' 9 7 88.2 | South Lopham 32 30-7 54. - | Tower . . , | 9o 8 59' 6 5 69.8 SouTIIwold { Telescope above surface 123° 3 feet. Brandon . 90 II 26.6 4 36°o ToweR. 35 tower 28' 3 feet. Q & A M f f BRANDON. Telescope above surface 39° 2 feet. Orford Cas.() Top | 9o 7 58.8 || 9 | 84-7 |- 86.9 elescop 39 Laxfield Tr. 90 o 49°4 || Io 93 °8 – 86' 3 tº O f f/ f/ Toft's Tower º 90 4 58 ‘9 Io 57°o |–203 °o Ely Minster Top 9o 2 56°o 16 204' 6 tº Gorleston Tr. , go 8 4-5 | 10 | 87.7 – 75.9 |Hingham Tr. ºn 99 3 24. 9 ... – 78' 9 | Swaffham Spire (') 90 o 54-5 9 |IO4°o |+ I49°o Tol l fac - f Tharfield . . H 9o 8 29-8 II | Io'o |— 29' 5 ... [Telescope above surface ... 94.5 feet. Bunwell Tower". go 6 8-o 8 || 78.8 |+ 69.6 On Ford CASTLE: 33 coping of tr. 9:8 feet. S.Lopham Tr. Top go 4 17.2 8 : 69.8 + 75°2 O / fº Af Lawshall |. , 89 58 48' 7 || II || 75°2 |+ 78 7 Walton Tr. Top 90 6 2.5 | 3 || 91.5 – 6.2 |Lawshall Tr. 89 58 59° 5 || 5 || 75' 7 |+ 79-7 Otley Tower , | 89 59 Io'o 8 || 72°8 —61 - 9 Laxfield Tr. , O I IO "2 I 2 93 ‘8 || – I 7 t Southwold Tr. , | 9o 6 23°o 6 | 95°o + 1 'o STORE TOWER { Telescope above surface 125° 3 feet. 3) roof . I9' 3 feet. LAxFIELD ſ Telescope above surface Io?' I feet. Q iſ fif wº w * Walton Tr. To O II ALO " I I 5 ||— 60-2 T ſº y bat t feet. p 9 40° 5 I3 91 ° 5 9 OWER { 3. attlements I 3 '3 fee º T. ,, . 89 # 51 6 || 13 || 75°2 Iº. - O / / / f/ G OWCT tº O 2O * IO 2 * O | – I IO " | Otley Tower” 90 4 36' 5 9 72°8 |— Io9'2 iº Sp. Top ; 3 ; 9 ſº * % Mickfield Ch. Naughton Tr. , 9o I I4'8 9 || 45 °o tº Tower” 90 4 27:2 12 || 58°7 |–157'3 South Lopham 60 8 86 - Tower . Top 9o 7 I 3 '4 9 9 8 – 8b ‘o Telescope above surface . 97° 3 feet. Bunweli Tower, go # 38.3 16 75.0 – 76.0 | WAITON Towei: { 35 battlement 5'8 ſect. Toft's Tower”. 90 Io Io. 5 | 16 62 5 – 106-7 Norwich Sp. Top 9o 6 18-6 | 12 .307 o ſº ſº is C fi jà Southwold Tr. , 9o I I I I 19 95° O – 35.3 §.". Top . 5 .# § #: †: Orford Castl * 5 | 84. 7 ||— 54." { 2 IO " tº tº : * astle , 90 I I I 3, 2 I5 4 7 54 7 §º º, 90 3 *:: % #. I}. - VGT LO tº * X | are A, X, * BUNWELL {Tºwn above surface 94 7 feet. St. %. Tr. º ; # 3. 3 #: -: ToweR. 33 battlements 19° 7 feet. Orford Cas. Tr. , 9o 8 23:2 9 | 84-7 | —25'8 O J & J ..T. Orford Obsy. , 90 7 51:8 || 4 || 97.5 | + o-6 Norwich Sp. Top 9o 2 4-7 || 13 |307'o tº ſº ſº - Hingham Tr. , 90 1 29°8 Io tº ſº tº tº ſº. y Laxfield Tr.” 90 7 28°6 | 12 94' 3 – 1 'o ST. PETER'S { Telescope above surface . 86.6 feet. Toft’s Tower* go Io 26°5 7 | 85 °o |— 20 I TOWER. 33 battlement 9-3 feet. Baconsthorpe” . . 9o 8 37° 3 9 || 6o 5 – 48.7 * f f Swaffham SP. Top | 90 4 29°3 to 154-8 |+169°4 Paddlesworth. . 8; 56 2.3% o Io –1594 South Lopham Frittenfield ._H 90 o 28°3 || 5 | ... — 122 5 Tower . . . . . 9o 6 58°7 | 12 69.8 – 112.2 walton Tr. Top 9o I4 2 I '9 9 || 91 ° 5 |+ 5.5 Brandon . . H | 9o Io 38°5 | Io 36: o –102-9 Danbury Sp.” . . . 9o 14 13.3 5 ... - 77° 3 Mickfield Tr.” 99 75.4 || 6 || 57.4 - 75.5 | Norwood . . H go $ 56.3 2 – 132° 5 Do. . Top 9o 7 50'4 || 5 || 57°o – 76.3 () Flag. * Heliostat Top. () Top of Tower. * Heliostat Top. OBSERVED ZENITH DISTANCES. 525 i. y Object tº Object Stations observed. Mºh §: º: Reduction. Stations observed. Mºh §:s. º Reduction. Surface. F Surface. FRITTENFIELD. Telescope above surface 37' 5 feet. DANDURY SPIRE-continued. Fairlight Down. H 96 1: 33.2 II 2 °4. –55°8 Lawshall Tower”. 93 12 23.4 4 |IoI ‘4 – 23.4 Beachy Head. H | 9o 17 15:4 12 o° 5 —35' 3 || Naughton Tr.” 90 I4 5o 'o 4 || 45°o – Ioo' I Crowborough. II 9o 8 55' 0 || 11 2 : 3 —43' 8 || Stoke Tower Top 9o 13 52' 6 17 |III 3 – 22 7 Leith Hill Tower 9o 15 2.5 9 || 45 ‘8 + 6' 2 || Walton Tower” . . 9o 18 45° 5 || 12 92 5 – 39°o Leith Hill Tr. H go 15 50.4 9 o' 9 —27-3 || St. Peter's Tr. Top | 9o 20 I 6 || II 77° 3 – 42 3 Wrotham . . . H 9o 5 45’7 15 || 23 5 —21.8 | Norwood . . H | 9o 14 43' o 17 28' 5 – 158-6 Danbury Spire 90 16 35' 5 7 119.9 +86-8 Frittenfield . H | 9o Io 27°o II 32 o – 97° 7 Norwood . . . . 9o 2 I 4o'o 6 29° 5 —21 7 - Walton Tower II 90 24 59-6 || Io 91 5 +42' 6 St. Peter's Tr. Top go 20 31 °o II | 77°3 +56°4 || SevenNDRoog {* above surface . 68.9 feet. Paddlesworth , go 6 7' 5 I5 32 °3 - I4'o TOWER 53 top of battlement 6' o feet. o a Jº Leith Hill . H | 8o 58 37 ° 4 II * O | – O2 * IPADDLEswortTII. Telescope above surface 37' 5 feet. Leith Hill Tr. Top ; ; §: I I #3 |- ...; Q f { Banstead . . H 90 § #3 | 4 || 24°3 I: Fairlight Down. H | 9o 12 19:2 13 2 * 4. –491 St. Ann's...; H 90 16 26-7 7 I 4 – Io2 Crowborough H 90 13 40°4 12 2 3 | – 31 ° 9 Hanger Hill Tr. R 99 15 33.5 15 38:8 – 73°5 Frittenfield. Top St. Paul's Cath. () 9o 7 23-4 : 6 352-8 2. of Stage 90 5 13° 5 9 39.8 + 6'2 Berkhampstead. H | 9o 8 26' 5 II 104°o + 63.5 Walton Tower" . . 9o 23 43’5 Io 91.5 +42 3 ; la º 90 I3 § II sº —219 'o St. 's Tr. T ſº ºn ſº ſº. * ºppingUupola. Top 9o 7 48' 8 Io 9° 3 – 22 5 St. Peter's Tr. Top 9o 20 45° 2 | 12 77.3 +73. 3 Gºsiń' I 90 12 56° 5 II I 3 -148.4 Wrotham . 89 5o 6'o 19 33°6 – 97.2 } Norwood. Telescope above surface 31 feet. © J J A * {{ Wrotham . . II | 89 56 13 3 4 I5 °4 – 24 7 Gad's Hill () . . . 9o 4 6-9 I ... — 75-8 Danbury Sp. Top 9o 3 46°4 II 119°9 |+ 146' 5 Walton Tower" . . 9o 16 13 ‘8 || 14 92 “o |+ 64-8 St. Peter's Tr. Top 9o II 13° 3 9 77° 3 + 70 ° 9 Prittenfield . H. 89 49 16’ o Io 4' 5 — 71 ‘8 TILAXTED SPIRE { Telescope above surface 178° 3 feet. GAD’s HILL. Telescope above surface 5-8 feet. *m-. O f & J. &# Severndroog (*) 90 o 22 °4 18 62 9 |+ 125°2 Epping Cupola. H | 9o 5 47 9 || 12 6o. 3 + 85-6 Danbury Sp. Top go 2 2-8 14 119°9 |+208-o Norwood . . [I 90 7 sys I9 4-8 – 2 7 33 spire . 4° 3 feet. Q W */ J/ Epping Cupola H. 9o Io 37°2 II | 6o 7 Berkhampstead. H 9o Io 46°o 2 I 96-9 Tharfield. Top of Pole . . . . 9o 3 39°o II | 3o ‘o Balsham. Top of Observatory 90 7 o' 2 | 17 | 77°o Stoke Tower . II | 9o 12 53°o 8 |142.8 Danbury Sp. Top 9o 8 29° 2 16 |II9'9 Lawshall Tr. , 9o II 9° 5 18 75' 2 ſº above surface 73' 5 feet. BALSIIAM TowPR 33 tower 5° 5 feet. * ; * * * * * * * * Telescope above surface . 124-8 feet. O # // Af DANDURY SPIRE #." 35 #: feet. Tharfield . . . . . . 90 34.9 || 4 || 30°o Cambridge Obs. (*): 90 24 22-6 II 1.6 $ _ * r * r * O / / / ,, . Ely Minster Top 9o I3 42 “o I4 204' Ş. () tº 90 12 5’ o 2. ... – 227' 5 ś. ,, . 9o 16 22 °2 8 |104 °o S . `... r. 90 3 55 ° 5 9 42 °o – Io9' 6 || Swaffham Sp. , 9o 15 12 5 4. Iş4-8 i.º.º. 90 IQ 9-8 Io 67°9 – 79° 1 || Lawshall Tr. H | 9o 7 29° 5 || Io Ios '9 ... #. sºlº, 99 8 47 9 14 | 66.5 |–117-3 || Thaxted Sp. Top go 3 8-5 9 [I74 o || “. **P. ºop 90 7 24-2 || 15 174-0 + 106-3 || Keysoe Sp. . , go 13 46.5 5 | . . . . tº º º * Heliostat Top. (*) Top of Obelisk. * Heliostat Top. () Top of Cross. (*) Top of Tower. (*) Top of Dome. -- 526 PRINCIPAL TRLANGULATION. ſean Zenith N Object ſº Object Stations observed. M #. ‘ā. º Reduction. Stations observed. Mºh à. º Reduction. -, *, *, * * * * * * i Surface. - - - - w Surface. 4. sm ſ Telescope above surface . 219. 3 feet. LEITII HILL ToweR-continued. ELY Misstem ( - 33 battlement 14. '7 feet. IT o , u - w *m- Q iſ ſy JJ Epping Poor Ho. H | 96 24 45-5 9 60° 7 + Io' 3 ICeysoe Spire Top 9o 9 5-2 || 15 * … ºr Wrotham . . . [I 9o 16 4-8 || 10 15.4 —44-3 Tharfield . . H | 90 4 3o'8 I5 2 * 5 Crowborough. 90 I4. 45 ° 5 9 tº º & –79° 4 Lynn Old Tr, Top | 90 13 18:9 || 11 88.2 Beachy Head . 90 22 26-7 7 : ... —47' 6 Swaffham Spire . . 9o 7 19:9 | 12 104°o Bitºlling 'ix 90 I3 44 ° 9 9 || Io'o —69' 5 Brandon . . . . . 9o 9 44°o 21 º, º is St. Paul's (), . . . . 90 24 35' 5 8 |352.8 tº º ſº Cambridge Obs. () go 12 io. 7 7 + tº Hanger Hill Tr. H 9o 29 58 4 6 || 4o'.5 | – 14' 5 Balsham Ch. Tr. Top 90 1 5' 1 | 16 | 68' o - flºws: 90 II 42 - 3 || 23 86.8 CHINGFord. Telescope above surface 6' 3 feet. Bºters . To o 13 24-8 II | 81 o o ſ ſº - f/ p s 3 St. Paul's () . . . 89 55 26-8 6 |352.8 tº º º Leith Hill. . H | 90 1 20-8 3 || 4 - I - 2 °4. FPPING CUPola. Telescope above surface 63 °o feet. Berkhampstead . 89 53 53 - 5 4 97°o |-|-359' I Wrotham . . H | 89 56 36-4 % 34°4 + É O J. ". º 4. º tº 8 2 * O 6 • I + 184' Severndroog . H 9o 4 59° 2 8 : 62 9 ||— or 2 Severndroog 9 55 43.9 | 3. Leith HillTower.H | 9o 7 22 I | 13 ... – 58' 2 Banstead . . H | 9o 2 2-2 2 I 9 – 7 I St. Paul's . . 90 6 4.3 % #. . . . º. º. - Bººl ; : ;: 6 *::: t’É. BROADWAY ToweR. Telescope above surface 56' I feet. Dunstable . . II | 9o 3 32 °3 5 tº º tº dº ſº. , , J # Danbury Spire 90 4 54°2 13 128' 5 + 131 - 9 || Cradle. . H. 90 2 11-8 27 o' 3 —39' 6 Gad's Hill (*). 90 Io 45°o 2 ... – 99 o |Malvern tº º 89 58 56-6 || 15 5'8 —887 Wrotham . . . . . 9o I o' 7 II || 42: o – 29-6 || Malvern_... . H | 89'59 4' 3 || 33 I 5 —96.3 Wrotham . . . H 90 1 22 °o || 4 || 24-9 – 53.7 Arbury Hill ..., H 9o 18 42-3 || 20 4'o —67. 9 Thaxted Spire . 90 5 15:4 || 17 |174-6 |+220-7 | WhiteHorse Hill.H 9o 16 52° 5 24 I ‘7 —64-3 Tharfield . . H | 90 5 14' 3 5 ... — 108.6 || Bardon Hill . H 90 21 46*6 23 o'o —4I '8 Tharfield . . 90 3 5 I 6 9 3o'o - 56' 9 * * * - - - MALVERN. Telescope above surface 5' 5 feet. THARFIELD. Telescope above surface 37' 5 feet. n O / // , Cradle. . . | 85 43 479 8 ... – 6.1 Reysoe Spire . . . 9o 14 43' 8 II ... ' |- 63 I Arbury . . H | 90 26 8-o 8 5°o – o '4 Berkhampstead. H 9o II 25-6 || Io IoI. 3 + 135°2 | Broadway Tr. Top 9o 17 6' 3 || 4 || 44' 9 +69' 5 Dunstable . . H 9o 3 7° 3 I5 ... — 61' 3 || Broadway Tower. 90 18 59' o 7 ... – 9 7 Ely Minster . 90 17 36' 2 | 13 204' 6 +223 3 | White Horse Hill.H | 9o 25 14-1 7 – 4° 3 Brandon . . H. 9o 20 59' I 6 36: o – I 5 || Long Mount Pole. 9o 8 32.7 8 — 5' 7 Balsham Tower . . 9o II 50-3 8 | 68°o |-|- 69'9 - Thaxted Spire 90 Io 6’ 3 5 |I74°o |-|- 320' I - - Epping Cupola . . . 9o 12 48.8 5 59' 3 + 37' 6 CRADLE. Telescope above surface 5' 5 feet. Hanslope Spire 90 I3 I9'8 4. ... — 42 6 A f/ f/ - B.º. 963; 58°4 6 . . ; – 3 '7 - º Paracombe . H | 90 33 59' 2 6 . – 3' 5 *...*{**.*::::: ; ; ; ; ; ; ; ; ... = 3; - * * 33 3 & foet. Mendip . H 9o 4o 9'8 2 — 3' 8 O J WA , T Plynlimmon . 90 19 Io' 3 9 — 4° 7 Butser. . H | 9o I3 41 °4 Io 2-9 || –61 o | Cader Idris 90 I9 23' 4 6 – 3' 5 Inkpen . . ... II | 9o 18 30°5 13 4-3 || –36. I Snowdon . . . . . . 9o 24, 19° 3 4. — 2 5 White Horsehill.H | 9o 23 I ‘5 11 24-6 –16-6 Long Mount Pole. go 30 9.8 6 — 5' I Dunstable . . H | 9o 20 41' 3 9 ... —4o 2 || Malvern . . 9o 36 I3°o 5 – 6: I Berkhampstead II | 90 24 6°o 11 |IoI 5 +48.9 | Broadway Tower. 9o 39 35-4 4. – 3 9 Soverndroog . II | 90 23 12-6 || 13 62.9 + 19. I White Horsehill.H | 9o 42 42.9 8 — 3 ‘o Frittenfield . H | 9o 23 38°3 8 || 41 7 || – 5'8 Arrenig . . 90 24 44' 4 || - 2 ... – 3 ‘o () Top of Dome. (*) Top of Obelisk. () Top of Cross. OBSERVED ZENITH DISTANCES. 527 Zenith Object tº N Ş. Stations observed. Mr. §: º Reduction. Stations observed. - Mºh ô.s. O . Reduction. Surface. i Surface. PRECELLY. Telescope above surface 5' 5 feet. BANSTEAD. Telescope above surface 37' 8 feet. Snowdon . 93 15 5*8 7 – 246 Leith Hill EI 83 J. *6 ' [O - A." 2 —lic" Cader Idris. 90 II H.3 8 º 3 * 4. º: . H ; t; : 6 #: T}} ºlºmºn H 90 II 55" 4 7 T 3.9 || King's Arbour H go 27 i. 5 7 || 23°4 —36'9 Cradle. º 90 18 Io'4 5 T 3...? | Hampton Poor- DunkeryBeacon.H 90 27 47° 3 5 — 2 9 house . . 90 37 35° 5 Io 3o'o -30°3 | Paracombe . H | 9o 26 14.5 2. T 3.1 || HangerHillTr.Top go 22 o'o 7 || 31 ‘8 — 15' 7 Paracombe . . . . . 9o 26 22-9 2 T 3...? | St. Paul's () . . go 13 27 o' I 362-8 º, º º High Wilhays H 9o 31 38.8 6. tºº 3.3 Chingford . . . H 9o 17 23° 5 IO 1 ° 2 — 59'8 Lundy Island. H 9o 35 9:8 5 T 4.2 | Epping Cupola H go 15 5-3 || 8 || 6o 3 | +28-9 Tara . H 9o 36 53°o || 4 ~ *.7 | SeverndroogCastle go 11 36°o 7 62 9 +62 - 5 Rippure . H 9o 35 I2 3 2. T *.2 || Berkhampstead H | 9o II 39°o 2 I IO " 2 tº it ſº Forth . . . 90 37 37' I 3 — 2 7 ... * * * * * * * sº Mount Leinster 90 29 30 9 I - 2 ° 2 -- HANGER HILL ToweR. Telescope above surface 41 - 8 feet. LUNDY ISLAND. Telescope above surface 5' 5 feet. O & MA - - º, Leith Hill Tower. 89 48 19-7 || 12 45'8 |+ 6' 5 Hensbarrow : H | 9o 13 31 7 || 1 | 3°8 — I 3 || Hampton Poor- Trevose Head H 9o 20 21 “4 II 2 “o — 3 o house . . H 9o 16 23°o 3 || 35°o — 36' 2 Precelly H | 9o 4 I5'o 21 I 3 | – 3 1 || St. Ann's . . H 9o 6 31 °o II I 2 – 12 I 5 Paracombe H | 89 52 44' 3 8 I ‘o — 5’ o King's Arbour H 90 13 54'8 2 35 ° 5 - 34’ o Paracombe . 89 52 42° 3 || 3 ... – 6' I | St. Paul's (*). . . . 89 59 3’5 5 352 '8 tº ſº tº High Wilhays H | 89 53 20' 6 19 —7'o –11: 1 || Severndroog Tr. H | 89 56 39°5 12 69° 7 |+ 68°2 Brown Willy. H 90 o 3' 3 || 8 || 12: o + 6'4 Wrotham . . H | 89 58 3-4 7 34°4 – 9 9 Brown Willy . . . 9o o 14° 9 || 3 . - 5' 4 || Banstead . . 89 5o 52 “o 8 ... —I Io' 9 PARACOMBE. Telescope above surface 5' 5 feet. Winte Horse HILL Telescope above surface 37' 5 feet. High Wilhays . . 9o 3 51 I II ... I — 6' 2 § - d ...". - . ." #º §". H 3. 2: 3.5 || 7 || 13: o + 5.7 ||Yenip . . . 93 ° 3.3 || 3 || 43.7 tº: * * jº Cradle. . H 9o Io 28 - I IO I "O I9' 9 Brown Willy . 90 20 56' 9 4. ... - 4.' I 6. •= ? ſy." - * ... . . Malvern . . . . 9o II 29 9 7 tº ſº. 29' 7 Lundy Island. . . . 9o 33 5’ 6 7 ... I — 6' I f 8 . * 8 8 --- º. † ... Broadway Tower. 9o 8 18°o II 44'2 | f | 8 | Precelly . H 90 2 1 56-4 Io I o — 2 7 Hill . H | qo i8 46 o 9 80 ‘8 +35.7 Cradle. . H 9o II 32 6 12 || 1 | 3 || – 2 7 ãº. II ; I9 *::: II ... } -30°2 Dunkery Beacon . 89 57 32° 2 | 16 —so Icith Hill. . H' 90 20 46' 9 14 I 6 —23 9 *=– - - - - Inkpen 90 2. 39'5 I5 . -91° 4 WROTIIAM. Telescope above surface 37' 5 feet. - * O / dt * * * * * ve surface 37' 5 feet. Crowborough. H 96 7 19: I II 2' 3 —72 6 DUNSTABLE. Telescope above su 37' 5 feet Ditchling . . H 9o II 2 9 || Io 41 ° 4 || -- 4:6 O J &M A f Leith Hill Tr. H go 6 48.1 zo 45.8 || 4-16-7 || Hanslope Sp. Top 9o 15 55’7 5 ... —69°o Epping Cupola . go 18 AI-1 || 9 | 66.5 4-40-9 |Leith Hill Tr: , 9o 15 23:9 || 3 || 45'8 + 6.7 Hanger Hill Tr. H go 23 3o-o 16 | 40-3 || 4-'4-6 |Leith Hill. Surf. 90 15 57.6 8 ... -39'5 Fairlight . . H go 17 o' 5 14 2.4 -46-7 || Arbury Hill . H | 90 15 38'4 8 ... – 38' 5 Berkhampstead II 90 I9 40° 5 1i 101.5 +71 - 1 || Tharfield . . . . 9o I4 59' I 7 30°o – 12:3 Panbury Spire Top go 18 5.3 4 || 19.9 |+ 106.2 | Tharfield . . . . . 90 15 42.9 3 —61 3 Frittenfield . H go 12 52-6 || 1 , || 41.7 | H. 6.5 |White Horse Hill.H. 9o 17 46' I 9 –3o 2 Dunstable. . H go 18 4o-o 2 29.8 – 5-6 || NasebyCh.Tr. Top 9o 1647.5 7 ... T-35.3 Sevºjnºg • H 9o 21 6.2 || 17 | 62.9 +66.9 | Epping Cupola 90 19 46' I 3 59' 3 +28: St. Paul's () . . . go I9 41 ° 7 Io 352 '8 * † : . Borkhampstead H 9o 1940'6 5 |IoI 5 +3. Soºyºº. H go 23 #5.8 9 || 39.5 –12.7 Wrotham : ...H | 9o 1953: 5 || 6 —23.3 Gad's Hill (*). 90 32 43 - 9 6 H. L. L. -** Reysoe Spire. Top 9o 21 20°2 9 —54 “I () Top of Cross. (*) Top of Obelisk. () Top of Observatory. (*) Top of Cross. 528 PRINCIPAL TRLANGULATION. Stations observed. Mean Zenith Distance. No. Obs. Object observed above Surface. IReduction. Stations observed. Mean Zenith Distance. No. Obs. Object observed above Surface. Reduction. INRPEN. Telescope above surface 20.4 feet. Dean Hill . . Beacon Hill . . Wingreen . H | Westbury Down . Upcot Down . Butser . H Dunnose . . H White Horse Hill Leith Hill . H Nodes Beacon 90 90 90 90 90 90 90 90 90 90 20 43°4. 18 37'o I5 4o'6 I6 3 - 5 9 47' 6 I4. I7' 5 22 I 9 11 15-6 I8 20 "o 24 43'8 38°o BARDON HILL. Telescope above surface 5' 5 feet. SouTII LoPHAMr Tower. Telescope above surface 89' 3 feet. Lawshall Tr. Top 96 2. 2. ‘ O 3 75°2 —27 ° 2 Lawshall Tr.” 90 2 6'o 8 || 75-7 || —26-2 Brandon . 90 7 18: 2 2 || 36 o º º Brandon . . . . 9o 7 2 I '8 3 || 33° 7 Brandon . . H. 9o 7 28°o 4 36°o Brandon . . . . 9o 8 46' 2 I º, tº º Swaffham Sp. Top 9o 3 27-7 4 |154'8 Hingham Ch. Tr., 9o I 4I 3 6 º º tº ſº tº | Bunwell Tower , 9o I 47 'o I3 75'2 | –63-4 Laxfield Tower , 9o 6 6' 9 3 93.8 + Io'6 Laxfield Tower”. 90 6 9' 3 6 94-3 || + II 5 Mickfield Tower *| 90 4 23°4 Io o'o —82 ° 9 Tilton . . . od 12 3%2 —io" Broadway Tower ; I8 37. : ºmº ; Malvern . . . . 9o 16 57-8 3 — 3' 6 Mowcopt . . FI 9o 14 11.9 3 — 4' 6 Axedge . . 9o 3 25 °3 3 — 4.8 13ack Tor . . . . 9o 6 32° 5 I — 4° 2 Lincoln Minst. Top 90 24 Io'o 6 ºr ſº º Arbury Hill . II 9o 16 35' 5 7 – 6: 3 Long Mount . II 9o 17 9'5 I – 3: 3 Buckminster Spire, Top 9o 18 I 3 3 — 8°o Naseby Tower , 9o 14 19 9 3 – 8:3 ST. MARTIN's HEAD. Telescope above surface 5' I feet. w O J * I Al Peninnis Windmill 90 4 28.2 18 || 25.8 * Telegraph Tower | 89 51 13° 2 17 || 41' 5 º º Beacon Hill, Tres- COW . • . . 9o 3 2 °o 7 tº . . . –59°o Karnminnis . H | 90 1 2-7 || 12 ... - 5' 5 I(arn Galver . II | 89 58 19° 1 22 2 * 5 – 3' I Pertinney . H | 89 57 58.8 17 2 5 || – 3' 5 Wolf Rock 90 II 48' 3 7 ... – 9 7 MICRFIELD ToweR. Teloscope above surface 84-7 feet. Naughton Tr. Top Lawshall Tr.” Lawshall Tr. Top S. Lopham Tr.” . Bunwell Tr. Top i Bunwell Tower” . Laxfield Tower () Otley Tower. Top . . O . 2. 2 I 9 I2 I2. IO I8 2O 27 45 ° 75' 75' 73. 75' 76. 93' 72. –1465 - 2 O "2 —2 I 3 –32 °4 — 19:6 — 17' 2 +29'8 —77° 3 IPENINNIS WINDMILL. Telescope above surface 31 8 feet. LONG MoUNT. Telescope above surface 5' 5 feet. Cradlo Plynlimmon . Cader Idris Snowdon . | Cyrn-y-Brain | Axedge . H Malvern . ſº Mowcopt . . H Dardon Hill . II Arronig º 90 90 89 90 90 90 90 90 90 90 1. 23's I 25 °4. 58 44-8 3 36' I Io 53°2 2 I 5 °4. 19 8-6 25 59'8 31 32 '6 o 29°8 I5 II 8 4. : f : St. Agnes' Light- house. Top Beacon Hill, Tres- COW . . . . Telegraph Tower ICarn Galver . II St. Martin's Head Day-mark . IPertinny . . II Wolf Rock 89 90 89 90 89 89 90 54 36' 5 o 44.' I 3I 20° 3 o 29° 3 53 32 ' I 59 56' 2 II I5' 7 I 2 I I I5 I 2. I5 ** OTLEY TOWER. Telescope above surface 88.6 feet. Stoke Tower. Top Naughton Tr. , Mickfield Tr. Laxfield Tr. Laxfield Tr.” . Orford Castle. Top Walton Tower , 33 '. 4 i ;3 i ; I3 I3 I 3 3 I3 23 22 III 3 45° 57' 93' 94.' 84' 9I i +497 +13.7 +18 °o — I I "O + 5'7 * Heliostat Top. () Top of Pinnacles. * Heliostat Top. OBSERVED ZENITH DISTANCES. 529 it! Object { } Object Stations observed. Mº. 1. §: º Reduction. I Stations observed. *...* à. º Reduction. ! Surface. Surface. TILTON. Telescope above surface 5' 5 feet. o a f/ WINGREEN. Telescope above surface 5' 5 feet. Naseby Tr. Top 9o 8 13.7 Io - I2 * O Bardon . . 9o I 57' I 4. – Io. 9 Ö ſ ſh Af Buckminster Spire 9o 17 44'o 2. ... – 16-6 ||Westbury Down ; 90 12 36.7 8 ... – I I 3 Easton Ch. Tr. Top | 90 23 35'2 I | 72-8 ... Inkpen I 9o 13 4-4 | 16 3 : 3 – 2 2 Keysoe Spire 3, 9o 20 28-3 || 8 || "... Inkpen ..... . . . . 9o 12 56-6 || 4 || o'o - 5’7 Arbury Hill () 90 12 6-3 2 27° 3 Beacon Hill . H | 9o 15 42 'o 5 I o – 8 ' I Dean Hill . H | 9o 20 33.8 7 2 5 – 5'8 - Pillesdon . . H 9o 12 19:7 8 31 °o -- 29°3 WALPOLE, ST. PETER's ToweR. Telescope above surface | Mendip. Top of 91 5 feet. Stage . . . . 9o 5 II* 7 || II 97° 5 |+ 144 ° 2 O fif T Mendip . . .; 9o $ 50.9 4. o “o – 8 6 Easton Tower.Top 9o 5 35'8 7 72-8 ." | Butser . H 9o 18 45' 6 15 ... - 4 * 4. Boston Tower , 9o I 44 °3 9 tº $ tº Bunnose . . FI 9o 19 33°7 12 I ‘3 – 3-5 Docking Tr. , | 89 59 18°7 I2 º Horton’s Gazebo, Lynn Old Tr. , 9o 2 22 °3 || 15 88" 2 º Top 90 37 58°o Io — 19:8 Swaffham Spire (') 89 58 34-7 9 |14I '8 Coringdon 90 16 12 3 18 — 8-6 Ely Minster. Top 9o 3 36°o 9 |204' 6 º º º Swyre Barrow 90 15 43 I 16 — 8-2 Nodes Beacon 90 20 28°4 6 — 6' 5 SwaffirAsſ SPIRE. Telescope above surface 135.8 feet. Lynn Old Tr. Top IHingham Tr. , Walpole St.Peter's Tower. Top Boston Tower , Baconsthorpe'I'r., Ely Minster. , Brandon . . II S.Lopham Tr. Top Bunwell Tr. , Lawshall Tr. , Lawshall Tr. * 96 90 90 90 90 90 90 90 90 90 90 1; 2% 7 52 16 33’ I5 43 * I I I I " I2 I5' I3 42 ° I2, I2 * II 30° II 38' 5 I2 4° 5 : 88 - 2 f f WESTBURY DOWN. Telescope above surface Io 3 feet. Dean Hill. Telescope above surface 38' 3 feet. -— Southampton . H Wingreen . . . WestburyDown H Stoke Hill. . H Milk Hill . . H Beacon Hill . H nkpen . . H Old Sarum Cas. H Four Mile Stone . Old Lodge . H Coringdon . H Swyre Barrow II Horton's Gazebo. Top Butser IHill . H Dunnose . II Nodes Beacon 96 J. J. f 25 Io" I 52 i i 4. i + 39. – 74." 52 ° 57° 54." – 130° — 59: — 18o' 4. O i 90 90 89 90 90 90 90 f . 5 i i IO IA." 15 60' o' 5 : OLD LODGE. Telescope above surface 22' 6 feet. –4 | Milk Hill . . . () Top of Observatory. * Heliostat Top. Upcot Down . H Upcot Down . Milk Hill. Stoko Hill * Inkpen . . II Beacon Hill . II Beacon Hill . . Dean IHill . . II IDean Hill. † Wingreen . . . Old Lodge . H Four Milo Stone . Mendip . H Mendip Dean Hill . . H Wingreen . . . Old Sarum Castle. Old Sarum Gun Four Mile Stone . Westbury Down . Westbury Down . Stoke Hill. . II Stoke Hill. Beacon Hill . . Milk Hill . . H Inkpen 93 89 90 90 90 90 90 90 9 O 6 1348 58 50' I 18 38.7 33 40 °3 8 27.2 3 28° 3 3 3 I 9 2 49° 2 2 46 o 5o 5' 5 53 46' 9 53 48' 2 51 15'8 :I 2 33' 5 6.5 14°o 3-o 3.8 + 59' 3 — 39' I — I 18.7 — 88: 9 — 96°4 – I4 °4. — 38°o I ºf — 4.3" —1876 — 38'9 — 46'7 — 51 ‘8 3 X 53o PRINCIPAL TRLANGULATION. zºn | No lº º Object Stations observed. Mº. à. O .." Reduction. Stations observed. Mºh §. º IReduction. Surface. Surface. DUNKERY BEAcon. Telescope above surface 5' 3 feet. IIENSBARRow. Telescope above surface 5' 5 feet. High Wilhays 93 § 21.7 9 , , , , - #. 5 Tr He; C} f { } * 4 Brown Willy. 90 25 32 '8 5 tº º ſº. – 3' 5 #. H : # $7.3 * © -ºš Paracombe . . . 9o II 59' 3 | II ..., | T *7.5 Brown Willy . . 89 53 I2 tº tº — I2 - 5 Precelly . H 90 26 58' 5 4. o' 8 || – * 4 || High Wilhays H | 8 3 $.3 9 º: • 8 - • 6 { } — 2 8 ºg unay - 9 59 28 3 9 I 5 – 3 Cradle . . . II 90 9 3 I I3 I 2 2 High Wilhay 8 º Mendi II 9o 26 53' 6 12 || 2 I 3 | + 13 '8 g ays, 9 59 20 °4. 8 ... – 5 2 i.n . . Hiſ 33 37 33. I8 I "C) — 3 * Maker Tower. Top 90 24 36.8 || 3 || 69.4|+88.7 º º 90 27 48' 3 9 3 3 | Barrow Hill . 90 25 9°o | Io 19° 5 || + Io. 7 É. . . H . : #. º ... I – IQ I º tº º 2 * 2 || - AL * MENDIP. Telescope above surface 37' 5 feet, Kºi. tº ; ; 3.3 IO º * §§ - f // – Pertinny . . H | 9o 19 55'8 6 2 °o – 3 3 Pillesdon . . II 9é I3 41 ‘8 Io 1 5 —45-4 | Pertinny . . . . . 9o 1952 '5 3 ... - 5 ° 2 Pillesdon . . . . 9o 13 51:8 2 * † & –47-3 || Karnminnis . II | 9o 17 I’9 15 2 “o – 4. ‘o High Wilhays II 9o 18 32 I 6 ... – 19.8 || St.Agnes'BeaconII. 9o 22 7.7 7 II ‘o + II '7 Dunkery . . . H 9o 6 9' 3 3 I 3 | – 31 ° 2 Dunkery . . . . . 9o 6 26' I 9 ... - 32° 3 Cradle'. . II 90 2 15-8 II I “o —25' 3 .TREvose HEAD. Telescope above surface 6-8 feet. Malvern . . H | 90 18 #.3 I4. I 5 —22 7 WhitcLHorse Hill.H. o 19 30 3 7 34' I – 2 7 O & #1 f/ Inkpen . . . II ; 17 18: 9 8 || 45' 5 + 6-6 Lundy Island H | 9o 13 49' 5 33 2' 6 — 3-6 Westbury Down . go 16 8: o II ... —83 °o Brown Willy, Top Beacon Hill . II | 9o 19 #3 I2. 2 ” O I: Hºw Top 89 28 34°5 20 | 13: o + 12 6 Wi º I I º I sº - ºf X " º ingreen 90 5 | 5 58 9 sº 89 30 48' I I3 II 7 || + 12.8 ...Agnes lieacon, RYDER's HILL. Telescope above surface 5'8 feet. Top of Pile 89 54 I4' 3 | 12 II “o + 8:8 ICarnminnis . H | 9o I I2 3 || 20 I 3 | – 6.6 Deadman . . H 96 35 5šo 6 5 °o || – 6.7 Kºº Top 90 3 I2 7 7 — 7' 2 Hensbarrow . II | 9o 26 13° 2 || 14 I 2 | – 4'4 Brown Willy. H | 90 18 30:6 ; I 3 || – 5’ 6 Brown Willy . 90 18 13 9 I3° 5 + 9°4 - tº gº - . Af-A fº High wº . 89 47 51 7 II | 19°o +38'2 DEADMAN. Telescope above surface 9 'o feet. Pillesdon . . . H | 9o 29 4-6 I5 I 3 | – 3 5 * f Barrow Hill . . . 90 46 13.6 12 19°1 | # 7.9 | Hensbarrow, Top O / / / f Darrow Hill . . . 9o 46 34.3 3 º: -12.8 |_ of Pile ... . . . 89 26 14-8 18 || 11 7 | + 9'4 Blackdown . H 9o 32 II ‘8 12 4 || - 2.9 |Brown Willy, Top Swyre Barrow H | 90 37 34°4 9 3° 5 || – I 2 of Pile . . . . . 89 45 38-6 || 14 | 13 o + 5'8 Goonhilly. . EI 9o 37 36'2 2C) -* *ºmºmº High Wilhays H 89 54 34 7 24. I 5 || – 6 - 2 Ryder's Hill . H | 89 57 20-6 22 1 - 3 – 6-8 Higir WILLIAys. Telescope above surface 7'o feet #iº 90 7 57'7 18 ... – 17 ‘o - – n f/ of Pile. ". . . 89 51 46-o 14 | 11-o | + 4:1 Paracombo . . 9o 2 I 38' 6 7 Io. 5 + 4*o | St. Agnes, Top of - Paracombe . II 9o 2 I 51 ‘7. 5 2 3 | – 5' 3 Pile . . . . 89 59 26:9 || 14 || 11 °o + 4 o Lundy Island. H 9o 39 46°4 15 o' 8 || – 5-4 Deadman . . # 90 4o ;: 4. 5 * 5 || – I'2 Hensbarrow . H | 9o 31 38' 3 I2 I 2 | – 5' 5 d * Tol t t; º Brown Willy . . . . 9o 26 7°o | II | 13 5 || + 9-5 ICARN GALVER. Telescope above surface 5' I feet. Precclly . H 9o 36 16-6 || 14 I 5 || – 2 3 O M MA Af Dunkery . . . 9o 19 32 °3 || Io 20°o + 13° 5 Pertinny . . 90 IS 29° 2 22 ‘8 +43 : 3 ...” . H 9o 36 38°o 12 || 2 I 2 | + 7.5 St. Agnes Light- 9 9 43 °3 Pillesdon . . . H | 90 33 35'6 17 I 4 || – 4' I house Top 90 25 34’ o | II – 5' 3 Ryders Hill . . . 9o 2 I 55".7 I4 II 5 + 13:2 Peninnis Wind- Biackdown . H | 9o 36 13°o 6 5' 6 — or 8 mill . . . Top 9o 25 42 6 | 12 || 25'8 +22° 7 Swyro Barrow H | 90 41. 41'9 8 2 5 || – 2 I | Telegraph Tr. , 90 24 27°o 12 41'5 | +49-9 * * * * * ; " OBSERVED ZENITH DISTANCES. 53 I Zenith Object | º Object Stations observed. *. §: - º Reduction. Stations observed. * §: º Reduction. Surface. Surface. RARN GALVER—continued. NASEBY ToweR. St. Martin's Head & #1 º Arbury Hill . 9& 4. 45° 5 6 tº º ºr .." Daymark ...Top 90 24 42-9 12 4o'o +42.5 Arbury Hill .. 90 3 55 ° 2 4 25 “I tº º Beacon Hill, Tres- Bardon Hill Obsy. 9o 3 55' 5 || 5 || 8° 5 | .. COW . Top 9o 25 48-9 Io ... - 5'6 | Tilton . . . . go 5 18:2 . Io ... tº tº º Trevose Head H 90 24 17 | 1.4 I 5 || - 3' 8 || Easton Tower Top go 18 15' I 6 | 72-8 tº e tº Rarnminnis . . . 9o 4 43-6 || 25 II ‘o +56-8 || Keysoe Spire. , go 18 14.8 4 tº º ſº. tº º º Hensbarrow . H | 9o II 26' 9 14 ... - 5’2 || Hanslope Spire, 9o 12 39' 3 5 e s - Karnbonellis . . . 9o 6 5o 8 21 II "o + 13 5 - - Goonhilly . . II 9o 21 57' 5 I5 I • – 6: 7 BOSTON TOWER. TELEGRAPII Tower. Telescope above surface 43' 6 feet. Peninnis Wind- f f mill . . . . Top 9o 31 40°3 15 25.8 St. Agnes Light- house . . Top 9o Io I 9 12 Beacon Hill, Tres- COW" . Top | 9o 14 22 5 12 St. Martin's Head Daymark Top 9o 3 41 ° 5 || 19 || 4o'o St. Martin’s Head Daymark . . . 9o 12 36' 5 3 tº a tº Karn Galver . H | 9o I 3 '9 22 I 5. Pertinny . . H | 89 59 53°7 14 I 5 Wolf Rock Top 90 13 34°4 15 & º º ! Faston Tower Top Buckminster . , Lincoln Minster, Docking Tower, Swaffham Spire, Lynn Old Tower, Walpole, Saint Peter's . Top 93 16 & 1 | 10 90 4, 57° 3 I2 go 6 9-8 21 90 8 27' 2 6 90 12 8' o 3 90 13 II '8 3 90 13 54°8 || 6 15.8 88 - 2 -8I 'o - * 72°8 ... EASTON Toweſt. Telescopo above surface 79°o feet. Telescope above surface 6' 3 feet. BEACON IIILL. Coringdon. . H 93 15 #2 I5 4 ° 2 || – 241 Swyre Barrow H go 15 42.7 9 || 23 5 +15° 6 Wingreen . . . . 9o o 52 2 15 ... – I I 3 Mendip . . H go 7 29' 3 || 15 17' 5 + 12:3 Westbury . . H go 4 15-5 14 || 2:5 – 7.7 Milk Hill, Top of Beacon . . . . 89 51 31 '8 6 ... } – 17°o Milk Hill . . H | 89 52 8-5 6 4° 5 || – 4'8 Inkpen . . H | 89 53 55.1 | 18 I 5 — II 5 Butser Hill ... II 96 9 3: o 19 I 5 – 5' 3 Dunnose . . II go 13 16.3 13 2 : 7 — 3 I Dean Hill. . . . go 13 22.5 11 ... -22 3 Stoke Hill . II go 3 36.3 6 2 °o — Io'4 sº Hill, Top of §acon . . . . . . 9o 2 35 'o 2 25' I +46 o Old Sarum Gun II sº 6 • - T * o: Sarum Gun, 90 43 2 °3 5 5 I 3 op of Beacon. q. * > º Sarum Old Castle, 90 4o 54." I I3 24’ 2 + IoI 2 Axis of Inst . . oo º * oºi...º.º.º. 9° 3.47° | 4 || 37.8 Beacon . . . . . 9o 13 23. 6 * Four-mile Stone II §§ # 6. *: 3. =2. - Four-mile Stone . . 9o 16 $5.5 3 tº º –33-3 Naseby Tower Top Tilton . tº º Buckminster Top Boston Tower , Walpole, Saint Peter’s . Top Ely Minster . , Keysoe Spire . , 93 14.9 89 49 3 7 89 54 53 '8 90 I3 I4' I 90 17 18:o 90 I5 51 ‘8 90 Io 4'4 : 81 o 204' 6 º w’ Telescope above surface 5 'o feet. CROWBOROUGII. C l Aſ ºf f/ Leith Hill. 90 4 35' 5 2 — 8' o Wrotham . 90 8 o' 5 2 — Io' 3 Fairlight . 90 I5 29°o I — 8' 2 BERRILAMPSTEAD GAZEBO. Telescope above surface 98.8 feet. * tº y O I f f f f Leith Hill Tower. 9o 7 26 o 6 tº º tº tº º º Dunstable. 89 53 2 I o I 44 °o gº º tº Chingford. 90 13 47' 5 2 tº ºr tº 9 * Wrotham . . 90 6 49' 5 4. * * * * * & St. Paul's (') . go 7 35-3 || 3 |352 '8 | -n Tharfield . . 90 I 23° 3 2 5o '5 º () Top of Cross. . 532 PRINCIPAL TRIANGULATION. Object * Zeni No. lobs d * Stations observcd. Mºh Obs. . Reduction. Surface. Stations observed. Mean Zenith Distance. Nn. Obs. Object observed above Surface. Reduction. NAUGHTON ToweR. Telescope above surface 64° 3 feet. $. O f * * * Af Broadway Tower 9o 3 47.4 2 44 ° 9 || +27' 5 Droadway Tower | 9o 4, 57. I 4. ... - 3 I ‘I | Malvern . . . . 9o 9 28' 5 6 — 19: I | Bardon Hill . H | 9o 9 35.9 7 ſº Naseby Tr. Top 9o 6 45°o I tº º º Hanslope Sp. , 90 13 48°o I —51 6 Dunstable . H | 9o 13 8.7 7 tº ſº E. tº Dunstable 90 13 16. I 3 ... -24 ° 5 PARROW HILI {Tº above centre stone 23' 6 feet. mºm- O f { / ºf 4 - 4 33 surface 2 I 5 feet. Stoke Tower Top | 90 ; 4I 4 || I5 *::::: Otley Tower . , 9o 4 I 9 7 2 * - * * , , ...". iº !. \!. Tower , 9o 12 57.8 8 #. 5 #.ºr; º . I I 42.7 º s: tº-º-º: 15.3 Walton Tower II | 9o 12 39' I 1o 92.3 "...º. r. (') 9o 9 12.5 5*4 |+ Io'7' 5 * tº iº Ryder's Hill . . . 89 29 32-9 20 | 11 : 5 – 18.5 LawshallTowerTop 89 59 33 9 19 || 75°2 Pillesdon II | qo I * I 2 it. 4. MickfieldTower, 9o 8 43-3 || 17 | 57°o º finckdown . H . # 33 I2. ::: – 14.3 Thaxted Spire ,, 9o 6 58.8 || 11 |174'o * fl0RCIOWI) . 9 3 5 I 3 ' I Danbury Spire ,, 9o 8 II : 5 3 |II9'9 tº tº º * ... ſ Telescope above surface 73° 3 feet. Telescope above surface 86°2 feet. BackDows: 92 top of monument 2 °o feet. Mºtownſ 3 J. battlements 16'8 feet. 33 pinnacles o “8 feet. tº O 1 ſ f Af Darrow Hill . H 9o 26 24' I 21 ‘7 |— 46-2 O M M W , Ryder's Hill . H 9o 12 59-6 6 I ‘5 – 46-4 Deadman . . H 9o 12 15° 5 20 5'7 High Wilhays II 9o II 30°5 16 2 °o – 43 °4. Hensbarrow . II | 89 57 o' I 28 I 3 Pillesdon . . . 9o 3 I7°2 9 ... – IQI ‘o High Wilhays . 89 26 21 3 || 11 | 16 o Horton's Gazebo. 9o 21 57 o I . . . . -ICO "2. IBarrow Hill . H | 9o 9 4°o 24 3 ‘o Nodes Beacon H| 9o 21 35.8 13 I 3 – 63 - 5 Dunnose . . H 9o 22 29.2 17 4 * 5 - 45° I Coringdon . 90 I4. I3 °o Io ... — I I4. 9 ARBURY HILL. Telescope above surface 23-8 feet. Swyre Barrow 90 I3 I 2 | 13 I37'9 PILLESDON. Telescope above surface 38'4 feet. CLIFTON IBEACON. Telescope above surface 5' 5 feet. Back Tor . . . 85 25 33.7 5 —13.6 Holme Moss . . . 89 36 37.2 5 — 7.7 Gt. Whernside. H 9o I 7'o I ... - 3 - 7 York Minster. Top 9o 16 58.8 3 Igg 3 # , º, Acklam Wold 90 II 55 °o I ... – 4'8 Crowle . . II 9o 20 43' o 5 — II " I Gringley Beacon. 9o 14 o' 7 7 — 15 ' I Lincoln Minst. Top 9o 12 32 °8 5 — 6-7 With the 3-ft. Theodolitc. Telescope above surface 5' 5 ft. S. End of IBase . 96 28 5*o I —1%6 Gringley Beacon . . 9o I3 4o'o I – 15 ' I N. End of Base . . 9o 32 57°o I – IS ‘5 Barrow Hill . II | 9o 23 48.2 6 2 3 —23.6 High Wilhays H | 9o 5 51 3 || 13 —6°o —33. I Dunkery . . . II | 9o 3 18: 3 || 17 I 3 – 35' 3 Mendip . II | 9o Io 30°3 15 2 I 6 —21 °o Coringdon . H 9o 19 10-2 18 3° 5 – 34° 9 Wingreen . . II | 9o 13 11 - 3 16 I I —42 '8 Swyre Barrow . . . 9o 17 17:6 13 | 18.3 —22.2 Blackdown . H go 12 7.6 20 I 5 —96'o Hol.M.E. Moss. Telescope above surface 5' 5 feet. Axedge 93 13 3éo 4. * —1é I Mowcopt . 90 29 I5°o 3 tº tº – 6.6 Cyrn-y-Brain 90 25 39°o 3 * . . . – 3:4. Whittle IIill . 90 21 24'8 7 tº — II 9 Pendle Hill . . . 9o 13 2.7 4. * * * * – 7:6 Gt. Whernside H | 9o 11 14-8 8 tº º – 5 'o Rumbles Moor . go 25 55'o 2 tº dº — 8' 5 Garforth Cliff H go 49 15.5 2 tº tº — 8°o Clifton Beacon H | 90 47 39.8 3 — 7.7 Back Tor. 90 I4 2 I 5 — 19°o (*) Top of Pinnacles. OBSERVED ZENITIJ DISTANCES. 533 Stations observed. Mean Zenith Distance. No. Obs. Object observed above Surface. Reduction. Stations observed. Mean Zenith Distance. No. Obs. Object observed IReduction. above Surface. LINCOLN MINSTER. WIIITTLE IIILL. Telescope above surface 5' 5 fect. Telescope above surface 238° 5 feet. BuckminsterSpire, " ' " " . Axedge 96 6 16-o 2 – 6.6 Top 90 6 57. 4. Delamero . . 90 30 23 °o I – 6: I Dardon Hill . . . 9o 11 % : 8 Bºom! - 90 I7 #: 2 — 3' 6 tº º h º C:l IQ º 90 7 47 'o I — 3 - 2 flºº. . . : : #| | Pendle Hill 89 51 38'o | II — I5' 3 Clifton Beacon . . . 9o 11 II •o 6 Fº: : ###| || – º É. Tr. T. ; ; ; ; ; Gt. Whernside 89 58 57'2 | 6 — 6 o º p 9o I4. 7 IIolme Moss . 89 53 Io' 6 7 —II 9 MowcoPT. Telescope above surface 7' 4 feet. Telescope above outside base of C. W. W.' Af Yomoſissiºnſ building 203-8 ft. Long Mount Pole. H| 9o 9 42 °4 I5 I 5 || – 4'8 l 35 battlements . 4 5 ft. Cyrn-y-Brain 90 2 43° 5 8 ... – 7 2 i. º 90 7 3.; 3 I5' 5 + : Clifton . . H 93 § 342 I4. 9°o J/ § †hin H 90 * §. 9 ::s | T'3. Garforth Cliff H 90 2 22:8 20 7'o i. º. º 90 4. .9 19 I-8 — 5-8 Gt. Whernside H | 89 4o 8-8 12 4 '7 Holme Moss . . . 89 55 47' 5 3 :- | T 3.3 | Botton Head 89 44, 31 7 | 13 Holme Moss : H | 89 55 42.6 14 5.9 | T *.9 |Adjam wold' 8 * I2. tº º ºr Bardon Hill . H go 20 6-6 || 14 2.5 — 4.1 |* W9 9 4o 4' 5 Axedge . . . 89 31 38-8 31 ... –2 I 2 LLANELLAN. Telescope above surface 5' 5 feet. PENDLE HILL. Telescope above surface 5' 5 feet. © f { } f/ Arrenig 89 2 I 48°o I – 9°2 * -- ~~". * { Garreg . . . . 9o I 7 35 °o I — II 9 iº, º ; : ...; ; dºm- 13 Gt. Orme's Head. 9o 4o 57°o I –29 2 Sca Fell 90 2 56'8 8 – 3: 9 Cyrn-y-Brain 89 52 57°o I – 7:8 Ingleborough . 89 5o 25°7 9 — IO ".2 Gt. Whernside . 89 54 54'4 || 8 – 9: I le: ab f * 5 feet. Rumbles Moor 90 23 46' 9 7 — II • I GARREG. Telescope above surface 5' 5 fee * Moss . 90 º ; % mº 7. Snowdon 85 23 *o I – 6°o XCdge . . 90 9 — 4.' *... . Whittle Hill . 90 18 30°2 8 – 15 3 ãº, Head : ; #: – ; : Gwaunysgaer. 90 19 36°o I –49°o SNOWDON. Telescope above surface 5' 5 feet. &#Biº ; # £: : E.}} o u ,, . Delamcre . 90 I4 57°o I – 8:3 Precclly . 90 44 40 °4. 5 — 2' 6 Tara . 90 53 28°o 3 – 2 3 IGippure 90 4 I 40 °o I – 2 3 MoELFRE ISSA. Telescope above surface 5' 6 feet. º 90 53 56°o I — 2 - 5 - Slicve Donard 90 43 50 °o 3 T * * : Gwaun * - d -4. W. ". tº ey e aunysgaer . . . 9o 28 36°o I –24° 3 sº ºrule * 90 45 5.8 3 㺠2.7 Great Orme's Head 90 24 6'o I —16'7 à l'Cil . 90 38 27' 5 2 T * * | Llanelian 8o 58 o'o I – 22 * I Black Comb . 90 44. I6' 5 2. — 2 - 5 anelian . . 9 58 O 33. Ingleborough . 90 45 23 5 || 4. I ...? | Cyrn-y-Brain 89 43 39°o I — 9 '9 Y. Hill . 90 46 58' 5 4. – 2 - 5 xcdge . . º - * * 6:Bin tº 3. ; #3 : º ; ICAST END of BASE. Telescope above surface 5'5 feet. Long Mount Pole go 43 25° 5 4. – 3 °4. © f f/ # / Plynlimmon . 90 29 50 - 5 || 4. – 5-0 | West End of Base | 89 59' 51 "o I 22°4 || "..., | Cader Idris 90 25 I 1 - 3 I5 — 8 ' I | Moelfre Issa . 87 5o 34’ o I ... -4.9 Arrenig . . * O 7 – 12 °4 Gwaunysgaer. 88 13 15 'o I –54." I 534 PRINCIPAL TRLANGULATION. West End of Base º Object g Object Stations observed. * à. º:d Teduction. Stations observed. * §: º Reduction. Surface. Surface. WEST END of BASE. Telescope above surface 5.5 feet. CRoCIIAN. O f # / J/ * d & f* Jº Moclfre Issa . 86 43 3 ‘o I * † tº –64'4 Kippure.... . 89 47 23: 5 2 Orme's Head . . . 89 27 37°o I ... – 18 7 Lyons Hill . c. 90 I3 49 2 5 IEast End of Base 9o o O I 2 I 5 tº ſº º Mount Leinster . 89 57 43 “o I Gwaunysgaer. 89 8 7'o I ... – 27°o - wºm-- | BENCORR. GWAUNYSGAER. Telescope above surface 5' 5 feet. C & fi Af Nephin . . . . 9o 9 27°4 5 O / ſſ a | Slieve More, Achill 9o 16 o' 6 5 Garreg . . . . 89 45 47°o I -49.9 Keeper . . 9o 3o 24' o 2 Moelfre Issa . . . 89 39 56°o I ~23.9 | Baurtregaum . 90 29 43’5 2. 90 59 12 “o I –27°o DUBLIN OBSERVATony. WordESLOW. Telescope above surface 5'8 feet. f Gt. Whernside H Merrington Tower, Top Water Crag . II Brandon . . H Collier Law . . Cheviot . H IEasington . . Easington . H Burleigh Moor H lłotton Head . . Botton Head . H 85 58 52.1 90 I 53° 89 49 I4' 89 51 50° 89 38 5’ 89 53 27- 90 9 49° 90 9 37° 90 Io 38: 89 55 28: 89 55 47' * : ; * 5 : 3 ‘o I 3 I "O Hºmº I' ‘z I IASINGTON. Telescope above surface 5-7 feet. Botton Head . Water Crag . . Collier Law . H Wordeslow ... EI Cheviot . H 30 1% o o o' 5 3 56°o I2 I5'o I3 40 °o 86 90 90 90 90 i : }º f ! i i GARFORTH CLIFF, Telescope above surface 5' 5 feet. Holme Moss . . Great Whernside York Minster . Acklam Wold H Crowle . H 85 33 &o 89 38 54°o 90 Io 9 'o 90 2 42 “o 90 16 8 o I I5°o I99° 3 + . : º Howth 86 49 58°o I — 19 2 Kippure 88 28 18 °o – I4. 9 Lyons Hill 89 43 2 I ‘o –20:4 HowTII. Lyons Hill 93 4 28.4 8 —io" 7 Rippure 88 54 42 °4. 7 — 12 4. Slieve Donard . 89 54 41 °o I — 3 '8 Dublin Obsy () . . 9o 17 58' 3 3 — 19:2 Dublin Obsy (*) . 90 18 28 o I IKIPPURE. O f J/ f/ IIowth . 91 18 11 °o I – 12 '4 Lyons Hill 9I 47 46'7 7 —18.7 South Berulo . 90 4o 4.5 "5 2 - 2 * 2. Slieve Donard 90 23 33°6 5 — 3 °o Croghan . . . . 9o 42 20°7 3 – 5' 3 Dublin Obsy () 9I 42 24 °o I – 14 ° 9 | Snowdon . 90 27 22 °o I – 2 3 Ballycreen 90 17 30° 7 3 tº ſº ſº Reeper 90 33 I I ‘o I Tara . 90 44, 33' 3 3 Lyons IIILL. Rippuro . . . . . 83 26 51 °o 2 # / Dublin Obsy () . . 9o 23 48°o 2 Howth . . 9o Io 16° 5 2. () Top of Dome. (*) Base of Dome. GRINGLEY BEACON. Telescope above surface 5.4 feet. South End of Base South End of Base North End of Base North End of Base 964; 44.5 90 46 27.2 90 2 I 47' 5 90 22. 59' 4 : 17° 3 13' I 33° 5 2O "O #f OBSERVED ZENITH DISTANCEs. 535 Mean Zenith N Object N Object º can Zenit O. lobserved º º - Mean Zenith o, lobserved º Stations observed. Distance. ô. ..." Reduction. Stations observed. Distance. 6. ... “Reduction. Surface. Surface. MoELFRE ISSA. Telescope above surface 5' 6 feet. Gwaunysgaer Llanelian . Llanelian . . . Great Orme's Head I –24°3 6 ... —33 I 4 || I4 "o +49'9 9 ... — 16'7 SOUTII BERULE. Telescope above surface 5' 5 feet. NortII END OF BASE. Telescope above surface 5' 5 feet. Gringley Beacon. South End of Base Clifton Beacon 85 43 13°o 90 I 3 'o 89 44 12 5 I [ . . . –25°6 3 ... -43 "I 2 || | – I 5" 5 SouTII END OF BASE. Telescope Clifton Beacon Gringley Beacon . North End of Base 8; 43 58.5 89 16 27°o 90 2 Io'7 I I Telescope above surface 16 feet. Gringley Beacon. Gringley Beacon. 85 16 & 9 89 16 55 'o 4 II 3 ||— 48 7 4. 5°3 – IIo 7 GREAT WHERNSIDE. Telescope above surface 5' 5 feet. | Pendle Hill Ingleborough . Sca Fell - Cross Fell Water Crag . Botton Head . : tº-º-º: 4. I INGLEBOROUGH. Telescope above surface 5' 5 feet. Pendle Hill . Great Whernside. Black Comb . Sca Fell =mºm- 93 25 15°o 90 9 I7' 5 . . . 9o 22 24 °o 90 I 33 °o f/ 2 — IO " 2 2 – I 3 '3 I — 5-6 I — 5-6 Sca FELL. Telescope above surface 5' 5 feet. Black Comb . Ditto . . . . 91 I 32." South Berulo . 90 39 50 ° Merrick 90 29 2 Criſſol. . 90 36 34' Hart Fell . 90 3o I Wisp, . • 9o 35 43 * Cheviot 90 34. 2 I Cross Fell 90 17 56. Water Crag • 9o 3 I 35' Great Whernside. 9o go #3. | Ingleborough . . . . 9o 28 41. Whittle Hill . II *— f f/ 9I I 33° 90 4o 47' 5 I f £o - - - - - , ... • - - . . . 41 - * + Af Kippure . EI 93 28 47: I 16 2 5 — I 2 Howth EI 9o 36 43' 6 7 I ‘o – 2 °2 Slieve Donard EI 9o 3 13' 2. I o' 3 – 4° o Ditto . . . . 9o 3 Io'7 3 ... - 4 ° 2 Divis . H 9o 23 6'o 9 I4 * 4 || + 5° 5 Trostan . . . 9o 29 5' 5 4. ... - 2 ° 5 Trostan . H 9o 29 25 °o I2 1 I o + 2 - 5 Merrick . II 9o 14 18°4 16 2 ” O – 2 °C Ditto . . . 9o I4. 9° 5 3 º, tº tº — 3 I Criffel. . H. 9o 22 43 9 18 ... - 3 ‘I Sca Fell . . . . H | 9o. 6, 4:3 – 17 o’8 — 3 'o Ingleborough . H | 9o 27 36' 9 || Io 3 *2 — I ‘o Black Comb . H 9o 15 31 “4 24 ... - 3 ° 9 Snowdon . H | 9o 12 24-7 || 20 I 5 || – 2 o WATERCRAG. Telescope above surface 6-8 feet. O f // Ji Cross Fell 89 49 Io'o I . . ~ I I " I Collier Law 90 22 12 “o 2. . I — II " I Brandon Down H | 9o 4o 2 I 5 3 2 : o – 6-7 Wordeslow . H | 9o 39 54°o I 2 °o — 4*7 Merrington Tower, º - Top 90 46 I'o I ... - 9 '9 Easington . . II | 90 37 56° 3 3 2 : o — 3' 6 Botton Head . 90 26 8-o I . – 6'4 Great Whernside. 9o 3 2 I ‘o 2. — 13 5 SLIEVE DonARD. Telescope above surface 5' 5 feet. O W * Af Sawel . 90 30 o'o 2 dº º ſº. tº . . . Divis . º 90 38 12 ‘o 2. * * * tº gº tº Vicar's Carn . 90 56 18-7 3 º E ſº tº º Cuilcagh . 90 34 2 °o 2 º º tº tº º Trostan 90 32 35 °o I tº $ tº tº º º Howth . 90 46 21 ‘o I * † tº tº º º South Berule . H 9o 34 4°4 I3 I 5 – 5' 4 South Berule . 90 34 4'8 5 ... - 4 ° 2 Rippure 90 29 I5°o I tº º º DIVIS. O. f // ºf Slieve Donard 89 44. I2 °5 4. Sawel . . . . . 9o 5 I ‘o 4. Inocklayd . . . 9o 12 13° o 3 VICAR’s CARN. Slieve Donard 85 25 27° 3 4. Divis . 89 56 21 ‘o 4. 2 Sawcl . . . 89 51 46°o 536 PRINCIPAL TRLANGULATION. wer ºn so ºn Object º can Zenitil O. ODSCrV e º º Stations observed. Distance. Obs. s: Reduction. I Stations observed. *...* §: º Reduction. & Surface. SAWEL. PERTINNY. Telescope above surface 6' I feet. - O 1 ºf Wolf TRock § 46 #1 8 —º N. End of Lough " | Telegraph Tower, 90 4o 7 17.8 Foyle Base . . . 91 Io 29' I Top | 9o 22 41 8 º º Slieve Snaght % I5 #: Ž sº º Day 9 4I 4 4I 5 | +43° 5 ICnocklayd O 2 3 4.2 ° 2 ark . Top 9o 22 52 º º Trostan ; : §§ 2 Beacon Hill, Tres- 52 “5 Io 4o'o +45° 2 cow . . . . . 9o 23 49' 3 3 . . . . - 7 ° #º fºº # |##|# ey • II " O 24." CUILCAGH. Goonhilly . . . . . 9o I9 §: 6 tº ſº º tº: Goonhilly . . H 9o 19 I5'6 24 I 5 — 8-5 O f ºf Hensbarrow . H | 8o Io 43' 2O I " 's — AL * Slieve League 90 2d 55 ° 3 6 " | Karn Galver . 89 47 #: 5 º –33 Sawel ; 90 19 3 7 6 jº. Donard 90 23 6' 5 2 - sº ; § #! É GoonLIILLY. Telescope above surface 5'8 feet. Vicar's Carn . 90 27 54 “o I O W WA f/ Croghan 90 38 16 o I Wolf Rock 90 18 33°2 6 Rippure 90 32 36°o I Ditto Surface of Water. 90 18 53' 5 3 ... — 7'8 £º : *|####| | | ||= } * O tº º & = T fº * SLIEVE LEAGUE. ICarnbongllis . . . 89 : §§ # II 5 I: Hensbarrow . H. 89 55 23 'o 7 I 2 – 6.3 O f / # / IIensb º 8 º tº º §'s tº ht 90 f 34° 3 3 * flºw : # sº ; º tº: 16V6 S11:tº Il O 2 I 3 I " ſt - º = 1 ſ fº * Croghan g tº ſº. ; 2. *::: : arn Galver 89 53 24' 3 5 tº ſº tº Io. 7 Slieve More (in Achi º cº . : : .. : Brown WILLY. Telescope above surface 7 feet. | Knockalongy . 90 I5 35°o I C & WA H. : * : ; #| | | | | | = . º º º 2 I . . . - I S. " IXarnbonellis . H ; : ;: 9 2. "O º NEPHIN. St. Agnes I3ea- O J & Kºimi #1; 26 55.8 || | | | : - 8:3 Croghan 91 28 16-5 4. º Trevoss Hai IH 90 25 32.2 I5 I 5 || – 4' 3 Knockalongy . . . . 9o 3o 17°o 3 IRyder' Íñi 90 45 19°o I4. I 5 — I I 2 Cuileagh . . II 9o 27 42 o 2. # jº. º 90 4 3 I 5 || Io II 5 + 5° 5 Slieve League 90 27 I 1 - 5 2 #. H. .# º 89 52 58.8 17 19 'o + 17' 5 Slieve More (in º y Islan ight Achill) . 90 20 32 ° 5 2. º P * * 9° 37 34.2 13 ... I — 6'8 Tawnaghmore 90 53 33 °o I • * aracombe . H. 9o 15 45 ‘o 2 I 5 || – 4' I DEACHY HEAD. Telescope above surface 5.5 feet. ST. AGNES BEACON. Telescope above surface 5' 5 feet. o , u | *m-m-m-- B. : : * : ; ; ; ; ; ; "|- . Rarnbonellis . 8; 47 15°o I –2% o fittenfield . It : #. 3.3 : 6.2 −1. P. ... • 3. I4 IS ‘o I — II I | Leith Hill Tower, 5 36' 2 +29-2 arm Iſlin IllS 9 57 45 ‘o I — I 3 '4 T ſº * º Trevose Head. 90 19 30°o I — II 6 || Leith Hill. op ; § 6; # 45 8 *:::: Hensbarrow . 89 51 52'o I —II 7 || Fairlight . 90 5 8*6 27 º Tº: OBSERVED ZENITH DISTANCES, 537 *— Zeni º f g Object Stations observed. Mºh §: *:::::"Reduction. Stations observed. Mºh §: º Reduction. Surface. Surface. DoNIFACE DOWN, Telescope above surface 5' 5 feet. JBUTSER HILL–continued. *--—- * O / #4 If tºwn; * : #: # . " |####".T. . .'; ##| || || 3 | I].” CCK lyOWIl 90 4o tº tº ſº - * nº Wroxall Down 91 58 *::: 2 tº ſº Crowborough . H | 9o 19 Io' 7 || Io 3’ 5 ... Nodes Beacon 90 I7 54° 2 5 dº ſº Shanklin Down 90 42 16°o 3 tº ſº tº CoRINGDON. Telescope above surface 6' 2 feet. Dunnose . . . . 9o 9 38' 3 6 tº * O f f/ f/ BonifaceDown, S.E. 92 55 31 : 5 4. Swyre Barrow (') 89 58 46.8 14 ... -49 O Black Down . H | 9o 5 4o 6 7 3 3 – 4' 5 Pillesdon . . . II 9o Io 11 - 2 I5 3 *o – 3 2 WEEK Down. Telescope above surface 5' 5 feet. Beacon Hill . II 9o 14 23 2 9 tº ſº ſº — 6' o *-*- f Wingreen . . . H 9o 2 29° 5 || 13 I 7 — 7'o Nodes Beacon . 93 I4. 4.3 °o 3 — 15 ' I Horton's Gaº 8 I 3 '' { . Shanklin Down . 89 52 Io'7 6 Tº...? | Dean Hill % 90 I #. # ... -15. Boniface Down 89 24, I '8 4. – I 35 “I i. un. . II 92 & 33.9 3.3 || – 3:6 Littletown Down 9o 16 55' 5 6 – I49' 3 R. SCT . . 9° 5 19.9 15 3 * 5 – 2 I DonifaceDown, S.E. 89 34 33 °o 5 — 131 '8 odes Beacon, Top 9o 12 4-7 4. . . . . - I 2 * I | Dunnose . 89 36 38-3 4. — Ioo 3 Dunnose . . H. 9o Io 34°5 | 16 2 5 – 4 I |D . Tel :l DOV f: • 7 feet. IIIGII Port CLIFF. Telescope above surface 5' 5 feet. froming, relescope above sur e 20-7 fee H - - ,, . Dunnose . . H 93 16 18.6 . 17 2 5 -14.5 BonifaceDown,S.E. 76 39 46°o | Io –433°8 || Butser . . H | 90 13 15-4 II | 4: 5 – 16-4 Littletown Down . 78 54. 27°o II —427 6 #. Towei, ; : #.: | % #. #: l:MI) • e l'l CO I2 2 I " 24. "O * T Crowborough (). go 5 36.7 9 18 o — 6'7 LITTLETown Down. Telescope above surface 5' 5 fect. Fairlight . I 9o 16 45'3 13 || 2:4 –22:4 • , , º f f i.; ind. To 90 16 49' 3 4. tº ſº –25° 4 Week Down . . . 89 47 25' 5 6 ... - I49' 3 º op 6 co- ~. • 6 Boniface Down 84 47 17:9 || 7 || 3.8 |–262-6 || '9" tº . . 9o Ib 59°o Io Io'o - 2 I BonifaceDown, S.E. 85 23 34’ o 7 ... -93.5 °7 | - High Port Cliff . Ior 9 o' 7 7 3 ‘8 – 136. I DUNNose. Telescope above surface 6' 6 feet. BEAcON HILL, TREscow. Telescope above surface 5' I feet. | St. Agnes, Lae house Karnminnis Rarnminnis . II Pertinny . . . Pertinny . . . H Top | Telegraph Tr. Top .iºm- 89 57 34° 2 90 2 38' 3 90 2 53 ° 2 89 59 15°o 89 59 35' I 89 44, 34'7 I4. 4. 25 18 17 i i : i ſ 5 I BUTSER HILL. Telescope above surface I2 8 feet. Dunnose . . II Dunnose . Nodes Beacon Coringdon . Ii Ditchling . . H | Ditchling . Wingreen . fi Inkpen . . . H Dean Hill . . H 90 I2 45°4 90 I2 25 o 90 19 18:8 90 21 28-7 90 15 25-8 90 I5 24' o 90 17 46.8 90 Io 4.3 °4. 90 19 19.8 17 5 3 I 2 24 I I8 I 3 5 .. . —17.2 – I 5' 3 Hºmº 7'o – 9:6 — 12 9 — 6-7 — IO "O - • , a WF Week Down, . . 90 27 I I 5 2. ſº —º : Swyre Barrow II go 16 8-7 8 2-8 – 3' 8 Coringdom . II 9o I5 I ‘7 12 2 - 5 – 4' 6 Black Down . H 9o 21 36' 6 II I "O – 3 7 Nodes Beacon 90 17 56' o . — 16'7 Horton's Gazebo, Top 90 21 6" o 2 ... – 6' 9 Wingreen . II 9o 15 54'8 13 I I — 4' 6 Dean Hill . H 9o 18 o' 9 15 2 : 8 — 4'2 Beacon IIill . H go 18 39.3 5 I 5 – 4'4. Ditchling . . II 9o 17 52- 9 Io ... – 5 'o Southampton . H | 90 27 8.4 17 . — II 5 Inkpen . . H. 9o 17 2-4 18 4’3 — I '8 Butser. . . H 9o 7 12 I 19 2 9 – 5'4 Beachy Head II 90 26 3-4 13 o' 5 – 3 '7 i | DUNNOSE. 18-in. Theodolite. | O f f iſ ** Boniface Down . . 89 52 29° 5 3 ... – 247 ‘o Wock Down . 90 26 38-3 4. ... — I2O 'O Shanklin Down . 91 37 4o'o 2 * * º ºg tº Wroxall Down 9o 28 8'o 2. ... —216' 3 – I 3 ' 5 () Top of Cross. 3 Y 538 PRINCIPAL TRLANGULATION. º Object Object Stations observed. Mººn §: º:d Reduction. Stations observed. Mºh §: º Reduction. Surface. Surface. FAIRLIGHT. Telescope above surface 7 I feet, Swyn E. BARRow. Telescope above surface 6' 3 feet. O J f/ WA o 4 m | | | ||...wn # 33 4 98 || 3 || 3.7 || 4:3 Beachy Head . . . 96 8 15' 3 8 Io'o + 6 1 || Wingreen . . H | 90 4 o' 5 12 I o – 7:8 Beachy Head . . . 9o 8 30°3 5 ... — 14' 9 || Dunnoso . . FI 9o 12 52 “o 6 3'2 – 3' I Ditchling . . II 9o 7 3' I 12 o: 5 – 8 i | Dunnose... . II 9o 12 io'o 9 2 * I — 4.' I IPaddlesworth. II 9o 9 31 I 13 | 1.3 – 8.2 | High Wilhays II 90 18 25.7 | 16 —6'o — 5:7 Crowborough. H go 3 32-6 7 2'3 – 7-8 |Pillesdon . . .II 90 7 9'? 5 35°5 + 32°4. Crowborough . . go 2 46.5 % ... – 11 7 || Horton's Gazebo, - Frittenfield H go 7 54-7 17 4' 5 — 4.' I ... Top 90 18 20:5 4. ... – 13 ‘I Frittenfield . . 9o 7 2-8 3 39.8 +52. 1 || Beacon Hill . II 9o 15 35'9 | 12 I 3 || - 4.' 5 Wrotham . . H 9o 8 58' 7 14 2.5 – 5:3 |Dean Hill , H 90 I6 6-8 I2 3' o – 3' 6 | Coringdon. . . . 9o 5 I ‘9 II : é.6 + 2.7 ICARNMINNIS. Telescope above surface 6' 9 feet. ICEYsor, CIIURGII SPIRE. Q f Af Aſ Pertinny . . . . 03 & 48°6 | 1 .8 || -- 145 | Dunstable . H. $95; 53-3 || 4 | ... . ... §."ºis Day 9 3 3 || 9 ** |juj. . . . § 3 ;-3 || | | . tº ſº tº Mark . . Top 90 24 12-8 6 4o'o +35.7 | Punstable, ..., 89 59 20'o I 4o 5 +58' 5 Trevose Head . 90 23 4.6 || 10 11.9 + 4-š Hanslope.Sp. Top | 89 59 57.5 5 • * * • * * Brown Willy . . . 9o Io 21 ‘o 2 I3 5 + 5 2 Naseby Ch. Tr. H 90 o 34.8 6 tº tº St. Agnes Beacon 90 14 3'4. Io | II o + Io'o Tilton. . H go 4 34’ o II tº º º * - ſº Hensbarrow . H 9o 8 28' 9 || Io 1.5 – 6.2 | Tilton . . . . . 9o 4 33°o I 8' 5 + Io' I Hensbarrow . . . 9o 8 I '9 5 II '7 + 5° 5 Tilton . . . . . 9o 6 7'o I dº ſº º tº º §º. . . . ; ; ; ; tº tº |##.."4. . ; ; ; ; ; ; P- | º *** {\{* * { º º O , 12 O.A." ICarn Galver . 89 57 56' 5 6 tº tº º 4 |Tia. . .” 90 2 47' I 6 +. NoDES BEACON. Telescope above surface 5' 6 feet. Telescope above surface 79' I feet. { 33 33 LAWSIIALL Cir. Tit. | tower 3: 9 feet. Swyre Barrow H 93 3 56.5 Io I 3 — 69 f • PTw § 2 - ". | º &# Swyre Barrow Ii 99 3 57.5 2 º: . -º 8:3 lº ; ; #. ; º: * §. ... ii 92 5.9 # | 3.8 I 3. Brandon . . H. 33 ºf £1.3 || 1: 3é-o tº ſº #ºn II ; º #3 8 I * 2 - §: Swaffham Spire. H 90 13 12 3 3 132.3 tº º . º * is tº º-is III crl { w * - - º lº §º #|; ; ; ; ; ; – #|jº Hº ; ; ; ; ; nkpen . . Il 9o Io 29° 3 4’3 - || | | \rickſ. T.' wº .2 sº . H 3. I9 33. 3 5 52 I + Ioo' 3 Nº. †. º ; º ſ: i. #: Tº ſº €Clº l NOWIl , , * O 2 • , , — I S. * ~ +,-1-2. ' r º * tº ºr IButser . . H . # s: 21 3 * 4 || – 3.3 Stoke Tower () . go 10 37.8 12 111 3 Dunnose . . . . 89 53 31 ‘8 17 ... – I4' I LYNN ToweR. { Telescope above surface 94' I feet. 33 , lower 5' 9 feet. SILANRLIN Down. Telescope above surface 5' 5 feet. O - Ely Minster. Top go 5 22 - 5 || 11 204-6 f/ Week Down . 93 12 13 o 2. –1149 sº *sº 89 52 22 °5 7 154's ;I, ; 34. ; : * | “ Tă.3 || Peter's () . . . . 9o 4 13.3 || 5 || 91.5 Onliil CC LWOWIl 9 2 I I4. 4. “ TºQ74 || Boston Tower.Top go 4 13.5 8 & tº º DockingCh.Tr. , | 89 53 53'5 9 • * *, BoxIFACE DOWN, S.E. Telescope above surface 5' 5 ft. ACKLAMI Wold. Telescope above surface 5' 5 feet. Littletown Down. 94 57 I 2 6 ... AA * o f iſ f/ Week Down . ; 29 35' 7 6 : ... §n . H 9o 25 28 ‘o 3 i – 7: 1 Wroxall Down 9I 5 20°o I ... Ş. º: eacon H 9o 20 33 °o 2 ... } – 4'8 Nodes Beacon . . 9o 16 57.7 6 ... ork Minster. Top 90 29 52 'o' 6 (199: 3 |+558-3 Doniface Down 87 16 25' 5 6 3.8 Botton Head . 89 53 o'o 5 ... – 7-8 High Port Cliff . Io9 24 Io" 2 6 3.8 | ſ (*) Top of Battlement. OBSERVED ZENITH DISTANCES. 539 Stations observed. Mean Zenith Distance, No. Obs. Object observed above Surface. Reduction. AXEDGE. Telescope above surface 5' 5 feet. Mowcopt . . . 9o 39 26.5 | Mowcopt. Cross 9o 38 11.9 Pendle Hill. . . . go 16 23:0 Whittle Hill . . . 9o 17 20.5 Holme Moss . . . 9o 4 3o'o Back Tor . . . . . 9o 7 51 o Lincoln Minster'Top 9o 36 3 o Bardon Hill . 90 29 28 °o Snowdon . . . . 9o 19 35°o Cyrn-y-Brain. 90 19 12 “o : 33°o ; d f i : T BLACKcoMB. Telescope above surface 5' 5 feet. Snowdon . . . 96 2O I2 °C) Criffel . . . . . 9o 18 57'o Sca Fell . . . . 89 8 48' o Ingleborough . 90 6 52 “o Water Crag 90 9 49' o Pendle Hill . . . 9o 20 22 o Whittle Hill . H go 26 3o'o South Berule. 90 24 32 ° 5 Morrick 90 20 II “o I I | ... i ; : Collier Law. . . Wordeslow | DurhamObsy Dome BRANDON Down. Telescope above surface 34° 3 feet. Great Whernside. Water Crag . . Easington . . . Burleigh Moor. H Botton Head . MerringtonChurch Tower . Top 89 55 5°o 89 39 50°o 89 22 6' o 90 18 57 "o 9I 34 47°o 90 17 I ‘o 90 18 50' o 90 I 23°o 90 23 52 “o I ; i | | // CoLLIER LAw. *=– Telescope above surface 7 I fect. Water Crag . . : Cross Fell . . . Cheviot | Cheviot Ii i Wordeslow . II. Durham Obsyl)ome I3randon Down Easington . . . II MerringtonChurch Tower . Top Botton Head . II 89 55 I4°o 89 29 30°o 90 4 38' o 90 4 20 °o 90 38 37' o 9I I 28 °o O O | 9o 47 23. 90 31 20° 90 44 57°o 90 19 19 'o l : 3 tº tº 1.5 —11°8 — 13 3 – 5'7 ºmº 3.8 – 9: 9 – 17 9 –23° 3 tº- 4'8 — 16:8 — 5 'o Object Stations observed. ** i à. º Reduction. Surface. CRIFFEL. Telescope above surface 5' 5 feet. | O d MA f/ Goat Fell . . . . 96 1949°o 3 — 2 8 Hart Tell . . . . 89 57 3' 6 6 — 6'4 Dunrich . . . . 9o 9 I4. ‘o 5 º — 4' 6 Wisp . . . . 9o II 16’ o 6 º – 6: I Cross Fell 9o 3 Io'o 7 * @ – 4'4. Sca Fell , . 89 5o 18°o 9 ... — 5' 7 Blackcomb . . . 9o 16 14 o 4. – 4 4 South Berulo . go 27 58' o I . – 3 I Merrick . . . S9 56 57 "o II ... – 6'o IBurnswark 90 4 I 4' 5 2 | ... - I2 3 | CRoss FELL. Telescope above surface 5' 5 feet. d {{ f/ Sca Fell . . . 96 7 12'o 8 — 6'4 Criffel . . . 90 3 I 55 °o 2 – 4'4. Merrick . . . . 9o 3o 56°o I - 2 - 5 Hart Fell . . . . 90 24 8 o 3 – 3 5 Wisp . . . . . 9o 3o I5'o 3 | – 4'8 Dumrich . 90 27 36°o I – 3" 2 Cheviot 90 23 8' o 4 | – 3 9 Collier Law . 90 46 38' o 2 | — I O 2 Botton Head . . . 9o 37 2 o 6 : ... — 3' 6 Water Crag . . . 9o 29 19 'o 4. ... , – 9 'o Great Whernside 9o 25 Io'o 6 ... — 5: I Ingleborough . . . 9o 23 46°o 2. ... – 5'8 Burnswark . . . 90 46 1.8 I ... - 5 2 CRowLE. Telescope above surface 5' 5 feet. | O f iſ iſ - f/ Clifton Beacon H 89 53 53°o 6 ... - II " I Garforth Cliſſ' . . 9o I 46 o 6 ... — 8' 5 Great Whornside 89 57 16'7 I ... - 3 5 Acklam Wold . 89 56 33’o 6 ... – 7' I Lincoln MinsterTop 90 1 28°o 4. º º — 7' 5 | CYRN-Y-BRAIN. Telescope above surface 9-3 feet. Snowdon . . . 85 43 4. 'O I6 I5' 5 + 6.5 Delamere . . . . 9o 42 48' o 9 9°o – o '4. Axedge . . 9o 18 33° o 7 ... – 6'9 Mowcopt . . II 9o 26 42'o 13 5'5 – 3' 6 Long Mount . 90 I5 47°o I6 20°o + II 5 Arrenig 89 44 II •o 17 | 20°o + 16-6 Llanelian . 90 27 7"o II | 20°o + 15' 2 Moelfre Issa . 90 3 I 35' 3 18 20' o + 19.' I DELAMERE. Telescope above surface 5' 5 feet. Cyrn-y-Brain. 85 34 gºo 8 — 9 'o Arrenig . . . . . 89 48 36 ‘o I tº ſº tº Whittle Hill . . . 89 55 6'o 4 — 6' I Holme Moss . 89 52 29 'o 3 — 5 4. Mowcopt . 89 51 6' I 6 — IO "2. 3 Y 2 54O PRINCIPAL TRLANGULATION. INDEX TO THE ZENITH DISTANCES. Names of Stations. I?age. Names of Stations. Page. Names of Stations. I’age. Acklam . . . . . 538 || Collier Law }ringle { * Arbury Hill . . . . 532 || Coringdon tº : # gºº Il tº $ tº ; ſº Arrenig . . . . . Corryhabbie . 518 || Hampton Poor House tº Axedge ſº 539 || Cowhythe 516 || Hanger Hill Tower 527 I3ack Tor . tº . iº º ſº. Cradle . 526 Hanslope Spire Daconsthorpe Tower 523 || Criffel . 539 || Happisburgh Tower 523 l3alsham Tower . 525 | Croghan . 534 || Hart Fell e 52O Balta . 514 | Cyrn-y-Brain . 539 Hensbarrow . . . . 53o Ballycreen ... Crocghiubhais 515 IIigh Port Cliff . . . 537 IBanstead . . 527 | Cross Fell. 539 || High Williays 53o 13arrow Hill . 532 || Crowborough . . 531 || Hingham Tower . 524. IBardon Hill 28 | Crowle 539 Holme Moss 532 | Bauriregaum . ... Cuilcagh i. 536 || Horton's Gazebo . ... I3eacon Hill 53 I | Cundtham tº . 522 || IIowth • * 534 I3eacon Hill, Trescow 537 || Danbury Spire . 525 || Hungry IIill . tº . . Beachy Head . 536 || Dean Hill . {º 529 || Ingleborough . 535 l}on Choilt 5 I 5 || Decrness . . . 515 || Inkpen tº ſº º 528 Ben Clibrig 516 || Ditchling . . . 537 || Jura . . . . . . 520 Bencorr i. 534 || Divis . . . . 535 Karnbonellis . tº ſº tº Den Heynish . 520 | Docking Tower 524 || ICarn Galver . 539 Den Cleugh 519 || Doolieve . ... I ICarnminnis 538 Den Lomond . 520 | Delamore . 539 || ICeeper . . . . tº º º Ben Hutig 515 Deadman . 53o IXeysoe Church Spire. 538 T3en Lawers 519 Drung Point . 522 IKing's Arbour † Don Macdui * 518 | Dublin Observatory . 534 I(cllic Law 52O IBen More, South Uist 5 18 | Dudwick . . . . 5 17 || Kippurc 534 Ben More, Mull . 519 | Dunkery Beacon . 530 || ICnock . i. 517 -Ben Novis 519 | Dunnet Head . . 515 Inockalongy . tº is ſº I3en Tartovil . 522 | Dunnose 537 l{nocklayd 522 Ben Wyvis tº º ſº. 5 16 | Dunrich 521 || ICnockmealdown . Berkhampstead Gazebo . 53 I | Dunstable. * 527 | 1Qmocknadober I}lack Comb . * * 539 Durham Observatory ... Knocknagante 13lackdown . º: 532 | Basington . 534 || ICnocknaskeagll #ºn tº º 52 s - º Lomond . 519 || Knockanaffrin tº tº UIC II 1 || . tº I Saston Tower . I r Boniface Down tº ſº. ; 37 | Ely Minster . . #; Fºllº * 538 Doniſaco, South IEast . 538 || Epping Cupola 526 #. 1C OWel 524. l}oston Tower tº 531 Fairlight Down 538 #. "Hill in..... " 5 : Dotton Head . . . . ... | Fair Isle #. Hºllºwer 52 Brandon Down º 539 || Fashven . . . 5 IS Lincoln Minster . 533 Brandon Hill . . tº º º º Feaghmaan . . tº º º Littletown D OWII . 537 Drandon (Suffolk) i. 524 || Fetlar . . 5 I4. Little Stirling 5I 7 Irassa tº º i 514 || Fitty Hill. ;: | Hºng ſount . 528 I3rimmond sº º 518 || Foula . tº º 5 I4. Llanelian . . . . . . . . . 533 Droadway Tower 526 || Four-mile Stone . 523 L. Foyle Base, North End 522 Brown Willy . i. 536 || Forth . . . † tº L. Foyle Base, South End 522 Duckminster Spire tº ... I Trittenfield 525 Lumsden . . . . . 52 I Bunwell Tower * 524 || Gad's Hill 525 Lundy Island . 527 Burleigh Moor { } tº ſº ſº. Galtymore * * * Lynn Tower wº 538 Burnswark 520 || Garreg . . . 533 Lyons Hill 534 Butser Hill 537 || Garforth Cliff . 534 Maker Tower . 532 Cader Idris ... I Gerth of Scaw 514 || Malvern . . 526 Callcrbarnagh ... I Goatfell tº gº 521 || Mamsuil 518 Calton Hill tº gº 516 || Goonhilly . . . . 536 || Mendip 53o Cambridge Observatory . ... I Gorleston Tower . 523 || Merrick tº 52O Carrigſadda tº º ... Great Ormes Head ... Merrington Tower * - ſº Cheviot 521 || Great Stirling 517 | Mickfield Tower . . 528 Chingford . 526 || Great Whernside . º 535 | Milk IIill . . . . . . 523 Qleisham tº 516 || Greenwich Observatory . ... | M. C. lxase, North End . 535 Clifton Beacon . 532 || Gwaunysgaer 534 || M. C. Base, South End . 535 * *. INDEX TO THE ZENITH DISTANCES. 54.I ſi Names of Stations. Page. Names of Stations. Page. Names of Stations. Page. * 5 Ronas . . . . . . 514 || Storr . . . 517 Moclfre Issa #| . . . . . . 516 || Swaffham Spir 529 Monach 515 Rhuddlan Base, East End 533 Swyre Barrow 538 Mordington 520 | Rhuddlan Base, West End 534 || Start Lighthouse . ſº ſº ºn Mormonth . 516 || Ryder's Hill i.e. 53o | Taur . . . * * * * Mowcopt . . 533 Sarum Castle . 523 Tarbathy . 518 Mount Battock 519 || Sarum Gun 523 Tawnaghmore * a Mount Leinster ... I Sawel . 536 || Thaxted Spire 525 Mount Sandy 522 | Saxavord . 514 || Telegraph Tower. 53 I Nivo Hill . tº º Sayrs Law 521 | Tharfield . 526 Naseby Tower 531 St. Agnes 13eacon 536 || Tilton . 529 Naughton Tower 532 || St. Agnes Lighthouse ... I Tofts Tower 523 Nephin 536 | St. Ann's . . . . . . ... I Tara { } { } º Norwich Spiro 523 St. Martin's Head . . , 528 || Trostan 522 Nodes Beacon . . . . 538 || St. Paul's Cathedral . tº tº Trevose Head . 53o North Ronaldshay Lighthouse ... St. Peter's tº 524. Upcot Down 522 Norwood & Q & ºt 525 | Sca Fell 535 | Vicar's Carn . . . . 535 Old Lodge ſº tº 529 || Scarabin . 516 || Walpole, St. Peter's Tower . 529 Ordnance Map Office ... Scournalapich 517 | Walton Tower º 524. Orford Castle . 524 | Severndroog 525 Wart Hill Hoy 5 I5 Otley Tower . 528 Shanklin Down 538 Watercrag 535 Over Hill . . 518 Slieve Donard 535 | Week Down 537 IPaddlesworth . 525 | Slieve League . . 536 || Westbury Down . 529 Paracombe 527 | Slieve More in Achill ... I Whitehorse Hill 527 Pendle Hill . . . . 533 | Slieve Snaght 522 || Wingreen . 529 IPeterhead Old Windmill 517 | Snowdon 533 Wittle Hill 533 Peninnis Windmill 528 || South Berule . ſº 535 || Wolf Rock tº ſº º Pertinny 536 | South Lopham Tower . 528 || Wordeslow 534 Pillesdon . 532 | South Ronaldshay 515 Wrotham . 527 Precelly 527 | Southwold Tower 524 Wroxall Down * ... tº Plynlimmon ... | Stoke Tower . 524 || Wisp 516 Reform Monument Stoko Hill 522 || Yell ... • - 5 I4. Rona Stronsay 514 || Yorkminster . . 533 ! Coefficient of Refraction, THE coefficient of refraction may be determined either by direct observation, as when the heights of the observing point and the point observed are known with exactness, or it may be deduced from pairs of reciprocal observations. In the former case, the coefficient required is simply tho ratio of the excess of the observed above the true zenith distance to the angle subtended by the two stations at the centre of the earth. The following table contains the values of coefficients of refraction observed in this manner, the weights in the last column but one being proportional to the square root of the distance and to the number of observations:— No. | Stations. Isºld zºº. Nº Lºgrºmis a Tººh Z–2. º: w. k w Height. 3. Obs. Distance. Z. }. a } --sºms. |##" ::::::::::::::: ; sº |*|;; *::::::::::::: §§ • ?:, ; ; ; ; *.*.*|*|ssssss sº, º 'º' ~~ *** s|##" | #3; ###|*|sºn ºf 3:3:#;|#### 4|## , ; ; ; ; ; ; sºngs 3379.9 |:::::::::::::::::: ; ; ; s|#." |###|: ; ; ; ; ; sees, 1966's #: ; ; ; ; ; ; ; ; 6|#.": ; ; ; ; ; ; ; ;&l |43.3% |: ; ; ; ; ; ; ; ; ; ; 7|#º": ; ; ; ; ; ; ; ; ;sos |*|#########|#### 8|#;" || “...; ; ; ; ; ; ; ;38;9|21464 |: ; ; ; ; ; ; ; ; ; ; 9|#. . . ; ; ; ; ; ; ; 2571. 1778's . . ; ; ; ; ; ; ; ; ; ; to $º" . . . ; ; ; ; ; ; ; ; 2643; 1896.9 |; ; ; ; ; ; ; ; ; ; ; | 1 |#. . . . § 3 ; ; *..}|...}|s:43606 |2685* : ; ; ; ; ; ; ; ; ; }; I2 Yºmi #: ; º ;: : 5 * 40979 || 2527° 4 ; º #} ::::: ...; # 3. **: ######|*|*|############ ** : ::::::::::::::::: ***, *::::::::::::::::::::::::: wººl; ###|*|*|#####:####, **ś.: ; ; ; ; ; ; sº sºlº # 3: $.33%;|3}} Mcan value of k = o-o?92. COEFFICIENT OF REFRACTION. 543 .| i : The largest value of the coefficient of refraction is at Swyre Barrow, in the observed zenith distance of High Wilhays, which slightly exceeds one-tenth. The next in magnitude is at Ben Nevis. The mean reading of the barometer at this station was 25.233; and it is worthy of notice, that for about a fortnight during the stay of the observers on the hill (when the greater part of the observations were made) the state of the atmosphere was unusually calm ; so much so, that a lighted candle could often be carried from the tents of the men to the observatory, whilst at the foot of the hill the weather was wild and stormy. The coefficient resulting from the observations at Dunnose to Ditchling is considerably greater than the mean, as is also the coefficient at Malvern. The range of the whole is from # to #, and the mean in - When the coefficient of refraction, k, is derived from reciprocal observations of zenith distance, we have (see page 5 II)— * z' -- 2 – 18o° º where 2 and 2' are the observed zenith distances, and v the angle subtended by the two stations at the centre of the earth. The weights assumed for the separate determinations are directly as the square root of the distance and inversely as the sum of the reciprocals of the numbers of observations at the two observing stations. 1 — 2 k = The following table contains the calculation of 112 values of k – Coeff. of . . No. Stations. º §: pº ty. * is: | 1 – 2 k. Rºston 70 J. w 1 || Monach. . . . . 93 3. 244 * s. 36 6 º • 8 •o'78 † Ben Cibrig . . . 3, 4; 26.; to 5'5°599 || 3619-3 || 305+ 9.843° | **785 27 | *1195 Corryhabbie . . . . 90 22 37.9 31 s.6 º i. • 8 † 'Aq28 * Ben Clibrig . . . . . 24.3 °3 5'60487 3959.2 3342.5 o'8442 || 0-9779 |32 || 2:49: abbie . . . 8 6.6 * . . 3 gº tº it ; ; 4o" 2 # 5' 51742 3237. I 2746.8 o'8485 orož58 21 || 1 '5918 4. jºr ich ; % ; º 5' 60864 3993.8 || 3359'o o'841o o'oZ95 16 | I 2720 S alapich . . 6-8 5||...'...uſuiº ||3: ; ; ; ; ; ; 5.64709 || 4363-6 3678.9 o'843 || 0-0785 |73 || 6′1230 Den Nevis . . . . qo g 6 iºsimuli ; # #: : 5'68727 4786.6 3992.8 o'8342 o°o829 49 4'o621 Den Nevi o 42 58' I , sº ; : ; ; ; , ; 5.58509 3783-3 || 31677 o'8373 o'osi" |42 || 3:4188 8 || Sayrs Law 90 36 43’5 || 7 | .. • 8 ICellie Law . 89 43 23 ‘9 29 5' 17099 || 1458. I 1207-4 o'8281 o'o66o 22 I '8920 Lumsden . . 6. * 9 || Kellic Law * . ; 4 §§ : 5' 23296 I68 I 6 1415 o o'8415 o'oZ93 39 || 3'0927 Lumsden. * * : * * | Mount Battock . ; .. #: § 5' 59737 3891 6 || 3245'4 o'834o o°oS30 28 || 2 ° 3240 Ben Clibrig . 6 34. 6 † ** | Storr. g ; # #. 1% 5'63913 || 4284-0 || 3600-o o'8403 o'oZ99 || 39 || 3' +16+ 544 PRINCIPAL TRLANGULATION. * - “ºlº. . . … -, *| | . I 2. ºr sººn ; ! #: ; 5' 37.556 sº lºss. o'8257 o'o672 | 73 | 6’ 3656 13||.” |: ; ; ; ; ;74794 ssors 4573. ossos | c.9846 ||37 || 3:30: | º 4|***|: ; ; ; ; 5.65536 423,7| 354.s o'869 o'esis|6. 3:09. IS §º : # #3: 5' 16171 1427. I I 190° '834o o'o630 || 44 • 6520 17 i. ſº ; : ;: º 5' 33717 | 2137' 5 1787' '8361 o'o62o 22 '8040 I8 àn. ; .# #: # 5' 31659 2038.6 1706' '8368 o'o616 || 38 • Ioo& I9 sº ſº ; s: : *; 5'493 Io 3060°8 2559: '8362 o'o619 || 36 ‘9484 zo ..." ; ; ; ; ; 5'5774; 3716-6 || 3996-9 o'833, o'o634 16 || 1:3344 2 I *...** ; ; #3 *: 5' 36705 2290°o 1952'4 ‘8526 o' of 37 20 ° 4740 22 ś. ; s: 3: º 5'42890 2640.8 2228.8 '844o o'oZ8o 50 ‘90oo 23|{... . . . . ; ; ; ; #|5-26425 | 1897.9 || 1:27's o'8453 o'o", 29 || 2:2446 24. É.iii. tº º : # #. * | 5:37384 || 2326’9 1988-2 o'8545 o'oZ28 || 23 || 1:6744 25 ||...}, . . . ; ; :}; § 5:42952 2645'2 2207'o o'8344 •esis|ss | * 26 Hºli. ; : $3. *: 5' 46416 2864-7 || 2291.8 ‘8ooo o' Iooo 22 * 2 OOO *|† : :::::::::#|sº sº, was sº sº, e -º as ||..." ; ; ; ; ; ; ; 27016 | 1832-6 || 1537.9 o'839. o'oso | 8 || 1:447, 29 |#." ; ; ; ; ; ; ; 5:4594 || 333-6 || 4-77 o'8;68 || 0-6716 |33 || 2:36.8 3o łº ; : º: º 5:45528 2806' 6 2357.8 ‘84ol o'o6oo 22 7600 3 I Fº ; : #4 5'5437. 3446's 2888.7 o'8396 orogo, 17 | 1-3634. 32 #.º. ; : s: ; * 3099.9 2627-2 o'847; o'oyās 43 32809. COEFFICIENT OF REFRACTION. 545 * - i{ i :3 sº sº. "Fººl: º, . . . . . . .-, * ~ * O / If & J. JJ º 33 Hºw"; ; : ; ; ; 5:49749 309.6 2397.9 o'8398 o'cºol ||37 || 2:9637 34 ;: ; : 33 | | 3:56:37 || 3:35.4 266-2 o'849; o'oys; 23 17365 as Hººd ; : ...} | . 553283 || 3340"o 284-0 || 0.8569 o'oz,6||33 || 2:4596 36 ºver is ſº ; # *::g º 5'63569 || 42.5o ‘8 3566-5 o '8390 o'o605 | 66 5' 313o 37 §º ; 3. sº j 5'60szz 396,-8 || 333i's o'8457 o'oz7. 16 I 2352 38 |...} : ; ; ; ; ; ; 5.4986; 2520' | 2:33.9 o'8467 o'ozó7|29 || 2:2243 39 gº tº ; º ; % 5*40925 2523 7 || 21 19' I o'8397 o'o602 || 22 I '7644 4o ºn ; : ; # : º 5'591.02 3835' 3 || 3291 °o o'8581 o'oZIo 28 I '988o 4. I Fº : * § # 5' 60836 || 3991 5 3199.8 o'8016 || o' ogg2 32 3' I744 42 Hº: ; : #4 º 5'65297 4423°o 3770'8 o'8525 o'oZ38 | 19 || 1:4022 43 *i; § : #. 3. 5' 35288 22.16°4 1857.8 o'8382 orogog 62 5’ or 58 44. Nº. ; : #: ; 5' 39684 2453-3 || 2120°5 o'8644 o'o678 |31 || 2 Io48 45 ; : u º ; ; ...} ; 5'42430 2613.4 2199°6 o'8416 o'oZ92 34 2°6928 46 Fº ; : 33 º 5.43919 2704. 6 || 2328’4 o'8609 o'o696 || 43 2'9948 47 Fºº ; ; ; ; ; 3:37996 || 3339.8 1977's o'8379 o'osi" |29 || 2:3519 48 #. ; # *:: : 5 : 36717 2291 3 || 1970-4 o'8599 o'oZoi | 40 || 2 '804o 49 |; ; ; ; ; ; ; ; ; ; 137;6|| 1349's 1564 o'857, o'oſis 4 || “935 so |º ; ; ; ; ; ; ;size 3749.3 || 3:43.7 o'838; o'osos | 7 || 3.73% 5 I § ; ; ; i; 5.56598 || 362o.2 3046-2 o'8415 o'oZ93 || 78 || 6’1854 sº ||...": ; ; ; ; ;|#|sºss || 2:3:6 seſs's esses oº |79| * 53 º: tº , º ; : #4 ; 5.61443 || 4047° 5 || 3421 - 1 o' 8452 o'oZ74 5* 4’ o248 3 Z 546 PRINCIPAL TRIANGULATION. º - Coeff. of +. Observed Zenith No. 1 Log. 2 + 2' • No. Stations. ºut. ë. Diº. t}, — 180°. 1 – 2 k. Reſºrtion 10. k w. alapicl § 4 dº * jJ j/ 54. jºriº ; # ; ; 5'32 Io9 2059.9 1744.3 o'8468 o'o.766 | 89 6'8174 Scournalapich 90 I4 48°8 29 || -. 8 2016.” sº s' 55 | Ben Macdui . 90 26 55' 9 28 5 °472O 2916' 3 || 2504'7 o'8589 o'oyoó | 78 5' 5068 \ lani 8 i. ;6|Sºl ; : #: ; 4°54′49 || 34-2 || 320-3 || 0-936, orogao 16 o-size JBon Novi 6. 6 - | 57 j. . ; * ...; : 5:26093 1793'5 | 1541 ‘5 o'8595 o'oZo8 57 4'oo?1 8 || Ben Nevis. . . . 9o 44, 34'8 14 | .. g 805 - • 8 † - * 5* | Ben Cleugh . . . 9o 2 II " I 27 5' 52480 3292-9 2805'9 o'852 I o°o?40 53 3'9220 B N * tº º • 6 - - 59 |##. . . . . ; ; ; ; ; 5.45432 2799's 23887 o'8533 o'oy;4|97 || 7-1198 i Ben Macdui . o 20 2 1 - 8 || 42 , or : 6o i. i. º ; IO #: # 5. 34547 2178 9 1884-7 o'865o o'o675 87 5'8725 | 6p || Ben Lawers . 99 44 °7'4 19 || 3.2126 iº º •8 gº * | Merrick. | | 6a 3, 26.4 16 5’71495 5975.9 || 4313 8 o'85oo o'oZ5o 57 4'275o 62 #º ; # #: ; 5' 65121 4405' 5 3726'5 o' 8459 o'oZ71 || 45 3:4695 63 㺠; t; 3. ; 4 ° 99047 962 - 2 818.6 o'8508 o'oZA6 20 | 1.4920 L . 8q 28 22 64 Fº i. : : *::: ; 5' 19654 1546'4 1296-9 o'8386 o 'oSo? 30 || 2:42 Io 65 | Elimäden, . 90 Io 3o 7 || 8 || -. * * . * 5 | Blackheddon. 3G s 39.4 18 5'9554* | *74 9599 || 0 8591 o'oZo.5 | 19 || 1:33.95 Cheviot . . I 2 - 6 21 . . sº .* 66 Blackheddon. § : 48° 3 18 4'8673o 724-6 590’9 o'8155 o’og23 26 || 2 3998 67 sº ; # #: # 5:23766 17oo'o 1435-8 o'8446 o'oZ77 26 || 2 ozoz Cheviot . 18 40- | 68 |}. . ; : §. º 5' 33872 2I45'5 1785’7 o'8323 o'o639 15 1 - 2585 Ben Hutig . 8 6-6 || 8 * 69 #. §: ſº ; * . 33 5' of 847 1151 3 987:6 o'8578 o'oy11 22 I 5642 Ben Hutig . 8 sº - 70 #." ; #. ; 5 : 4'870oo 729 'o 612 7 o'8405 o'o'798 || 7 || o' 5586 Ben Hutig . 90 20 4." i. ſº 71 jhis . . . ; ; ; ; ; |4-95785 | 892.4 || 759 o'8596 o'oZAZ || 8 || 0:5976 Ben Clibrig . 90 48 6. 7 || 1 * * * - 7* | Fashven g 89 : ;4 % 5' 1816I 1493-9 1265. 9 o'8474 o'oj63 | 19 || 1:4497 Ben Clibrig . O * 2 . . . 73 ||...” § 3; ; ; ; 5' 19896 || 1554.9 1343.9 o'8643 o'có79 |35 || 2:376; Cnoc-ghiubhais . 88 2 I 32. 6 sº 74. . & 9I 4. I *::: ; 4'25345 176.3 159' I o'9026 o' o487 4 o. 1948 COEFFICIENT OF REFRACTION. 547 * º - Coeff. of Ob ºd 2 + 2' º No. Stations. †"|3. Diº. . sº. – 21 |* | * | *w. Den Lawers . & 46 1% 4 * iſ f 75 Ben Cleugh . ; ; '; § 5' 20427 I574° 2 1344°8 o'8543 o'oZ29 || 62 || 4' 51.98 Ben Cleugh . . 6. 76 j . . . . ; *...} : 5'5409a || 3417-4 2881-6 o'8432 o'oz84 || 35 | 2:7440 Ben Cleugh . 90 16 20' I 9 {} º | -. 77 | Dunrich 90 18 39° 5 || 4 5*40510 || 2499-7 2099°6 o'8399 o'o601 || 14 || 1: 1214 8 Ben Cleugh . 90 19 33 ‘8 || 8 º ſº 2060 • 8 º wº - 7° | Goat Feli 3o 23 &g | 6 || 5'55°or 35057 29907 || 0-8445 o oz78 20 | I 5560 6 8 . º 79 flºº º : ; ...; s 5'46828 2891 - 2 2369°5 o'8196 o'ogoz 27 || 2:4354 {- 24, 28 so |º ; ; ; ; ; ; 5.61129 || 4918.6 3377.2 o'8404 o'oj98 || 36|| 2:8;28 Ben Macdui . • 8 * 81 #. §. º ; 4; : ; 5-51034 || 3185°o 2703-6 || 0-8489 o'oZ56 |57 || 4:3092 Ben Macdui . 2 • 6 82 Mamsuil º ; : #: 4 5 °4744. I 2932 °o 2507. I o' 8551 o'oy25 24 I 7400 8 Ben Macdui . . 99 45 4 39 || 3.298 º 614.' •86 •o6 * . 3 Mount Battock . 89 41 52-3 ||34 || 5 °7 87 | 1869. I | 1614’3 o'8637 o'o682 77 || 5:2514 Mamsuil . 90 2 I 30 6 21 || -. i. º • 8616 off 8 *4 |iºn invers . ; :: *5. ..., | 5'50952 3179°o 2739°o o'8616 o'o692 58 4'oisé Mormonth . . . . 8q 56 4.5" - ~~ g 85 jito... . . . ; ; ; ; ; ; 5:44233 || 27-3-2 || 23997 || 0-8482 o'oZ59 |46 3.4914 º 6 I 3 '' - 86 §. : 3. º: : 5' 23842 1702.8 1455'8 o'8549 o'oZ26 || 38 2.7588 tº º te 6 • - t tº tº 87|#ºn ; : ; : ; 5' 38595 || 2392 “o 2003°7 o'8377 o'o612 52 || 4-2224 6 tº - * tº - 88 Hºl. : ; #3 ; 5'41838 2577°4 2128: I o'8257 o'o672 || 36|| 3: 1392 89 iſſiºn. ; # £: : 5' 23217 | 1678-6 || 1438:7 o'8571 o'o.715 24 || 1:716o Corryhabbio. . 90 12 Io. 1 || 49 | .. ſº • 6 o '86 'o608 || 66 || 4 - 6068 9° Mount Battock . 3. i. i.; : 5°23'34 1675-3 || 44 o' 8bo5 o' obg 4' bo Pill tº • I º - 9I §. º ; . 33.3 º 5' 31368 2025'8 1723'3 o'8507 o'o.747 || 37 2 '7639 | 92 Mººn ; ; #.” i. 5' 29968 || 1961 : 5 17oo'o o'8667 o'o667 || 44 || 2 '9348 Wingreen . Ç. º 93 Butser Hill . ; º #: # 5:41479 || 2556.8 21814 o'8532 o'o.734 || 42 || 3 ob28 Inkpen . . - ſº & 94. #. IHill . . : ; : # 5' 2462 I 1734° 3 1468.8 o'8469 o'o';66 27 2 oô82 IBeachy Head * 2. º 95 ; iº ; ić #: # 5.3354o 21297 | 1809-3 o'8496 o'oZ52 |31 || 2:3312 | - 3 Z 2 548 PRINCIPAL TRIANGULATION. º ff. Of º Observed Zenith| No. Log. 2 + z' Cºeff. No. Stations. Distance. Obs. | Distance. 1), – 180°. 1 — 2 k. Rººm 10. kw. 96 * . # #: ; 5'41263 || 2544.' I 2162-6 o'8501 o'o.749 |34 || 2:5466 h: & Cº º 6 IQ 8 I 97 }. º, º ſº. : º #. : 5' 25ooo 1749'5 1513° 2 o'8649 o'o676 30 || 2: o38o 8 Beacon Hill . . . . 9o 7 41 9° Mendip . . . . go 18 52. : #| 5-27651 1859-6 || 15944 o'8574 o'oy13 29 || 2:0677 Pillesdon . . . . * º * 99 Hºwiny. tº : ; ;: § 5'44131 2717'9 || 2329°7 o'8572 o'oZ14 || 39 || 2:7846 Pillesd * G - º º º º IOO j. tº ſº. º. ; . #: {{| 5:33595 2132-4 1828°o o'8573 o'oZ14 || 4 || 2: 9274 IOI º, . . . ; : §§ ; 5' 21570 | 1616' 6 || 1387'o o'858o o'oſio 27 | 19170 IO2 Hºy, . : #3 ; 5:26086 1793.8 1529 o'8525 o'oz88 ||25 | 1.8450 Io3 flºw ; : : ić #: # 5' 27038 1833-6 || 1476.9 o'8055 o'ogy; 16 I 5568 toº ºf... . . ; ; ; ; ; 5.49954 3016 || 387.9 o'8496 o'oys. |34 || 2:3568 slºg |; ; ;|#|sºms use, sº ºw: *, * * Ioé Bº ; : : ; ; ;: ; 5' 30783 1998: 7 | 1695'o o'8481 o'oyāo 34 2 5840 Io'7 #. Twº . ; '; §§ : 5' 20088 1562' 4 || 1339'3 o'8572 o'oZ14 27 | 1 9278 |ios ºjº, . . . ; ; ; ; ; 5.43903 27°3′o 2.86% o'8458 o'oſi 55 || 4-249s Io9 #. . ; º #: ; 5' 22518 1652 3 || 1398. I o'8462 o'oZ69 29 - 2 2301 is ſº ; ; ; ; ; ; ;|sº | * *s, *s, *, *| rºse, - Severndroog . . . . 8 O 2 22 | . . iº º º * III Leith Hill Tower i. ; # 31 '7 f 5 I6066 1424 2 I231 9 O 865o - O o675 3 I 2 ” O925 Leith Hill Tower . . 9o 20 1- |*| Dunstable . . . go 15 28: § # 5'40466 2497'8 2129°7 o'8526 o'oZ37 28 || 2:0636 In the first 35 of these cases it will be seen, on reference to the map, that the ray passes for a considerable portion of its length over the sea, and in the next 13 cases the ray passes also over the sea, but for a smaller proportion of its length; in the remaining cases the ray is inland. From the first 35 we have k = o-o801; from the next 13 we have k = orož78; and from the remainder we have k = o'oZ44. - In the preceding table of 31 coefficients obtained from levelled heights (page 542), if we separate those rays which cross the sea from those which do not, we get for the former COEFFICIENT OF REFRACTION. 549 { j;&!* l f Jura . . . . . . 2566 | Sept. 30 Nov. 12 | 1st to 2nd 27°53 || 48 23rd to 24th 26' 67 || 36 || 27.288 k = .0817, and for the latter k = 'oZ72; or if we omit the case of Ben Nevis, in which the atmosphere” was apparently in an abnormal state, k = 'oZ56 for rays not crossing the sea. These * It is much to be regretted that the observations of the barometer and thermometer on the tops of the hills in Scotland were not made with systematic regularity. The following results of the observations at some of the highest points may be interesting, but it is necessary to premise that the index error of the instrument in each case is not exactly known. It is an almost unavoidable result of travelling that small bubbles of air are introduced into the vacuum, and thus all readings will require a positive correction, which at some of the stations may amount to nearly a tenth of an inch. Period. Maximum Pressure. Minimum Pressure. * Corres. Corres.|| Mean | Mean | No. Name. Height. Temp. Temp. Pressure.}Temp. Obs. IFrom To Date. Amount. Date. Amount. O O O * - t to 6tl - th & 16th Ben Nevis . . . . 4406 || Aug. 1 | Nov. 14 º 25' 62 58 '%. 24°37 || 35 || 25-233 || 45 || 16 June 29 21st to 24th to July 2 26. Io 58 June. 25° 15 38 || 25' 713 || 47 71 Ben Macdui . . . . 4296 || June 6 Aug. 16 21st to 22nd Goat Fell . . . . 287s Aug. 13 || Dec. 2 || “...“ 27:37 56 || Oct 5 26-27 | 37 || 26,754 42 too 12th to 14th Scournalapich . . . 3773 || July 15 Oct. 25 September. 26.63 54 || Oct. 6 25' 15 38 || 26°o52 || 48 |223 ! Corryhabbie . . . . 2569 Sept. 30 | Nov. 21 12th to 13th 27°43 || 4o Oct. 28 26- 60 October. 35 27°oo.4 38 |Io9 | Hart Fell . . . . 2638 Sept. 30 || March 4| * 27°68 || 30 ‘...." 26°54 || 43 27°oj6 29 98 Cheviot . . . . . 2669 || June 16 || Sept. 13 º 27°65 55 * 26' 61 47 27° 21 1 || 51 |Ioo Mount Battock . . 2555 May 1o July 3 | º, 27°81 59 June 14 26'72 45 27°231 5o |168|| October. October. 4 I 89 N.B.-The maxima and minima here given are not single readings, but the mean of the readings during the period of maximum or minimum pressure. From the usual formulae connecting the heights of stations with the readings of the barometer, and assuming that the thermometer falls 1° for every 275 feet of altitude, we may derive this formula— - b (1 + #) 2O5 = —; R log k (1 + #) - which gives the height, b, of the barometer at the altitude, h (= 62137 k), above the level of the sea, when the height of the barometer at the level of the sea is b, and the temperature 50° -- r. If we assume 29.850 as the mean height of the barometer in the latitude of Scotland at the level of the sea and temperature of 50° Falirenheit, the corresponding height due to different altitudes will be as follows:– Altitude Height of Altitude Height of in Feet. IBarometer. | in Feet. Barometer. in. in. 2COO 27° 7'oz + °oo72 r 35oo 26- 173 + °oroo r 25oo 27, 185 + °ooS2 r 4ooo 25°68o + oro8 r 3ooo 26-675 + °oog1 r 45oo 25° 193 + of 16 ºr At Storr in the Isle of Skye (2341 feet high) the mean' height of the barometer was 27.464 inches. The most severe weather ever encountered by any of the observing parties was at this station, which was only completed after the most extraordinary perseverance. Shortly after the commencement of the observing, a storm of wind carried away the wooden houses of the men, and left the observatory roofless. Three observatory roofs were subsequently demolished at different periods, and for some time the observatory was used without a roof, being filled with snow every night and emptied every morning. The instrument was protected under shelter of the cooking-house. 550 PRINCIPAL TRLANGULATION. determinations agree satisfactorily with those from the second table. The individual determina- tions in the first table would seem to be entitled to the most confidence, being directly observed, but the number of determinations in the second table is considerably greater; we may make these respective advantages counterbalance, and assume the mean as true; namely, Coefficient of Rºain'ſ = o.o.809 for rays crossing the sea. = o-o/50 for rays not crossing the sea. With one or two exceptions, all the coefficients in the preceding tables are derived from observed zenith distances of very distant objects; and the results are, upon the whole, tolerably consistent. The same consistency, however, is not found to exist among coefficients of refraction deduced from the observations of objects at short distances: the values are very irregular, and, indeed, "cannot be represented with precision by any mean quantity. A great deal depends upon the nature of the ground over which the ray passes: as a general rule, when the distances are small the ray passes near the ground, which would tend to increase the coefficient of refraction, as is evident from Struve's formula (page 512); and this agrees with observation, for the mean value at short distances is certainly not under o. IOOO, one-tenth of the arc-distance, with an uncertainty of at least half that quantity. Fortunately, however, the shorter the distance the less will the resulting altitudes be affected by error in the assumed refraction. Altitudes above the Mean Level of the Sea. : In the summer of 1842 a system of tidal observations was instituted by the late Major- General Colby round the coast of Ireland, in order both to improve the theory of the tides and to ascertain the relative advantages of using high water, low water, or the mean of high and low water, as the plane of reference for altitudes. Observations of the tides were made with great regularity for the space of two complete lunations (during the months of June, July, and August) at 22 stations round the coast of the island, the stations being connected by lines of spirit-levelling. These observations have been fully discussed by the Astronomer Royal in a paper which will be found in the Philosophical Transactions, Part I., for 1845. The relative heights of the surface of the sea round Ireland, which have been deduced from them by means of the connecting system of levels, are exhibited in the following table”:— Spring Tides. Neap Tides. Mean Height Stations. of Mean Water. Mean Height | Mean Height | Mean Height | Mean Height of Of of of k High Water. Low Water. High Water. Low Water. Fect. Teet. ” Feet, Feet. Feet. Kingstown . 8' 395 I4 35 2 * II "2 I • 26 Clogher Head . 8, 184 I5 .# § II º: # 3. Ardglass 8.638 I6'431 I ‘oo5 I2 °53 I 4' 503 Donaghadee 8: 745 I5' oA6 3 'o61 II '910 5' 39 I Glenarm 8. 709 I2 - 681 5' 336 Io 68I 6:700 Ballycastle . 8’479 Io'864 6- 601 8-651 7.726 |Portrush 8 : 682 I2 °234. 5’ 674. 9°og4. 7' 634 | Carrowkeel. 9 “O29 I3° 447 5' 187 ro' ro7 7' 532 Buncrana 8° 369 I5’ og I I '911 Io. 566 5 °791 Mullaghmore 9 OAZ I5' 538 3'o';8 Io'993 6- 668 Old Head . . . 8 725 I5'28o 2 - 460 Io 8 Io 6°26o Cashla Bay . . . 8-899 I5'98o I '820 II '735 5°998 Galway. º 8’48o I5'853 I' or 3 II '403 5' 39 I IXilbaha. 6' 578 I3' IQ9 - O " IOI 9°279 3 * 709 Kilrush . º 7° 358 I4 * 4 I2 o'o'79 Io 423 4’ or 6 Foynes Island . 8°og2 || 15' 627 —o' 603 11 : 672 3. 809 Limerick º 8: 567 I7' 502 —2 o88 I2 ° 935 2-516 Castletownsend . . 6' 660 II 954. I '984 9° 55 I 4" or 4. Passage West . 6'934 13. 601 I 3 II Io' 5 I4. 3.601 Dunmore East . 6'753 || 13°og9 o' 699 9°879 3' 629 New ROSS 7.667 I4'822 I 256 II 3oo 3° 737 Courtown . 7' 598 9°849 6' 139 7° 732 7'407 A glance at this table shows that mean water is more nearly on a uniform level round the coast of Ireland than low water of spring tides, to which the altitudes on the Ordnance maps in that country have been referred. The mean sea level appears, indeed, to be rather higher round the northern than round the southern coast of the island, but the difference is small, and it would pe difficult, considering the very small number of stations, to say how far it is real. A very close approximation to the true height of mean water at any station may be obtained from a few observations of high and low water at any period of the lunation, and Mr. Airy has * See the volume entitled “Abstracts of the Principal Lines of Spirit-levelling in Ireland,” published by Order of the Master General and Board of Ordnance, 1855. 552 PRINCIPAL TRLANGULATION. shown that the irregularities in its height from day to day, which appear to be chiefly caused by irregularities in the atmospheric pressure, are nearly the same on every part of the Irish coast at the same time. In consideration of the advantage of mean water as the plane of reference for altitudes, it was adopted by Major-General Colby for the levels and altitudes of the Ordnance survey of the north of England and Scotland, which are all referred to mean water at Liverpool. When the observations of the general triangulation were resumed in the north of Scotland, in the summer of 1838, by the late Lieutenant-Colonel Robe, R.E., several tidal stations were formed and the height of mean water ascertained for the determination of the heights of the trigonometrical stations.” The distances of these tidal stations with respect to the trigonometrical stations were determined by special triangulations, observed with 5 and 7-inch theodolites. It seems unnecessary to give more than the results of these operations, which are as follows:– Height above Mean Ilevel of the Sea. Names. Log. Distance. From º 5143882 | Ben Hutig. IRoan Island . . . . . 243'88 {{. # 199 || Ben Clibrig. ſº ſº • 670078 Fashven. Rispond . . . . . 7o 13 {{...; Ben Hutig. { 4’ ob43398 || Cnoc-ghiubhais. 4' 394.7377 | Fashven. Berriedale Tower. . . 187° 76 4' 362 Io23 || Scarabin. Brock . . . . . . 9I o2 3.9539667 | Dunnet Head. Loch Seaforth, Cottage . 33°65 4' 304.1556 | Cleisham. Callernish . . . . . 46.86 4. 1315796 || Ben More, South Uist. Clashcarnach . . . . 228" I2 * The descriptions of these stations are as follows:– Roan Island Tide Station.—The graduated tide-pole was erected in a quiet inlet on the eastern coast of Roan Island, in the Kyle of Tongue: a Bench-mark was cut on a rock, at the level of 8.250 feet above the zero of the tide-pole. From the observations of 14 high and 14 low waters, the reading of mean water on the tide-pole was found to be 6' 63 feet. Thence, by levelling, the height of the Tide Station was found to be 243'88 feet above the mean level of the sea. Iłispond Tide Station.—The graduated tide-pole was erected in a quiet inlet about 1oo yards west of the Tide Station, which was on the small headland forming the western promontory of the entrance to Loch Eriboll. From the observations of 34 tides, the reading of mean water on the tide-pole was found to be 7' 16 feet. Thence, by levelling, the height of the Tide Station was found to be 70- 13 feet above the mean level of the sca. Clashcarnach Tide Station.—The tide-pole was erected in a small inlet to the east of Cape Wrath Lighthouse ; the Tide Station being on the cliff above it. At this point only three tides were observed, and, by levelling, the height of the Tide Station was found to be 228 - 12 above the mean level of the sea. Berriedale Lower Tower—The tide-pole was erected in a small rocky inlet on the east side and immediately under the ruins of the old Castle of Berriedale, in Caithness-shire. The mean of 41 tides gave 8' 911 for the reading of the pole, corresponding to mean water. A hole was jumped in the rock corresponding to Io'75 feet on the pole. The height of the bottom of the tower was found by levelling to be 187° 76 feet above the mean level of the sea. Brock Tide Station, near Dunnet Head—Record of the tidal observations defective. The Tide Station is found by levelling to be 99'93 fect above lowest tide, or 91 oz above mean water. - Loch Seaforth Tide Station, Island of Lewis-The graduated tide-pole was erected about a quarter of a mile south- west of Sir Frederic Johnstone's cottage, at the first rocky point projecting a little into the Loch. The mean of 51 tides ALTITUDES ABOVE THE MEAN LEVEL OF THE SEA. 553 * Of the stations composing the principal triangulation, the heights of the following have been obtained by spirit-levelling:— Height Height Names. M ãº,el Remarks. Names. M.. vel Remarks. of the Sea. * . of the Sea. Feet. - Feet. Arbury Hill . . 735'26 Surface. IIensbarrow . . . . Ioz6'99 Surface. Beacon Hill tº ſº º 668-74 }} High Wilhays. . . . 2039' 61 5, ' Blackdown . . . . 790: oo Monument 861 38. Ingleboro' . . . . . . 23.73° 49 3) Ben Lomond . . . . . .3192: 16 Surface. ICarnminnis . . . . 799 - 78 33 Ben Nevis. . . . . . 4406: 31 3 * Lincoln Minster . . . 475 ° 35 Pinnacles. Botton Head . . . . 1489' oo 35 Maker Church . . . 366° 35 Surface. Burleigh Moor . . . 581 Io J} Malvern . . . . . . 1396-20 33 Calton IIill . . . . 349' 60 JJ Merrick . . . . . . 2764- 80 }} | Clifton Beacon . . . 460 ° 90 }} Monach . . . . . 813 '83 3 J. Coringdon . . . . . 655° 55 3) North Rona . . . . 355 ° 20 31 Cowhythe . . . . . 272 75 Above low water. Old Sarum Castle. . . 404' 68 }} Criffel . . . . . . 1866 - 60 Surface. Old Sarum Gun . . . 24. I 3 I }} Ditchling tº ſº tº . . 814' 17 }} Pertinney º, º ſº º tº 735 °47 25 Dunkery . . . . . 1706:44 35 Precelly . . . . . 1757. 9o 33 Dunnose . . . . . 771 ° 90 32 Sayrs Law. . . . . 1753 'oZ 3 y | Dunstable . . . . . . 8oo 25 33 S. End Lough Foyle Base 88 oo 39 East Lomond . . . . I471 ° 30 92 Southampton . . . . 78. oo 33 Garforth Cliff. . . . 342 O4. }} Saint Paul's . . . . 417 '91 Top of Cross. Gerth of Scaw. . . . 7o' 20 3} Swaffham . . . . . 372 '60 Telescope. Great Stirling . . . 26o 5o 33 Swyre . . . . . . 674° 40 Surface. Great Whernside . . . . 2310-30 95 Trevose . . . . . 242 58 $ 2 Hanger Hill . . . . 2O I " I 2 3) York Minster . . . . 53 Io y? In order to show the degree of reliance to be placed upon the determinations of heights by means of observed zenith distances, we shall now give in detail part of the calculation by which the heights of those of the principal stations which have not been determined by levelling have been ascertained. - - We shall commence with the stations on the north coast of Scotland, whose heights are determinable with sufficient accuracy by means of the tide stations described in the last page. The heights of the tide stations at Rispond, Clashcarnach, and Roan Island are 70. I, 228. I, and 243.9 feet respectively above mean water. Assume the height of Ben Hutig 134o + æ, of Fashven 1495 + y, and of Cnoc-ghiubhais 976 + 2, then by means of the reciprocal observations of these stations, and their observations of the tide stations, we have eleven equations for the determination of a, y, z. These equations are thus obtained: the difference of height of Ben -—-mºsº gave 8 °30 feet as the reading of incan water on the tide-pole, and, by levelling, the height of the ground at south-West corner of tho cottage was found to be 33 65 feet above the mean level of the sea. Callernish Point, in South Uist.—The graduated tide-pole was erected in a sheltered situation about 200 yards north-east of the Ku Callernish Pile. The result of 28 observed tides gave 10-48 feet for the reading of mean water on the pole ; and, by levelling, the centre stone in the Callernish Pile was found to be 46-86 feet above the mean level of the Sea. 4 A. 554 PRINCIPAL TRIANGULATION. Hutig and Fashven is, by the observations at the former station, 156.3, and by the observations at the latter, 154.7; these quantities supply two equations, namely, a – y— 155 + 156.3 = o a — y + I-3 = o Or In general, it is convenient to assume for the weight of an equation the number of observations upon which it depends, divided by the arc (; – k) v, expressed in minutes: this quantity being proportional to the distance, and of a convenient magnitude. In thus estimating the weight, it is by no means necessary to calculate it with precision. Thus the weights of the equations just written down are each taken equal to unity. The reciprocal observations at Ben Hutig and Cnoc-ghiubhais give the equations— w a — y — o-3 = o a — 2 + 1.7 = o *: a; – 2 + O. I = O - - The weight of either may be taken at .75. From the eleven equations that may be deduced in this manner between a y and z, we have finally, by the method of least squares, the following— 27.5 a - 2-o y – I-5 z + o-o = o — 2-o a + 22-o y – 9-o 2 – 18-O = o — 1.5 ac – 9-o y + 36.52 + 18.8 = o From these we have a = + o-o; ; y = + o-68; z = — or 35; whence, Height of Ben Hutig . . . . . . . . . 134o.o Feet above Mean Level of Sea. 33 I’ashven . . . . . . . . . . I495.7 35 35 35 Cnoc-ghiubhais . . . . . . 975-7 53 35 These values satisfy the observations with much precision, and therefore the determinations may be considered as satisfactory. The height of the tide station Brock, near Dunnet Head, is 91.0 feet above mean water, and the height of Berriedale Tower, near Scarabin, was found by levelling to be 187.8 feet. By means of these data we may fix the heights of Dunnet Head, Ben Chielt, and Scarabin. Assuming the heights of these three stations to be 420 + 4, 940 + y, 2054 + 2, we have six equations for the determination of a, y, z, which when combined, having respect to their weights,” form the group— 41.25 ac – o-25 y – I'oo 2 + 77.52 = o . — o-25 a + 4-oo y - 3.752 – 2:55 = o — 1 -oo a; - 3.75 y + 24.75 2 + I.O.3 = o Whence we have a = — 1.88; y = + o-48; z = - o'o.4. Applying these corrections, there results— * Height of Dunnet Head . . . . . . . 418. I Feet above Mean Level of Sea. 33 JBen Chicle . . . . . . . . . 94O-5 33 33 35 Scarabin . . . . . . . . . 2O54'o 35 33 We may compare these results with what would have been derived from Ben Hutig. The reciprocal observations at Dunnet Head and Ben Hutig (two observations at each) give 917 feet for the difference of height: this applied to the height of Ben Hutig as just determined, namely * When the weight deduced, as explained above, does not much exceed tº the corresponding equation is rejected. ALTITUDES ABOVE THE MEAN LEVEL OF THE SEA. 555 1340 feet, would give the height of Dunnet Head 423 feet, showing a discrepancy of 5 feet. The reciprocal observations at Ben Chielt and Ben Hutig give 415 feet as the difference of height of those stations: this quantity applied to the height of Ben Hutig gives 925 feet for the height of Ben Chielt, which is probably too small by 15 feet. And finally, the ten observations at Scarabin give 744 feet for the difference of height of that station and Ben Hutig: this applied to the height of Ben Hutig would give the height of Scarabin too great by 30 feet. - The height of Ben Clibrig may be determined very satisfactorily from Fashven, Ben Hutig, Scarabin, Dunnet Head, and Ben Chielt; and also by means of the observations at Ben Clibrig of the Roan Island Tide Station. We have thus ten determinations of the required height; of these, six are between 315I and 3158 feet; the others are 314o. 6; 3162. 1 ; 3170. 6; and 3168. o. Thus the height of Ben Clibrig is found, by giving to each determination its proper weight, to be 3157.6 feet. - From the levelled heights of Ben Nevis (4406.3 feet) and Ben Lomond (3192.2 feet) we may determine the heights of Scournalapich (3774 + v ), Mamsuil (3862 + y), Ben Lawers (3984 + 2), and Ben Macdui (4292 + w). This system of points supplies twenty equations for the determination of the four unknown heights. These equations resolve themselves into the following system— 30.5 a - 23-o y + . . . – 2.5o w -- 42.70 = o — 23-o a + 28.5 y – 2-o- 2 – o-75 w — 20-35 = o { } - 2'o y + I3-25 z – 5-o w -- 16.40 = o - 2.5 a - or 75 y – 5-o z + II-75 w — 45-45 = o Whence— a = – I-24; y = — o' 18; 2 = + o-Io; w = + 3.64. So that we thus have— Height of Scournalapich . . . . . . . 3772.8 Feet above Mean Level of Sea. , Mamsuil . . . . . . . . . 386.1.8 3 y 33 33 Ben Lawers . . . . . . . . 3984. I § 3. 33 33 Ben Macdui . . . . . . . 4295-6 ». 33 The greatest discrepancy here brought out is in the connection of Mamsuil and Ben Lawers. We have obtained, as most probable, their difference of height, I22.3 feet; but the observations (twenty in number) at Ben Lawers give 161.4 feet for the difference of height, and the observa- tions (twenty-one in number) at Mamsuil give 85.4 feet for the difference of height. If, however, we calculate the difference of height by means of the difference of the observed zenith distances, instead of using a value of the coefficient of refraction, we get 124 feet, which agrees satisfactorily with the heights we have assigned. And similarly with respect to Ben Lawers and Ben Macdui;” the differences of height calculated independently are 289. I and 332.4 feet, but if we combine the zenith distances and thus eliminate the coefficient of refraction, the result is 31 I feet, which agrees exactly with the heights assigned as most probable. * Ben Macdui, or, as more correctly spelt, Beinn-muic-dhuibh, has been sometimes stated as the highest mountain in Great Britain ; but as the probable error of the height here given can scarcely amount to 10 feet, Ben Nevis has the advantage by at least Ioo feet of height. 4. A 2 556 PRINCIPAL TRIANGULATION. The difference of height of Ben Clibrig and Ben Macdui is thus 1138 feet. These points are mutually visible, and ten observed zenith distances at Ben Macdui give 1162 feet for the difference of height, while four observations at Ben Clibrig give I Io; feet; the mean of these results, having respect to their relative weights, gives 1146 feet for the difference of height. This is sufficiently satisfactory when the distance, 85 miles, is considered. The points Ben Macdui and Scarabin are also mutually visible. By means of seventeen obser- vations at Ben Macdui, the difference of height is found to be 2301 feet, while a single observation at Scarabin gives 2208; the former exceeds the probable truth by 60 feet, the latter is in defect by 33 feet: the distance is 80 miles. By eight observations at Sayrs Law, distant 93 miles, the height of Macdui is 4314. o feet. The station Knock is well observed from Cowhythe, whose levelled height is 267.7 feet, and may be safely determined from that point alone. We thus obtain 1416.9 feet for the height of Knock. sº. The heights of Mount Battock and Corryhabbie may be safely determined by their connection with Ben Macdui, Knock, and Cowhythe. Putting 2557 -- a and 2555 + y for the required heights, we have ten equations for determining a and y, which resolve themselves into the equations— I 2.25 a - 6-o y + Io9.2 = o – 6.o a + 18.5 y – 270. I = o from which there results a = — 2. Io, y = + 13.92. Consequently, Height of Mount Battock . . . . . 2554.9 Feet above Mean Level of Sea. 3 3 Corryhabbie . . . . . . . 2568.9 33 33 These determinations represent the observations with tolerable exactness. The heights of Corryhabbie, as deduced from Knock, Cowhythe, and Ben Macdui separately, are 2582, 2559, and 2571, the mean differing by 3 feet from the most probable height just deduced. Yet on comparing this with the height of Ben Nevis a very large discrepancy is brought out. The true difference of height is 1837.4 feet, whereas nineteen observations at Corryhabbie give 1957.4 feet for the difference of height, and fourteen observations at Ben Nevis give 1948. 4, either of which, notwithstanding the great number of observations, must be more than a hundred feet greater than the truth: the distance is very nearly 80 miles. A similar effect is observed in comparing Corry- habbie with other distant stations, all tending to show an unusual amount of refraction at Corry- habbie. This extraordinary refraction may perhaps be satisfactorily explained by the circumstance that the top of the hill is an extensive flat. The height of Ben Wyvis may be ascertained from Ben Clibrig, Scournalapich, and Mamsuil, without having recourse to more distant stations. We thus have five determinations, all lying between 3402.6 and 3426.6, which, when combined with respect to their weights, give— Height of Ben JPyvis . . . . . . . . 3422.5 Feet above Mean Level of Sea. The observations at Scarabin give 3410.4, at Ben Macdui 3419.7, while from Ben Nevis forty- two observations give 35ol. 2, and twenty-seven observations at Corryhabbie give 3479.4. From Ben Lawers, Ben Lomond, Ben Macdui, Mount Battock, East Lomond, Ben Nevis, and Sayrs Law, we may obtain fourteen determinations of the height of Ben Cleugh, ranging between ALTITUDES ABOVE THE MEAN LEVEL OF THE SEA. 557 2327 and 2366, from which the height required is found to be 2352.5 feet. The greatest discre- pancies are shown by the distant points Ben Nevis and Ben Macdui. Nine determinations of the height of Glashmeal may be obtained from Corryhabbie, Ben Macdui, Ben Lawers, Ben Cleugh, and Mount Battock. The values range between 3564 and 3482, the greatest value resulting in each case from the observations at Glashmeal, which are few in number, and therefore of small weight. The greatest discrepancy amounts to 62 feet, and results from the three observations of Corryhabbie at Glashmeal, a distance of little more than 33 miles. The most probable height of Glashmeal from these determinations is 3501.7 feet. - By means of the known heights of Sayrs Law, Ben Cleugh, Merrick, and Criffel, and the mutual observations of Hart Fell, Dunrich, Wisp, and Cheviot, we may determine the heights of the last four points. Putting Hart Fell = 2640 + w, Dunrich = 2440 + y, Wisp = 1950 + 2, Cheviot = 2670 + w, we get twenty-eight equations for determining w, y, z, w, which resolve themselves into the following— 14.6 a – 5-o y – 3-4 z – I'o w – 16. I = o – 5-o a + 9.3 y – o-82 — 1.2 w -- 63-6 = o – 3-4a – o 8 y + 6.52 – 1.2 w — 13.5 = o – I'o a - 1.2 y – I-23 + 5-4 w — 4.6 = c From which we obtain— a = — I-6; y = — 7-8; z = + o- I ; w = — 1.2 So that we have— Height of Hart Fell . . . . . . . . . . 2638.4 Feet above Mean Level of Sea. 35 JDunrich . . . . . . . . . . 2432°2 33 55 * 23 Wisp tº ºn tº C & ſº tº ſº tº º tº I950. I 33 35 33 Cheviot . . . . . . . . . . 2668.8 33 35 The largest discrepancies here occur in the observations of Merrick at Hart Fell; Cheviot at Dunrich ; and Hart Fell at Wisp. Seventeen observations at Hart Fell give I 59.2 feet for the difference of height of Merrick and Hart Fell, which probably exceeds the truth by 30 feet at least. In the other two cases the discrepancies are also about 30 feet each, but depend upon a very small number of observations. The observations at Hart Fell present great irregularities; the range in many cases being so large as to render it difficult to say what is the most probable mean zenith distance of the object observed. 558 PRINCIPAL TRLANGULATION. A L TITU D E S ABOVE THE MEAN LEVEL OF THE SEA OF THE STATIONS COMPOSING THE PRINCIPAL TRIANGULATION. | Names. Feet. . Names. I'eet. Names. | Feet. * | Epping Poorhouse . . . . 371 Fairlight Down . . . 583 Faira . . . . . . 7II Fashven . . . . . . I495 Feaghmaan . . . . . . 88o' Petlar . . . . . . 52 I Fitty . . . . . . 55o' Foula . . . . . . . I 372 Four Mile Stone . . . 5 I 3 ' Forth . . . . . . 768. Frittenfield . . . . . . 632 Gads Hill (Base of Obelisk) 297. Galty more . . . . . 3907." Acklam Wold . . . . . 765. 9 | Bunwell Tower Ground 189: Arbury . . . . . . | 735' 3 || Burleigh Moor. . 581 Arrenig . . . . . . 2816'8 || Burnswark . . . . . . 929.’ Axedge . . . . . . 1809-6 || Butser . . . . . . . 882 Back Tor . . . . . 1764' Cader Idris . . . . . . 2959 Baconsthorpe Tr. Ground 263 3 || Calherbarnagh . . . . . 22.31 Balsham Tower Ground 378' I | Calton Observatory (B.M.) | 349." Balta . . . . . . . I43’5 | Carn Galver . . . . . . . 826' Ballycreen . . . . . . 2167 2 | Carrigfadda . . . . . IoI9' Banstead . . . . . 572 Cheviot. . . . . . . 2668 Barrow Hill . . . . . 447' Chingford . . . . . . 299' Bardon . . . . . . 902 Cleisham . . . . . . 2622' Baurtregaum . . . . . 2788' Clifton . . . . . . . 460' Beacon Hill . . . . | 668.7 Cnoc-ghiubhais. . . . . 975-7 || Garreg . . . . . . . . 808° Beacon Hill, Trescow . . I 2.2 ° Collier Law . . . . | 1685 Garforth Cliff . . . . 342 ° Beachy Head . . . . 532 ° Coringdon . . . . . 655 Gerth of Scaw. . . . . 7o: Ben Cheilt . . . . . 94 o' Corryhabbie . . . . . 2568 Goonhilly 367. Gorleston Tower Ground 34." Great Ormes Head . . . 683. Great Stirling . . . . . 260: Great Whernside . . . . 23 Io' Greenwich Obsy (Vane) . 214' Gwaunysgaer . . . . . . 694' Gringley . . . . . . 275' Glashmeal . . . . . 35o I' Goat Fell . . . . . . 2874' Ben Clibrig . . . . . 31.57° Ben Corr . . . . . . 23.28° Ben Heynish . . . . . . 473 | Ben Cleugh . . . . . 2352 Ben Lomond . . . . 3192' Den Hutig . . . . . . I34o Den Lawers . . . . 3984' Ben More, South Uist . 2034. Ben More, Mull . . . 3185. Cowhythe" . . . . . . 267' Cradle . . . . . . . 2660' Criffel . . . . . . . 1866. Croghan . . . . . . 761 Cyrn-y-Brain . . . . 1843' Cross Fell . . . . . . 2927' Crowborough . . . . . 893" Crowle . . . . . . 63 Cuilcagh . . . . . . 2180° Den Macdui . . . . . 4295' Cundtham ſº º & C 756: Hampton Poorhouse . . 57° Ben Nevis . . . . . . 4406’ 3 || Danbury Spire . Ground 366-7 || Hanger Hill . . . 2 O I " Ben Tartevil . . . . . 743 - 4 || Dean Hill . . . . 512 "o Hanslope Spire . Top # i. I Ben Wyvis . tº . Berkhampstead Gazebo. Ground 352. Black Comb . . . . . 1974. Blackdown Mont . Top 861. Ground 790. Blackheddon . . . . . 656. Blue Hill . . . . . . 465. Boniface Down . . . . . 483. Boniface, South East . . 755. Boston Tower . . Top 286. Botton Head . . . . . 1489. Brandon Down . . . . 866. Brandon Hill. . . . . 31 19- Brandon, Suffolk . . . . . 163. Brassa . . . . . . 737' | Happisburgh Tr. Ground Hensbarrow . . . . . Io27' Hart Fell . . . . . . 2638' High Port Cliff . . . 134' High Wilhays . . . . . 2039.' Holme Moss . . . I925 ° Hingham Tower . Top | 312 ° IHortons Gazebo . Top 354' Howth . . . . . . 555 ° Hungry Hill . . . . . 2243' Ingleborough . . . . . 2373' Inkpen . . . . . . . 972 Jura . . . . . . . 2566. ICarnbonellis . . . . . 808- ICarnminnis . . . . 799' Reeper . . . . . . . 2270." Reysoe Church Spire. Top 358 King's Arbour . tº ſº 84' Rellie Law . . . . . . 595 Kippure . . . . . . 2465’ Deerness . . . . . 282 Ditchling . . . . . . 814' Divis . . . . . . . I559' Docking Tower . Top 357' Doolieve . . . . . . 592 Delamere . . . . . 572 Deadman . . . . . 372 Drung Point . . . . 55 ° Dudwick . . . . . 562 Dunkery . . . . . . I706' Dublin Observatory . . . 272 Dunnet Head . . . . . 4.18' Dunnose . . . . . 77I Dunrich . . . . . . 2432 Dunstable tº £ tº tº 8oo' Durham Observatory (Dome) 360' Brimmond . . . . . . 859' Easington . . . . . . 683. Broadway Tower . . . . IoA5' East Lomond . . . . . . 1471. Brown Willy . . . . . . I 364' I | Easton Tower . Ground 287. Buckminster Spire. Top 586' 6 | Ely Minster . Ground 5 I 3.422 ° * The altitude of this point was found, by levelling, on August 25, 1813, to be 272-75 feet above low water : 5 feet has been deducted to refer it to the mean level of the sea. ALTITUDES ABOVE THE MEAN LEVEL OF THE SEA. 559 Names. Feet. Names. Feet. Names. Feet, ICnock . . . . . . . I I49' Norwich Spire. Ground 19.7 | Slieve More in Achil . . . 2196'4 Knockalongy . . . . . I77o'o Nodes Beacon . . . . . 483 o | Slieve Snaght . . . . 20II •o Inocklayd . . . . . . 1677. North Ronaldshay Light- Snowdon . . . . . 3590' I Rnockmealdown . . . . 26or " house . . . Ground 25° South Berule . . . . 1598' 3 Knocknadober . . . . . 2258. Norwood . . . . . 258 South Lopham Tr. Ground | 160-4 IXnocknagante . . . . . 21.78: Old Lodge . . . . . 562 South Ronaldshay . . . 383 : 3 Ordnance Map Office . . 78. Orford Castle. . Ground 39.' Otley Tower . Ground 179' Over Hill . . . . . . 449” Paddlesworth . . . . . . 626° Paracombe . . . . . . I 572 ° Pendle Hill. . . . . . 1816. JPeterhead Old Windmill . 74° Peninnis Windmill . . . Ioy' Pertinney . . . . . 735' l’illesdon . . . . . . 909" Inocknaskagh . . . . . 1398. Knockanaffrin . . . . . 24.70. Lawshall Tower. Ground 335- Laxfield Tower. Ground 152. Layton . . . . . . . . Leith Hill . . . . . . 967.' Lincoln Minster . Top 475 Littletown Down ... • Little Stirling . . . . 312' Long Mount . . . . . 1696. Llanelian . . . . . . . . Io9 Lough Foyle Base, N. End 17. Southwold Tower. Ground 38-4 Stoke Tower . . . Ground | 188: 1 Stoke Hill . . . . . . 731 “4 | Stronsay . . . . . . I48° 4 Storr . . . . . . . . 2341 ° 5' | Swaffham Spiro Ground 236.8 Swyre Barrow . . . . . . Start Lighthouse (Base of ... Cupola) . . . . . . Io9' Tāur . . . . . . . 1321 Tarbathy . . . . . . 168. O o Precelly. . . . . . . 1757: 9 || Tawnaghmore . • . . I roj-3 Lough Foyle Base, S. End 80° Plynlimmon . . . . . 2481 Thaxted Spire . Ground 324.8 Lundy Island . . . . 466 Reform Monument. Top 243'o Telegraph Tower. Ground 159.7 Lynn Church Tr. Ground 18° 5 || Rona, North . . . . 355 2 | Tharfield . . . . . 55o'o || Lyons Hill . . . . . . 644°o | Ronas . . . . . . . 1474-8 || Tilton . . . . . . . 755 'o Lumsden . . . . . 737 Ru Rea . . . . . . . 953° Tofts Tower . . . . 98’o Maker Church Tr. Ground 366-3 || Rhuddlan Base, East End. 21 - 3 || Tara . . . . . . . 817 ‘o Malvern . . . . . I 596 Rhuddlan Base, West End. 20:2 l Trostan . . . . . . . 1802 "o Mamsuil . . . . . 3861 - 8 || Ryders Hill . . . . . 1696 o | Trevose Head . . . . . 242 6 Mendip . . . . . . . 979' Old Sarum Castle . . . . 404-7 | Upcot Down . . . . . 890°o Merrick . . 2764.8 || Old Sarum Gun . . . . 241 - 3 || Vicars Carn . . . 8o0 o Merrington Ch. Tr. Top 698. Sawel . . . . . . . 2228. o | Walpole, St. Peter's Tower. Mickfield Ch. Tr. Ground | 194'6 | Saxavord . . . . . . 937. I Ground 8. Milk Hill . . . . . . 966-7 || Sayrs Law. . . . . . 1753 - 1 || Walton Tower . . . . 74° M. C. Base, North End . 8. St. Agnes Beacon . . . . 597'3 Wart Hill Hoy . . . . . I559' M. C. Base, South End . 8. Moelfre Issa . . . . . Iod 6’ Monach . . . . . . . 813' Mordington . . . . . . 649 Mormonth . . . . . 743 * Mowcopt St. Agnes Lighthouse. Top | 157.6 || Water Crag . . . . . . 21.87° St. Anns . . . . . . 207. I | Week Down. . . . . . 690° St. Martin's Head . . . . 150' 3 || Westbury Down . . . 754' St. Paul's Cathedral, Top Whitehorse Hill . . . 850° of Cross . . . . . . 417 - 9 || Wingreen . . . . . . . 913' tº p & ſº º St. Peter's Tower . . . . 154' 6 || Wittle Hill . . . . . . I529' Mount Battock . . . . . 2554 Sca Fell. . . . . . 3229' 6 || Wolf Rock . . . . . 2O" Mount Leinster . . . . 2602 Scarabin . . . . . . 2054.0 | Wordeslow . . . . . . . 635' Mount Sandy . . . . 56°o | Scournalapich . . . . . . 3772°8 || Wrotham . . . . . . 774' Nive Hill . . . . . 524 o | Severndroog Castle. Ground 406-4 || Wroxall Down . . . . . . 725° Naseby Ch. Tower. Top 714-6 || Shanklin Down . . . 717 7 || Wisp . . . . . . . I95o' Naughton Ch. Tr. Ground 277 I | Slieve Donard . . . . . 2788: o Yell . . . . . . . . tº Nephin . . . . . 2638'o | Slieve League . . . . 1956°o | York Minster . Ground 53° : : Fº g sECTION X. CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. THE information we possess as to the figure of the earth has been obtained by methods singularly dissimilar, but agreeing with great precision in the resulting values of the eccentricity of the meridian. The theorem connecting the figure of the earth with the law of gravity upon its surface, enables us, after ascertaining by means of the vibration of a pendulum the actual or rather relative amounts of gravity at a great number of stations, to determine that figure or amount of seccentricity which will best represent the observed variations of gravity. But we cannot by this method, nor by the observed effects of the eccentricity of the earth in producing a disturbance both in the latitude and longitude of the moon, assign anything beyond the ratio of the axes. The actual dimensions of the earth, or the nature of the irregular surface within any given limits, can only be determined by the connection of geodetical and astronomical observations, whereby we obtain respectively the lengths and curvatures of lines traced upon the true surface. § I. I. The comparison of the results of corresponding geodetical and astronomical observations has almost invariably brought to light discrepancies that from their magnitude could not, even in the earlier operations, be ascribed to the errors of observation alone; nor has the greater perfection to which instruments and modes of observing and calculating have been brought, up to the present time, removed these discrepancies, but on the contrary, they are exhibited in more unmistakeable reality. The source of these discrepancies may be a combination of errors of observation with either of the following: first, deflection of the plumb-line by local attraction, caused by inequalities of the visible surface of the earth at or near the station; second, deflection of the plumb-line by unequal distribution of density at small or very great depths below the surface; third, irregularities of the earth's figure or surface. The third of these sources differs from the other two in the quality of extent only; for the local attraction, whether originating at or below the surface, that produces a deflection of the plumb-line also produces an irregularity in the mathematical surface: there may be irregularities of different orders of magnitude. That stations may be chosen unsuspectingly in such positions that the astronomical results shall be very materially affected by the first of the above sources of error, namely, that of the inequalities of the surface, is proved by the selection of the position of several stations even in the present triangulation; for instance, Burleigh Moor, or the south end of the Lough Foyle Base. It will be proved further on that the high ground to the south of each of these stations produces a dis- turbance that renders the astronomical observations quite erroneous. As another instance, we may allude to the station Takal Khera, in the vicinity of the Mahadeo Range of Mountains. The face of this range, which lies east and west, is distant about twenty miles north (very nearly) of the astronomical station, and in consequence of this great distance it was considered by Colonel CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 561 * : Lambton that no effect could be produced upon the plumb-line at Takal Khera. It was, how- ever, proved by Colonel Everest, by actual calculation, that the mass was sufficient to produce a deflection of the plumb-line to an amount far exceeding the possible errors of observation.” When we consider the heterogeneous nature of the crust of the globe, it is in no way remarkable that the surface to which geodetical operations are referred (that of the sea, pro- duced in imagination) should present small irregularities, but, on the contrary, the d priori probability that the surface of the earth should be found to agree precisely with any single formula is really very small. - 3. The discrepancies between geodetical and astronomical observations are brought out principally in one or other of the following ways;–either in the determination of the figure of the earth from different combinations of measures, whether of the meridian or of parallels; or in the comparison of the observed latitude, longitude, or bearing of the meridian at any point, B, by means of the observed latitude, longitude, and bearing of the meridian at another point, A, transferred geodetically on assumed elements of the earth's figure to B. Suppose A and B to be the trigonometrical stations, and suppose that at A there is a disturbing force acting which draws the vertical through an angle, 6, then it is evident that the apparent zenith of A will be really that of some other place, A', whose distance from A is 6× earth's radius; and similarly if there be a disturbance at B to the amount 3', the apparent zenith of B will be really that of some other place, B', whose distance from B is 3' x carth's radius. Hence we have the dis- crepancy, that while the geodetical operations deal with the points A and B, the astronomical observations belong to the points A' and B. Should 3, 3’ be equal and parallel, the displacements AA', BB' will be equal and parallel, and no discrepancy will appear. 4. By the comparison of two meridian measures we may determine values of the axes of the spheroid, affected with errors of observation and the probable effects of local attraction. If a", a , be the measured lengths of two meridian arcs, whose astronomical amplitudes are p, q}, and their mean latitudes x, x, we shall have— O 1 = a (I * = m) (?, — 3 m sin +, COS 2. 2.) a", = a (I — m) (i. — 3 m sin 4, cos 2x) omitting the square of m, which is the ratio of a - b : a + b. If we suppose the arcs small, so that sin & may be replaced by p, we shall have— 7, 4. a 3, cos 2 x – cos 2 x, 3 m = 0- Or ++ cos 2 x, — ; cos 22. a ( — n) = *. I cos 2 A, - COS 2 A2 * In connection with this it is worthy of remark, that the correction to the latitude of Takal Khora, deduced by M. Dessel in his determination of the Figure of the Earth from meridian measures, is + 3"'537–See “Astronomische Nachrichten," No. 438, p. 115. * 4 B 562 PRINCIPAL TRIANGULATION. Now suppose that, in consequence of local attraction, the terminal latitudes of the arc a. are affected by errors ar,' and r, then the arc p, is affected by the error a,' — ar, ; and similarly suppose b, to be affected with the error wſ – v., then the deduced value of 3 m will be affected with the error— - a', (4, + æ,’ – a.) * 2 Ps O’r (?, + +.' -º- +.) * OT: qº, COS 2. M – COS 2. Aa P p ar, - ar, , 2.2 - 22 = —t —t cos 2 AI - COS 2 A, Let the arcs ®, b, expressed in degrees be r r, , and suppose w, w, w, v,' expressed in seconds, then the error of the ellipticity will be— f f ar, - ºr, ar, - ºr, + mmºm- 2 I - 72 7": - 3 36cc a sin(x, TX) sin(x, FX.) a',' – ar, ar,’ – ar, +- + *-*-*mº 72 7"I - Io8oosin(x, -- x.) sin(x, — ».) If we suppose each of the independent errors w to have a probable amount s, then the probable error of the deduced value of the ellipticity is— - - * + - -- ( 5 ) ºr ºf r r” + r,” + \108oo/ sin(x, TX) sin(x,− x.) - * Suppose, now, that we compare two arcs of a degree each, situated in mean latitudes, and close to each other, say about five degrees apart, the probable error of the resulting value of the compression will be approximately— 5 V4 E ºmmº * 3 = + *mº Io8oo sin 5 5oo so that if s = 2" the probable error of the deduced value of the compression will be actually greater than the compression itself. Hence, in comparing small arcs not widely separated in latitude, it will be nothing remarkable if negative values of the ellipticity should be obtained, provided the probable disturbance due to local attraction should amount at each station to 2" or even a smaller quantity. - - - Should the two arcs be continuous, that is, suppose the northern terminus of p, to be the southern terminus of p, , then ar,' = a, , and the error of the deduced value of the ellipticity— z,' ſ I . I Jºr * sem, wa —_ + * gºmº 7"a 7", 7", 7°r TTEETC.T.) in (x, — Aj Va (#4 #4 +) W. +- 5 r,” Tº t ºr, T Io8oo sin (A, + x) sin (A, - A,) and the probable error— CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 563 * { { 6& which is approximately equal to— r * * +- V I + I + I º 5 Hºmºmº **** f r.” r.” 7"I Ta 15 T (r. -- ",) V2 by putting x, — », - half the combined length of the two arcs. Let us estimate from this the probable error of the ellipticity that would result from a comparison of the arcs Dunnose to Arbury and Arbury to Clifton. Their lengths expressed in degrees are r = 1.6 r, - 1.2, and x, - 51° 25' x, = 52° 50'; so that the probable error of the deduced value of the ellipticity is— * e A/1,606 -T- + 42 ºr w/ 2 cosec (x, -i- x.) sec (14° 15') g I42.7 Therefore if we suppose the probable disturbance at each station to be even less than a second, the probable error of the resulting ellipticity will be twice as great as the ellipticity itself. = + 5. The anomalous results deduced from the English arc extending from Dunnose to Clifton, as given in the second volume of the “Account of the Trigonometrical Survey,” have given rise to much discussion. It was found that in proceeding from the southern to the northern extremity, the length of a degree diminished, which seemed to indicate a negative value of the ellipticity. General Mudge remarks upon this discrepancy between the expected and the obtained results:—“I think it is probable that an error in the whole distance, of 197. “ miles nearly, does not subsist to an amount of more than Ioo feet, corresponding to one “ second in the amplitude of the whole arc, and I also think it probable it cannot amount to “ half that quantity. The supposition of the zenith distance of the stars being generally “ erroneous at any one station cannot be admitted, unless it should be imagined that the plane of the sector's limb was not got into that of the meridian. Such an idea, however, can scarcely be entertained after a careful examination of the several observations, and a due attention to the means by which the instrument was made to assume its right position. Perhaps, also, I should not fail to observe in this place, that although the instrument was always brought into the plane of each meridian by means of the telescope attached to the side of the great tube and the azimuth circle, yet, having two good chronometers in my possession, I repeatedly verified the truth of the sector's position by observing the transits of two stars north and south of the zenith at the greatest distances my arc would admit of But, to return: if there be an error in the amplitude of the total arc from a deflection of the plumb-line at either of the stations, it is not probable that any such deflection existed at Dunnose, as the deviation of it towards the north, from a deficiency of matter towards the channel, would tend to diminish the inequality between the lengths of the two degrees; this will be evident on consideration. I am therefore disposed to believe that the plumb-line was drawn towards the south from the action of matter, both at the northern extremity of the arc and at Arbury Hill, but more particularly at the first-mentioned station. If this 4 B 2 - * & 4 & & © . & C {{ & & & & { % {{ & 8 {{ { % 6 & 564 PRINCIPAL TRIANGULATION. “ were partly the case, and both Dunnose and Arbury Hill were free from any such prevailing “cause, the total arc must be too great, if taken at 2° 50' 23”. 38, by about 8", nearly answering “ to 2" on each degree. A deviation of 8” from the true vertical is a large quantity, nor can “ the cause of it be assigned, unless it be also supposed that the matter producing that “ deflection extends in a southern direction beyond Arbury Hill. If the error, though not “ probable, as above observed, be supposed to exist at Dunnose, it must amount to more than “ Io", and that, too, from the effects of attraction in a southern direction, where the deficiency “ of matter would lead us to believe the reverse would happen . . . . . . In short, the “general tenor of the observations seems to prove that the plumb-line of the sector has been “ drawn towards the south at all the stations, and that by attractive forces which increase as “we proceed northwards.” * In the Philosophical Transactions for 1812 there is a paper entitled “Observations on the “Measurement of Three Degrees of the Meridian, conducted in England by Lieutenant-Colonel “ William Mudge,” by Don Joseph Rodriguez, in which the author endeavours to prove that the discrepancies in question arose from errors in the astronomical observations at Arbury. Assuming certain clements of the earth's figure, which are far from the true or most probable values, he finds that the arc Dunnose to Arbury should, from its geodetical magnitude, have an amplitude of 1° 36' 23”. 34, and the arc Clifton to Arbury an amplitude of 1° 13' 58”.63, and com- paring these with the observed values the resulting errors of the observed amplitudes are—on the southern portion — 3”. 39; on the northern portion + 4”.77: on the total arc + 1". 38. From these quantities the inference of the author is that the observations at Arbury Hill are erroneous to the extent of 5". But the only true inference is this: If the earth be a perfect. spheroid, without appreciable irregularities, and if the elements used be the true values, then the observed amplitudes are from some cause erroneous. But even admitting the hypotheses, which are false, the conclusion that error is at Arbury Hill is not legitimate. It should also be remarked, that had the station Blenheim been allowed an “influence in the deduction, it would have been necessary to ascribe to that station an error corresponding in amount to that ascribed to Arbury. Of this paper, as it has been considered by the highest authorities to throw no light what- ever on the subject, and to be deficient in demonstration," no further notice need be taken. It would appear, however, that the discrepancy was generally attributed to a deflection at Arbury Hillf to the amount of 5", as is evident from Captain Kater's remark at page 188 of the account of his operations to determine the difference of longitude of Greenwich and Calais in * DELAMIRE, Conn. des Tems, 1816, Additions: AIRY, Encyclopædia Metrop.; “Figure of the Earth,” page 237. # It is worthy of remark, that in a letter to Colonel Mudge (in 1816) the illustrious Schumacher wrote :-" You, “ who know the ground, are best able to judge where local attractions are most probable; but on my part I must confess “ that I should suspect them rathcrat Dunnose than at Arbury Hill. And further, it seems to me that in any “ hypothesis it would be very difficult to establish a perſectly regular figure for the carth.”—Memoirs of Major-General Colby, Royal Engineers, by Colonel Portlock, Royal Engineers-Professional Papers of the Corps of Royal Engineers, Vol. III. New Series, page xxvii. CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 565 1821 (Philosophical Transactions, 1828); and similarly at page 236 of the treatise on the Figure of the Earth by the Astronomer Royal, in the Tncyclopaedia Metropolitana. 6. Let us now examine the data of this arc, in order to ascertain as far as possible what are the deflections most probably due to each of the stations. The data, as we find them at page Ioz of the second volume of the “Account of the Trigonometrical Survey,” are— - I?artial Arcs. Léngth in Feet. *:::::::: Dunnosc to Greenwich . . . 313696 & 5i 3*39 33 Blenheim . . . 446498 I 13 19 69 33 Arbury . . . . 586320 I 36 19: 98 32 Clifton . . . Io:36337 2 50 23:38 Latitude of Dunnose 50° 37' 7" If I — n : 1 + n be the ratio of the axes of the elliptic meridian, the length of the arc between the latitudes x + , p and 2. — p is— - tºº wº-ºº º — mº 2 ” + . . . º i. 2 A + . . . a = a (I m) (1 w) (1 + in +. ...) (? 3 m sin & cos +- ) and the length, A, of a degree in the mean latitude, A, is therefore— = a( – ) ( – ’)(; +3* + . . ) (#–3 win; coax + . . ) A = a (I — n) (1 w)(; +3* + ) (; 3 m sin is; cos 2 x + Put x, for the latitude of Dunnose, and let the corresponding value of A be A., then, neglecting quantities of the order a n pº, we have— º 18o. 4 I — 3 m cos 2 x ºr I — 3 m cos 2 Ao But supposing the arc q to be measured from Dunnose, x = x. + # 3 the latitude of the middle point, or rather the mean of the extreme latitudes; hence, supposing q to be expressed in seconds— a = As * n 3600-a = Ao ‘t (1 + 3 m ſcos 2 x- cos (2 Ae -- •)) * =A, 2 (1 + 6 nsin (2x. + i º) in ) = Ae 4. ( + 4 sin 3” sin (2 ×e +++)n) Let 3648oo feet be an approximate value of Ag, and let the same quantity, increased by the multiplier I + u, be the true value, then by substituting this value— , #;" = p + 4* sin 3" sin (2 ×e + # 4) . n + 4 w •) 566 - PRINCIPAL TRIANGULATION. In this equation a is the length in feet of an arc measured from Dunnose northward, and corresponding to the amplitude P. Let us suppose that at each of the five stations named in the table there is an uncertain amount of local attraction, and that in consequence the latitudes have to be increased by small quantities w w, w, w, v, a corresponding to Dunnose. Therefore to the four amplitudes given in the above table we have to append the unknown quantities. a', -a, w, - a, w, - a, and 4, - w, Hence, supposing a, to be the length and p, to be the tabular amplitude of the i” partial arc- * * * F. . . . #" = }, + æ, - a + 4* sin 3" sin (2 x + , t) n + 4, u * 2' = # – 4, - tº sin 3" sin (2 x + 3 +) n — 4, u + æ Substituting in this equation the numerical quantities given in the table of data, we have the following set of four equations, in which, in order to diminish the number of figures, the values of n and u have been multiplied by Jooo- f ar, - 4.29 — or 1361 m – 3-og I w -- a a', a 6.54 – o-2755 m – 4:4oo u + æ A. i- (A) a's = 6.07 – o'47.52 m 5.78o w -- a a', - 3-63 — I-4832 n – Io.223 w -- a These four equations contain all the necessary relations between the radius of curvature of the arc, its rate of variation, and the five effects of local attraction. If we eliminate n and u we shall have two equations of condition between the five quantities a . . . . , so that if we assign any arbitrary values to any three of these quantities the other two can be determined. But the most probable values correspond to those values of n and w which make the quantity a” + ar,” + ar,” + ar,’ + æ,’ a minimum; this is, in fact, determining that particular elliptic curve which will best represent the observations. Making the differential coefficients of the quantity just written with respect to a n and w respectively zero, we have— o = a + r + r. -- a, + æ, o = 6.1361 a, + o-2755 r, + o-4752 r + 1.4832 r, O E 3'og I a"r -H. '4°4OO £2 + 5.78o *3 -- Io.223 24 *... • * and performing the multiplications, we get— o = + 20.53 — 2.370 m – 23:494 u + 5-ooo a o = - 114.23 + 19.542 m + 166.832 u - 23.494 r o = — Io.65 + 2.520 n + 19.542 w – 2:370 r Solving these equations, and restoring to n and w their proper values, namely, a thousandth part— z = + o-oč4 w = + o-oo:2088 n = — obligo9 CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 567 and the apparent corrections necessary to the observed latitudes— Dunnose . . . . . . . . . -- cog * Greenwich . . . . . . . — o-48 Blenheim. . . . . . . . . -- o-69 Arbury . . . . . . . . . – o 28 Clifton . . . . . . . . . . + o-or These are the smallest corrections that can be applied to the observed latitudes in order that they may agree with the corresponding geodetical arcs in representing any elliptical curve. The ratio of the axes of this curve are— 4 – 1 + n – 41-48 b T I – n T 42.48 • *- and the length of a degree— 368 125 + 13152 cos 2 × . - - - - This is the result most consonant with the observations and measures in this arc, and must be taken as the true length of a degree anywhere between Dunnose and Clifton, provided it be assumed as most probable that the latitudes of any points between these limits determined astronomically would fall in with this curve we have determined; that is, supposing it most probable that there is a large irregularity of the earth's surface between Clifton and Dunnose. But the small number of five stations is quite insufficient to give probability to this hypothesis; and as in general we must assign a greater probability to small irregularities than to great ones, let us ascertain next what are the smallest effects of local attraction that must be attributed as most probable to the different stations, in order that the expression for a degree along the arc may not indicate a large irregularity of the earth's surface. And for this purpose assume an ellipticity of #, which is very near the mean value for the whole earth; on this supposition n becomes ::, and the equations (A)— a', a 4-off – 3-ogi u + æ ar, a 6-oš – 4:40o u + æ r, a 5.28 — 5:780 u + æ a, - 1.16 – Io.223 u + + = + ... ſo I6.58 + 5-ooo a - 23:494 ...} º {. 81.68 – 23.494 c + 166.832 w º' - - 3-oo - u = + -oooooo.8 whence the apparent corrections for the effects of local attraction are— - */ Dunnose . . . . . . . . . – 3•oo Greenwich . . . . . . . . -- o'85 * * - - - * * * * * * a tº - * * * * * * * and the formula for the length of a degree— - 364469 — 1832 cos 2A 568 PRINCIPAL TRIANGULATION. Here the length of the degree exhibits no anomaly, and the probable disturbances at the different stations are not singularly large, the largest falling to Dunnose in a southern direction, whilst at Arbury the disturbance does not amount to two seconds. 7. We conclude, therefore, that the data of this arc as given in the second volume of the “Account of the Trigonometrical Survey” do not indicate as probable any general irregularity of the earth's surface, nor do they require the supposition of a very large disturbance at any of the stations, as supposed by General Mudge. If we correct the observed amplitudes accordingly, and thence deduce the lengths of a degree at the different mean latitudes, they will be as follows:— º Partial Arcs. *::::" | . . . .tº. in jail Dunnose—Greenwich . 313696 3093-24 5í Ž 5% 364852 | IoI 348 Greenwich—Blenheim I32802 1310-23 || 51 39 32 || 364888 to 358 Blenheim—Arbury I39822 1379-40 || 52 I 57 || 364912 || IoI 364 Arbury—Clifton 450017 || 4438-99 || 52 5o 28 364962 | Ior 378 In obtaining these results we have assumed a value of the ellipticity; they would not, however, have been materially different had we assumed any other value near the truth. This arc is particularly illsuited to be used in determining a value of the ellipticity, inasmuch as its situation in latitude renders the coefficient of the ellipticity small. 8. Let us next suppose that in the whole arc there is an error of 170 feet, as now appears to be the case. The equations will be altered to— a', a 4.06 – 3-091 u + a a, a 6.08 – 4:400 u + æ a, - 5.28 – 5.78o u + æ a', a 2.84 – Io.223 w -- a nº ... ſo = + 18.26 + 5-ooo r - ...} * ſ: {. = — 98.85 — 23.494 a + I66.832 tº – 2.565 w = + o-oooz313 JC = and the apparent corrections for the effects of local attraction become— Dunnose . . . . . . . ‘. . — 3.56 Greenwich . . . . . . . -- o.78 Blenheim . . . . . . . . -- 2.50 Arbury. . . . . . . . . . -- 1:38 Clifton . . . . . . . . . . – 2.09 CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 569 -t These quantities are all smaller than before, and the apparent deflection at Dunnose is now reduced by nearly half a second. The length of a degree is also increased to— - - 364529 – 1823 cos 2 x or about 60 feet greater than before. - It appears, then, that the error in the geodetical operations has had a sensible influence in magnifying the discrepancies. 9. As Dunnose is the southern terminus of the arc, it was considered necessary that additional observations should be made at other stations in its neighbourhood, in order to throw light upon the supposed probable existence of disturbance at that point. Three stations were therefore selected by Captain Yolland for this purpose, and the observations for ascertaining their latitudes were made with Airy's Zenith Sector. The stations Week Down and Boniface Down are connected directly with Dunnose, see triangles 46, 47, page 472, and the distance Dunnose to Highport Cliff is determined by the calculation of the following triangles:— - Names. Angles. Log. Sines. Log. Distances. Boniface Down, South East . 17; ; 46.96 8'929.0573 3°4963342 High Port Cliff . . . . o 48 36'48 8' 1504,198 2*7176967 Boniface Down . . . . 4 3 42°56 8' 8502344 3°4175 II.3 18o o o 'oo Boniface Down . . . . . 145 8 13: o3 9° 757 Ioso 3'9173428 Dunnose . . . . . . 12 31 29°oš 9' 3360964 3°49.63342 * High Port Cliff . . . . 22 20 26-92 9'5799 I5 I 3°74O1529 18o o o' oo At Dunnose the observed bearing (page 106) of Boniface Down is 3° 40' 12".69, which becomes, by applying the correction + o”.92 (page 403), 3° 49' 13"-61. The reading of the referring-object at Dunnose is 339°12' 19".99; but on referring to the results of azimuthal observations, page 177, we find that the true azimuth of the referring-object is 339°12' 12". 59. All the readings, therefore, at Dunnose, as given at page Ioff, have to be corrected by the application of the quantity – 7”. 40 to reduce them to the exact meridian. So that we have, At Dunnose, azimuth of Boniface Down . . . . . . . . . 3 40' 6%, S.W. Angle: Week Down—Dunnose—Boniface Down . . . . 45 Io 21.33 ..". At Dunnose, azimuth of Week Down . . . . . . . . . 48 5o 27-54 S.W. Angle: Boniface Down—Dunnose—Highport Cliff . . . I2 31 20.05 ..'. At Dunnose, azimuth of Highport Cliff . . . . . . . . 8 51 13.84 S.E. The distances being very small we may neglect the curvature of the surface in determining the meridional distances of Dunnose—Boniface Down and Dunnose—Highport Cliff; we have therefore only to multiply the distance by the cosine of the azimuth in order to get the distance - - - + 4 C • *, * -*. ... - . w 576 : ... & F.' ' ', ; ; ; ; , . PRINCIPAL TRIANGULATION. . . . . . . of the parallels. To convert this into seconds of arc, it is almost immaterial what elements are used; the logarithm actually used is derivéd from the elements of the figure of the earth given by the Astronomer Royal in his treatise in the Encyclopædia Metropolitana. Dunnose— | | | Dunnose— * . . g ...]. ... Tunnose- Boniface Down. | Week Down. . . .” -- ; ;. • ?:, . º: . * * º • rr. ‘’’. . . . … * * - High Pört Cliff. Azimuth . -- 3. o' é 48 56 28 § 5: 14 Log. cosine 9°999.Io9 || 9°818324 || 9-994794. Log. distance . 3°74or 53 || 4°os3569 || 3’917343 Tabular log. . 7°994O95 7°994O95 7°994O95 Log. diff, lat. . I '733357 I '865.988 I '906232 Diff, lat. 54". 12 73"'45* 80” 58 ºf . To obtain the true difference of latitude of Dunnose and Week Down, a small correction must be added to the quantity 73". 45 just obtained, dependent upon the distance, D, of Week Down from the meridian of Dunnose; this correction is— . . . . . . . . . . . . . . . . . . 1 (#) tan x t *g * --—77 * 2 \lk / sin I’’ * ! * - *-* * * * -- IR being the radius of the earth, and 2, the latitude. The amount of the correction is + o'.oz.” The station Highport Cliff is not identical with the point (called Port Valley) at which the astronomical observations were made: the latter is 263 feet from the former, and in a line between it and Boniface Down, S.E. station. The azimuth of this line is 30° 22', so that the meridian distance is 227 feet, and the difference of latitude 2". 24, which quantity has to be sub- tracted from the latitude, 50° 35'45". 52, of Port Valley, to reduce it to the station at Highport Cliff. * Names. Latitudes. Ast Amp. Geo. Amp. - O f f ; J/ Wſ Dunnose . . 5o 37 7" I 5 56-60 54." I2 Boniface Down .. 5o 36 Io' 55 * - - 75-73 73°47 Week Down . 5o 35 5I '42 3. High Port Cliff so 3s 43-28 || 83°7 | 89°58 Now let a, w, w, v, be the disturbances at these four stations due to local attractions, then, * } . 56-60 + -a, -a, - 54. 12 : ' ' ', 75-73 + æ, - a, = 73.47 83.87 + æ, - ſº, s- 80.58 Qa = 0}, + 2.48 a. * *, + 2-26 - & = 0}, + 3.29 : . . . . . • * * : *.* + æ,’ + æ, + æ,’ = a,” + (x, -- 2:48) -- (a, + 2.26)*-i- (x + 3.29) “” - " " . . . " CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 571 and the value of a which renders this function a minimum is determined by the equation—º º . . . . . . . . * 4 a., + 8.03 = o . . . . . . . . . . . . .3 ... ac, - – 2 OI. r . . . . Therefore the disturbances at the several stations, as far as can be determined from these observations alone, are most probably as follows:— - . . . . . - & / Dunnose . . . . . . . — 2-ol IBoniface . . . . . . + o-47 Week Down . . . . -- o-25 Highport Cliff . . . -- I-28 Io. The agreement of this result as to the disturbance at Dunnose with that deduced (– 2". 56) from the original data of the arc Dunnose to Clifton, corrected for the error in the geodetical measure, is very satisfactory, and seems to prove that there is a southern deflection at Dunnose to the amount of about 2". It is also worthy of remark in this place, that the correction assigned to the latitude of Dunnose by M. Bessel in his determination of the figure of the earth (Astronomische Nachrichten, No. 438, page 115) is — I’’.816. “. . . . . . . . In deducing these results for the four stations in the Isle of Wight, the latitudes used are independent of the assumed declinations of the stars observed; they would have been almost exactly the same had we made use of the latitudes deduced from assumed declinations. II. A fact of the highest importance is also here brought out. We have seen that at Dunnose there is probably a deflection of 2", or to the south, and at Highport Cliff a deflection of I". 28 to the north, and that between the two stations the effect of local attraction alters to the amount of 3”. 29, whilst the distance of the parallels of these stations is not much more than a mile and a half. Therefore, if in the original operations the station at Highport Cliff had been used as the southern terminus of the arc instead of Dunnose, the results deduced from that measure would have been very different. And in general it is unsafe to form any conclu- sion as to the curvature of any entire arc merely from the observed latitudes of its extremities, for it cannot be said with any degree of certainty that there are not many intervening irregu- larities. To illustrate this, suppose A P B to be an elliptic curve passing through the terminal points A B of an arc, at any point P in this curve erect a perpendicular PQ proportional to the deflection (considered positive when the attractive force is to the north, and negative when the attractive force is to the south) at that point. The curve traced by the point Q will inter- sect the elliptic curve A P B at all points at which there is no local disturbance, and will lie alternately above and below A P Q. By the observed latitudes at A and B we have the direc- tions of the tangents of this irregular curve at those points, and this is all. And if from these data we form a conclusion as to the general curvature of the actual surface between A and B, . . . 572 - PRINCIPAL TRLANGULATION. the probability to be attached to such a conclusion will correspond to the probability there is in the assumption that the point Q does not trace any irregularities, but a continuous curve of slowly but evenly varying curvature. The fact that the country between A and B is free from all external causes of disturbance, could not legitimately be brought forward as an argument against the existence of irregularities. Such a conclusion would be unsupported by observation. By observing the latitude at a great many points between A and B we shall ascertain the directions of the tangents to the curve A QB at the corresponding points, and thus we shall be able to determine some regular curve A P B which shall most nearly agree on the whole with the curve traced by Q. *: 12. The irregularities we have been considering, though doubtless in many cases they may be accounted for satisfactorily by the nature of the country around, must still be considered as probably intimately connected with the internal constitution of the earth, of which we know little or nothing with certainty. An important suggestion has been brought forward by the Astronomer Royal” relative to the probable effects of extensive mountain ranges in producing deflection of the plumb-line. It is as follows:— The general regularity of the physical surface of the earth, the smallness of its elevations and depressions, and the exactness with which it can be represented by a spheroid of revolution, have induced most physicists to suppose either that the interior of the earth is now fluid or that it was fluid when the mountains took the present forms. Of the probable thickness of the hard crust it would be unsafe to express an opinion, but, for the sake of fixing the ideas, suppose the earth a fluid mass covered with a solid crust Io miles thick. Now suppose a mass of mountain or table land Ioo miles broad in its smaller horizontal dimension and 2 miles high throughout to be placed on the surface; will this mass be supported, or break through the crust and sink partly into the fluid In the adjoining. e V $. figure let a b c d be part of the earth's crust, e.g. f the table land, and . Ct. H d suppose the rocks to be separated by vertical fissures, as indicated by b hi i k. * the dotted lines, and conceive these fissures to be opened, as they would be by a sinking of the middle of the mass, the two halves turning upon their lower points of connection with the rest of the crust. Let W.be the weight of a square mile of the rock and C the cohesion, or force necessary to separate a square mile. Then the cohesion at h = Io C and at i it is 12 C, also the superincumbent weight of each half is 2.5o W; therefore considering one half only, as eg, and taking the moments— . - * - - - 10° C + 12° C = 2.50° W _ 5000 T 244 ..". C W or about twenty times the weight of a cubic mile of rock, so that the cohesion would have to be sufficient to support a hanging column of 20 miles of rock. Had we supposed the thickness of * Philosophical Transactions, 1855, page [101]. CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 573 . $º the crust Ioo miles we should have had, cateris paribus, C = W nearly. Even in this case the force of cohesion necessary is greater than can be supposed to exist, and therefore the table land will not be supported by the crust. * It appears, then, probable that such mountain masses must be accompanied with corre- a 22-Tºsº a sponding solid depressions, as ef', or indentations into the fluid, in - e' # =e, order to preserve equilibrium. Now if we suppose a station at a, near *sº the table land e,f, there will be a disturbance northward owing to the attraction of the superincumbent matter e,f, but owing to the substitution of the lighter matter e'f' for the denser fluid matter there will be a negative attraction northwards. ...The diminution of attractive matter below will be sensibly equal to the increase of attractive matter above, and if the point a be not very near to e,f there may be no disturbance at all; but if a be close to the table land, and especially if the crust be anything like Ioo miles thick, there will be a very sensible disturbance, but less than that which would be due to the attraction of the entire table land. - { • . . . . . . . . “The general conclusion, then, is this: In all cases the real disturbance will be less than “ that found by computing the effects of the mountains on the law of gravitation. Near to the “ elevated country, the part which is to be subtracted from the computed effect is a small “ proportion of the whole. At a distance from the elevated country the part which is to be “subtracted is so nearly equal to the whole that the remainder may be neglected as insignificant, “ even in cases where the attraction of the elevated country itself would be considerable. But, “ in our ignorance of the depth at which the downward immersion of the projecting crust into “ the lava takes place, we cannot give greater precision to this statement. “In all the latter inferences it is supposed that the crust is floating in a state of equi- “ librium ; but, in our entire ignorance of the modus operandi of the forces which have raised “ submarine strata to the tops of high mountains, we cannot insist on this as absolutely true. “We know (from the reasoning above) that it will be so to the limits of breakage of the table “ lands, but within those limits there may be some range of the conditions either way. It is “ quite as possible that the immersion of the lower projection in the lava may be too great, as “ that the elevation may be too great, and in the former of these cases the attraction on the “ distant stations would be negative. . * “Again reverting to the condition of breakage of the table lands as dominating through “ the whole of this reasoning, it will be seen that it does not apply in regard to such com- “putations as that of the attraction of Schehallien and the like. It applies only to the “ computation of the attractions of high tracts of very great horizontal extent, such as those to “ the north of India.” ..º. 13. This theory, which has great d priori probability, receives strong corroboration from the comparison of the observed effect of the Himalaya Mountains in disturbing the plumb-line at the northern terminus of the Indian arc (Kaliana, in latitude 29° 30' 48") with the dis- turbance that would result from the apparent mass and extent of the mountains. The observed effect of the attraction of the mountains is 5”. 236, or more probably - 3". 343, as stated by 574. . . . PRINCIPAL TRIANGULATION. Colonel Everest at page clºxviii of his account of the Measurement of the Indian Arc; the exact amount, being dependent on the assumed elements of the figure of the earth and other circumstances, cannot be positively assigned. But the attraction of the apparent or super- incumbent mass of the Himalayas at that point is sufficient to produce a deflection of 27”.853, as calculated by Archdeacon Pratt, of Calcutta.” ‘. * But the theory does not seem to be borne out in the case of the Alps, where disturbances have been observed of very large amount. I4. The greatest discrepancy ever observed is that brought out by the arc of Beccaria, measured in Piedmont. The terminal stations, Andrate and Mondovi, are situated at the foot of lofty mountain ranges, the intervening country being flat. This measure gave for the length of a degree 57,468 toises,—a quantity much larger than it should be, and corre- sponding to an error of more than 41’’ in the amplitude. In consequence of this anomaly, Laplace and other geometers resolved to make no use of the arc in the determination of the dimensions, of the earth, as it was very doubtful whether the observations of Beccaria were not erroneous. In order to throw light on the matter, and to settle the question whether the discrepancy was due to the defective operations of Beccaria, or had a real existence resulting from the attraction of the mountains or the uneven distribution of density in the terrestrial strata, the latitudes of Beccaria's stations at Mondovi and Andrate were re-observed by MM. Plana and Carlini during their operations in that country in 1823. The observations; were made with an 18-inch circle by Troughton, and appear satisfactory; the latitudes of the terminal stations were found to be— . . . . . . . * , , Andrate . . . . . . . . 43 3: 13:36 . * * * * ... ' - Mondovi . . . . . . . . 44 23 45.38 - Amplitude . . . . . . . I 7 26.98 f This quantity is less than the amplitude assigned by Beccaria by 13". The geodetical con- nection of these stations, which had been partly revised by the French Geographical Engineers in their operations in 1809 was now completed, and the length of the arc found to be 126394.6 mêtres, 38 mêtres greater than obtained by Beccaria. The geodetical latitudes—that is, the latitudes calculated on an assumed figure of the earth, and based on the observed latitude of Paris, are—, , . r -- f f/ . * : * Andrate tº gº tº ºn tº º ſº tº 43 3I 40°45 y * # Mondovi . . . . . . . . . 44, 23 25.63 Amplitude . . . . . . I 8 14.82 which exceeds the astronomical amplitude by 47".84; showing a deflection 287,09 to the north at Andrate, and 19".75 to the south at Mondovi. - * “On the Attraction of the Himalaya Mountains, and of the elevated Regions beyond them, upon the Plumb-line in India.” By the Venerable John HENRY PRATT, M.A., Archdeacon of Calcutta–Phil. Trans. 1855. * f “Opérations Géodésiques et Astronomiques pour la Mesure d'un Arc du Parallèle Moyen.” “Tom. II. CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 575 their action. . . . . . . . . . . . & ; : . . . . . . . . . . . . . . . . . If external causes could suffice to explain these disturbances, they would naturally be sought in the existence of the chain of the Maritime Alps to the south, and of the chain of the Graian Alps to the north. But it is possible, also, that this singular phenomenon, may be partly produced by irregularities in the densities of the crust of the earth. There. is a difficulty, in ascribing the whole amount, of the discrepancy to the action of the superincumbent matter of the mountains, inasmuch as the geodetical and astronomical connections of the Observatories of Parma and Milan show a discrepancy of 20°.4,” although these places are situated in a plain, and so remote from mountains that such a discrepancy could not be explained by * -: * * f ; : " . . y: , , - § II. On the Deflections produced by given Masses. I5. Although the law of gravity, or of the attraction mutually exercised by all material particles, is in itself very simple, yet, when it is traced to its consequences, whether. in the form of motion or mere attraction, difficulties are encountered which, in the present state of analysis, cannot be rigorously overcome. It is only in the most simple cases that exact results can be obtained; in all others, recourse must behād to approximation. Fortunately, in all the important cases that arise in practice, in which it is necessary to trace the effects:of attraction, the conditions of the problem are such that the method of approximation can be applied. When a particle is attracted by a body which subtends, at the particle, a very small angle, then, supposing there is no great disparity between the different dimensions of the attracting body, the attraction will be sensibly the same as if the mass of the body were condensed in its centre of gravity. We may generally get a rough approximation to the true attraction of a body by this rule, but the error will increase rapidly with the increase of the angular magnitude of the body at the attracted particle. '... … . . . . . In order to calculate exactly the attraction of a mass—such as a mountain—at any given point, it is necessary to have the equation of the surface, together with the value of the density at any point w y z in the mass. It is therefore at once evident, that to calculate the attraction exercised by masses of uneven ground upon the plumb-line is theoretically impracticable; but as it is in no case necessary to know the precise amount of attraction, we may have recourse to methods of approximation, which may be carried to any degree of precision that may be necessary. ...; wº sº. * . . . . - 16. The deflection of the plumb-line caused by a local attraction whose amount is A, is measured by the ratio of A to the attraction of the earth, or the force of gravity, f. If x be. - # • *. * f # * （* * * * * * * * * * * * * * . . i** . . . . . ." . . . . . ; T * . . . . . . . " ... * * * * * p. * Opér, Géod. & Ast: Tom. II, page 348. * . - . . . . .27. ... . . . . . . . .”. f The plumb-line is acted on by gravity G in a vertical direction, and by the disturbing force:A acting,” “. hori- zontal direction : the resultant of these forces = v.A.E.G acts in a direction which makes the angle tan" *† with the direction of gravity. When A is very small in comparison with G, this angle is identical with its tangent. 576 PRINCIPAL TRIANGULATION. . . the latitude of the place of observation, P. the mass of the earth, whose major and minor semi- axes are a and b, s the ellipticity of the surface, and m the ratio of the centrifugal force to gravity at the equator, the attraction of the earth is (see Airy's Mathematical Tracts, pp. 167, 173)— - * P. º – 3 L (5 – )sin. b” I 8 #m +(in 8 || SIIl x) =; (1–3 m +(#m-)sin x) the values of m and s are is and is respectively. For the purpose of estimating the amount of disturbance caused by local attraction, it will be quite sufficient to use the principal term only, omitting the terms in m and s. If 6 be the mean density of the earth, P. may be taken as the mass of a sphere whose radius = Val and density = 6, consequently the attraction of the earth—— - § ={-s} = -(a) r Therefore if we take 3956 miles as the mean radius of the earth, the deflection 4 caused by an attraction A, will be— - or, expressed in-seconds— v=#A = 1.47% (1) 17. Let us now investigate the attraction exercised at a given point by an elevated table land whose upper surface is tolerably even, and of which the form is nearly a rectangle. Let the attracted point be taken as the origin, and let the attracting solid be bounded by the planes— . a = a y = o z = o a = a' y = b z = h so that the dimensions of the parallelopiped are a' - a, b, h. We shall also assume h to be small in comparison with a a' and b. If g be the density (assumed uniform) of the solid, and a y 2 the co-ordinates of an element of the mass whose sides are da dy dz, the attraction exercised by this infinitely small mass at the origin is— g de dy dz 3:2 -H 3/* + 2” The force in the direction of the axis of w is equal to this quantity multiplied by the cosine of the angle contained by the direction of the element at the origin, and the axis of w; it is, therefore, equal to— - gda, dy dz-z (a + y + 2*): CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 577 Integrating from y = o to y = b, we obtain the attraction in the direction of the axis of * of an elementary rod parallel to the axis of y; this attraction is— - ob dº bac-da, dz da, dza ſº-º-.. = g .GIſ, Ia) - (<āT: ) (TWTſ), Summing in the direction of a we get the attraction of an elementary slice of the solid parallel to the plane of ay equal to— gdºſ" a; da; 2\}. a (a.” + 2*) (2 + b + 2*) The general integral is— (a.” -- 2'); gdalog fi +(b" + 22 + 2*): which taken from a to o' is equal to— 2 2. 2. a” + 2 b -- W bº + a” + 2* (2) Assuming 2 to be small in comparison with b and a and a', we may neglect quantities of the order z'; and therefore the quantity within the larger b = a cot p = a' cot ºp' g dz log {(##. *.0 + V bº + a” H} brackets becomes, if we put 2° nº 2” I + = cot q, + Voice” +: + £ / , , 2* I a; J Cot qº' + cosec *q- + ..., 22 22 l- tº I -- #7, cot 4 + cosec 3 + ##, sin - 2* . I + #: Cot º' + cosec p’ + #jasin dy Now we have— I + cos ? Cot q + cosec q = sin q = cotº @ and therefore the above expression becomes— cot # 4. (1 + #( sin” (p. – )–3; sin’ & — )) cot; p’ * a” \ I + cos q * aſ” \ 1 + cos q' _ cot # 4, + 2” (º: q' cos *) ) I *º- tº-º- cot # 4' 2 \ a” a” Therefore the attraction of the elementary slice parallel to the plane of w y is— - cot # 4. 2* /cos ?' cos ?) * ºdºlog{# (; +: (#–**))} in which quantities of the order 2 have been omitted. Since log (1 + wy = w when u is a small quantity, the above expression becomes— - cot & q' a” a” e dºlog{#} + , , , is {**-*.* * - 4. ID 578 r * PRINCIPAL TRLANGULATION. Integrating from z = o to 2 = ſt, we have the attraction of the whole mass equal to— t + ! --- # ºlog{#}} + #2 * {*-*.*} (3) a.” (i. 18. By the application of this expression we may find the components of the attraction of a table land upon any point. Let ABCD be the rectangular mass of height h, which is small in comparison with PE. Let PE = a, PF = a, EC = b, EA = }, S /* so that the dimensions of the rectangle are a' — a and Y + 5. e- * Let the age. C D PCE = q. PAE = 6 PDF = 4: . PBF = 0. then the attraction in the direction PE is— cot #0 cotº, h" ſcos 0' + cos ?' cos 0 + COS *)} **{log:# cot & q' + 3 ( a” . . . * a” * and the attraction in the direction perpendicular to PE is— * {1 a got (45 - # 9) dot (45 - # *) + & (ºr – sin 6 sin it' - sin *) * Tºji=Tº-ºy" 5 lya b The corresponding deflections* expressed in seconds are by equation (I)— = "o"., a £ a cot # 6 cot lº (e. 3' + cost cos 0 + cos *) } !, = 12",447; h {log cot. Gſco. 37 t 6 a” tº 0.” (4) imº "º. = "… . J' = I2”.447 § h {log cot (45 – #6') cot (45 – # 4 ) " 6 b/2 . b? If the deflection in any particular direction as PS be required, then if SPE = a, the required deflection y is— a cof (45 – # 6) cot (45 – 4 º') ... hº (in 6'.— sin 6 sin 4' — sin *) } p = p, cos & + 1/sin & . The absolute amount of deflection is VW-FV, and the direction in which it takes place is determined by the angle whose tangent is the fraction / ; ), * * * *r- * * * * * * These may be put in the following form : If a and y be the co-ordinates of P measured from the centre of the rectangle parallel to BA, AC respectively, the deflections will be— * , , ſ , 4.7 it (#) . . .';* (#) * = **** * ' (; ; H). 1 + x/ + (#) 1 + x/ + #) + x/ 1 + (+.) in which 2a and 2b are the sides of the rectangle AB, BD. W = 12" 447 #h log CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 579 19. Let us now ascertain the actual amount of disturbance that would be caused by a given mass. Suppose a table land whose form is a rectangle of twelve miles by eight miles, having a mean height of 500 feet, and being of half the density of the earth; and let the observer be at a point two miles distant (perpendicularly) from the middle point of the longer side. ` In applying the formula the height h must be expressed in miles, as that is the linear unit used in obtaining the equation (1); and if p be the modulus of the common system of logarithms, we shall have— - r 252. e i () ſº (#) 5286 p.’ “**\cot # 4' - J,' = o The term in hº may be neglected, as is easily seen, and the angles p and p", which may be found by construction, are about 18° 30' and 59° o'. Hence the numerical value of the deflection due to the mass is— ” - ** * * - - - - - º, - I2”.447 .*. • * r * , - w - b, - I’.472 r , As we approach nearer the mass the deflection increases, being 2". 20 at the distance of one mile. Had the height been a thousand feet instead of five hundred, the term in hº might still have been omitted without materially affecting the result. ~" * ºr wº 20. The attraction of a prism of indefinite length, whose section is a trapezoid, upon a point in the plane of one of the parallel faces, admits of a simple expression, from which we may obtain the deflection that would be caused by a rectilinear range of mountains of a some- what regular section, at a point in the plane of the base. 'Let the attracted point be taken as the origin of co-ordinates, and let the prism be con- tained by the planes— . . . . . . . . . . 2, E O - 2 = * = a + a 2 , a = a + a' z then the attraction of the prism, g being its density, is— * a de dy dz , , , * f.ſſa; + y” + 27); the limits being y = o to y = co; a = a + & 2 to a' + & 2 ; and 2 = o to 2 = h- - a de de g w - eſ dz {log (* + (a' + cz' =y) — log (z” + (a + a 2).) } tº ' -s an eye z” + (a’ + c.' 2). d 2” + (a’ + cz' 2). * = , = lºg #H# – º ſº. £ lºg+H: #; d. --- -- ' ' ... As A2. ~/ .../ . T 2 - : 2 log º f (* + & 3) a” + a” cº" 2 mº a” + a cº 2. **** = +& H = + , ſ = Hº-3 aſ a F&H =y — . . ... * + (a' + 2 2) a’ cº’ -- * : * ...- * + 2* a) — g z log 2” + (a + c, ; + ###, log (* + (a’ + cz' =y) + Hatan 1. (= aſ + * - - . . . . . . . . . * * º I + 2* | •y r, “ . . . . . . . . . . . . g a & • 2. g d._ tº n* * , * - a) * -- . . . . – H. log (a +(a + a 2)) – ## tan’ (= -ā- + al * 58o PRINCIPAL TRIANGULATION. Now put u = 2 + (a + & 2)" and w” = 2 + (a' + & 2)"; then the definite integral will be— sº - zS IFºº /a:N1 + 2* /w’N ** 2 o aſ h } = p 1 (...) ſº #) * . (; * * *— tax- ( b ) – 2 9 a. * I l g log \; (É 2. + 7 + c,” tan- 1 a’ + cz' h I + cz” tan a + c, h (5) which is the value of the attraction required. This expression is much simplified by the consideration of the adjoining figure, which is a section of the prism passing through the attracted point O. * H H' If HB, H'B' are perpendicular to OAA', we have— O _2^ N FIB = h = H'B' A B Bf Af OA = a OA' = aſ OB = a + c, h OB' = a' + cz' h OH = w h" + (a + 2 h)" * † OH' = y hº + (a' + a hy If therefore we suppose OH and OH' to be joined, and put - HAB = 0, H'A'B' = 0, HOB = p, HOB' = @" 2. a sin a 2 h - A = * { (#) ſº (#) º (#) } + 2 g {a' dº' sin 36' – a q, sin”). (6) If O coincide with the foot of the range— * a h a' sin a 6' A = glog. #) (#) + 2 g a' d' sin "0" If the section of the range be a triangle, so that H and H' coincide and q = q', the attraction at any point, O, is— a' sin 2 9 a sin 20 OAf OA. / cºrn 24/ : … 2 º:G; * (#) } + 2 g : {a sin '0' — a sin 9] (7) If the section be an isosceles triangle, the attraction at O is— a' a n sin a 0 OA' OA 3- 2 / glog. { (#) * (#) } + 2 g º sin '6 (AA') (8) From these expressions we may ascertain the disturbances existing in the vicinity of a range of mountains. It is true that in no case can the formulae be supposed to give exact results, but they will serve, as in the following hypothetical cases, to give a general idea of the amount of deviation. We shall suppose the matter of which the disturbing mass is composed to have a density equal to half the mean density of the earth; and in the first case suppose a range of indefinite length, whose mean height is a tenth of a mile, or 528 feet, and breadth at base four- teen miles. Suppose, also, that the slope of the range on either side is th (or tan - ;). The deflection produced by such a mass at a station at the foot of one of the slopes would be 3”.6. At the distance of one mile from this point the deflection is diminished to 2". 5, and at five miles is equal to I". 3. If we suppose a range whose mean height is a third of a mile, or 1760 feet, having equal slopes of, and a breadth at base of fifteen miles, such a mass would produce a deflection of CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 581 7"-9 at a point situated at the foot of one of its slopes. If we remove the station from the foot of the range to a distance of five miles, the deflection at that point would be 3”. 5. As a third instance, suppose a range whose section is triangular, the height of the ridge being eight-tenths of a mile, or 4224 feet, the breadth of the base fifteen miles, and the slopes # and #. The deflection produced by this mass on a point at its base would be 12"-o; at a distance of five miles the effect would be diminished by about one half, at ten miles the deflec- tion would be 4”. 2, and at fifteen miles would be diminished to 3”. 2.* 21. Hitherto we have neglected the geometrical consideration of the curvature of the earth's surface as affecting deflection. This, indeed, may generally be done with safety, even in the case of a range of mountains when their breadth and the distance of the observer are small compared with the dimensions of the earth. But if it be required to ascertain the disturbing effect of a large tract of country of considerable elevation, the curvature of the surface should not be neglected. Its influence may be determined as follows: * The attraction of a mountain whose form is that of a solid of revolution can be obtained only by series. Let the co-ordinates originate at the attracted point, the plane of aſy coinciding with the surface of the earth, and let w = a, y = o be the equation of the axis of the solid which is perpendicular to the plane of ay. The attraction of an elementary slice of the solid contained between the horizontal planes 2 and z + dº respectively is— * * dy dy p dz ..{ wº-ſº where r is the radius of the circular plate k” = a + r + 2*, w” = r" – y”. By the binomial theorem this expres- sion is transformed to— 2 p dz ſº r s #######" (;) i- k ſ's 1.2.3 .... (2 i – I) Å;2 dy where i takes the successive values 1 2 3 4. . . . . ; but we havc- w * a – * -> 2 : I - 3 - 5 - - - - - (2 i – I) J. “ • dy = r ;:...T(zi) = Substituting this in the expression for the attraction of the circular plate, and integrating with respect to z, we have the attraction of the mass equal to— * - ſ's; I • 3.5 . . . . . (4 i – 3) (#)”:'d. " ; k 23.4° . . . . . (2 i — 2)” \ k” tº where r is a function of z, and is determined and expressed by the equation of the attracting surface. If the mass be a paraboloid, the radius of the base = b and height = h, the attraction is- *{ + b – º – 15 º' - 24 tº a 4- 16% + . . . . . . 4 a” 128 at } Suppose h = 2640 feet, b = a mile and a half; at the distance of a mile and a half from the foot of such a mountain its attraction would produce a deflection of 17.30; at five miles the deflection would be only * quarter of a second. - 582. . . . . . . - ‘ PRINCIPAL TRLANGULATION. " In the adjoining diagram let C be the centre of the earth, A the station at which the A . T attraction is required, AN the meridian of A, AP any other great circle - passing through A in azimuth a, so that NAP = a, and AT a tangent to the great circle AN. Let ACP = 6; then if we consider a and 0 as P N the co-ordinates of P, the element of the surface at P will be the rectangle r dº r sin 6 do.; and if h be the height of the actual surface of the ground at P, the element of the volume of the superincumbent matter at P is h r" sin 6 dº do. Consequently the attraction produced by this prism at A in the direction AP is— -- , . gh r" sin 6 d6 da 4 r" sin” # 6 which resolved in the direction AT is— . . . . . gh sin 6 d6 do. 4 sin” # 6 gh cos” # 6 2 sin # 6 cos # 6 cos & = cos & d6 do. From this expression we may easily find the attraction of a portion of the surface contained between two vertical planes passing through A in azimuths ø, and o! and two small circles having the centre A and radii 0, and 6', supposing the surface to have an even height and equal to h; the attraction in question is— g * . . h 9 / a cos’ \ 0 *.ſ. ſ Tº cos & . d6 da 2. 6, a, sin # 6 = g h (sin &' — sin a,) (log # + cos # 6' — cos ?: 0) (9) When 9 amounts to no more than three or four degrees, we may without fear of error omit the higher powers of 6; the corresponding deflection will therefore be, supposing the mean density of the attracting mass to be half that of the earth— / 6”.223 h (sin a' — sin •)log; - . . . . . (Io) f 22. We shall now apply this formula to the station Tawnaghmore, on the north coast of Mayo in Ireland. If through this station we draw on a map of Ireland a line in a north-east direction making an angle of 75° with the north meridian line, and another line due south, and describe two circles round the station as a centre whose radii are respectively Io' and 2° 30'; . these four lines so drawn will inclose a space which may be taken as equivalent in attraction to the mass of Ireland, supposing the space to be filled up with rock to the height of the mean level of Ireland. Now in Ireland there are 13,243 square miles of country whose height is between o and 250 feet, 11,797 square miles whose height is between 250 and 500 feet, 5798 square miles whose height is between 500 and 1000 feet, and 82 square miles whose height is above 2000. Prom these numbers we may infer that the mean level of Ireland is 4oo feet. But the part of Ireland which is more immediately south-west of this station does not attain to the mean level of the country. The mean height of Sligo, Mayo, and Roscommon is 320 feet; CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 583 : | we shall therefore use this quantity instead of 400 feet as the mean height of the disturbing mass. Consequently the deflection caused by this mass at Tawnaghmore is— sº Z. r) 32O º O ty' 6”.223 (...) an 75 log. 15. or o'.984 south. We have here neglected the local attraction due to the form of the ground within ten or twelve miles of the station, as that requires more exact data, and will be subsequently considered. Similarly it might be shown that at the south end of the Lough Foyle Base the deflection due to the mass of Ireland is nearly two seconds, neglecting the consideration of the purely local attraction. n - There is another consideration that must not be overlooked, which is, that the mean density of the sea being less than that of rock, the above effects should be increased 3 but as the amount depends upon the mean depth of the sea, it cannot in general be very exactly ascertained. The deflection due to this cause will probably be considerably smaller than that due to the land. º 23. We now proceed to consider the method by which the local attraction due to the form of the ground in the immediate vicinity of a station is to be calculated. As it is impossible to find an expression for the surface of the ground, the method that naturally suggests itself is the division of the attracting mass into a large number of parts, of each of which the attraction resolved in a certain direction is to be obtained, and thence the sum of all the partial attractions, or the total attraction, or resultant. The case of the computation will materially depend upon the method or law according to which the attracting mass is divided. The method adopted in the calculation of the attraction of the mountain Schehallien by Dr. Hutton is perhaps the most simple and expeditious that could be devised. It is as follows: Having a map showing the nature of the ground, its elevations and depressions, or contours, for some distance round the given station in every direction, draw through the centre of the station a series of radial lines, and describe a series of concentric circles, having the station as their common centre. The ground is thus divided into a number of compartments, whose separate attractions are easily obtained; but before stating the law according to which the circles and radii are to be drawn, we shall investigate an expression for the attraction of the prism of matter standing over any one of these compartments. Let a horizontal plane be supposed to pass through the given station, and let this point be taken as the origin of co-ordinates r & to any point in that plane, and let 2 be the vertical co-ordinate; let also a = o correspond to the north meridian line. Let it be required to find the attraction of a mass contained between the horizontal planes z = 0, z = h, the two vertical planes a = a, , , = 2, and the two cylindrical surfaces r = r), r = r. The volume of an indefinitely small element of the attracting mass being rºda-drºdz, if g be its density the corresponding attraction at the origin is— - • , , " . . . . . . " > * - > g r-do, dr dº * * * - * , * * * - 4 - .” * * * = - * * + - - - * * , ; --- l - * * . " * * * • * * * * * ºf * , , , a. - r" + 2* . . " * . _ " ' " . . . . . . . . . . ; *... . . .' ' ' ' ' " i ...’. > 1. *. 584 wº PRINCIPAL TRIANGULATION. and therefore the attraction of the mass in the direction of the meridian is equal to— * /* /? r* cos & da dr d2 ſ/ſº the limits of 2 being o and h; of 2, 2, and 2'; of r, r, and r’— :- -.' rº r” dr d2 = g (sin Cº." - S111 •oſſ:#; : - ..? º h dr = g (sin c.' – in-)ſº r' + W r" + h” r, + Wr,” + h" If we expand the logarithm, this expression becomes— º º h (2 7” — h’) (r’— 7" ). P f tº- mºmºmº- f tº tº dº g (r’— r) (sin & sin c.) AZFT,”+ h” ( + 24 (r. + h'). + ) = g h (sin a' — sin &,) log, (II) in which r = 4 (r' + 1). Therefore taking r' — r, sufficiently small in comparison with r' + r, we have, putting A for the attraction— - A = g (r' — r.) (sin a' — sin & h ..) WFTE (12) This expression suggests immediately a law of division, for if we make the successive radii of the concentric circles drawn round the station to have a common difference, and also draw the radial lines so that the sines of their azimuths shall be in arithmetical progression, then the attraction of any part of the mass is - (constant) (sine elevation), because the last factor of the above expression for A is the sine of the elevation of the middle point of the upper surface of any compartment as seen at the origin or given station, supposing the uneven surface of that compartment to be smoothed down to an even surface or mean level. The whole calculation therefore requires merely the sum of the sines of the elevations of the different compartments. Unless the ground be very steep it will be unnecessary to retain h", so that in this case we may take— A = g (r' — r.) (sin a' – sin a); (13) 24. Let (r) and (s) stand for the common difference of the radii and sines of the azimuths; let r, be the radius of the nº circle, H, the sum of the heights of all the compartments on the north side of the station between the n” and (n + 1)" circles, H', being the corresponding quantity for the south side of the station; then since # (r., + r. 1.) = n (r) + 4 (r), we have— A = g(s) > . #. Consequently if be the deflection— - 4 = 24".894 ; (s) > H, - Hº, (14) 2 m + I where 3 is the mean density of the earth; H and H' are to be expressed in miles. CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 585 There is another law of division which may be used when hº may be neglected, for in this case we have— n tº * . 7' A = g (sin a' — sin c.) log, ; : I Af If therefore the radii of the circles be in geometrical progression and the sines of the azimuths be in arithmetical progression, the total deflection will be— # * = 24.7%) (r) (H-H) * ºr - - (15) where (r) is the Napierian logarithm of the ratio of the geometrical series in which the radii of the concentric circles are drawn, H the sum of the mean heights of all the compartments on the north side, H’ the sum of the mean heights of all the compartments on the South side. - Of the Disturbance produced by a Mass of great Density and compact Form, situated at a short Distance below the Surface. . 25. The mathematical surface of the earth being at every point perpendicular to the actual direction of gravity at that point, every disturbance of the direction of gravity must be accompanied with an inclination of the mathematical surface at that point to the mean surface. Thus every mountain or series of mountains produces necessarily a wave on the mathematical surface of the earth, and the same effect is also produced by irregularities in the density of the matter below the actual surface of the earth. Suppose, for instance, a mass of very dense matter to exist at a certain place at a small distance under the surface of the earth, and, for the sake of illustration, suppose the position of the disturbing mass to be covered by a large lake, then it is clear that the attraction of the dense mass would have the effect of collecting the water towards a point vertically over the centre of the attracting mass where it would accumulate in a permanent wave. The magnitude of the wave will of course be a function of the magnitude and depth of the disturbing mass, and if the latter be given the nature and details of the former can be concluded. - Theoretically therefore, as the matter of the crust of the earth is not of an even density, and the actual surface is everywhere uneven, the mathematical surface of the earth must be a continued series of waves. This is evident & priori, but it remains for observation and calcula- tion to ascertain whether these waves are of sufficient magnitude to be detected. 26. The effect of a small and very dense mass below the surface of the earth in pro- ducing an irregularity in the mathematical surface in the neighbourhood may be thus investi- gated. Suppose the earth a sphere of a radius = a, and let all be the depth of the centre of the disturbing mass, and put I — k = h. Let M be the disturbing mass, and P any point of the earth's surface, its distance from the centre of the earth being = r, and let the angle sub- tended by M and P at the centre of the earth be put = 0. We shall suppose the disturbing force to be so small in comparison with the attraction of the earth that its square may be 4 E 586 - - PRINCIPAL TRLANGULATION. neglected, consequently in estimating the effect of the disturbing force at Pwe may neglect r — a, or the height of P above the undisturbed surface, and put— PM = a (1 + k – 2 k cos 0) - Also if q be the angle contained at P between PM the direction of the disturbing mass, and the vertical— - - - * - PM sin q = a k sin 6 Hence if we put M for the disturbing mass, its attraction at P resolved horizontally is— M k sin Ó a” (1 + k” – 2 k cos(); The ratio of this force to the attraction of the earth will give the angle through which the direction of gravity is displaced by the action of the disturbing force. Now if p be the ratio of the disturbing mass to the mass of the earth, the attraction of the earth will be expressed by— M_ P. a.” hence the angular displacement of the direction of gravity is— p. It sin 6 (1 + k” – 2 k cos 0): The mathematical surface is always perpendicular to the actual direction of gravity; hence r, 0 being the polar co-ordinates of the curve formed by the intersection of this surface, with a plane passing through M and the centre of the earth, we have— dr — p. k sin 9 Fä - (TTFE. Così), *... I ſº — p k sin 6 dº tº ſº ogreſs, + k” – 2 k cos 0): ” — ſº Or e º s o log z = (1 + k” – 2 k cos 0): + C As the square of p is neglected, so also may the square of r – a ; thus the equation of the curve becomes— 7° E (I {++(HF =#E) -- c} (16) C being a constant, which is necessarily of the order of the disturbing force: this constant is quite arbitrary, as there are an infinity of surfaces perpendicular to gravity. But if we take for the mathematical surface of the earth the surface of the Sea, or still water connected with the sea, then we may determine the constant by the assumption that the volume of the surface generated by the curve (16) is equal to the volume of the sphere whose radius is a. Now the first is equal to— 2 " … si = * 3 ºr 3 * **ſ. r3 sin 6 d6 #zaſ. {1 + 30+ (Hººsingdº =;-2ſ2G + 3 C)+ 62% CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 587 and since this is equal to ; ºr a we have C = — tº ; hence (16) becomes by putting y = r – a, I - v=a+(G+H=ay-1} (17) The greatest value of the elevation y of the disturbed surface is that vertically over the disturbing mass, or corresponding to 0 = o, where its value is— I — h h or, as we are considering only small depths h, and Y is a small quantity— Y = a pº _ 0 }. x = + (18) The deflection of the plumb-line due to the disturbance of the mass at any distance 6 is— — p. A sin 6 J = (1 + k – 2 k cos 0): (19) Or since the effect of the disturbing force is only sensible at a distance which is small com- pared with a, we may neglect higher powers of 6 than the square; thus— * = ſ.ſ. #y (20) When } = o the deflection is zero: as 0 increases, the deflection increases up to a certain point, and afterwards diminishes indefinitely. The value of 0, which corresponds to the maximum deflection, is obtained by making— - -- d!, h” – 2 9” dó = p. (FIG) E O and therefore the maximum deflection takes place at a point whose distance from the radius of the earth passing through the disturbing mass is to the depth of the disturbing mass as 1 : V2. The maximum value of the deflection is— ^{* = sº * #. (21) 27. We now proceed to show, that although a disturbing mass below the surface may be sufficient to produce a very large deflection, yet the actual height of the wave in the mathe- matical surface produced by its action is quite inconsiderable as regards the figure of the earth. If we suppose 4, the maximum deflection, to be expressed in seconds, m the depth of the disturbing mass expressed in miles, a the ratio of the volume of the disturbing mass to that of the earth; then if the excess of the density of the disturbing mass above that of the surrounding matter be equal to half the mean density of the earth— *—--- (£) 180-60-60 T 3 v3 \ m – & 3. ºr p ºn? ** = -2 (Easy The volume of the disturbing mass is therefore to the volume of a sphere a mile in diameter as, ºr "P" ºn? 94/3 4. 4 E 2 588 † - PRINCIPAL TRIANGULATION. If we compare Y, the greatest height of the wave expressed in feet, with y, the greatest deflection expressed in seconds— = 34/3 ºr w m _ II ºf 9 m 2. I8o.60.60 T 3Oow/3 Suppose now the disturbing mass to be a sphere of a mile in diameter, the excess of its density above that of the surrounding country being equal to half the density of the earth, and suppose the depth of its centre to be half a mile, then— w = 2×3 = % so that although the deflection would amount at the maximum to very nearly five seconds, yet the actual vertical magnitude of the wave would be only two inches. If we had supposed the centre of the mass to be at the depth of three quarters of a mile, the result would have been— - 4. w/ 3 \; - = 2". 20 7r I x = -33 = + nearly 3OO 9. - We may from these calculations draw this important conclusion,-that a large observed amount of deflection may arise from, or rather accompany, an irregularity of the surface of the earth whose actual magnitude, as regards height at least, is of an extremely minute order. 28. The above calculations are necessarily only roughly approximative, since the form of the mass is assumed such that its attraction upon any given point is nearly the same as if the whole mass were collected into one point at its centre. The general deduction will, however, remain true. - Let us now examine the effect of the disturbing mass upon the curvature of the surface. The equation of a principal section of the wave we have seen to be— T = a + 1 + const. pſ a (h’ + 5°) and if R be the radius of curvature of this curve— ( ** + #) - d62 F. (#)-; It = d6 but since we may neglect the square of the disturbing force— IR E i d? r d 62 CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 589 - Here we may also neglect r – a, and therefore— HR = (! tº a r -- – . h” – 2.6% (22) I + p. (FTE), The radius of curvature will therefore be a maximum or minimum according as (h' – 26°) (h’ + 5°)" is a minimum or a maximum. The differential coefficient of this quantity is— 30 (?? - 3") o (h' + 6-); Tºmº and therefore the maximum and minimum of the radius of curvature correspond to G = 3 hº and 3 = of hence— * * º - - - Maximum of R = C. I - 8v 2 p. 254/5 hº Minimum of R = C. - Ł I -- Ji? Or expressing tº in terms of * the greatest deflection, the greatest and least values are— O. and 0. 25 V5 h 2 h The difference of these values is— "If 3• 124; (I “p I + 2.072 r + tº º º ' If we suppose y to be expressed in seconds and the depth m in miles, then the difference in miles between the maximum and minimum radii of curvature is— 2a2+ 42 : 2 + + - I + o-O4O 77? The inference from this formula is very remarkable, for if we suppose a disturbing mass to be placed at one mile below the surface, then the difference between the greatest and least radii of curvature of the disturbed mathematical surface will be proportional to the maximum deflection, and at the rate of 240 miles per second. The curvature of the mathematical surface of the earth is therefore affected to a very con- siderable amount by a disturbing mass of no very great dimensions below the surface; and consequently if the existence of such disturbing masses be admitted, it will follow that if the curvature of the surface could be determined at many points of the earth, such curvatures would exhibit very great discrepancies. 29. Let us now inquire whether the disturbing mass which produces a sensible amount of deviation in the plumb-line can also sensibly affect the rate of the seconds pendulum. If L be 590 PRINCIPAL TRIANGULATION. the length of the pendulum, g the force of gravity, n the number of vibrations in twenty-four hours— - - º +--- * * - a (804oo \* g *=(* ) # dn dg: - * F = # Now the vertical component of the disturbing force at the distance a0 from the point of the surface directly over the mass M is— º M 7, = d. a’ (h' + 91): T 9 Also g = #, therefore if v be the number of seconds the pendulum is accelerated— * – –tº– or – 260. p h 2 = (HTF), or, y = 12.60.60 (FIG). (23) The disturbance is a maximum for 0 = o, or when the pendulum is just over the disturbing mass, the amount of the greatest acceleration is— N = I2.60.60 # (24) the greatest deflection y in seconds is # # by (21), consequently— . . N – T V 3. ...— . 7 – -i- (25) The number of seconds of time which the pendulum is accelerated is therefore, at the maximum, about half the number of seconds of arc in the maximum deviation of the plumb-line. 30. Instead, however, of comparing the mawimum effects we may compare the mean effects in the following manner. Suppose P that point of the surface of the earth which is vertically over M the disturbing mass, and with the centre P and any radius b describe a circle on the surface; draw also a meridian line through P. Let r be the distance of any point of the surface within this circle from P, & its azimuth, and the meridional component of the deflection at that point. In (20) put 0 = h tan w, then tº expressed in seconds is— I5 N 2 J = 7- Sin u cos “w cos & - ºr h where N = 12.60.60. p. Now the mean value of , within the distance b of P is— 4. ſfºrd, do. ºr bº the limits of a being o and , t , of r, o and b. But r = ah tan u ... r dr = a lº sin w sec *u. du ; consequently the mean value of p is— 60 N a? * u, r sin *M. 2 *mmºmºmºmº OS 2. du do. 212 02 iſ. ſ. COS 2. C 6o N a” a” / dit d := -- – — COS 7t 7° b” Jo \cos w u) =&#. (log cot (45 –3) – in u) . . . . (26) CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 591 which is the mean value of the meridional component of the deflection within a distance b = ah tan w of P. - - Similarly we may obtain the mean value of the acceleration of the pendulum within the same limits. By (23) we have— -- - * * * w = 7; cos ºu. = Wi And the mean value of v is therefore— 2. 18 : #ſ.ſº in ududa = ** (, — cos w) Hence the ratio of the mean value of 9 to the mean value of 9 within any given distance of the disturbing mass is— - 1. * * lóg cot ( -:) — in a H ( A 36.1% “(45 T2 (27) y ) T ~2 I - COS 2. ſº . . . b IRatio: º 8 IRatio: . b IRatio: . tº: tº 1. Depth Mean iſ . Depth Mean tº Depth Mean J, of M Mean v of M Mean v of M Mean v being = 1. being = 1. being = 1. O O © O O" OO o' oo || 30. o' 58 I 12 | 60 | I '73 2 '74 IO o' 18 o' 36 40 o'84 1 : 56 70 2*75 3.68 2O o:36 o'72 50 I 19 2 : o3 8o 5-67 5 °34 Of the Disturbance produced by a Mass of great Density and elongated Form, situated at a short Distance below the Surface. 31. In the preceding case we have supposed the disturbing mass to be of such a form that. we might, without much altering its effect, replace it by a massive point at a certain depth below the surface. But the results will be different if the disturbing mass be a long prism or cylinder of dense matter; for this reason, that the attraction of a material point acts inversely as the square of the distance of the attracted point, whereas the attraction of a small prism or cylinder of indefinite length upon an external point is inversely as the distance and not the square of the distance. This circumstance is easily explained by considering, that as the point attracted moves away from the cylinder the more distant parts of the cylinder, beginning to act less obliquely, have a greater effect, and therefore the diminution of attraction is not so rapid as in the case of an attracting material point or sphere. 592 PRINCIPAL TRIANGULATION. The attraction of a cylindrical shell of indefinite length whose density is g, radius r, and thickness dr, upon a point whose distance from the centre of the cylinder is k, is— É'ſ dr iſ.” 2 k (R – reos 6) d6 k o k” + r* – 2 k rºcos 6 =#rdr. h The attraction of the whole cylinder of density g is therefore— 2 * * g# g (28) Let us apply this to the determination of the wave that would result from a long range of very dense matter under and parallel to the surface of the earth. Let, as before, a be the radius of the earth, r the distance of any point P in the curve formed by the intersection with the mathematical surface, of a vertical plane perpendicular to the axis M of the disturbing mass from the centre of the earth. Then 6 being the angle subtended by MP at the centre of the earth, and h the ratio of the depth of A to the radius a of the earth, the attraction of the disturbing mass at P is— º 2 ºr cºg a(RTG), where c is the radius of the section of the disturbing mass and g the excess of its density above that of the surrounding matter. This attraction resolved horizontally is— - 26 cºg ºr a (h’ + 6°) The attraction of the earth being $ in a 3, the deflection is— 7 dé) 4 & a” h’ + 0° (29) – log r = 44; log(le 4 0) + C &º 4, 8 a” If we suppose that at the distance 0 = 0, , r = a, then— • * = 33 & a lº' -- 0:” f log a T 4 3 a" log li” -- 0° (30) which is the equation of a transverse section of the wave. The maximum value of the deflection takes place when H; is a maximum, that is, when 0 = h : the greatest deflection is therefore— — 3 g c | * = #: 7 We may express + in seconds, and put m for the actual depth of A in miles, c being also expressed in miles; then— - w = 3. É 162. ' 4 8 ºr 'm g. cº = 38”.7 8 . m (31) CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 593 If y be the height of any point of the wave surface above the undisturbed surface, g the maximum value of y— a rºy 4 & a tº h” -º-º: 2 2. 2 2 = 2 = 3.9 ° logº + 6 0. 4 & a′ h? 62 9 – ?) = aſ w log(1 -- #) - (32) If G be large compared with h- g — y = 2 ah k log; 32. If the excess of the density of the disturbing mass above that of the adjacent matter be equal to half the mean density of the earth, and g — y be expressed in feet— // cº * - I9 '37, 2 \} g — y = c log ( I -- #) , approximately. Suppose c = }, m = I, then the greatest deflection = 4".8, and— At Io miles g – y = o'58 feet. At 20 miles g – y = o'75 feet. At 30 miles g – y = o-85 feet. In this case therefore, also, a very large deviation of the plumb-line may be due to an irregularity of the surface of which the magnitude is small compared with the dimensions of the earth. 33. Let us now examine the curvature of this wave. Returning to the equation of the curve, we have— * = — a 34* r * d6 28 a” h’ + 6° d?r Ji? – 6” alò : - 2, ah Ap (FTF). If R be the radius of curvature— IR = 7° 1 – . ºf r d62 omitting the square of % ; we may also omit r — a in this expression; then— R = a - -º-º-º: }* – 6” (33) I + 2 h ºf (FTF); 4 F 594 PRINCIPAL TRIANGULATION. This will be a maximum or minimum according as– h” – 6? (h’ + 6’), is a minimum or a maximum; the differential coefficient of this is — 20 (3 hº — Gº) (h’ +9°)-', therefore the values required correspond to 6’ = 3 hº and to 0 = o, so that— Maximum R = * * - II. Minimum R = *: *If 1 + + The difference of these values is— 9 : a 4 h 7 * I (P \" I + 4 h 2. (#) or if y be expressed in seconds, and m be the depth in miles of the centre of the disturbing range of matter, the difference of the greatest and least radii of curvature is, in miles— “y 175 in 1 + “O34 • ; – “oool 9 (#) (34) sº The disturbance of the curvature is therefore nearly proportional to the area of the section of the disturbing mass, and inversely as the square of its depth below the surface. 34. The maximum effect of the disturbing mass upon the number of vibrations (n) of the pendulum is— 3. - i. . . . . . . . . . . . . dº — 3 g º I — 2 H = # 7 = 2* Therefore if * be expressed in seconds— . N = 4. . * * $º I5 (35) so that in this case, as in the preceding, the maximum increase of vibrations per day in the seconds pendulum is about half the number of seconds in the maximum deflection. 35. If we wish to have a fair representation of the relative effect of this disturbance upon the plumb-line and upon the pendulum, we should not compare the maximum effects upon either, as there is an infinite number of chances against the maximum being observed in any CàSe. Let us suppose, then, that a point is taken at random within a certain distance from the crest of the wave, and let it be required to ascertain the probable amount of deflection at such a point. The probable deflection will evidently vary with the given distance; if that distance CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 595 be very small, the probable deflection will be very small; as the distance increases the probable deflection increases; but when the distance is great and increases, then it is clear that the probable deflection will decrease; within a distance that may be determined the deflection to be expected will therefore be a maximum. n ~f_ - - T--— O —; .* à - Let the curve OHKP be such that at any distance OQ from O the ordinate QP shall represent the deflection at that point, O corresponding to the crest of the wave where the deflection is zero. Draw OV perpendicular to OQ, and through any point v draw whk parallel to OQ, cutting the curve in h and k. If the point taken at random between O and Q (O and Q being the limits) fall within hk, the deflection will be greater than Ov, otherwise it will be less; consequently— hk hk OQ. and 1 – OQ. are the probabilities that the deflection that will be encountered will exceed or fall short of Ov. If we take Ov such that hk = y OQ, which may be done by means of the equation to the curve, then the probabilities of exceeding or falling short of Ov are equal, and consequently Ov represents the probable deflection. - - . If Vbe determined so that VH = HK, being parallel to OQ, then as P moves up to K, Ov increases to OV, but if P be taken to the left of K the probable deflection will begin to decrease. The distance VK is therefore that within which, a point being taken at random, the greatest amount of deflection is to be expected. If O, q be the stated limits, then the probable deflection is evidently that which corresponds to the abscissa ; Oq, for, for all points in the right half of Oq the deflection is greater, and for all points in the left half of Off the deflection is less, than at the middle point. 36. In the case we have last considered, if be the deflection at any distance a from the crest of the wave, 4 the greatest value— 4. - 4 = + -º- arº + ºn” For each value of there are two values of a ; these values are determined from the quadratic- J, - ºpe 2. a:” – 2 m -- a -i- m” = O from which we have— - 2. – nº tº 2 - º o, = m ++ w/º L. J. J, 4 F 2 596 . : PRINCIPAL TRLANGULATION. And between these values of a the deflection is greater than without them. These values are equal when y = *, as is otherwise evident. When w, = 2 a., , which determines the point Kin the curve— g r * * + Wºº-Jº = 2 * – 2 WTJF ‘. Jy = 'y 2 V2 The corresponding value of a, = WK = m wz : consequently if the point be selected at random within this distance of the crest of the wave, the probable deflection will be the greatest, and equal to # of the maximum deflection. If r be the given distance (> m V2) within which the point is to be taken, the probabilities that the deflection will exceed or fall short of J, are— 2 m wº- tº 1 – 2 m w ł. - % 27—y- , 7° J, When these are equal— *p *=y, +(#) This, then, is the deflection that may be expected in taking at random a point within the distance r from the crest of the wave, m being the depth of the disturbing mass. 37. Let us now obtain the number of increased vibrations per day that may be expected within the same limits. The ratio of the increased vertical attraction to the attraction of the earth is at any distance w— dn 3 g c 2 a m 2 – = 4. Ö a? m” + 22 Put dm = y, then— _ _ n m” fººms m* + 3:2 It is evident that for all positive values of a, # is negative, and 9 diminishes continuously as a increases. If therefore we form the curve whose ordinate is v to the abscissa w, it is clear that all values of 9 between a = o and a = 3 r are greater, and all values of v between v = } r and r = r are less, than the value of 9 corresponding to a = }, r, or— 7, "J" r? I *= -- 4 m” - and this, therefore, is the probable increase to the number of vibrations per day to be expected within the distance r of the crest of the wave, taking a point at random. y E CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 597 Comparing this with the probable value of J, we have— 4 = 4G tº 9 I + + q’ where q = # and is supposed greater than v2. If y be expressed in seconds, we must put for J- ºr 2 ºr * 155.55.65 = Wi. and therefore— ** = -- ſº *!, I5 q* + 4 t § III. Ö Observations for determining the Attractions of Mountains. The first attempt to determine the amount of the attraction of a mountain was made by the French Academicians MM. Bouguer and De la Condamine during their operations in Peru. The great mass of the different mountains in that country invited the experiment, for it appeared that if the attraction of a mountain were at all sensible it could be nowhere apparent in greater amount than among these mountains, though on the other hand, considering the volcanic nature of the country, it was a matter of much doubt whether the probable existence of large internal cavities might not diminish the weight of the result derived from the observa- tions. For this purpose the mountain Chimboraço" was chosen by M. Bouguer: its height above the level of the sea is 32.17 toises, but above the plane of the surrounding country 1700 or 1800 toises; at the base the diameter is about ten or twelve thousand toises, and at half its height the diameter is about 35oo toises. The summit is flat, and three or four hundred toises in diameter. º: From these dimensions M. Bouguer estimated the volume of the mountain to be about 20000000000 cubic toises, or the one 74oooooooo" part of the mass of the earth, whence he inferred that at the distance of 1700 or 1800 toises from the centre of the mass its attraction would amount to the 2000" part of the attraction of the earth, or would produce a deviation of I'43". In order to ascertain by observation whether the actual amount of deviation would at all correspond with this rough calculation, a station was chosen on the south side of the mountain as near to the centre of gravity of the mass as convenient, and a second station was fixed upon at about 3700 toises to the east of the first, at which point it was conceived that the meridional component of the attraction of the mass would be very small. The meridional altitudes of several stars were observed at both stations with the quadrant, but unfortunately the observa- tions were few and very discordant, owing to the very inconvenient circumstances in which the observers were placed. The result of the observations, such as they were, gave 7":5 for the * “Ila Figure de la Terre, déterminée parles Observations de Messieurs Bouguer et de la Condamine, &c. 1749.” Page 368. 598 PRINCIPAL TRIANGULATION. deviation produced by the attraction of the mountain, which is probably erroneous to a con- siderable extent, and very little weight was attached even by the observers themselves to this experiment. Schehallien. In 1772 the Astronomer Royal, Dr. Maskelyne, undertook to repeat the experiment, and after careful search, and the examination of many hills, Schehallién, a mountain of 3000 feet in height, in Perthshire, was selected as the most favourable that could be found in the country. The form of Schehallien is regular; the summit is an inclined ridge, presenting from some points of view a conical appearance, and rising to the height of about 2000 feet above the general level of the surrounding country. A station was selected on the south side of the hill at about 1200 feet below the vertex, and another station on the north side at about 250 feet below the level of the former. At these stations in 1774 Dr. Maskelyne determined the latitudes with a sector made by Sisson. At the south station 73 observations were made face east and 93 face west; at the north station 68 observations were made face west, and Ioo face east. The difference of latitude was found by Dr. Maskelyne to be 54".60, which agrees with the result given by the Baron de Zach in his work on the “Attraction of Mountains,” from his own reduction of all the observations. * The survey was made in the years 1774–75 and 76, by the direction and partly under the inspection of Dr. Maskelyne. Two base-lines were measured with deal rods whose lengths were ascertained in terms of the Royal Society's brass 5-feet scale; the length of the base on the south side of the hill was found to be 3011.4 feet, that on the north side, in Rannoch, was found to be 5895.4. By means of a triangulation founded on these bases, the distance between the parallels passing through the two astronomical stations was found to be 4364-4 feet, which corresponds to a difference of latitude of 42".94. * This last quantity, determined by geodetical operations and independent of the attraction of the mountain, shows that the effect of that attraction was to increase the astronomical ampli- tude by 54”.6o — 42". 94 = II”.66, which last quantity is the sum of the angles through which the plumb-line was drawn inwards towards the mountain at the two stations. *. Mimet. In 1814 the Baron de Zach published a work on the Attraction of Mountains,” containing a detailed account of observations made by him in the south of France for ascertaining the actual amount of the deviation caused by a disturbing mass. The mountain Mimet selected by him. for the purpose, is nine or ten miles north of Marseilles, its height is about 25oo feet above the level of the sea, and one of the observatories was situated on the southern face of the mountain, where the ruins of a convent offered some shelter. The second station was in the small island of Planier, nine miles south-west of Marseilles, at which distance the attraction due to Mimet * “L'Attraction des Montagnes, et ses Iºffets sur les fils à plomb, &c. Par le Baron de Zach.” Avignon, 1814. OBSERVATIONS AT ARTHUR'S SEAT. 599 would be insensible; so that the attraction of the mountain would be represented by the excess of the geodetical over the astronomical difference of latitude of the two stations. The observations for latitude were made with a repeating circle by Reichenbach, of twelve inches diameter. The three stars observed were on the same side of the zenith, and were observed 874 times at the northern station, and 896 times at the island of Planier. º The geodetical operations for connecting the two stations were conducted with great care and minuteness. The base-line was measured with a system of three deal rods of ten feet in length, which were guarded against moisture of the atmosphere by coats of oil and paint; the final length of the line was 1182 toises. The angles of the triangles were observed (each being repeated ten times) with an 8-inch repeating theodolite by Reichenbach. The mean error in the sums of the observed angles of the triangles is 3”. I7. The direction of the meridian was determined both at Mimet and Planier by numerous observations of the Sun. th From these observations the difference of latitude was calculated, using an ellipticity of #, to be 12' 13”. 11, which exceeded the amplitude derived from the astronomical observations by 1”.98, which is the apparent effect of the attraction of the mountain Mimet. But it has been shown by M. Arago, in the Additions to the Connaissance des Tems, 1819, that the repeating circle used by the Baron de Zach for the purpose, was scarcely adequate to the determination of so small a quantity, and that consequently little weight should be attached to the result of these operations. - ARTHUR's SEAT, EDINBURGH. The next experiment upon the attraction of mountains is that by Lieutenant-Colonel James, Royal Engineers, in 1855. The hill is the well-known “Arthur's Seat” in Edinburgh, a compact and abrupt mass rising to the height of 822 feet above the sea. In the choice of this hill there was a second object in view, also in connection with the subject of local disturbances. It has been known for some time that the astronomical latitude of the Calton Hill Observatory, Edinburgh, differs very materially—between five and six seconds—from the latitude inferred by geodetical operations from several other astronomically-determined points not very far distant. This circum- stance rendered it very desirable that the latitude of some other points in the immediate vicinity of the Observatory should be determined astronomically, thus to trace the course and magnitude of the disturbance. In the selection of three stations on Arthur's Seat, this object was accom- plished, as well as the determination of the attraction of the hill itself: and as a third result, a value of the mean density of the earth was obtained. In form, Arthur's Seat is particularly well adapted for the problem of attraction; the mass, however, is considerably smaller than could be desired, especially for the determination of the density of the earth. A very convenient place offered itself for the southern station, almost exactly on the meridian passing through the apex of the hill (see plate XX.), and close on the south side of the road called the “Queen's Drive.” This station, is nearly on the contour ‘375, and therefore at about one-third of the effective height of the hill. In selecting stations for the observation of the attraction of a hill, those two points have to be determined, one on the north side and the 6oo. PRINCIPAL TRIANGULATION. tº other on the south, at which the horizontal components of the attraction of the mass resolved in the direction of the meridian are the greatest. These points will not generally be at the base of the hill, but between that and the top, and can only be determined in any particular case by an examination of the ground. In such a mass as Arthur's Seat, the maximum attraction is pro- bably at about a third of the effective altitude, that is, the altitude above the adjacent ground. On the north side of this hill there is more difficulty than on the south in obtaining a favourable position; that chosen for the purpose, and at which it was supposed that the attraction would not be far from the maximum, is in a small hollow to the east of and above the Ruins of St. Anthony's Chapel, and about fifty feet below the horizontal plane passing through the south station. A third station was also chosen on the top of the hill: this point is distant fourteen feet from the Trigonometrical Station, and bearing 18° north-west. The observations for the determination of the latitudes of these three points were made with Airy's Zenith Sector in the months of August, September, and October, the weather being generally very favourable. The apparent declinations of the stars were obtained principally from the British Association's Catalogue and the constants therein given. The refractions were computed from the tables given in the Appendix to the Greenwich Observations for 1836. The following table contains an abstract of the results:— LATITUDES. AMPLITUDES. Name of Star. No. No. No. | South Station SummitStationſ North Station South Station. of |Summit Station. of North Station. of and and and Obs Obs, Obs. |North Station. South Station. SummitStation f O Af O f ºf O & // | o f tº O / / / 59 Cygni ... ... f" |55 56 26’ 63 || 4 |55 56 43-92 || 8 | O O I7 "29 |o , , 3416 Groombridge. 25'68 2 42 "3o | Io I6' 62 | 23 Cephei . E 27° 36 4 4.3 ° 93 || 2 | ° 16' 57 3692 Groombridge. 23 °og I 42 '98 || 2 19'89 3 Lacerta: . . Ø 28° 39 2 46'34 || 4 I7° 95 37 Cassiopeiae .. 6 24'82 2 43' 47 || 6 • 18: 65 39 Cassiopeiae . x 27-27 || 6 44' 17 | 8 16-90 362 Groombridge . 25°63 || 3 42 52 | 8 | 16-89 44. Cassiopeia: . 25 '26 || 6 42 '85 || 8 i I7°59 I Persei. * 24'98 || 4 42 of 8 I7 - og 9 Cephei {º 45' 52 || 6 |55 57 Io'34 || 4 | o o 24'82 13 Cephei . . p. 42' 33 || 8 8° 52 || 4 26- 19 25 Cephei . . . 44' 37 || 6 9' 61 Io 25°24. 4077 Groombridge. 45 ° of 2 Io 5o 2 25° 43 3224 B. F. . . . 44'96 || 4 Io I5 4 25° 19 3 Persei. tº ſº 42 - 1 1 || 6 6'99 || 2 24'88 531 Groombridge . 46"69 || 4 II '73 2 25 "O4. 13 Persei . () 43 71 || 6 8°75 2 25 “O4. 590 Groombridge . 43 ° 93 2 8°os 2 24” I2 | 391 B. F. . . . . . . 46’ 6o 2 Io'97 || 2 | 24° 37 634 Groombridge . 44' 47 || I 6'64 || 2 22 - 17 33 Persci . . a 44° 34 4. 9° 25 2 24 '91 45 Draconis - d. 27°59 4 Io'o6 || 2 ||o o 42°47 46 Draconis , : c 24° 73 || 5 7'48 || 4 | 42 °75 2677 Groombridge. 22° 38 || 3 4'72 || 2 || 42:34 47 Draconis . 0 25-86 || 6 7. 97 || 2 | 42 " II 2718 Groombridge. 25'89 || 2 8'72 2 | 42 '83 OBSERVATIONS AT ARTHUR'S SEAT. 6of LATITUDES. AMPLITUDES. * | Name of Star. iNo. | No. No. ||South Station SummitStation|North Station South Station. of Summit sation. of | North Station. of and and and ow. | Obs. Obs. ||North Station. South Station. Summit5tation 48 Draconis . 55 56 27-80 || 3 55 57 1685 2 |3 o 43°os o a © M fº 49 Draconis . . . 23 I 5 4. 8' 15 2 45 °oo 2777 Groombridge. 28° 52 2 Io '90 2 42 38 53 Draconis º 27 ‘95 2 9°29 || 6 4 I 34. 54 Draconis • 27' 64 2 | Io'os 2 42 °4 I 2836 Groombridge. 26 - 16 2 | 9° 33 || 6 43 I? Io Cygni . . i* 26.75 2 8.70 || 2 4 I '95 2865 Groombridge. 27 o'S 2 Io'oz 4 42 ° 94. 2894 Groombridge. 24 °42 2 : 7°24 2 42 '82 I3 Cygni . . . 6 23' 67 || 2 t 5 ° 9o 2 42 ° 23 16 Cygni (1*) . cº 28° 23 || 6 r Io. 68 7 42 ° 45 16 Cygni (2nd), c’ 26.70 || 6 . 9° 18 7 42'48 43 Cygni . . wº 23'20 | 6 7' 03 2 43 ‘83 I 137 Oxford, 1843. 26' 90 4 ! 9' 57 4 42'67 2 Cephei ... 6 26'78 4 | Io '83 2 44' os 20 Andromeda: . ), 25 3 I 4. | 8-27 | 6 42 96 7 Cassiopeiae 9 26-64 6 9' 17 | 8 42 ° 53 9 Cassiopeiae 28° 32 2 Io'96 || 6 42 64 31 Groombridge 26.63 8 9° 32 8 42' 69 | 8 Cephei 25° 7 3 9° 38 6 43' 61 3524. Groombridge. 26-48 2 Io'83 || 2 || 44' 35 | 80 Cygni , art 25'65 || 4 7:84 2 42 " IQ 20 Cygni . . d 28'97 || 6 |55 56 45-46 || 6 11.71 || 6 42 '74 |o o 16°49 |o o 25°25 2996 Groombridge. 25'98 || 6 43 28 2 '8' or | 6 42 "O3 17° 30 24 73 66 Draconis tº 26' 35 | 6 43° 26 || 6 8’42 || 6 42 of 16-91 25' 16 30 Cygni . . of 28 - 12 || 2 45 ° 9o 2 *6'63 4 *38.51 17-78 *zo'73 31 Cygni . . oº 27 ° 90 2 45 ° 59 2 Io 33 2 42 "43 1769 24 ° 74 68 Draconis 26:45 2 43 °47 || 4 8 : 6o 4. 42° 15 17 oz 25° IS 71 Draconis ſº 27°34 Io 44' 13 | 8 9.75 | 8 42 °4 I 16'79 25' 62 3205 Groombridge. 27 ° 99 3 44 ° 30 4. 9-76 4 41 77 16' 31 25° 46 46 Cygni . . .3 27°46 3 43 - 58 6 9° 2 I 3 4I ‘75 I6' 12 25°63 50 Cygni . . . . 26-72 Io 44. "Io 5 9-66 8 42 ° 94. 17:38 25° 56 | 3 Cephei . . . . . 26.70 || 6 44° 12 8 9° 50 4 42 '8o 17°42 25° 38 7268 B. A. C. . . 28'93 || 6 45' 67 || 4 10'76 || 6 41 ‘83 16'74 25' 09 63 Cygni . f* 28° 23 || 8 44 ° 9o Io Io'49 || 8 42'26 16.67 25° 59 3415 Groombridge. 26-31 || Io 42 °47 5 8’ Io 4 4I '79 I6' 16 25' 63 5 Cephei . , c. 27 OA. 7 43 '8o 12 9:25 8 42°2 I 16.76 25 ° 45 1256 Oxford, 1842. 25°32 2 43' 82 4 9° 53 2 44 ° 2 I 18° 5o 25'71 71 Cygni . . g . 25'56 3 42 '76 4 8' 34 I 42 78 17 zo 25° 58 io Cephei . . . . 25' 63 || 6 42.70 || 8 8.70 || 10 43° of 17'o'7 26 oo 3606 Groombridge. 27°53 7 4I '93 I 8'22 || 8 40' 69 I4 * 40 26' 29 3652 Groombridge. 27. 58 || 8 43°47 4. Io' 33 I2 42 °75 15°89 26.86 7736 B.A.C. (1*star) 27°52 2 44'54 || 6 Io' 43 I2 42 ° 91 17 oz 25'89 | 7736B.A.C. (2ndstar) 28. 18 3 45' 18 || 6 II - I 5 I2 42 ° 97 17'oo 25' 97 27 Cephei (1*) 8. 29' 35 | 2 45°81 4 Io' 58 Io 41 ° 23 16:46 24*77 27 Cephei (2nd) 8° 27 63 2 45' 12 || 6 Io' 19 Io 42° 56 17°49 25" of 9 Lacertae tº 27 ° 93 4 44 ° 23 2 Io 14 || 6 42 ° 21 16:30 25 ° 9 I 3o Cephei . & 25'38 || 4 44' 56 2 Io 65 2 45 ° 27 19° 18 26°og 3882 Groombridge. 24 ° 25 || 4. 42 - 26 || 6 7. 12 8 42.87 18° of 24'86 3147 B. F. . . . 26.68 4 43.88 || 6 9' od 8 42 36 :7: | #.;; I Cassiopeiae . 25 “O2 4. 42 "40 2 8' 26 || Io 43°23 17:37 *#. 8 Andromediu . 25: 71 4. 42°48 4. 8: 57 IO 42-86 16-77 26 o9 * Not used in mean. 4 G. 6oz PRINCIPAL TRIANGULATION. IATITUDES. AMPLITUDES. Name of Star. No. 1 - No. No. | South Station SummitStation|North Station South Station. . of Summit Station. of | North Station. of and and and obs. Obs. Obs. son Station. South Station.jSummitstation = * * * | | º O * * * O # * * © & M.J. c iſ ºf O J iſ O / If 4. Cassiopeiae . 55 56 28°45 || 4 |55 56 45°os 4 55 57 II o2 | 8 |o o 42.57 |o o 16' 60 ſo o 25' 97 16 Andromedae. A 27 '89 4 44' 37 2 Io 24 Io 42 °35 16:48 25'87 5 Cassiopeiae 7. 26'46 4. 43 IQ 4. 9° 7I 4 | 43° 25 16.73 26'52 12 Cassiopeiae . . 26'96 || Io 43 o9 2 9°53 || 6 || 42 °57 16. 13 26°44. 15 Cassiopeiae . k 27' 59 || 8 45' Io 2 Io'oz | 6 | 42 °43 I7' 51 24 ° 92 18 Cassiopeiae . c. 27'39 || 8 44' 51 6 Io 15 || 6 || 42-76 17: 12 25' 64 24 Cassiopeiae . . 26-32 | Io 42 73 || 8 9° 30 || 4 || 42 98 I6'41. 26. 57 27 Cassiopeiae . y 26’ 65 Io 43'54 Io 9° 32 || 4 | 42' 67 16.89 25-78 3o Cassiopeiae . p. 26-42 Io 43’51 i 8 8-94 || 4 || 42°52 17’ og 25° 43 287 Groombridge . 27°o: 4 44' 2 I | 8 9 Io || 2 || 42 of 17: 18 24'89 34 Cassiopeia: . p 28.63 Io 45' 72 || 8 Io 51 || 2 || 41 '88 17’ og 24 '79 5 Persei h 29' oo 2 46' oo 6 I2 74 || 2 || 4.3 ° 74. 17°oo 26'74 • { If we assign to the result given by any one star, a weight equal to the number of observa- tions of that star, we get the following results for the latitudes of the three stations:— Station. Latitude. No. of Obs. South . 53 56 26.69 427 Summit 55 56 43°95 42.5 North . 55 57 9°50 4 II These results are affected by the errors of the assumed declinations: in order to avoid these the following method is adopted:—Put a for the amplitude or difference of latitude of the first two stations, y for the amplitude of the second and third. Let the stars observed at the first and second stations only, give the values v = a, w = a', w = a”. . . . let the stars observed at the second and third stations only, give y = b, y = 0, y = b”. . . . let the stars observed at the first and third stations only, give a + y = c, a + y = c', a + y = c''. . . . and lastly, let the stars observed at all three stations give a = a, , y = b, , w = a,’, y = b,'. ... . . . Let d, e, and the same letters accented, be taken to represent the number of times the stars of the first set are observed at the first and second stations respectively. Let f, g, and hk, represent the same quantities for stars of the second and third sets; and let n, p, q, and the same letters accented, be taken to represent the number of times the stars of the third set are observed at the three stations respectively. & The probable values of a and y are those which render a minimum the function— de ..Y 1 s (...ſº º hk s # (, – dy) + 3 º,0-y) + s #! (, 4 y – cy). + = (#; G - a) + =Gº;g-º) OBSERVATIONS AT ARTHUR'S SEAT. 603 Making the differential coefficients of this quantity with respect to a and y separately = or we get— Ha! -H ISy — L = o I(x + My — N = o where— de hk np j? hk pſy -: S S ; M = S ( zº- > ( → º-ºº-º-º-º: H = 3 (H. + h + k + (#) M (#) + (#) + 3 4 + q hk - f - E = X h + k The quantities L and N are affected by the errors of observation. Let (d. s) be taken to represent the sum of the errors of the d observations of a star of the first set at the first station, and let (e.s) be the sum of the e errors of observation of the same star at the second station. Then, denoting the other sums of errors in a corresponding manner— . L = 3 (H. d) + s #; a) + 3 (H. e -- d. n + p d (e.g.) — e (d.s.) n (p-s) — p (n-s) h (k's) — k (h-e) + 3 (*H ) + 3 (tºº) + 3 “H N-s (ſº < ſ 720 hk Af(g-s) – g (fs) p (7-5) — 7 (p.s) h (k-s) — k (h's) +s ( f + 9 ) + s ( p + q ) + s ( h + k ) If we require the probable error of r + p.8), tº being any given multiplier, we have— L (M — w KY + N (tº H – K * + 2y = ** # # ) To find the probable error of r + p y, we must form the sum of the squares of the coefficients of the errors as they exist in this expression. This sum will be found equal to— (M – º Ky H + (, H – Ky M + 2 (M – º K) (; H – K) (K–P) (MH – Kº)" . where— < * np ſ/ - " (n + p) (p + q) Consequently if E be the probable value of an error of observation (as determined by the discrepancies between the mean and individual results for latitude given by a single star), the probable error of a + p y is— — # MII — IX* {A: (m — Kº + 2 RF) - 2 p. (R (MII — K*) + p (MH + Rº) + p.” (th — IC” + 2 r)n] IP = The values of H, M, K, P and L, N are— II = 168.93 MI = 168.52 K = 46.06 L = 362.40 N = 182-20 P = 49.34 * * 4 G 2 604 PRINCIPAL TRIANGULATION. We have, therefore, for the determination of the astronomical amplitudes w and y, I68.93 r + 46.06 y — 362.40 = o - (a) 46.06 a + 168.52 y – 182-20 = o by the solution of which, r = 17"-oo: y = 25".53; a + y = 4.2”.53. At the South Station the sum of the squares of the apparent errors of observation, 427 in number, is 265.6; at the Summit, the sum of the squares of the apparent errors of observation, 425 in number, is 202.7 ; and at the North Station the sum of the squares of the apparent errors of observation, 411 in number, is 243.8. From the sum of the whole we find the mean square of error = o'. 56, and therefore the probable error of an observation = o'67 Wor;6= o”. 50. o”.5o 263.4 3. Probable error of r + up = {520.5 — 544-7 p. -- 522°o *} } = o”.o.43 { – I-off tº + *} The probable errors, therefore, of the astronomical determinations of the amplitudes w, y, or a + y, are each equal to + o”. O4. Geodetical Amplitudes.—The stations were very carefully connected by a small network of triangulation based upon the minor triangulation of the Ordnance Survey of the county of Edinburgh. It seems unnecessary to give more than the results of this operation, which are these:— From To Piº in Bearing. tº. º i C} f JJ Summit South Station . 1426'7 179 42 7 (Trigonometrical Station) | North Station . 2490°o 6 o 17 | The bearings are measured from North round by East. The corresponding amplitudes (derived from Airy's Elements of the Figure of the Earth) are 14”-06 and 24”.40. But the Summit Station in the last table is the Trigonometrical Station, which differs o”. 13 in latitude from the Sector Station; therefore the amplitudes corresponding to the astronomical observations are 14". 19 and 24”. 27. * | ; : Astronomical ' Geodetical sations. Amplitude. Amplitude. A —G. Af f South and Summit . . 1% CO I4 IQ 3.81 Summit and North . . 25" 53 24'27 I 26 South and North . . . . 42 °53 38'46 4 o'7 It appears, therefore, that the sum of the angles through which the direction of the plumb- line is deflected by the attraction of the hill at the North and South Stations amounts to 4".o.7, with a very small probable error. OBSERVATIONS AT ARTHUR'S SEAT. 605 Mean Density of the Earth. At the same time that the attraction of Schiehallien was observed astronomically, trigono- metrical operations were carried on over its surface, by means of which its mass might be accurately known and its attraction computed and compared with the quantity observed. The altitudes of a great many points on the hill were carefully determined and laid down upon a plan showing also the position of the Observatories. Through each station on the plan a series of 48 radial lines were drawn, the sine of the azimuth of the (n + 1)" line being equal to the sine of the azimuth of the m” line + . A series of concentric circles was also drawn round each station as centre, the radius of the (n + 1)" circle being equal to the radius of the mºh circle + 666.6 feet. Thus for each station the mass of the hill was divided into 960 prisms. The attraction of any one of these prisms is # 9 sin s x 666-6, where g is the density of the mass and s the elevation of the top of the prism: the deflection for either station is therefore— o”. 1310 : S (sin s) where 3 is the mean density of the earth. Dr. Hutton found for the North Station, X (sin e) = 88.644, and for the South, X (sin s) = 69.967: this gave— Deflection at North Station = 11”.61 ; 33 South Station = 9”.17 ; The sum of these must be equal to the observed quantity II".66; this gives 20.78 g = II. 666 ... à = 1.78 g. If therefore the density of the hill be 2.75, the mean density of the earth would be 4. 9. º - It is to be regretted that the inner circle of 666 feet at cach station was not subdivided, as it is probable that this might have modified the result sensibly. Had the calculation been extended to a greater distance, the high ground to the south might have diminished the cal- culated attraction by an appreciable quantity which would have the effect of increasing the resulting value of the mean density of the earth. This calculation was afterwards carefully repeated by Playfair in connection with his lithological survey of the mountain, and from it he obtained 4.713 as his final result.—(Philosophical Transactions, 1811, page 376.) The experiments of Cavendish with the Torsion Balance gave 5.448 for the mean density of the earth (Memoirs of the Royal Astronomical Society, Vol. XIV., page 91), with a probable error of + o-o33. These experiments were repeated in 1836, with some improvements, by Professor Reich, of Freiberg in Saxony, and from his calculations he obtained 5.44, with a probable error of + o-o23. The volume of the Memoirs of the Royal Astronomical Society mentioned above contains the full account, by Mr. Baily, of his own experiments with the Torsion Balance, conducted at the public expense (a grant of 50ol. having been applied for and obtained by the Astronomer Royal), and with every imaginable refinement. The result of these valuable experiments was 5.660, with a probable error of + o-oo:3. 606 PRINCIPAL TRLANGULATION. If we suppose the earth a sphere of radius a, having mean density 6, the force of gravity at its surface is— g = : ºr a 3 - If we descend below the surface to a depth ah which is small in comparison with a, the force of gravity g, at that depth is— _ + ºr a” 8 – 4. T a” ah g 9, - a” (1 — h)" where g is the density of the superficial parts of the globe; consequently— 9, - tº-º g # = 1 + 2} 3 h; Now if a pendulum make n vibrations per day at the surface, and n + q at the depth ah, 1 + 2} =%. , = ( – #) So that by observing the rate of a clock at a known depth below the surface and comparing it with another at the surface, the mean density of the earth may be compared with that of the superficial rocks. By this means the Astronomer Royal in 1855 obtained 6. 566 + o- or 8 as the mean density of the earth; the acceleration of the seconds' pendulum at the depth of 1256 feet being found equal to 2°. 24 + o'-ol.—(Philosophical Transactions, 1856.) - Mean Density derived from the Attraction of Arthur's Seat. If we add the amplitudes as determined from equations (a) to the observed latitude of the South Station, we get the following values for the latitudes of the three stations:— Latitude of South Station 5 3. 56 26.69 33 Summit , 55 56 43.69 33 North , 55 57 9'22 - Now the observed latitude of the Calton Hill Observatory is 55° 57'23"-20, and the geodetical amplitude of the Observatory and the Trigonometrical Station on Arthur's Seat is 39.64; consequently the geodetical differs from the astronomical only by o'-38. It is therefore evident that the disturbing force that acts in a southward direction at the Calton Hill exists at the summit of Arthur's Seat to the same amount very nearly ; this may be termed the “general deflection,” and exists at each of the stations distinct from the attraction of the hill. The attraction of the hill was calculated in the same manner as in the case of Schehallien, with only this difference, that the distance of the successive circles is 500 instead of 666.6 feet. The calculation has also been extended to a much greater distance round the stations than was considered necessary for Schehallien. Round the North Station sixteen circles were drawn upon the contoured plan, having their radii in arithmetic progression, the radius of the last being 8000 feet. After these circles, another series of circles was drawn in continuation, having their radii in geometrical progression, the ratio being #; so that the radius of the (16 + n)th circle OBSERVATIONS AT ARTITUR'S SEAT. 607 is (;)" × 8ooo feet. The South Station was treated in a similar manner, as also the Summit Station, with this exception, that at the latter there were only twelve circles in the first (or arithmetic) series, so that the radius of the (12 + n)" circle is ()" × 6000 feet. At each of the three stations the inner circle of 500 feet was subdivided by four other circles, the common difference of whose radii was Ioo feet: thus each station is surrounded by three series of circles. If we put X, for the sum of the sines of the elevations of the tops of the compartments to the north of a station (up to the end of the second series of circles), S, for the corresponding quantity on the south side: and put H, for the sum of the altitudes of all the compartments (in the third series of circles) to the north, H, for the corresponding quantity on the south side, then the deflection to the north is (by pages 584,585) + o”.org64 (X, − S.). 2 for the first series, + o”.og82 (S. – E.). 2 for the second series, + o”-oooo.3027 (H, - H.). 2. for the third series; where 2 is the ratio of the mean densities of the hill and the earth. * By means of the contours on the map the following results were obtained:— TABLE I.—First Series of Circles. N South Station. Summit Station. North Station. 0. of Ring. 2n 2, 2n >. 2n 2. 1) + 1-689 — I '796 — 7 118 -3° 524 - 2 * OO2 +4'867 2 +5'448 || – II 294 | – II 281 –9° 164 –8: o38 +4° 347 § +7° 705 — II '808 — II '845 —8*603 –8-856 +3* I 59 4. +9°og8 || – II 360 — 12 ol.4 –7°436 –8°424 |. --2 179 (5 +8.845 — Io-oor — II '719 —6°421 –6'973 + 1 ° 932 TABLE II.—Second Series. South Station. Arthur's Seat. North Station. No. of Ring. 2n >. 2n 2, 2n >, 2 +6.614 –6. 299 —Io' 560 — 5' 143 –4°644 +2 °oog 3 +3° 187 —3’531 — 7'996 —6-634 -3°994 | + I '695 4. + 1 o88 –2 °536 – 5'85o —7° 715 —2 '859 +o 978 5 +o oz.5 —2 oz.6 — 4'656 —6'425 –2 361 +-I o28 6 —o’og 5 —I '713 - 4'474 -5 °295 - I '954 + I 195 7 —o'o.88 — I 488 — 4' 570 —4' 549 | – I 623 +o '745 8 —o' 418 – I 309 - 4" 209 -3°994. — 1 “422 —o. 361 * 9 —o'926 — I 149 || – 3 '839 —3'587 | – I 25 —o' 747 IO —I ‘oo4. —o '985 – 3:467 —3°234 —I 176 —o'671 I I —I of 7 —o’844 — 3 I Ig -2 ° 93 I — I 117 —o' 604 I2 —I ‘ooA. —o. 729 — 2-883 —2' 667 — I of 8 —o' 575 I 3 —o'908 —o' 625 —o' 996 —o"558 I4 -o'843 —o' 539 —o' 941 -o' 525 I5 —o' 828 —o' 4.72 —o '935 —o'488 I6 —o 8o0 –o "4:34 —o'894 -o'449 608 PRINCIPAL TRLANGULATION. TABLE III.-Third Series. N South Station. Summit Station. North Station. .# f -º-ºsm Ring. Ha II, IH, H, H., II, I 3 +2643 +4645 I4. +224.5 + 5025 I5 + 1624 +5460 I6 + 904 +6obo 17 +2385 + 6060 + 548 +746o + 520 +4495 18 + 1685 + 6870 + 427 +8485 +385 + 5045 I9 -- 935 + 8295 + 148 +8845 +277 +5640 2. + 630 | + 901o – 92 +855o – 15 +6475 2 I + 465 + 89.25 – 132 +9595 - 2 OO +8ooo 22 + 18o + 8175 –320 +8175 23 - IO + Ioobo d –375 +8135 TABLE IV.-Results. South Station. | Summit sation. ! North Station. Series. . *— 2n-2, l)eflection. Xa-2, Deflection. . 2,-X, Deflection. i ; | s – , | | I ! +78'984 +1'551 2 —18-829 —o' 370 2. —50°777 —o. 997 : 2 +27. 636 | +2.714 z – 3:441 —o. 3382 —28'994 –2 '847 z Ha—H, Ha—H, TT.III, —— 3 —51665 – 565 - — 558 Io — I 691 z –45693 ! -1.393.2 35 33 The sums of the third, fifth, and seventh columns of this table give— Deflection at South Station = + 2.70o z Summit , = – 2.399 z North , = – 5-237 z We must now assume that the disturbing force which acts in very nearly the same amount at Calton Hill and the summit of Arthur's Seat acts equally at all the three stations on the hill in a southerly direction. — 5 - 237 2 – v. of the three stations are 2. — a , x, x + y, and also if x, be the geodetic latitude of the Summit, the geodetic latitudes will be x, — 14. I9, 2, , X, + 24, 27. (if we put x, — » = 2) a + v — 14, 19, a, a + preceding or calculated values there result— v - 2.70o z + cz + r – I4 IQ v + 2.399 z + & v + 5°237 z + 2 – y + 24.27 Thus the deflections become + 2.700 2. — v.; – 2: 399 2. — v and Now let x be the astronomical latitude of the Summit, so that the latitudes Then the deflections north will be 24-27 – y. By equating these with the : OBSERVATIONS AT ARTHUR's SEAT. 609 where w and y are known quantities. From this equation by the method of least squares— (5'999' + 7.937” + 2.833°) = = 5·999 (; – 1419) + 7.937 (+ + y – 38,46) + 2.838 (9 – 24:27) ... z = o'I3432 z + o- IIIo2 y – 4,6006 f Consequently, g being the mean density of Arthur's Seat, 6 the mean density of the earth, Ö it o: I.2432 a + sº 3y — 4,6006 By being put in this form, we see more clearly how to estimate the probable error of 6 as depending upon the probable errors of the observed quantities r, y, g. By the examination of a great number of specimens, Lieutenant-Colonel James determined the mean density of the hill to be = 2.75. Substituting this value, and the previously obtained quantities w = 17, oo, y = 25-53, we get 3 = 5.316. By means of the expression given for the probable error of a + by (page 604), we readily obtain, putting p = •83, the probable error of 6 depending on the probable errors of the observed amplitudes, namely + -oj4. If, therefore, s be the probable error of the observed mean density of Arthur's Seat, we shall have finally” Mean Density of the Earth = 5.316 + W3725 FT oozo § IV. On the Influence of the Irregularities of the Surface of the Earth on the Comparison of Geodetical and Astronomical Observations. I. Let the axis of revolution of the earth be taken as the axis of z, the centre of the earth being the origin, and let—. *: a’,” + y,” + (1 + s) 2,” – I = o (I) be the equation of a regular spheroid whose surface coincides very closely with the mathematical surface of the earth. Let the normal to any point a y 2 of the latter surface meet the spheroid in v. 3), 2, , and let v be the part of the normal intercepted by the two surfaces, then— ar, - a - Av : y = y — pºv : 2, - 2 – vy where 2, p. v are the direction-cosines of the normal. Substituting these values in the equation of the spheroid, we have— (a – Av) + (y – pºv) + (1 + e) (2 — vu) — I = o We may assume v to be so small that terms of the order v', s v, may be neglected, then the above equation becomes— a” + y” + (1 + s) 2" — 2 v (Az + py + v2) — I = o * “On the Deflection of the Plumb-line at Arthur's Seat, and the Mean Specific Gravity of the Earth. Commu- nicated by Lieutenant-Colonel James, R.E., F.R.S., M.R.I.A., &c., Superintendent of the Ordnance Survey.” Philo- sophical Transactions, 1856, page 591. - 4 II 6Io . . PRINCIPAL TRLANGULATION. but in the coefficient of v we may neglect s, Šo that w = x, y = p, 2 = y; therefore since x + p + v = 1, we have— r + - - - w = z* + y + (1 + s) 2" — 2 v — 1 = o (2) for the equation of the irregular surface of the earth, where v is the height of the latter at any point, above the surface of the spheroid (1) of reference, and is a function of a y z ; but as we may substitute for 2 its value in terms of w and y, v may be considered a function of a and y. 2. The equations of meridians and parallels upon this surface may be expressed as follows: A meridian line upon the irregular surface (2) of the earth is a curve of double curvature, and is the locus of all those points whose longitude is constant. Let to be this longitude, then the normals for every point in the meridian line are parallel to the plane y cos o – a sin a = o, or perpendicular to the line y sin a + a cos a = 0. But the direction-cosines of the normal are proportional to— t du du . du do. dv º * * * * iſ ºmº- d: dy - d. * - E : y - #: (1 + s) z Therefore we must have— – in a ( – ) + coe ( º #) E O dr dy and therefore the equation of a meridian line on the surface (2) is— º . dv dv – sun a + y to a + in a E – cose: – o (3) For the equation of a parallel whose latitude is A, we have— du” — so, , (duº , duº , duº f = sin” (E * iF + #) dv dv 2. G + i) = coex = 2 - 2 =# + y – 29; Or, I * dv dv (1 + i)=(H + coex)'—v 4 = } + yj - 1 = o - (4) which, together with (2), are the equations of the locus of all points whose latitude is a . 3. If through any point P on the surface (2) we draw a system of rectangular axes of co-ordinates é º 4, the first being directed to the north, the second to the east, and the third to the zenith, then— . . - r = a + 1, # + m, n + n, ; 3y = 3 + l, § -- m, n + n, & (5) * 2 = y + , ; . . . 4 n, where & 3 y are the co-ordinates of P, and l, m, n, l, m, . . . . . . the direction-cosines of the new axes. Hence we have— d = (, ; + lº) d; + (nº. + m, .) d" + (, ; + n, #) d; CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 6II At the point P dº = o ; also l, = — cos a sin x : 1, = — sin a sin A : m, = sin a m, = — cos a ; consequently at P− –– * = cos 24 + sin du sin x dº T da: *āy * = sin a * cos,” dº T da: dy The quantities # and . are the inclinations of the surface (2) to that of the spheroid of reference (I), measured north and east, or they are the deflections north and east, to use a term derived from the expression “deflection of the plumb-line.” If we put i, and i' for these differ- ential coefficients, the equation i, 3 + i + + 4 = o is. that of a plane passing through P parallel to the corresponding tangent plane of the spheroid. Let a vertical plane pass through P making an azimuthal angle & with the plane š , and put 6 cos & = & , 6 sin & = 1, then it is clear that the inclination of the two surfaces measured in the direction determined by the azimuth o is a i, cos & + i sin & . This may be illustrated mechanically, for if i be the magnitude of a local attraction acting at any point of the earth's surface, i, and i' the com- ponents of this force in the direction of the meridian and perpendicular to it, then in the direction of the azimuth & the attraction is i, cos & + i sin & . The maximum, or i, takes place for the azimuth tan -(?' : i), and is equal to y if +7°. By means of the above expressions for # and #. , the equations of the meridian and parallel become— tº - dv – a sin a + y cos a 4 + = o *] (6) - —— 2. \\ do $º — = (1 + ·) (H+ cot x) + cotxi + v + i = 0 4. The effect of the irregularities of the surface upon the curvature at any point may be traced in the following manner: Let the system of axes é º & originate at that point (P) on the surface for which the curvature is required. Let hk p be the co-ordinates of any point of * º - tº iſ . d the surface very near to the origin, then since at that point # = o and # = o, we have— dºg dº, dºg = F * º l. 2. : ry gººmsº + º 2 + tº tº º º ſº. p (h, k) 2 \d;" h "d; dº dº.” k ) Put now h” = (hº + k') cos ºoz, k” = (hº + K") sin *o., then— —#4– * -; d’; 2 ry d’é * d’; tº 2 tº ſº º º ſº dº h? 1 ź tºº, d:” COS “ct + * l; d" COS c. Sin & -- in’ Sin "c. -- Now if g be the radius of curvature of the vertical section of the surface by a plane passing through the axis of , and making an angle & with the plane of ; #, we have at the limit I'-H k = 2 pg. Also it is easy to show that at the point P or the origin— dºu du Cº. d’u du dº dºu ... du d’é à + i + = 0 ++, + i +; = * : * iF i = * 4 H 2 612 I PRINCIPAL TRLANGULATION. consequently by substitution in the preceding equation, and neglecting the sign of g, we have— I du 4- d’u (la d? - * e - e - 2, , ("tº {} d’ll si g dº d:" COS “c, -ī- 2 d: dº COS c. Sln & -- dºſ” sin ºcc (7) 5. By differentiating the equation w = a + y + (1 + s) ~ – 2 v — 1, we obtain through equations (5), and considering v a function of £ and m only— du dv dºw * d”v # d; - l, a: + l, y -- (I + s) l, 2 - d; # Ziº - l,” + l, + l,” (I + s) ſº d; lu dv d’at d’v l. au º wº tº i.e. * m #-- - - k *=- := 2 sº 2 ſº iº º ſº lºgº 2 dr, = m, a + m, y dm 2. dº.” mn,” + m, dº? l du . l dºu g-g 2 2 2 # = n = + n, y + (1 + ) , = ## = n + n + nr (1 + ) d’ut d°v ### = ſ. m. * 1 m. – i. But we have also the following necessary relations— l,”,+ l,” + l,” = m,” + m,” = n,” + n,” + n,” = 1 l, m, + l, m, = o and therefore since l. = cos x , dºu d”v 4 * = S “A — - º d:” I + = COS X d;" 1. º. - *- dºv : ** = 1 — tº * di: dº d: dº * dº? dº.” Also if we add the squares of the foregoing values of # #. # we shall have, remembering that at P the first two of these differential coefficients are zero, and making use of the equation to the surface, (2) 2 # = 1 + G + i) = + , , . 1 du — I + v • , ; ; = * 8 § ( – s in x) (8) I —- 5 - 6. If g, g, be the principal radii of curvature, p the azimuth of the plane of the former, and if we put x cos ‘o. 4-2 w sin a cos & + y sin o. for the reciprocal of g, we shall have— tº * , , º, I I . X cos "c, + 2 w sin & cos & -- Y sin “a = ; coe ( – )+; in ( – ) * * I 82 I I ... x + Y + (X - Y) cos 2 & + 2 w sin 2 & = + + --- cos 2 & (; – ) cos 2 & -- sin 2 q, (.-:) sin 2 & :* £r 92 91 92 \ 91 g2 whence we obtain— I I smºs — = X + Y 91 92 I I cos 2 @ (; – ) = x -x : in a (; – ) = 2 w 91 92 CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 613 If we put r, r, for the principal radii of curvature of the spheroid at a point whose latitude is x , these equations will become— d? lºv I, _ I dº L (179 (9) 7. Let us now consider the effect of the irregularities upon the astronomical determination º º e tº º º º {[. dw * of latitude, longitude, and azimuth. Writing i, and i' for # and ..., the equation— i, ; + iſ 1 + š + v = O (Ic) is that of the tangent plane to the spheroid (I) at that point (P.) of its surface which is the projection of P, the origin of the co-ordinates é º &. Through P draw PQ parallel to the axis of rotation,-this line must be in the plane à &; then, neglecting quantities of the order v i, the meridian plane of P, is that which contains PQ and is perpendicular to (Io): let o, 3 + o' m + 4 = o be this plane, then since this is perpendicular to (Io) we must have o, i, + cz' i' + 1 = of so that the meridian plane of P, is represented by a, i' # — (1 + 2, i) n + i' = o (II) The trace of this plane upon the plane & = o is, omitting quantities of a smaller order, * = 5 - c, č'. Also making in (II) m = o, since the result is the equation of PQ, we must have cº, - – tan x, x being the latitude of P. Hence the true meridian line through P makes a horizontal angle i' tan a with the meridian line traced on the spheroid through the point P, . . It is also easy to see that the plane (II) makes with the plane é º an angle equal to the borizontal angle i' tan a divided by sin A, or 'sec × . 8. It follows, then, that if A a be the latitude and longitude of P, x, w, the latitude and longitude of P., the projection of P upon the spheroid of reference, & the azimuth (measured from north round by east) of any object on the actual surface, a, the corresponding azimuth on the spheroid of reference— - - A = x + + 1 - d; * = a – #ssex (12) -- * = a + an a The first two of these equations are also evident by the consideration of the spherical triangle formed by lines parallel to the normals at P and P., and the axis of revolution; the third equation will also be evident by considering the spherical triangle formed by lines parallel to the directions of the meridian at P and P., and the axis of revolution. 614 PRINCIPAL TRIANGULATION. 9. In the operation of spirit levelling, it is clear that the resulting height of any point of the actual surface is the height above the irregular surface (2) of the earth, for the instrumental horizontal line at any point is determined by the direction of gravity at that point. In the measurement of a base-line, also, the horizontality of the apparatus is determined at every place by the normal to the surface, also the height of every part of the line is given with reference to the irregular surface; hence, theoretically at least, the length of the base-line as reduced to the mean level of the sea is the length of the curve traced upon the true mathematical surface of the earth by a plane passing through the extremities of the line, or their projections upon the surface, and containing the normal at either extremity. Let r = f(0) be the polar equation of the curve of intersection of this plane with the surface of the spheroid of reference, the origin of r and 6 being the intersection with the axis of revolution of that normal which lies in the intersecting plane. Then v the height of the true surface above that of the spheroid of refer- ence at any point in the plane of the base is also a function of 6; let g = r + v, then the length of the curve upon the irregular surface is— - s = f^{e de 4 dº =ſ+r de 4 dr} {1 +; } neglecting terms of the order edu: but if s, be the length of the curve of intersection with the surface of the spheroid— , = f^{r de + de) ‘. S – s; = ſo dº Consequently if v, be the mean value of v between the extremities of the base, the length of the measured line will exceed that of its projection on the speroid of reference by v. s. Io. Let us now consider the influence of the irregularities of the surface on the measure- ment of the angles of a triangulation. If we take two points A B on the surface (2), and project them upon the surface (1) of the spheroid of reference, then the azimuth of B, (the projection of B) as it would be measured at A, (the projection of A) exceeds the azimuth of B at A on account of the altitude of the pole by the quantity #. tan A : but if Ó be the arc distance of B from A, B is seen at a depression = }6, and is therefore displaced in azimuth by the amount of du du . l (; cos e – is SIIl •) tan #6 where c. is the azimuth of B at A ; therefore if a, be the azimuth of B, at A- d d * * = a + ... an x + (; cosa – in 2) tan; dm d; Also if & be the azimuth of any other point C, and 2,' that of its projection, we have— dv dv 2,' – a' + dv 6’ tan A ’ – ºf sin c." º dm an A + (; COS dº d; S1D1 2) tan 2. CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 615 The effect of the irregularity upon the observed angle is therefore— . (cos Cº. tan; - cos &'tan #) gº # (sin & tan : — sin 2' tan ...) Hence it follows that the observed angles of a triangulation differ from the angles of the triangles formed by the projection of the trigonometrical points upon the spheroid of reference, only by quantities which are of the second order in comparison with the inclination of the surfaces to each other. At the utmost this influence can never exceed a minute fraction of a second, and is overwhelmed by other sources of error. Hence in calculating the distance between any two points P, Q of a triangulation (the extremities of an arc of meridian, for instance) and using the observed angles, the result will not be sensibly different from the true distance of the projections P, Q, upon the surface of a spheroid whose surface is parallel to that of the spheroid of reference and at the mean height (v.) of the base-line from it. II. In tracing further the influence of the irregularities of the surface of the earth we shall write # * instead of the differential coefficients of v with respect to those quantities; thus, at any point # denotes the inclination of the actual surface to that of the spheroid of reference measured in the direction of the north; * denotes the inclination of the actual surface to that of the spheroid of reference measured in the direction of the east, the inclination being considered positive when the actual surface is elevated in the stated direction. 12. Now let A B be any two points connected by a triangulation, let x 7' be their observed or apparent latitudes, a their observed or apparent difference of longitude, and let the direction of the meridian be observed at each. The points connected by the triangulation are A, B, the projections of A B, then we have the distance = s, and also from the observed bearings of the meridian we obtain from the triangulation the azimuth of B at A = c and the azimuth of A at B = &'. We have then, the quantities A, A,’ & 2, w, referring to the points A, B, A1 = A + š x,’ = Aſ + š' 2, - c. -- m tan A c.,’ = 2 + n’ tan A' (13) w; - w — m/sec ×' + n Sec A - Let (x) (2) (al') be the numerical results which we should obtain for the point B by using the observed latitude of A, and the observed direction of the meridian at the same, together with the distance s, then— (x) = f(x, a, s) = f( x, — ; , 2, — a tan A, s ) (w) = f; (*, *, s) = f; ( At — ; , 2, - m tan A, S ) (2) = f; (*, *, s) = f; ( X. — ; , 2, - m tan A, S ) Hence— f F df df J (ºr , a, , s) = A, = (x) + š, ; + , an x; df. dr J. (A., a, , s) = w = (w) + = #4 anx # - f df. df. . J. (A : «, , s) = a,' = (2) + = }, + , an a # 616 PRINCIPAL TRIANGULATION. and by substitution— # = (x) = x + š + , an x + da, P º df. df. 7 SCC (a) — a + # da, + m tan A #: - . SCC A (14) f f df. df. f º ſº : 2 *:/ 2 * tan x = (2) – a + * ſix, +- tan»; 13. The values of the differential coefficients are to be found from the equations at page 249. If we introduce into these equations the condition that azimuths are to be measured from north, by east, and longitudes to be measured from east to west, we get— tan # (2,' + w, - g) = - #E: ; cot # 2, _ sin # (# * ~ * - 9) sin # (; T – A, + 6) s sin # (2,’ + c, - g) ; #H#G +3) tan ; (2,' — w; – 3) = cot # 2, (15) X,' – X = In differentiating these equations we may neglect the small quantity & ; and if q be the third side of a spherical triangle of which go” – A, and 6 are two sides including the angle cº, , then by spherical trigonometry we have— * – sin (2,’ + w,) cos” # 4 = cos (; T – A, - 6) cos (; ºr – A, + 6) sin 2, – sin (2, — w;) sin” # 4 = sin # (; T – A – 6) sin # (; T – A, + 6) sin a, By means of these equations we get— da,' ... dw, - - sin (2,' + w,) da;' da; — sin (a," – w.) da, da, sin cº, da, da; sin &, º tº tº tº º da,' + da, sin 6 sin &, da,' dw, sin 6 sin 2, da, ' dar 2 cos” # 4, dx, dx, T 2 sin” # 4. in a' – in a *. sin a da,' º-º-º: * I “mºmº dx,’ _ & I I da, dx,' S I da, do. = . (I + Q) in 2 l. (... ' : # = 1 – ; (1 + q) º f 1 9 2 sin” （, (2,' — «,) I g 2 sin” (2,' – 2,) And therefore since sin 6 sin cº, + sin (p sin a = o, and Q may be omitted, da,' sin a,’ cos w, do, cos 2.'sin w; do, sin a, da, T sin or, * – sin w; da, cos ? sin w; da, sin q. da, Sln q> dx.’ ?) , g dx.’ 1) . + = , sin a sin 6 # = 1 — # sin” w, I g I where v is the same quantity as at page 249, namely the normal for x, . We may here put v = 2, and sin b = cos x', and substituting in equations (14) they become— # = (x) — A' + ( COS CO ) : + (in a sin o), * * --- .* .../ — sec A' - m^ = w) — a + (an x in 2) (#: – see :) I6 r ( # + cot A cos A' . . ) ( ) tan X’. m’ = (2') – c.' + (— Sec X' sin w # + (* A COS e) - cos A/ CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONs. 617. 14. Let us now inquire into the nature of these equations and the information to be derived from them. In obtaining the equations— Ar = A + š a), - a - 7 SCC A : o:: *= a + 'y'-tan A it is evident that they do not in any way depend upon the coincidence of the axis of the spheroid of reference with that of rotation of the earth; the only requirement is that the axis of the spheroid should be parallel to the axis of rotation. If therefore, returning to the arc AB or A,B, to which the equations (16) have reference, we suppose the surface of a spheroid whose axes are 2 a and 2 b, of which the latter is parallel to the axis of rotation of the earth, to pass through the point A or a point A, at a very small distance vertically from A, and to have its surface inclined to the true surface at A at a depression – 5 northwards and a depression. – m eastwards,” we shall be able to determine the quantities 3' nº with reference to this spheroid for the point B. For if with the observed latitude of A and the observed direction of the meridian at that point we calculate the latitude, longitude, and direction of the meridian at B, and find that the calculated values exceed the observed by quantities s, s, s, , then we have from the equations (16)— º, #' = e, -- a, § + b, . º sec x, y = s, + a, § -- b, n : tan x' - ' = e, + a, # + b, . Therefore for any assumed values of 3 and we may obtain the corresponding values of 3 and ". If we make the surface of our spheroid of reference parallel to the surface of the earth. at A or A, , then # = o, m = o, and we have #' = s, , ſ = - e, cos x' = s, cot A’. 15. In examining more closely the coefficients a, b, . . . . . . we find that a, is very nearly unity, b, is a small quantity of the order of 6 (the arc distance AB); a, is of the order 6; b, differs from sec x', the coefficient of Y, by a quantity of the order 6; a, is of the order 6; b, differs from tan x', the coefficient of "", by a quantity of the order 6. Therefore the equations give but little more than— r #' — # = s. º — sec × (n' – 1) = s. * (17) tan A (n' — n) = e, - From this we see that the observation of difference of longitude gives no further information than is obtained by the observation of the directions of the meridian at both extremities, but is available as a check upon the accuracy of the work. * If h k l be the co-ordinates of the centre of the spheroid, its equation is— (* ~ *)' , (y – 8)' , (- - )'' H---- H-- + →-- = 1 It may evidently be made to touch any given place in a given point, for this is equivalent to making it pass through three given points, by which h k l may be determined. - 4 I 618 - PRINCIPAL TRIANGULATION. If there be besides B, a number of other points CD. . . . . . with respect to which we have by a triangulation their distances from A and also the observed latitude and direction of the meridian corresponding to each, then we have a set of equations— #1 – # = a, - m. – ) = b, #, - # = a, ma - 1 = b, #, — # = a, ms – m = b, #, – # = a, 7, - n = b, These equations will enable us to determine the position of the given spheroid of reference, that is the quantities é and n for the point A, so that it shall upon the whole coincide most nearly with the surface of the earth within the limits of the geodetically-connected points; or rather, we may determine that position corresponding to which the sum of the squares of the quantities # 7, shall be the least possible; for the sum of the squares is— #* + (5 + a.) + (; + a,) + . . . . . (# + a.)" + n’ + (n + b,)” + (n + b.) + . . . . . (n + b.)" ...{ (n -- 1) # = - s (a) (n + 1) m = — S (5) 16. We have supposed the points to be projected on one particular spheroid, and the resulting system of inclinations é º is peculiar to that particular spheroid. Had the calculation been made with reference to another spheroid, another system of values would have resulted, and it is sufficiently obvious that we may assign as many systems of values as we please, each with reference to a certain spheroid. The question, then, is to ascertain which of all the spheroids will represent most nearly the general surface contained within the limits of the triangulation. In this shape the problem can scarcely be solved, but we may ascertain without much difficulty the spheroid which will make the sum of the squares of the apparent irregu- larities the least possible, or in other words we can determine the spheroid which shall show on the whole the least total imount of discordance with the astronomical observations. 17. If with the latitude of the point A and the distance and bearing of the point B, we calculate the latitude and longitude of B and the back azimuth of A, with the given (numerical) elements of the spheroid, a, b, and would ascertain the same quantities for B with reference to a spheroid whose semiaxes are a + 6a, b + 8b, then we have to add to each of the numerically- determined quantities terms of the form m.8a + n. 6b, where the coefficients m and n can be assigned. By the alteration of a and b the angle 6 (which is subtended by the distance A,B, = s at the point of intersection of the normal of A, with the axis of revolution) is also altered, for we have— 6 = #(I — e” sin *) CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 619 -* º;. : neglecting smaller terms which are not here required; therefore if w be the result of any calculation made with the angle 0 = f(a, b) and w' the same when 0 = f(a + 3a, b + 6b), Y — du zd6 d6 It is, however, more convenient to use the variation of e” than of b, so that if we put 3a = Ya, be' = s, and differentiate 6 with respect to a and e”, we get, du sin” X w’ = w — - # H.H.) 6 # (y 4 + H+. r The calculated values of x, w, c.,’ will therefore become, since a, and cº,' contain 6 only, and explicitly— * * * (x) + fix,’ 2 (w) + # da,' (c.' ) + zig 36 By differentiating the first two of equations (15) there results, da,' * ~f~ -. f da, iſ = — tan X' Sin Cz, d6 . 30 = sec A' sin &,’ and referring to page 248 we find, × - x = ( – ’) 1) ty ... 8x,’ = + 84 + (q – A,) 8 (+ :* + ( – ’) (;) Now by spherical trigonometry we have these equations— sin q = cos 6 sin X, + sin 6 cos x, cos 2, cos 2, cos ? = sin 6 sin x, — cos 6 cos x, cos 2, Differentiating the first of these equations we get (A, and 2, being constant) cos & dq = — sin 6 sin x, d3+ cos 6 cos x, cos a, d4, which by the second equation = — cos & cos &, d3; therefore 6% = — cos 2, 3}. We have also— v {1 – e' sin # (*, + A.) (IE *) (1 – c' sin x.) from which we obtain, neglecting terms of higher orders— d /v I * * * .# º #(;) = Hyſ – ; irº + x) + ºx) g ... 8 ( ;) – e; (* ; x') e. Making these substitutions in the value of 67, we have— 8X,' = — ; cº-w + ; :=#. + 3 x') • Se” and from above, * - 2 Cº) sec x' sin a,’ 26 — tan A' sin c.,’ 89 2 Cº. º : 4 I 2 62o - PRINCIPAL TRIANGULATION. 18. The equations (16) thus modified become— # = (x) – a 4 ( COS CU ) i + (in x in -) - (; cº-) is 4 a. sº º sin 6 cos &’ — sec x' n' = (w a + (tan x in 2) (#– x) ( / -: ') : n' = (w) # + ºx, — seca) n + (see x sin a 20 - (18) tan A' - m' = (2) — «' -- (see X' sin w) § -- (*.**) tºº-ºº: (tan X' sin 2) 26 - where— — É A’ – A 2. l. f : ſ * = 5 (I-5 co- + (x + 3 x) | 6 sin” X 86 = — y - 6 — 1. . - * ! l y - 6 * I — e” sin” X 19. Let A and B be the extremities of an arc of the meridian, or rather, lying very nearly in the meridian, at each of which we have the observed latitude and direction of the meridian. Using the observations at A as the basis of the calculation and a spheroid whose semi-axes are a and b, let the latitude of B, and the direction of the meridian at that point be calculated, and suppose the quantities so calculated exceed the corresponding observed values by k, k, , then we shall have— o = k, + c, y + c,’s + £ — #’ o = k, cot A’ + c., m + m — m/ The second of these equations determines nothing further than the relation of the quantities " ". The first gives a relation between y and s not free from the influence of # and #'. 20. If there be a number of meridian arcs there will be a series of equations— o = k + c, y + c,’s + š, - #,' o = k, + c, y + c,’s + š, - #,' o = k + c, y + c, s + š, - #,' o = i, + c, y + c, + š, - #. - which cannot be all satisfied, but give n – 2 relations among the m quantities 5 – 3'. * . If there be a number of points ABC. . . . . . all on the same meridian, having observed latitudes and being geodetically connected, they will afford a system of equations— o = k, + c, y + c,' s + # — ;, o = k, + c, y + c,' s + š - #, s o = }, + c, y + c,’s + # — #, From these equations we may determine the values of y and s which render the sum of the squares of the quantities é a minimum, and these values of y and s correspond to and determine CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 621 the spheroid which shows the least total amount of discordance with the observed latitudes. We have— S (; ) = #’ + S (k -- c y + c’s + š)” The equations for determining the minimum are therefore— (n + 1) # + (c) + (c’) = + (k) = o (c) # + (c’).7 + (cc) s + (ck) = o (c) # + (cc) y + (c”) s + (c’h) = o and from these we obtain the axes of the required spheroid, and the inclination of the actual surface at each of the stations ABC. . . . 21. If the measured arc be perpendicular to the meridian, the second, or third equation, depending upon the observed difference of longitude or the observed azimuths, will alone give a relation between y and e, and this subject to the influence of " — m/, and a small multiple of 5. If the line AB lie in any azimuth, we have generally— o = k + a, § – #’ + b, n + c, y + d, s - o = h, + a, § – n' + b, n + c, y + d, s but if small multiples of 3 and n are omitted, the first equation will contain only 3 – š', and the second only " — ". . If we put # = # = n = n = o, the spheroid determined from these equations will have its surface parallel to the actual surface of the earth at A and B, and its axis parallel to the axis of rotation of the earth. * 22. The application of the equations (18) to the determination of that spheroid which, having its axis parallel to that of the earth, shall most nearly represent the surface of a portion of the earth covered by a network of triangulation, and having the latitudes of several points in it observed, and also several determinations of the direction of the meridian; presents no other difficulty than the assigning of the relative weights of the equations depending upon observed latitudes and the equations depending upon observed azimuths. Let ABC . . . . be points in the triangulation, at which the latitude has been observed; these will give a series of equations of the form— #, = }, + a, ; + b, n + c, y + d, - and if the direction of the meridian has been observed at the points A'B'C' . . . . there will be a series of equations of the form— 7,' = }, + a.' * + b,' " + c, y + d,' s In the latitude equations, the absolute term k is subject to two sources of uncertainty— namely, that of the observed latitude and of the transferred latitude. Again, the observed latitude is subject to two distinct sources of error—namely, theirregularity of the earth's surface, and errors of the astronomical determination. In the equations derived from observed azimuths, the absolute terms are also liable to the errors of observation and of transference, and are affected by the irregularities of the surface. Now the errors (of observation) of the observed azimuths are in general (certainly in the Present 622 PRINCIPAL TRLANGULATION. operations) considerably greater, than the errors of the observed latitudes, and the error of transference of azimuth through a long series of triangles is also considerably greater than the error of transference of latitude. Hence the absolute terms of the equations derived from observed azimuths will show discrepancies considerably larger than are shown in the absolute terms of the equations resulting from observed latitudes. If from the whole of the equations we determine à 7 y s so that S (ß) + S (nº) shall be a minimum, the values thus obtained give the elements of the spheroid most nearly representing, on the whole, the observations for latitude and also for azimuth. But the result will be that the azimuths are corrected at the expense of the latitudes, whereas it is more important that the latitude equations should be satisfied than that the azimuths should show small differences. Consequently, the spheroid which makes S. (#) + s (*) the least possible, does not most nearly represent the surface; but if we could assign a relative weight w to the azimuth equations as compared with the latitude equations, then the spheroid most nearly representing the surface would be that which makes a minimum the quantity— S (#") + w . S (n°) g \ 23. The spheroids which we have been considering in the preceding articles as “most nearly representing” the surface of the earth comprised within the limits of the operations, are evidently not osculating spheroids If geodetical and astronomical observations be made in conjunction at any part of the earth's surface in order to determine strictly the osculating ellipsoid, or the principal radii of curvature and the directions in azimuth in which their planes lie, such operations should be contained within very narrow limits, for the differential coefficients of the quantity v, as there is every reason to believe, may vary very irregularly within a small space upon the earth's surface. 24. I.et us suppose that with the object of determining the curvature of the surface of the earth at a certain point, and whether it may for a small extent be represented by a surface of the second order, astronomical observations for latitude and azimuth have been made at three or four stations geodetically connected and at small distances from each other. Let A be one of these stations—say, the central one; at this point let (v) be the value of v, the height of the actual surface above the surface of reference, and let the tangential axes of co-ordinates é originate at A, the formerlying in the direction of the north, the latter to the east. w 25. Since we assume v to belong to a surface of the second order, it must be of the form— w = () + ft 4 gº + A* + i = x + k} ... dw tº. ... dw * : # =ſ+ h; + in * : # = g + i + k, 26. Let B be a second point on the surface not far from A, and let a system of rectangular axes of co-ordinates é' " " originate at B, the first two tangential to the surface and directed to CONNECTION OF GEODETICAL AND ASTRONOMICAL OBSERVATIONS. 623 the north and east respectively, the third & to the zenith of B; then the relations between these quantities and # * are these— # = a + #' cos (; ;) + x' cos (; 1) + º'cos (; ;) n = 3 + #' cos (n :') + n’ cos (n n') + g’ cos (n g’) and therefore at the point B we must have— dv dv f dv ſ # = #cos (; ;) + #cos (, ;) dv # = # cos (; )') + #cos (" ") In order to ascertain the values of these cosines, let Aa, A'a' be the latitude and longitude of A and B respectively, then— - cos (; ;) = cos (; z) cos (#' a) + cos (; y) cos (#' y) + cos (; 2) cos (; 2) = sin A sin x' (sin w sin w” + cos w cos w') + cos A cos x' cos (n :') = cos (, z) cos (#' r) + cos (, y) cos (;' y) = sin x' (– sin w cos w' + cos a sin o') cos (; "') = cos (; z) cos (n' r) + cos (; y) cos (n' y) = sin x (- cos w sin wº + sin a cos o') cos (" ") = cos (n +) cos (n' r) + cos (, y) cos (n' y) º = sin w sin a " + cos w cos w'. Therefore if we neglect quantities of the order of the square of the distance of B from A, we have— - cos (; ;) = 1 = cos (" !") cos (n :') = sin a sin (a' — w) = — cos (; 7') But, the longitudes being counted westward, and the azimuth from north round by east and south, it is evident that sin a sin (a' — a y = sin (2 – 2), where a' is the azimuth of A as seen at B: hence at B– -- dv dv : - / ...? du # = #1 ºne-o: (19) du do ..., , , dv # = - # sin (a' – ) + # Let # = 3 cos 2 and m = 5 sin cº, then— # =ſ+ (, co, a + i in 90 : # = p + (ico, a + k in .)6 Substituting these equations in the foregoing, and remembering that cos (2 – 2) + i = 0 very nearly, we get— d tº iº *_ / .../ # = f + 9 sin (a' – 2) + h 6 cos 2 + i 6 sin (a' — 2 c.) + J. 6 sin a sin (a' - 2) d º # = g – fin (2 – 2) + k 6 sin a – i 6 cos (2 – 2 a) – i. 6 cos a sin (a' - *) 624 PRINCIPAL TRIANGULATION. W. If we return to the notation previously used—namely, writing # 1 for the differential coefficients of v, we have— # = # + , sin (2' – 2) + h 6 cos x + i 6 sin (a' – 2 2) + k 6 sin a sin (2 – 2) n' = n – # sin (a' – 2) + k 6 sin & — i 6 cos (2' – 2 2) — k 6 cos & sin (a' — 2) (20) 27. These equations express the values of the é, a belonging to the point B, in terms of those belonging to A and the three quantities h, i, k, which are to be determined by observation. By equations (16) we have, if we neglect quantities of the order 6'é, and put 3, and 8, for the excesses of the observed latitude and azimuth at B above the values as obtained by calculation from A– 3, - # — #' + sin A sin a m cot x' - 8, - " — " — cosec × sin w - # – cot a sin (A’ – A). " Substituting the values of 3' and "' in terms of h, ı, k into these equations, we have finally, o = ſ. 6 cos & + i 6 sin (a' — 2 c.) + k 6 sin a sin (a' — 2) + 8, -- (21) o = k 6 sin c. — i 6 cos (2' – 2 c.) — h 6 cos a sin (a' – c.) + 8, cot x' + 6 (– : sin & + n cos 2) cot x' 28. These two equations are supplied by the point B. A second point C whose latitude is observed, and also the direction of the meridian at it, will, by means of its geodetical connection with A, afford another pair of equations; and since the quantities 3 and 7, as they enter into these equations have small coefficients, they may be neglected, and thus the two points B and C connected with A, affording four equations between the three quantities h, i, k, will be sufficient to determine these quantities, and also an equation of condition between the calculated values, which equation by its fulfilment or non-fulfilment will determine whether the surface within the small limits of the triangulation can or cannot be represented by a surface of the second order. Having thus obtained the values of h, i, k, the calculation of the radii of curvature follows from the equations (9), for we have— & -- * = h : -ºº. – ; : * d:” d: dº dº? The appearance of the term 0 (– : sin a + , cos 2) cot x' in the second of equations (21) would make it appear at first sight as if h, ı, k were in some way connected with 3 and m, which is not true. The manner in which it has arisen is owing to its having been neglected in the expression for the observed azimuths of B at A, and reciprocally. Tor if we suppose the points actually to observe one another, we shall have to retain those effects of the irregularities of the earth upon the azimuths which depend upon the mutual depressions of these points, namely + || 0 (– 3 sin o. + , cos &). = k i S E C T I O N XI. DETERMINATION OF LOCAL ATTRACTION. 1. The maps of the Ordnance Survey afford the means of calculating with much precision the disturbing effect of the irregularities of the ground in the vicinity of some of the Zenith- sector Stations. Unfortunately, the number of Stations for which this calculation can be made is comparatively small, as the system of contours, which affords the data for this work, has been only of late years carried out. Sufficient data can be obtained for Dunnose, Clifton Beacon, Burleigh-Moor, Calton Hill (observatory), Kellie Law, Monach, and the South end of the Lough Foyle Base in Ireland. - In the six-inch sheets of Ireland the heights of a great number of points are given, which afford data for the determination of the deflection at Forth Mountain, Feaghmaan, and Taw- maghmore, but imperfectly, for each of these Stations being situated on elevated and uncultivated ground, the number of altitude points is smaller than usual in the immediate vicinity of the Station, consequently the calculation for these Stations is imperfect. At Hungry Hill the ground has been specially contoured within a circle of a mile round the Station, at Ioo feet intervals. Beyond this circle the altitudes engraved on the map must suffice for the calculation. 2. The method by which the local attraction at each of these Stations has been computed is as follows: Through the Station, as marked on the plan, draw a meridian line, and a system . of radial lines making angles— - sin- ; (#) , sin (#) , sin- " (#) , . . . . . in- (#) with the north meridian line on each side; and a similar system with reference to the south meri- dian line: altogether 40 lines. Describe on the map a series of ten concentric circles round the Station as centre, the radii being successively 500, Iooo, I5oo, . . . .4500, 5000 feet; and in continuation, another series of concentric circles round the same centre in geometrical progression, such that the radius of the nº circle of this series = 5000 × (#)" feet. So that if we draw altogether 25 circles, as is done in most instances, a circle of 9.55 miles radius will be inclosed, and this area divided into 960 parts, omitting the centre circle, as may be done in most cases. When the ground in the immediate vicinity of the Station is uneven, the inner circle of 5oo feet radius is divided by circles having radii of Ioo, 200, 300, and 4oo feet. 3. Then to find the deflection we have the following rule, as proved at page 584: If Ha be the sum of the heights of all the compartments between the nº and (n + 1)" circles of the first series, on the north side of the Station, H', the same quantity for the south side, the total 4 K ** 626 I’RINCIPAL TRIANGULATION. deflection north due to the form of the ground within a circle of 5000 feet radius round the Station is— d - H. — H', 2 71 + I where H, H' are to be expressed in miles; also g is the density of the disturbing mass, and 3 the mean density of the earth. - - The quantity g varies, indeed, from one compartment or prism to another, but it will be sufficiently accurate to assume a common value for all the compartments, and this must be the mean density of all the rocks within the space over which the calculation extends. - The mean densities of the rocks which exist in the vicinities of the different Stations for which the deflection has been calculated, may be taken as follows:– * - 2”.4894; s Limestone . . . . 2.81 Gneiss . . . . . 2,70 Trap . . . . . . 2.75 Quartz Rock . . . 2.65 Chalk . . . . . 2.72 Mica Slate . . . . 2.65 Mica • . . . . . . 2.71 Sandstone . . . . . 2.5o of which the mean value is 2.69. The mean densities of these rocks differ but little among one another—scarcely more than do different specimens and varieties of the same rock. For the mean density of the earth we have six independent determinations. Of these, the determinations of Cavendish, Reich, and Baily with the torsion-balance, and the result of the Arthur's Seat experiment, agree very satisfactorily among themselves (see page 605), the mean of the four being 5.46. The value deduced by Playfair from the Schehallien experiment (which must be preferred to Dr. Hutton's result), namely, 4.71, and that obtained by the Astronomer Royal from the pendulum experiments, namely, 6:57, differ so materially from the others that it is clear we are not yet in possession of the truth. ... - . . . - The mean of the whole six values is 5.52, which is not very different from the mean (5-46) of the four which agree among themselves. We may therefore take 5.5o as the mean density of the earth, but affected with considerable probable error, perhaps not less than + o- Io. . Seeing, then, that in the ratio g : 3 the quantity 6 is not assignable with precision, it will be sufficient to assume the relation 8 = 2 g, throughout the calculations. 4. If in the formula for the deflection we express the quantities H, and H', in feet instead of miles, and make 8 = 2 g, the deflection north becomes equal to— - - H. — H' IH, - H' EI, - H'. .. FIA – H' * o'-oooz ſ --—- ++-2 + +4–3 + . . . . . +. -3–2 - 3574 ( ... 3 + 5 f , 7 I9 ) t Also the deflection due to the conformation of the ground between the tenth and last circles, which are drawn according to a geometric series whose ratio is 7: 6, is— t? *2447#log.º. (K-K) K being the sum of all the heights on the north side, K the sum of all the heights on the south side, expressed in miles. Expressing these heights in feet, and making the same assumption as DETERMINATION OF LOCAL ATTRACTION. 627 :.- - \ previously with respect to the density, we have (since log, 7 = 1.94591 & log, 6 = 1 .79176) the deflection equal to + ". o”.oooo.1817 (K. – K') If the inner circle of 500 feet be divided by four intermediate circles, the deflection due to the conformation of the ground within this space is ".623s. 4.- (s-s) = "oup (S-s). where S is the sum of the sines of the elevations of all the prisms or compartments on the north side, and S' the sum of the sines of the elevations of all the prisms or compartments on the south side of the Station, and within the 5oo feet circle. - The whole deflection at the Station is therefore expressed by the quantity— *\ 1 -// H, - H', , H, - H', H. — o”.or 179 (S — S') + o”.ooo23574 ( 3 -H. 5 -H. I9 • In a few instances it is necessary to take into account the third power of the apparent eleva- tions or depressions, or, in other words, to discriminate between the sine and tangent. This may be done with sufficient accuracy as follows: Let h be the height of the Station, h, h, h, . . . h. the heights of the different compartments between the n” & (n + 1)" circles on the north side, then the deflection is proportional to— - 1 * * - * } z ("H") – ys (*#): Here 3 (h) = H.; and we may for h; in the second part of the above expression put ºf H, so that the quantity becomes— - — tº ſ tº — h 7" 7.3 2O H, - 20 h Io / H. ) t *mº + r. I6o H. I. Nº - – ; {H. – 2O * ºmº (a ni71 -- 1). (:: º-º #) } because r = 250 X (2 m + 1) : therefore to H., in the formula (I), must be applied the correction— z * - I6o EI, h N 3 T G Ty (; – #) tº º & (a) with a similar correction for H', on the south side. 5. If any one of the compartments consist of a depth h of Sea, then for this we must take * 5 - 5.5 T 2. supposing the mean density of the earth = 5.5. In this case, therefore, the coefficient given for a disturbing mass of rock must be multiplied by — ºr In the cases we have to consider, with one exception, the sea occurs only in the compart- ments formed by the outer series of circles, namely those whose radii form a geometrical series. If, therefore, D'be the sums of the depths of the sea in all the compartments covered by it to * * * +H:º) + o”.ooool 817 (K — Kſ) . . . . 4 K 2 628 PRINCIPAL TRIANGULATION. the north of the Station, D' the sum of all the depths to the south, the increment to the deflec- tion north is t * . – o”.ooool 156 (D – D') And in general, if *, * be the radii of the bounding circular arcs of any compartment, a, & the azimuths of the bounding straight lines, the deflection due to this compartment is— y For land . . . . . . -- o”.oo2714 (sin &' — sin a,) logie : • (mean height) For Sea . . . . . . . — o”.ool 727 (sin a' — sin a,) logie : • (mean depth) Af 6. The mean heights of the different compartments can be obtained with sufficient accuracy and without much trouble when the contoured maps are available for the purpose. Great accuracy in the determination of the mean height is not necessary, as may be seen from the following considerations : In the formula (1) each of the terms H. H., &c. consists of 20 esti- mated mean heights; and if we write E, E, E, E, &c. for the corresponding sums of the errors, the error of the centre part of the formula is— PA IE, - D', , B, - E', E. – E' occoa, {** +--- + . . . . == } Each of the quantities K K is the sum of 300 estimated mean heights (supposing that there are 15 circles drawn according to the geometric-progression law), and if E and E’ be the sums of the corresponding errors, the error of the last part of the formula is— º o”.ooool 8 (E - E) The error to which the first term of the formula (1) expressing the total deflection is liable, is small, inasmuch as the compartments being small, their mean heights may be estimated pretty accurately. We shall therefore omit that term, and the error of the calculated deflection is— D. - D', +- D. - D', -- - - - - **) + o”.oooor8 (E - E): 3 5 19 + -- Here each of the quantities E, E'. . . . . are composed of 20 independent errors, and each of the quantities EE' of 300 independent errors. If we suppose, therefore, that each of the esti- mated mean heights is liable to an equal probable error e, the square of the probable error of the calculated deflection is— o”-ooozá. { O e” 4o e” = (o".oooo...) | #2 * . . . . 40 °l. + o”.oooo I8)” 6oo e” (o”.ooo.24) U 3” -- 5° + 19' ſ ( ) = , ſ •oooza) (3 + + . . . . -- 6oo (o. 8): ) = * {40 (o-ooozA) (; 5° -H. #) + (o-ooool.8) J == ſº º a ſ f 1. i. i. e º + 3. ') (o-ooo.24 e) (49 (; + 5° -H #) + 6oo (...) so that the probable error is equal to— . . 2. # + o",ooozA. 63 {40 (; + # + tº C tº ſº ; + #} -: + o”.ooo&2 s (2 DETERMINATION OF LOCAL ATTRACTION. 629 So that if all the estimated mean heights of the compartments be liable to a probable error of about 25 feet, the probable error of the computed deflection would only amount to about :E o”. o2. * * 7. The probable error of the determination of the mean height of a compartment will increase with the area of the compartment; and therefore, in order that the larger compart- ments may be estimated as accurately as the smaller, it is necessary to subdivide them. The probable error of the estimated mean height of a compartment does not appear to increase in proportion to the area (not subdivided), but perhaps as the square root of the area. Assuming this, let it be required to find the number of parts into which a compartment whose area is A should be divided, in order that the probable error of its resulting mean height should be equal to that of the estimated mean height of a smaller area a. If a be the number of parts, p the probable error corresponding to a, the probable error of the estimated mean height of one of the subdivisions of A is A. p * =º (I. T. and therefore the probable error of the mean of the mean heights of the w subdivisions is . . p. /A - 2. /A A/a: a & T as V. As this is to be equal to p, we have w = wº. So that if a compartment be in area equal to eight inches square, it should be divided into eight parts, in order that the mean height should be determined as accurately as a single estimation of a space whose area is one square inch. But in practice this rule cannot always be advantageously employed. ISLE of WIGHT SECTOR STATIONS. Boniface Down. Plate XXII, shows the contours of the ground in the vicinity of the four Stations, Dunnose, Boniface Down, Week Down, and Highport Cliff, surveyed at intervals of 25 feet vertically. There are two principal features, the one running north from Week Down, about two miles in length and about 700 feet high ; the other a curved ridge, having Dunnose Station at its northern extremity, and Boniface Station towards the south-western extremity: the height of this range averages 750 feet. The Station Highport Cliff or Port Valley is close to the sea, and lies S.S.E. from Boniface Down. The extent of the contours will only allow of 17 circles being drawn round each Station. The following table contains the heights of the compartments around Boniface Down:— 630 PRINCIPAL TRIANGULATION, IBONIFACE DOWN. North Sido, . Number of Sector. Number of H Circle. || 1 || 2 || 3 || 4 || 5 || 6 7 8 9 Io II | 12 || 13 || 14 15 | 16 || 17 | 18 19 20 1– 2 755 |75o |74o | 725 725 | 725 | 730 | 735 | 74o 750 || 755 755 || 76o 76o 765 775 780 || 78o 78o 78o 15060 2– 3 |675 65o 645 |635 630 || 630 || 64o 650 65o 655 | 660 670 690 7oo 715 | 725 | 735 | 750 770 78o 13655 3– 4 || 6oo |5Io|| 515 515 || 510 || 510 || 510 || 520 530 535 540 555 570 590 61o 625 | 64o 655 725 || 770 | 11535 4— 5 520 |435|430|440 || 45o 465 465 465 || 465 470 475 || 485 5oo 535 | 55o 58o 650 | 726 775 750 | 10625 5– 6|525 425 |385 |4|io || 435 450 || 435 425 || 45o 46o 465 || 48o 5oo 530 | 610 | 685 | 74o 750 | 730 | 685 | 10575 6– 7 |525 |410 |350 |355 370 || 385 | 400 || 435 | 475 5oo 51o 530 55o 6oo 7Io 75o 745 715 575 | 630 | Ioszo | 7–8 |540 |37o 330 |466 440 || 465 470 476 || 470 || 510 || 555 | 625 | 670 | 730 76o | 725 || 65o 575 5oo 575 ro83o 8– 9 |54o |390 |325|375 || 450 || 485 5oo 5io || 525 | 55o 625 | 720 | 730 | 735 | 725 | 675 530 465 375 5oo | Ioygo 9–10 |530 |390 |3.16||375|| 450 5oo 54o 565 575 6io || 675 | 725 7io || 605 || 585 | 625 520 | 35o || 3ro || 385 |Io;35 | Io–11 |430 |375 3oo 360 || 45o 530 | 660 | 680 | 665 7oo 750 | 730 | 630 || 515 470 520 | 520 | 375 26o 250 |IoIZo 11–12 |325|3oo |275|35o 435 | 540 | 625 | 61o 560 570 575 560 || 515 || 41o | 35o 375 || 48o 370 || 230 8455. 12–13 |410 |275|240 || 3ro || 375 || 450 || 475 || 430 || 390 || 375 375 375 | 365 || 345 || 3oo 275 375 || 38o 75 6595 13–14|600 || 335|25o 235 | 28o 345 || 335 | 335 | 270 || 25o 25o 275 25o 215 || 2 Io 18o 220 125 4960 14–15 625 |490 || 315 || 2 Io 200 215 225 || 25o 220 215 220 225 || 230 I75 I75 I45 4 I35 15–16|48o 515 3 Io 225 | 200 I5o 18o | I75 | I75 | 135 | I5o I75 || I35 | 125 | I25 | I Io 3365 16–17|325|325|215 16o | I5o 17o 135 | 165 I55 | 165 135 | 9o 9o IIo I2O 5o || 2560 IBONIFACE DOWN. South Sido, | Number of Sector. Number of II Circle. || 1 || 2 || 3 || 4 || 5 6 7 8 9 || Io II | 12 || 13 || 14 I5 | 16 17 | 18 19 20 1 – 2 | 730 650 |6oo 58o 560 56o 57o 570 58o 6oo 62o 630 || 650 670 | 685 710 | 730 750 755 770 | 12970 2–3 || 705 || 530 |450 |46o || 510 || 570 .62o 650 | 64o 61o 575 55o 525 || 500 || 5oo 51o 530 580 | 606 || 700 11310 3- 4 || 7ool 520 |400|420 5oo .55o 520 45o 38o 320 28o 265 26o 26o 26o 265 28o 35o 435 | 6oo 8015 4– 5 7oo |55o |38o |350 | 400 || 370 310|| 3ool 25o zoo 200 180 | 180 | 16o 18o 180 | 16o 18o || 366 || 490 | 6ozo 5- 6|68o 58o |425 || 315| 26o 230 220 155 150 | 135 | 17o 17o 16o 150 | 180 | 190 155 15o 175 | 400 || 5050 6- 7 || 64o 53o |450 |325 || 175|| 130 IIo | Ioo Izo 115|| 125 125 115 IIo Ioo 115 Iool IIo | 120 325 | 4040 7– 8 || 53o |465 |415 |27o 150 115 Ioo 75 5o 5o || 65|| 3o 20 5o | Ioo 26o 2745 8– 9 |48o |450 370 225 | 125 20 4o 17o 1880 9–Io |43o || 510 || 335 | 185| 125 12o 1705 Io–II 450 52O || 3oo I4o 35 – 40 – 60 – 60 – 70 – 70 - 7o |- 7o |- 7o - 70 - 70 – 7oj— 70 - 60 – 6o –40 1445 II — I2 || 5oo 460 185. 75 – 20 – 60 – 70 – 70 – 70 – 80 - 80 - 80 - 80 - 80 – 80–80 – 70 – 70–70 –7o I220 12–13 56o 4oo Iool-30 - 40 – 70 – 8o – 8o – 8o – 90 - 90 – 90 - 90 – 90 – 90 – 8o |— 80 – 8ol— 8o –90 Ioffo 13–14 625 35o 7o -50 - 70 - 80 – 80 – 90 – 90 – 100 - 100 – 100 – 100 — 100 – 100 – 90 - 90 - 90 – 90 – 90 1045 14–15 |479 |225 || 25 –6o - 70 - 90|- 11o |-12o [-11o - 15o!— 150 - 160 – 150|—-130|— 120 – 110 |- ſoo|— Ioo – 90 – 90 720 15–16|425 | 275 20 |-60 - 99|-rio |-140 – 170 -190 - 190 – 200 – 200|- 200|- 190|– 180|– 120 – 11o – 100 – 90 –90 720 16–17|335|250 |–40|-80 – 110 - 180 - 190 -200 -200 - 200 - 200 – 200 – 190|— 190|– 180 – 120 – 11o |— Ioo – 90 -90 585 N.B.—The Sectors are numbered from West to East, and the Circles from the Centre outwards. DETERMINATION OF LOCAL ATTRACTION. 631 g: The inner circle of 500 feet must here be subdivided, on account of the abruptness of the ground on the southern side, by drawing four concentric circles having radii of 100, 200, 300, and 400 feet. Thus we find for the south side S = — Io. 3. It is also necessary on the south side to calculate the corrections (a), page 627. These quantities are found to be— . - 45, 65, 185, 225, 195, 185, 190, 180, 150, and applying them with the positive sign to the quantities H. (South) in the table, we have— H, - H', = 20.45 H, - H', = 438o H, - H', - 7895 H, - H', = 228o Hs – H's = 5.330 IHs — H's = 8670 . H, - H', - 3335 H6 — H's = 6295 H, - H', = 848o R = 40240 IQ = 6795 S = o S’ = – 10:30 and the sum of the depths of sea to the south— D' = II930. Therefore, as far as the 17" circle the deflection is— o" or 179 × Io:3 + o’-oooz3574 × 4552 + o”.oOool 817 × 33445 + o”.oooo.1156 × 11930 amounting to I". 940 to the north. We may extend the calculation to the limits of the Isle of Wight in the following manner: In Plate XXIII. abcdef is the 17" circle drawn round Boniface Down; through a, b, and c draw the lines ad" bb' co" passing through the station, and making angles of 70°, 9°, and 33° respectively with the north meridian line, and let these lines be continued in the opposite directions, shown in the plan as did.' ge'ſſ'. Take aa' = dd = 9 miles, ce' = f' = 6 miles, and, with Boniface as a centre, describe the circular arcs a'b', c'b, and similarly on the south side. That portion of the island which lies south of the line aa' may be disregarded, and the two spaces ab a'b' and be b,c' may be considered as containing the whole of the effective dis- turbing force of the island, the opposite and corresponding spaces to the south and south-east being covered with sea. For the land, the mean height is to be taken at 150 feet, and the mean depth of sea estimated from the Admiralty Charts at about.90 feet (by giving greater weight to the nearer parts). This depth of 90 feet of water is equivalent to a hollow of + x 90, or 57 feet. Thus we may take account of the disturbing effect of the sea by adding, say 60 feet to the mean height of the land in the spaces ab a'b', be b,c', making that quantity 2 Io. The following table contains the calculation of the deflections due to these Spaces:— Space. h a' Cº. r’ 7" Deflection. 11.8 2-8 + 3.278 § aba'b' 2 IO 7o bcb,c' 2 IO 33 9 8-8 2 - 8 + o' I99 632 PRINCIPAL TRIANGULATION. Therefore the effect of that part of the island which is external to the 17" circle round Boniface Down is to produce a deflection of o” .477 to the north. * If we add this quantity to that previously determined, namely, I". 940, we get for the deflection at Boniface Down 2". 417 to the north. . IDunnose. The heights of the different compartments around this Station are given, up to the 17th circle, in the following table:— DETERMINATION OF LOCAL ATTRACTION. 633 :i DUNNOSE. North Side. Number Number of Sector. cº H ircle. | 1 - || |s| |*|, Io II | 12 || 13 || 14 15 16 || 17 | 18 19 20 1– 2 | 720 7oo 7oo | 685 |675 |660 |65o 62o 630 630 |630 |630 || 640 || 650 650 | 660 660 | 660 650 |630 || 13130 2–3 || 650 ||61o 6oo |575 |57o 570 560 |56o 520 |5io |5io || 5oo |5ool 500 5oo | 510 || 525 | 535 520 |520 19845 3–4 630 |520 480 |455|44o |430 |430|425 |360 410 |400|410 |415 |425 |415|410 |415 || 430 420 |400| 8729. 4— 5 630 520 435|400|375|375|38o |38o300|335|340 |335|350 |375|375|350 |365 38o |375 |350 7725 5— 6 |É. 475 420 |38o 325|310|325|34o |27o 285 275 285 31o 325|285| 3oo |300 320 |35o 310 | 6800 6– 7 565 430, 375 |345 3oo 26o 255 |29o 220 |230|235 | 27o 285 285 235 235 24o 240 |280 |275 585o 7–8 515 |4 to 375 |320|275 |260 |225 |230|235 210 |225 |250 |250 |26o |235|225 |200|| 2 io ||220 |280 5410 8– 9 425 |375 350 |330 270 |240 225 |230|240 180 |225 24o |230|250 |285 215 180 2 Io |200|280 || 515o 9–10 |375 35o 315|31o 26o 235 | 200 18o || 130 165 24o 235 | 200 220 235 | 215 165 200 | 180 | 3oo 47 Io 10–11 310|300 |230|260 |240 |210 | 199| 165|200|160 |230|230|200|165|200 150 16o 175 150 |250 || 41.75 11–12 225 220 2 Io ||230|220 18o 18o 15o 125 I4o 15o 18o I75 I4o I35 | 14o 12o 15o I Io 3180 || 12–13 || 2 Io 1731160 18o 16o 16o 16o 17o 15o Izo IIo I25 | 125 Izo Ioo 125 125 | 120 4o 2630 |. 13–14 290 |299||170 135 16o 17o | I5o | 165 | 165 15o 15o 9o 85| 8o | Ioo 12o 14o 90 26 Io 14–15 360 | 16o 17o 17o 130 125 15o 15o 17o 15o 130 Ioo 6o 7o 100 11o | Ioo 2.345 15–16 28o 14o Ioo 120 IIo | Ioo 130 16o 16o 17o 150 | Ioo 60 5o 8o 8o 30 2O2O 16–17 195 ice 75 || 75 8o Ioo ice as I5o iſsue * 7o 4o 5o Ioo 1640 | | DUNNOSE. South Side. Number Number of Sector. of H Circle. I | 2 || 3 4. 5 6 7 || 8 || 9 || 10 || 11 | 12 || 13 || 14 15 16 || 17 | 18 19 20 | 1 – 2 | 680 |65o 650 645 645 |650 |67o |675 700 |71o S715||725||730|735 | 735 | 725 715 7oo 675 |650 | 1378o 2–3 |625|57o 565 560 |56o 55o 560 575 ||615|635|675|| 706 || 720 | 735 | 735 | 725 | 685 65o 62o |55o 12590 3– 4 |625|54o 520 |515|510 |5io |510 |526 556|576|616 62o |675||735||755 75o 715 65o 660 |460 | 120co 4–5 |606 |5io |5oo 460 |450 |475 |485 |5oo 560 |500 520 545 |606 | 726 755 755 | 735 | 675 625 |48o 11390 5– 6 |560 |490 |485|425 |400|430 |450 |450 |460|475 |510 |536|600|70o|755 | 725 |65o 625 |6ool 525 | Io945 6– 7 |490 465 |450 |375 |44o |455 460 470 |490 |5oo 530 550 | 6oo | 725 || 755 7 Io 570 || 5oo 490 || 510 | 10535 7–8: 425 |400|400|360 |435|460 |485 |53o 575 6oo 610|600|62o 75o |755 |675|54o 425 38o |490 | IoS 15 8– 9 |376|350 |340 |355|365|455|536|Soo 686||720 | 720 |7ool 790 |775||990 575 |475 370 315|420 |19595 9–16 |320|360 |315|405 || 415 |475|6óoj690 |750 |775||775||770 |765||786|645; 476 |400| 3oo'265|345 ro562 10–11 290 38o |400|455 |48o 550 |67o |75o 760 |77o |78o |74o 7oo 650 |675 | 68o 56o 4oo 210 |240 || 1:149 I I-12 || 26o |425 | 525 |56o 62o 7oo |64o |54o 57o 55o 520 |450 |43o 430 |43o 420 |375 250 8o 8775 12-13 || 3 Io |35o |5oo 525 520 | 6oo 5oo |375 || 385 |260 | 180 18o 14o 14o 13o I5o I5o — rol-2 o|| 5395 13–14 425 || 390 375 410 460 440 | 3oo 17o | 120 | 1.5o | Ioo 60 || 30 –10 –10 –20 – 30 – 30 -30 -2° 3439 14–15 65o |575 |525 ||610|500 275 | 150 |—zo –40–60 |–60–60 |–70–70 —70—70—80 – 90 -80|-” 3285 15-16 || 5oo 55o ||610|410 |200| 40 –4c |–60 |–70|–70–80 –80 –80|–80–80 —gol–90 - 100-90|-3° 43'9 16-17 ||38o|450 |430 |230| 20 |–60 |–70 -80 |–8o!—80 |–90–90 –90 —90 —90–90 -90 —ies-º —30 | I 5 Io 4 I. 634. PRINCIPAL TRIANGULATION. From this table we find— * H, - H'. - — 65o H, ºm H', = - 3665 H,'— H', = — 5IOS H, - H', = - 1745 Hs – H's = – 4045 Hs – H's = – 5355 H, - H', = – 328o H6 — H's = — 4685 H, - H', - – 5850 IK = 18600 K’ = 35845 D' = 3230 The ground in the immediate vicinity of the Station within the 5oo-feet circle is not suffi- ciently uneven to require the calculation of S and S. We have therefore the deflection (as far as the 17" circle) equal to— – o”-ooo.23574 × 3133 — o”.ooool 817 × 17245 + o'-ooool I56 × 3230 or I”. ol; to the south. - It remains to add to this, the effect of that portion of the island which is external to the 17* circle. This quantity will not differ materially from the quantity obtained for Boniface Down, as is evident from the proximity of the two Stations: therefore if we deduct o”.477 from I". or 5, we obtain o”. 538 as the deflection at Dunnose to the south. Week Down. The heights of the several compartments around this Station are given, up to the 17" circle, in the following table:— DETERMINATION OF LOCAL ATTRACTION. 635 WEEK DOWN. North Side. Number of Sector. Number | ..of II Circle. || 1 || 2 || 3 4. 5 6 7 8 9 || Io II | 12 || 13 || 14 15 16 || 17 | 18 19 20 1 – 2 550 555 575 585 61o 635 655 67o 680 | 68o 680 | 680 | 68o 675 | 670 665 65o 630 || 605 || 655 12785 2— 3 470 51o 55o 58o 61o 635 | 660 | 675 | 68o 675 | 665 645 6oo 575 55o 525 515 || 510 || 510 || 575 I 1715 3— 4 445 5oo 57o 61o 650 | 675 | 68o | 68o 665 64o 6oo 55o 5oo 475 465 450 || 43o 425 || 420 5oo Io930 4— 5 |435|48o 575 62o | 660 | 680 | 68o 675 | 635 | 6oo 54o 599 || 45o 425 || 415 || 4 to 390 || 365 || 370 || 470 | Io975. 5– 6 4.45|5oo 556 58o 635 | 675 | 68o 660 || 3ro 55o 505 || 46o 425 | 38o 360 | 335 | 35o 396 || 4oo 475 9965 6– 7 |456|500|500 550 | 615 676 | 675 | 660 | 6oo 54o 496 || 45o 425 || 390 330 || 325 | 385 420 420 436 9825 7–8 |450 |465 || 485 515 586 625 670 67o gro 55o 46o 4ro 360 335 | 3io || 356 || 415 || 475 5oo 43o 9666 8– 9 |4|io |456|| 486 || 506 || 525 556 630 || 7co 570 55o 45o 4oo 35o 3oo 3oo 375 45o 55o 6oo 465 9715 9—Io 35o 470 470 455 440 || 5oo 6oo 7oo 690 560 44o 375 325 | 290 325 || 4oo 460 570 615 53o 9565 10–11 |320|425 | 385 390 490 55o 630 | 720 | 630 || 510 || 43o 345 || 3oo 26o 325 41o 435 45o 520 | 610 || 3:35 11–12 |280 315 325 || 470 53o 58o 675 690 535 | 425 || 370 325 275 25o 3oo 325 365 355 465 61o 8465 12–13 |230|276 || 325 || 4:30 || 4to 4oo 5oo 625 525 || 410 || 325 270 230 255 290 320 35o 355 430 58o 75oo 13–14|220 |25o 270 28o 3oo 325 43o 525 5oo 4oo 320 24o 2 Io 3oo 375 45o 590 455 465 6oo 7415 14–15 290 16o 17o 190 || 2 Io 275 325 325 || 3oo. 3oo 26o 200 || 2 io || 320 | 375 570 | 665 590 || 560 5oo 6795 15–16|360 |26o 25o 200 | 16a | 195 225 | 190 17o 175 2 to 190 200 24o 335 | 35o 480 64o 65o 38o 5866 16–17|200| 190 180 17o 16o 15o 16o 125 | 125 | 130 | 16o 17o 16o 21o 21o 220 28o 35o 425 || 175 3950 WEEK DOWN. South Side. Number of Sector. Number of EI Circle. | 1 || 2 3 4. 5 6 7 8 9 Io | II | 12 || 13 || 14 15 16 || 17 | 18 I9 || 20 1– 2 575 |600 615 635 | 640 || 650 655 655 650 635 | 62o 615 6oo 62o 590 58o 570 560 | 560 61o | 12:15 2— 3|4%;|520 556. 565 575 58o 585 586 575 566|| 535 | 510 || 475|| 46o 450 425 || 415 || 425 || 475 goo ro335 3–4|4%;|435 | 450 476 486 || 490 506| 495 || 486 || 470 450 440 || 425 || 385 365 365 4oo. 465 530 325 9145 4— ;|416|406| 400 | 400 410 || 415 || 415 || 466|| 390 375 370 360 | 34o 325|| 35o 375|| 4co 420 520 62o $975 5— 6|41o 38o 38o 385 385 || 38o 370 345 275 25o 225 225 220 220 225 24o 270 330 38o 555 | 6450 6– 7|420 |38o 375 375|| 375 360 | 3oo zi; 266|| 150 146|| 120 | 120 II5 | 120 | 130 | 130 175 28o 490 4979 7- 8 || 430 |375 375 4Io 4oo 3oo 2 Io 175 | 150 85 6o 5o 55 o 50 | 60 | 75 Ioo 200 45o 4070 8- 9 |430 360 4oo 45o 41o 235 | 17o 115 85| 6o 5o 30 3o 20 Io 30 8o 130 35o 3445 9-Io |400|350 | 405 || 435 | 3oo 200 | Izo 7o 6o zo 95 || 28o || 2735 Io-II 320 35o 390 370 23o I35 75 60 – 10 - 20 — 30 – 40 – 40 - 50 - 60 - 60 - 60 – 30 220 2 I5o 11–12 |330 |4oo 4io 250 135 75 – 10 – 20 — 30 – 30 – 40 — 50 – 60 – 60 - 70 – 70 - 70 - 60 - 40 || 129 1749 12–13 |400|455 330 14o 56 – to — 30 – 40 — 50 – 60 – 70 – 70 – 80 - 80 - 80 - 80 - 80 - 70 - 5°| 75 || 45° 13-14 335 |4 Io 25o 8o – 30 — 40 — 50 – 60 – 70 – 80 – 90 – 100 – 11o |-11o – 11o - 90 - 90 - 8o ſ— 6o 6o II 35 14–15 |300 325 70 – 30 | — 40 | – 60 – 70 – 80 – 90 –100 –120 |–140 – 150 |–150 – 140 -100 - 90 - 89 |T 60 — 20 695 15–16 325 3oo - 20 — 4o – 60 | – 70 — 80 – 90 – 110 – 120 – 150 – 180 – 190 – 190 -200 - 180 - 180 - ***|T 80 - 70 625 16–17|3oo – 30 – so | – 70 – 90 – 100 – 110 – 110 –120 – 140 – 180|–190 –190|–200 -200 -zoo -19°|T*|T 7° 3° - -- 4 L 2 636 PRINCIPAL TRIANGULATION. From this table we find the following numbers— H, - H', = 570 H. – H', = 2300 H,' – H', - 5590 II, - II", = 138o Hs – H's = 35.15 Hs — H's = 6270 H, - H', - 1785 H6 — H% = 4855 H, - H', = 6830 IK = 4906o IQ = 80.75 D' = 9030 The quantities S S may be neglected, as the ground does not fall abruptly either north or south; the deflection then is— o”.ooo23574 x 2770 + o”.ooool 817 x 40985 + o”-oooo.1156 × 9030 or I". 502 to the north, up to the 17" circle. To obtain the effect of the remainder of the mass of the island, we may apply the same quantity as obtained for Boniface Down, namely o”.477; this added to the former gives I”.979 for the deflection to the north at Week Down. Port Valley. This is the name of the point at which the zenith-sector was placed in connection with Highport Cliff. The heights of the various compartments are shown in the following table:— DETERMINATION OF LOCAL ATTRACTION. 637 PORT WALLEY. North Side. |Number Number of Sector. c; II "cle. || 1 || 2 3 4. 5 6 7 8 9 Io II | 12 || 13 || 14 || 15 16 || 17 | 18 19 20 * - 2 || 175 | 190 | 185 17o 170 | 16o 16o 165 165 17o 16o 15o 150 | 1.5o 140 | 130 | 125 | 120 | 11o 8o 3025 *~ 3 | 16o 200 2 Io 2 Io 2 Io 225 24o 245 245 25o 25o 225 | 200 17o 15o 125 Izo Izo II5 9o 3760 3- 4 || 2 Io 28o 330 4oo 45o 475 425 || 45o 46o 45o 43o 4oo 370 345 26o 23o 195 || 15o 125 4o 6475 4- 5 290 5oo 605 || 670 67o 7oo 675 65o 650 | 62o 55o 53o 48o 45o 420 35o 26o 220 14o 30 9460 5- 6|385 62o 585 655 750 78o 78o 78o 78o 755 || 700 65o 615 56o 490 410 || 35o 295 150 I logo 6-7|356 465 625 756 785 78o 780 770 || 765 || 775 || 78o 770 || 746 || 690 6oo 475 375 || 315 | 160 II 750 7-8 |365 |600|745 760 | 766 760 | 750 | 730 | 675 | 720 78o 715 615 630 || 7oo 6oo 405 || 320 | 150 11780 8– 9||540 |71o 675 675 670 670 650 | 62o 6oo 690 76o | 685 53o 45o 55o 570 4oo 225 5o Io.720 9-16 |5éo |660 556 556 550 55o 525 53o 570 | 685 75o 675 56o 425 || 425 45o 345 170 9530 | 10-11 || 525 |600 460 435 || 46o 465 465 490 565 | 720 | 720 | 6po 47o 33o 3oo 315 220 | 75 –3o 8215 11-12 |336|| 530 || 415 || 356 385 || 415 || 490 550 | 670 750 | 670 58o 45o 34o 275 18o –30 758o [2–13|450 |360 375 35o 465 || 510 || 530 62o 73o 625 5oo 5oo 515 450 33o 140 –25 –25 —4o 7630 13–14|44o |375 346 || 325 || 435 | 630 || 670 | 660 | 660 55o 425 | 325 || 325 4oo 365 6o —25 —30 ||—30 —40 6965 14–15 57o 34o 255 3 Io 415 || 55o 5oo 4oo 38o 355 285 25o 21o 2 Io –30 -30 || -35 | —50 5030 |*5-16 || 58o 550 285 220 285 34o 34o 255 24o 25o 25o I75 18o | Ioo -30 || -35 | –35 | -35 | —50 4050 16–17|450 6oo 410 25o 175 zoo 225 180 175 21o 150 | 125 | 125 7o –30 -35 | –35 | –40 —7o 3345 *— PORT WALLEY. South Side. *— C. N - Number of Sector. umber tº of II Circle. I || 2 || 3 4. 5 6 7 8 9 || 10 || 11 || 12 || 13 || 14 || 15 | 16 || 17 | 18 19 20 `--— - 2 | 135 | Ioo 70 || 65|| 45 . . " 415 || 3- 3 || 155 Ioo 60 – Io |— Io – Io | – Io |– Io |— Io - Io |- Io - IO |- io |- Io 315 3- 4 | 160 8o — 10 – 10 – 15 – 15 – 15 — 15 – 15 – 15 – 15 – 10 – 10 – 10 - 10 24o 4- 5 I IC 65 — 10 – 10 – 15 — 15 — 20 — 20 – 30 – 30 - 30 - 20 - 20 - 20 – 15 – 10 - 1 o J75 5- 6 Ioo # — 10 – 10 |— 15 – 15 — 20 — 20 – 25 – 30 – 30 - 30 – 30 - 20 - 20 – 20 – 20 – 2 o– zo I OO 6- 7 || 115 – 10|– 20 — 20 — 36|- 30|– 30|— 40 – 40 – 40 – 40 – 40 - 49–40 – 30 – 30 – 30 – 20 – 20 II5 - * 7- 8 95 — 20 – 30 – 30 — 40 – 40– 40 – 40 — 50 – 50 - 55 - 55 - 60 - 55 - 50 - 40 - 30 - 20 – 20 95 8– 9 150 – 10 – 20 – 30 - 30 — 40 - 45 – 50 - 50 - 55 - 6o – 65 — 65 — 65 — 6o l— 55 - 55 - 52- 2– 4o I5o 9-10 | 165|–20 – 30|— 40 — 50 – 60 – 60– 6ol— 70–70 – 80 – 80 – 70- 70 - 65|- 65|- 65 – Go |- 60 – 55 165 *9-11 |zoo –40 – 70 – 70 – 80 – 80 – 80–80 – 90 – 90 – 90 – 90 - 90 - 99|- 90 – 90 – 90 – 80 - 80 - 99 || 200 * I-12 270 —50 – 70 – 80 – 80 – 80 – 90|– 90 – 100 — Iool–1ool— 100 – 100 - 100-100]— 100–100 – 90 – 90 - 90 27o $2–13 3oo —60 – 70 — 80 – 90 – 90–100–110–120–130|- 130 – 120 – 120 – 120 – 110 – 110 – 110 – 100 - 90 – 90 3oo *3–14 275 —60]— 80 – 90 – 100 – 120 – 150–180 – 18o|- 180 – 190 – 190 – 180 — 180 – 150 – 120 – 110 – 1 oo - 90 - 9o 275 *4-15 360 –40 – 80 – 110]—120 – 180–180—1901–200|-zool—zool—zoo — 190|- 190 – 180|— 120 – 110 – 100 – 90 - 9° 329 15–16 275 –40 – 90 – 120 — 180 – 1901–2001–2001–2001–2001–190 – 190 – 180 – 150 – 120 – 110 – 110 – roof– 9°|- '99 275 16–17 326||—60|— tool— 150 – 190|—zool— zool–190–1901–180–150 – 120 – 110–110 – 100 – 100–100]- io9|- 9°|- *| 34° *— 638 º PRINCIPAL TRLANGULATION. On account of the great apparent elevation of Boniface Down at Highport Cliff, it becomes necessary to apply to the quantities H on the north side the correction (a); these are found to be Io, Io, 55, 130, 150, 130, Ioo, 55, 30, to be applied with the negative sign. - - Also to obtain the quantities H on the south side, the depths of water (up to the Ioh circle) are to be multiplied by ; and treated as hollows, or negative heights. We have then— H, - H', - 26oo H, - H', = 9330 H, - H', = I2046 H, -- H', - 3505 H. — H'. = 11066 Hs — H's = IIo72 H, - H', = 6285 . He – H's = 11855 II, - FI’, = Iooj4 IC = 42815 IK' = 1940 D = 815 D' = 1583o S = 19.co S’ = 6.48 the quantities S S having been obtained by subdividing the circle of 500 feet by four smaller circles. We have then, up to the 17" circle, the deflection equal to— o”.or 179 × 12.52 + o'coo23574 × 74.04 + o'-ooool 817 × 40875 + o-ooool 156 × 15015 or 2".809 to the north. To this we must add the deflection due to that part of the island which is external to the 17" circle round this Station. This may be taken as equal to the quantity calculated for Boniface Down, namely o”. 477, which added to the preceding, gives 3". 286 for the deflection to the north. - Clifton Beacon. This Station is in the north of Sheet 290 of Yorkshire. The country to the south is rather higher than to the north ; the ground in the immediate vicinity of the Station is tolerably even, and does not require the sines of the depressions or elevations to be computed. The following table contains the heights of the different compartments up to the 24" circle, the radius of which is 43273 feet, or about 84 miles. º i i r * - F - * = F *- : 21- -- * *_** * * *** * * * * * : * , *...* + ... ºn ºn a “**** * iº * **** - : * ~ * * **- : *-*----' -- * *-***** -º-º-º-º-º-º-º: tºrt:--------->>, >>r:-..yr - ºr-…-, : tº- • *-s ºa - - - ºr * * * * * ****** – * : :::::::::: --- : •f .*.** “. . . . .zz.w----> x2+...+* DETERMINATION OF LOCAL ATTRACTION. 639 CLIFTON BEACON. North Side. Number Number of sector. Circle. I 2 : | | | | Io II | 12 2O |, I– 2 |38o 390|400|4|io |425 |430 |435 |435|435|435 |435 |435|435|435 galaela, 43o |43o |440 |8505 2–3 ||350 |345|355 |365 |38o |405 |420 |426|420 || 415 |4|io || 415 || 415 || 415 || 415 |420 |425 |425 |425 |42o 8666 3- 4 |320|| 325 | 325 || 325 || 330 335 | 335 | 330 34o |345 355 |375 390 395 |4oo |405 |405 |4Io 415 || 415 || 7275 295 295 || 290 |299|295 |295 295 295 || 295 || 295 || 305 || 320 |355 385 |4oo |4oo |4oo |4oo |400|4oo | 6695 4- 5 5– 6|270 |265 |27o |270 |265 265 |265|27o 270 |275 296 |320|360 |385| 395 |4oo |4oo |4oo |4oo 395 |6436 6– 7 |250 |240 |245|250 |245|240 |240 |255 |265 275 |295 |320 |360 |385 |335|4oo |400|4oo 395 |393 |6245 7– 8 || 255 |225 | 215 |225 |225 220 |25o 275 275 |265|27o 300 |325|360 || 385 |4oo |4oo |4oo |38o |376|6ozo 8– 9 |27o ||225 |200|200|200|21o 25o 26o 265 |265 25o ||265 |290 || 3ro || 35o |375 | 390 |38o |370 |35o |5675 9–10 |275|225 |200|195 | 185|205 |220 |215|235 |240 |240|245|265|285|315|350 |375 |365 |360 |345|534o 10–11 |27o 24o 195|175 | 185| 195 | 185| 180 | 195 || 2 Iol 2 Io 25o ||26o 285 |300|3.15 335 | 345 |35o 330 || 5oſo 11 — 12 |250 265 |240 |200|| 165 || 17o 155 |200|250 |250 |255 27o 275 |275 275 275 27o 3 Io 325 325|5ooo 12–13 || 235 275 || -oo 225 | 195 || 175 190 I75 220 |25o 270 |27o ||26o ||250 |250 |250 |255 |290 |3oo 305 |490c 13–14|225 |265|255 |240 |230|235|230|| 195 | 160 |200|235|235|245|225 |225 245 |280 |300 |290 |290 4805 14–15 225 24o 245 275 |28o 275 265 |200|| 120 8o 15o 155|220 |225 |220 |225 |260 |28o 25o 235 |4425 15–16 195 || 155 190 220 220 |200|| 190 | Ioo 8o IIo 95 || 6o 16o 205 || 190 185|205 235 | 195 || 2 io || 34oo 16–17 | 125|200| 190|| 145 || II5 | 8o || 65|| 55 I5o |245|245 | 125 140|| 195 | 165 | 130 || 115 17o 150 |230|3035 17–18 125 | 15o Izo 7o 75 5o 5o 7o ||230|260 240 || 2 Io | 120 IIo 150 Ioo 8o 85 roo |200|2595 18–19 | So 7o | Ioo Io; I 15 55 55 I Io 25o 265 |225 | 180 135 | 85 | 130 Izo 85| 65|| 6o Ioo 2390 19–20 | 14o 90 135||130 6o 5o | IoS 275 |300 |265|225 | 195 || 170 II5 90 || 65|| 70 || 65|| 50 50 |2645 20–21 200 | 165 Izo 85| 6o | IIo 150 |26o 290 225 | 205 | 18o 130 Ioo 70 5o 5o 25 20 25 2520 | 21–22 |26o 16o 8o 85 Ioo | I 55 285 || 3 Io 26o 220 | 155 165 14o 75|| 35 | 3o 5o 25 | 20 25 2635 22–23 25o II5 Io; II5 150 |200|305 || 330 |27o 18o 14o 155 145 || 45 25 || 25 55 35 | 45 45|2735 23–24 290 14o | IIo|I45 | 160 |200|225 27o 27o 195 || 135 | 9o 35 25 || 25 25 45 || 45 || 35 | 55 2520 CLIFTON BEACON. † South Side. Number of Sector. Number - of —. Circle | 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10 || 11 | 12 *|| I5 *|, 18 19 20 H H 1 – 2 38o 385 |385 399 |390 |395 |400|4Io |415 |420 |425 |435 |440 |440 *** 45o |450 |445 |84oo 345 |355 |360 |365|37o |375 |375 385 |396 |4oo |416 425 |425 |425 |425 |425 |425 |425 |435|425 |7965 2– 3 3– 4 |336||335|34o |350 |355|365 |375|38o 390 |400|400|405 |4Io |4|io |415 || 415 |420 420 |420 |415 |775o – ;|3}o |326||325|335|345|355|365|375 |385|395|Aio |415|410 |4|io |405 |406|400|405 |400|426||7355 5– 6|290 |310|326||336||335|350 |355|373 ||375|395 |410 |425 |415 |410 |400|400|400|395|399|385||746o 6– 7 |275 |300 31o 325|335|350 |37o 38o |396 |400|410 || 415 |4Io 4oo |400|400|400|390 |38o |375 7415 7–8 |295|315|275|330 345 365 |38o |400|420 |430 425 |425 |420 |410 |4oo |4oo 4oo 390 |375 |365||7565 8– 9 |3io |325|325|345 |355|4oo |440 |445|450 445|440 |430 415 |405 |400|4oo 4ool 390 |370 |350 |784o 9–16|315|3oo |3ro |34o |38o|450 |475|465|455 |450 440 |430 420 |4oo 395 390 390 38o 365 |350 |790o Io—11 |300|285 305 || 330 |375|41o |450 |450 |450 |450 440 |430 415 || 395 |38o 365 |375 |360/345 335||7645 11–12 |27o 326||355|365 |385|400|440 |450 |450 |450 |440 |425 |425 |415 |385 |360 |35o |345|33o |315||7675 12–13 |245 330 |370 |375 |385 |400|415 |445 |450 |450 |445|446|430 415 |385|350 |33o |33o |305|305 |76oo 13–14|25o 320 |355 365 360 | 365 390 |440 |450 |450 |445 |425 |430 |495 |370 || 335 | 325|320|320 |320|7400 14–15 |3to 370 |385 |375 |375 |355 335|375 |425 |445|436 || 415 || 390 |385 |360 |34o |335|315|285 |285 | 7290 15–16|310|4|io 4oo |400|38o |34o 315|325|345|366 || 415 || 416 |38o |365 |37o |360 330 |290 |260 |265||7030 16–17|275 |405 |435 |375: 35o |355 |346||3.16||365 |3oo |336||34o |320|356|365 |345|360 |260 |225|245|3539 17–18|246. 395 |435|456|435|385 360 |34o |346|400|4|io |3}o |395 |345|3.16|296 |260 |z10 | 186|230|9678 18–19 || 190 35o |47o |47o |415 |375 |35o 36o |38o |400|4oo |375 |300 |280 |305 |25o 215 160 | 130 16o 6335 19–20 | 150 |275 |375 |390 390 |4oo |4oo 38o |365 390 |350 |3.16|265 |225 |220 220 | 195 | 16o 14o | I 19 |57:9 20–21 135 | 275 27o 25o 330 || 335 |375 |360 |35o 38o 35o 335 | 315 275 220 | 16o | I go I35 | | Io 59 5169 115 6o 45 |4995 Y 21–22 145 || 295 190|285 |285 |355 |365 |345 35o |35o |355 |360 |325|220 |210 | 1.75 | 165 22–23||75||35||5|*|335|3;3|375|352|335|345|33 ||372|393 ||315||92||73 ||38||38|*|*:::::::: |23–24 270 | 190 14o 2 Io |290 |28o 31o |35o 360 |360 |360 |315|230|| 190 17o 17o 150 | 120 95 7° 4b3o 640 PRINCIPAL TRIANGULATION. From this table we obtain— H, - H', = IoS H, - H', = — 860 H, - H', = — 1545 H, - H', = 95 H; – H'. = – 1030 Hs — H's = – 2165 H, - H', = – 475 H6 – H's = – 1170 H, - H', - – 2560 IC = 48615 IQ = 89590 Therefore by the formula (1) the deflection in seconds is— — o”.oooz357 × 658 – o”-oooor817 x 40975 = — o”.900 The apparent deflection is therefore o”. 90 to the south. Burleigh Moor. This Station is situated in the south of Sheet 7 of Yorkshire. The ground falls to the north, at first rapidly, and afterwards more gradually, to the sea, which is distant between two and three miles north. To the south the country gradually rises, until at a distance of nine miles it attains a mean height of about a thousand feet. The sea to the north, though not very deep, adds to the southern deflection: the depths shown with a negative sign in the following table are taken from the Admiralty Charts. At this Station the ground within the interior 500-feet circle, being uneven and falling to the north, was divided by four small circles whose radii were con- secutively io9, 200, 300, 400 feet. The sum of the sines of the elevations north was found to be — 22 30, and the corresponding.sum South – 12:45. DETERMINATION OF LOCAL ATTRACTION. 641 BURLEIGII MOOR. North Side. Number Number of Sector. of H circle. I | 2 || 3 || 4 || 5 6 7 8 9 || Io 11 | 12 13 || 14 | 15 16 17 | 18 19 20 1- 2 |375 385 |385 390 390 4oo 4oo 4oo 405 || 410 || 41o 410 || 415 || 420 425 || 430 || 435 | 460 | 5oo 540 | 8385 * - 3 ||325 325|325|325 325 325 | 325 | 325 | 325 | 325 325 | 325 || 325 || 330 330 345 35o 375 || 4to. 520 | 6885 3- 4 || 275 275 275 275 275 || 275 275 25o 250 || 25o 25o 26o 265 265 27o 290 3oo 325 || 4oo 470 5770 4- 5 250 |230|225 |225 225 220 220 220 | 210 || 2 Io 2 Io 225 225 22 235 | 25o 275 325 | 375 470 5050 5- 6 225 |200|200|200| 195 || 190 190 190 | 190 | 190 190 190 195| 200 || 2 Io 225 25o 285 35o 560 4625 6– 7 |225 175 18o 18o 176 17o 17o 17o 170 17o 175 | 17o 17o | I75 I90 195 220 | 265 345 530 || 4215 7- 8 225 I75 | 16o 170 165 | 165 | 16o 16o 155 155 155 155 | 1.45 15o I5o 17o 20o 25o 3oo 475 || 384o 8- 9 |225 | 16o 15o 15o 155 145 || 145 | 1.5o 150 | 1.5o 145 || 14o 130 | 130 | 1.5o 165 175 220 | 290 476 3595 9–Io 235 | 1.5o 125 14o 14o 130 || 130 | 130 || 130 13o 13o 125 Izo 125 I4o 15o 16o 18o 25o 45o 3270 Io– 11 |230|| 150 | 125 | 120 | 125 | 125 | 120 | 120 | 115 IIo 195 19ó | 190 125 13o 15o 16o 17o 220 365 || 2965 I 1–12 |235 | 125 11o 100 | 125 | 120 95 Ioo 9o 85 85 8o 85 Ioo Ioo 125 | 1.5o 16o 190 3oo 2526 12–13 215 IIo 95 85 8o 8o 8o 75 75 75|| 7o 7o 75 75 75 Ioo Ioo 15o 16o 235 | 268o 13–14 | 165 8o 75 7o 7o 7o 7o 6o 55 5o 55 55 5o 60 | 65|| 65| Ioo 125 | 1.5o 216 17oo 14–15 125 || 65|| 75 55 5o 5o 5o 5o 45 4o 4o 5o 5o 4o 5o 55 7o loo 15o 220 1430 15–16| 35 | 62 5° 45' 35 | .35| 35 | 35 | 35 | 35 35. 39| 20 to 20 14o 2 Io 925 I6–17 | 85 5o 35 | 35 | 3o "35 | 3o 25 25 20 – 5 – 5 – 5 – 5 || 4o 165 575 I 7–18 6o 35 || 25 || 25 2 O 25 25 2O I5 — 20 — 20 — 20 — 30 – 30 – 25 – 25 I4O 390 18–19 || 4o 25 I5 I 5 I5 25 20 Io – 25 — 20 – 20 – 25 – 30 – 35 – 30 – 25 | 130 295 I9–20 35 | 20 I 5 I5 Io — 20 — 25 – 35 – 55 – 55 – 60 – 60 — 55 – 40 - 35 25o 345 2O – 2 I - 5 – 20 | – 30 – 35 – 35 — 50 – 60 – 65 — 70 – 80 – 85 – 85 – 65 – 60 - 6o I4o 140 2 I — 22 - Io – 20 — 35 – 55 – 60 – 60 — 85 – 90 – 85 – 95 – 90 – 90 - 85 - 85 – 6o • 22–23 – 20 — 50 – 60 | – 60 — 80 – 85 – 90 – 95 – 110 – 115 – 115 – 115 - Ioo - Ioo - 85 - 60 23–24 – 30 — 40 — 65 | – 70 – 90 – 100 – 115 – 110 – 110 – 115 — 120 – 120 – 120 – 120 – 120 - 70 24–25 - 25 — 5o – 70 – 90 – 110 – 110 – 120 – 120 – 120 – 130 – 130 – 130 - 130 - 130 - 120 - I Io IBURLEIGII MOOR. South Side. " Number Number of Sector. of II Circle. || 1 || 2 3 || 4 || 5 6 7 8 9 Io 11 | 12 13 || 14 | 15 | 16 || 17 | 18 19 20 1 – 2 |375|38o 399 |400|| 416 || 440 |450 || 475 5oo 525 54o 550 55o 550 550 5oo 545 545 545 545 9815 2–3 ||325|330 |34o |350 360 | 375 385 4oo 420 456 460 || 480 490 5oo 5oo 5oo || 510 || 510 || 520 520 $725 3- 4 || 390 3oo 3oo 3 Io 320 25 34o 35o 37o 390 4oo 4Jo 43o 490 || 510 || 515 590 590 500 || 510 8160 4— ;|2.70 |280 |275 290 3oo 3oo 320 || 325 34o 35o 370 4oo 470 5oo || 45o 5oo 48o 460 5oo 535 | 7715 5- 6 275 28o 275 275 275 290 290 3oo 31o 35o 37o 41o 48o 5oo 5oo 470 44o 4Io 470 535 7505 6– 7 || 276|280 |275|27o 26o 26o 28o 290 3oo 325 380 || 450 5oo 500 || 475 435 | 400 || 4oo 45o 540 | 7340 7–8 275 |290 |275 |255 250 250 26o 275 275 | 325 | 400 450 500 || 460 || 425 | 375 35o 35o 4oo 510 | £950 8- 9|3.16||360 |260 |250 26o 250 25o 256 275 325 | 375 || 460 470 || 425 || 396 || 335 | 3oo 3io || 35o 490 £545 9–16|300|3oo 285 |275 275 275 275 250 256 306 || 356|| 360 360 | 396 || 35o 325 | 275 275 295 || 38o || 6′45 to-11 || 335|300 |280 |280 28o 28o 275 26o 260 |250 275 300 310 || 310 || 3oo 290 265 230 225 || 310 || 5615 I-12 345 31o 325|320|| 320 | 3oo 3oo 290 260 260 275 300 290 290 270 26o 24o 24o 150 || 250 5595 2-13 || 335 325 325|34o || 325 3oo 3oo 275 250 270 3oo 275 275 25o 220 24o 24o 24o 200 295 5499 *3-14|320 |34o 35o 360 || 325 || 31o 290 260 250 | 3oo 35o 325 285 275 265 275 28o 290 275 | *:9 #935 4-15 |350 |375 |37o 360 325 || 31o 28o 25o 290 320 385 350 310 || 3oo 320 || 390 420 420 439 242 6765 *5-16 || 395 |450 |420 |475 330 275 275 315 3io || 335 | 336|| 325 | 330 31o 4oo 6oo 57o 580 48o 290 7795 '6–17|450 580 || 510 |486 || 360 366 366 306. 300 || 325 | 34o 366 355 425 || 555 64o 625 || 5oo 522 || 34° 8485 Z–18|435|530|350 |350 31o 305 || 320 34o 34o #26 || 36|| 333 333 | #96 || 44; 4to 416 || 440 || 372 | *75 || 3:59 18–19 || 415 |625 |4|io |33o 390 || 365 375 520 | 535 | 725 $20 | 930 Šoo 615 $36 58o 6oo 999 || 45° : Io875 ‘9-20 245 53o 3ro 345 55o 6oo 590 75o 94o goo 95o 870 8oo 75o 75o 8oo 7 Io 660 525 365 I294o 29-21 | 160 |435 | 3oo 325|| 465 785 950 | 930 | 845 805 || 3ro roto 98o 935 | 90o 78o 6oo 579 49° 355 13590 21–22 | 1.45|336||395 |315|| 475 | 666 || 750 || 765 | 726 793 #55 39; $95 || $36 || $45 | #95 || 62o 582 479 || 385 2235 22–23 |13;|265 275 306 || 336 || 375 | 68o Šoć 62o Žo 675 | 66;| 765 610 || 746 | 845 | 735 | 668 #35 || 489 I IoGo 23–24 95 245 265 |27o 275 3io || 38o 475 61o 94o 826 836 806 | 725 635 | 790 785 | 735 615 535 | III 35 *4-25 | 85 |240 iss 24o 25o 305 || 375 45° 92.5 95o 11oo Iozo 65o 590 565 || 525 635 | 790 615 || 420 | IIoos *— 4. M 642 PRINCIPAL-TRIANGULATION. From this table we obtain— H, - H', - – 1430 H, - H', = – 2665 H, - H', = — 31 Io H, - H', - – 1840 H, - II's = – 288o Hs – H's = – 2950 H, - H', = — 2390 Hs – H's = – 3125 H, - H', - – 2875 IX = I3365 IQ = 1367 Io S = — 22.30 S’ = – 12:45 Also, the sums of the depths of the sea north— D = 7200 The deflection, therefore, due to the distribution of matter within a circle of nine miles and a half round the Station is— – o”.or 18 x 9.85 — o".oooz357 x 2516 – o”.oooo.1817 × 123345 – o'-ooool 16 x 7200 = – 3".o.33 or 3”. O33 to the south. But it is evident that if the table were extended to a great number of circles, an addition would be made to this quantity, for the high ground to the south continues for eight or ten miles further, whilst on the north there is an increased depth of sea; we may therefore proceed in the following manner: In Plate XXIV., B is the Station on Burleigh Moor, abmn the circle within which we have considered the effect of the ground, draw ag, ml (through B) making each an angle of 25° to the west with the meridian, also bh making an angle of 50° to the east, and nr perpendicular to the meridian; take ad = de = 5 miles, and ag = 38.5, and describe the cir- cular arcs ghrl, ef, cd. Now the whole of the space to the west of the lines ga, ml may be disregarded, as probably producing no meridional component of deflection at B, we have then three spaces left, namely, lm.nr., rnbh, and algh, to consider. Of these the second, namely nbrh, may also be disregarded, as the disturbing effect of the strip of land will be counteracted by the greater expanse of water. Within the space lmnr the depth of sea varies from 20 to 40 fathoms; the line of 30 fathoms depth runs parallel to the line of the shore, and about 12 miles from it: by giving greater weight to the depths nearer the Station, the effective mean depth may be taken at 30 fathoms, or 180 feet. Within the space abcd the mean height of the country, as estimated from the contours, is Iooo feet; within the space cdef the mean height, obtained in the same way, is 760 feet; and within the space eſgh the mean height is 240 feet, estimated also from the contoured maps. º The following table contains the calculation of the deflections due to each of the spaces — The sum of these small quantities amounts to — 1". 521: this added to the deflection due to the irregular distribution of matter within the circle of 9.5 miles radius, which was found to Space. a' 'a, 7' r, Deflection. abed | 1000 | 203 || 133 14.5 9-5 | – 3592 cdef 760 2O5 I3o 19° 5 I4 ° 5 – o' 315 efgh 24o 205 I3o 48°o I9' 5 – o '303 lmnr — 18o – 25 90 48°o 9° 5 Y-- o' 3 II be – 3".o33, gives – 4”.554 as the total deflection to the south at Burleigh Moor. t l 4 DETERMINATION OF LOCAL ATTRACTION. 643 Calton Observatory. This Station is situated in the north-east of the city of Edinburgh: Sheet 2 of Edinburgh- shire. The ground in the immediate neighbourhood of the Station falls abruptly on all sides: to the north it continues to fall gradually to the sea, which is at the distance of about two miles north; to the south there is a gradual rise, continuing to the borders of the county, where the mean height is about a thousand feet. The inner space of Iooo feet radius was divided by nine circles, whose radii were Ioo, 200, . . . 900 feet: the sines of the depressions were then calculated, and were found to be as follows:— Sum of Sincs between North. South. Centre and rico O * OOO O * OOO 7"ico - Tzoo 5' 38o 5’ og 8 Taco T 7300 5'813 4 ° 250 º T3oo - THoo 5'881 4 ° 250 T400 - 7 soo 6' 295 4' 386 7’soo T Téco 5'807 4- 366 7600 - ??oo 5' 543 3' 660 Too - ?’soo 4'868 3'846 78oo T 7 goo 4 "334 3'965 7 goo T Troco 3 '859 3 * 757 Total . . 47 '78o 37' 518 S = — 47.78o : S = — 37-518 The following table contains the mean heights of the compartments, from the Iooo feet circle to nine miles and a half round the Station. - 4 At 2 644 'orº PRINCIPAL TRIANGULATION. fºr if K. is : CALTON HILL, EDINBURGH. North Side. . Number of Sector. Number - of - * * H Circle. 1 2 3 4. 5 6 7 8 9 Io II | 12 || 13 || 14 15 16 || 17 | 18 19 20 I - 2 2— 3 | 180 | 165 || 145 || 145 || 140 14o 14o 14o 135 | 130 | 125 | 120 | 12o 1zo 115 115|| 130 150 | 18o 195| 2830 3– 4 180 || 14o 12o Too | II5 IIo | IIo Ios | I to 11o 115|| 115| IIo | I to 11o | Ioo | Ico 115|| 130 18o 2385 4— 5 | 165| 120 | IIo Ioo 85 8o 75 75 75 8o 95 95 95 || 95 95 Ioo Ioo Ioo 115 150 | 2005 | 5– 6 || 145 || IIo 85 | 85 75 75|| 75 75 75 75 8o 8o 8o 75 75 8o 90 95 Ioo Ioo 1730 6– 7 || 135 | 8o 75|| 8o 8o 8o 80 80 75 75 7o 75 7o || 65|| 70 75 | 85 90 Ioo Ioo 1640 7— 8 IIo 7o 55| 70 || 65|| 75|| 7o 60 || 65|| 55 || 5o 5o 55 6o 6o 7o 8o 9o | Ioo 1oo 14io 8– 9 IIo || 65|| 35 | 45 35 | 36|| 5o 5o 5o 50 45 45 45 5o 5o 6o 75 95 || 1 oo | Ioo 1185 9–Io 90 || 70 35 | 40 35 25 25 | 35 | 45 || 45 45 4o 35 | 45 50 | 50 | 70 | 85 Ioo 95 IoGo 10–11 85| 70 5o 45 4o 35 25 3o 35 | 40 | 40 35 | 30 35 | 40 || 45 || 65|| 8o 9o 95 Toro 11-12 || 70 8o 90 | 8o 7o | 65|| 45 || 4o 4o 35 || 25 25 || 25 || 25 25 30 4o 7o 8o 85 | IoA5 12–13 || 70 8o 95 go 8o 7o 6o 6o 5o 45 30 || 25 20 | 20 20 | 20 25 4o 7o 8o | Iojo 13-14 || 85 95 || Ioo 95 85 75 7o 55 45 3o 15| Io 5 5 Io | Io | Io 20 55 6o 935 I4-15 Ioo Ioo | Ioo 9o 75 4o | I 5 || Io I5 50 595 15–16 || 150 IIo 85| 45 Io 3o 43o 16–17 | 1.70 || IoS 65 5 – 2 O | – Io — Io – Io — Io i - IO | – I O - I O || - IO I - IO 5 || 35o 17–18 18o 8o 20 — 20 | – 20 — 25 — 20 — 20 — 15 – 30 — 25 – 25 – 20 | – 20 - 20 – 20 - 20 28o 18–19 18o 15 – 20 – 20 – 20 – 30 — 25 | – 25 — 25 – 30 – 30 — 30 | – 25 – 25 – 25 | – 30 – 25 | – 20 | – 20 195 19–20 I6o — 20 | – 25 | – 25 — 20 – 20 — 25 | – 20 — 20 — 20 | – 30 | – 25 — 30 | – 7o | – 4o | – 30 | – 30 | – 25 – 20 | 16o 2O - 2 I 90 5 — 25 – 20 | – 20 | – 20 | – 30 — 25 | – 30 – 30 – 30 – 25 – 25 – 20 | – 20 — 6o – 30 || – 30 — 25 – 25 95 2 I - 22 — 20 — 30 – 5o – 4o – 30 – 55 – 90 – 90 – 9o - 4o - 25 – 25 | – 35 | – 4o – 35 | – 30 – 30 22–23 — go — 6o — 90 | – 6o — Go || – 9o — 7o – 90 – 120 – 9o – 60 | – 7o – 40 | – 4o — 40 | – 35 | – 35 | – 30 23-24 — 8o — 70 2O 2O 3o 3o 8o 5o 7o 40 – 90 – 95 | – 7o – 70 – 60 | – 50 | – 40 | – 40 | – 30 340 24–25 3o 90 || 2 oo 18o 390 450 53o 450 | 3oo | 130 | – 60 | – 70 | – 70 | – 65 – 65 |- 65 – 55 — 50 | – 30 2750 CALTON HILL, EDINBURGII. South Side. | Number Number of Sector. of , H Circle. || 1 || 2 3 4. 5 6 7 8 9 || Ios | 1 || | 12 || 13 || 14 | 15 16 || 17 | 18 19 20 I —- 2 - 2– 3 || 235 | 220 | 1.75 | 165 155 15o 15o 2 Io 220 220 || 2 Io 215 220 || 2 || 5 || 215 215 220 || 2 Io 205 || 21o 4035 3–4|230 220 190 18c 165 175|| 180 195 || 2 Io 200 200 185 180 17o 16o 155 155 15o 155 | 16o 3615 4- 5 |225 | 200 200 200 200 2'io 205 220 235 | 200 | 180 185| 16o 155 15o 14o 14o 135 | 135 | 11o 3585 5- 6 2 Io 225 270 290 25o 245 || 2 Io 24o 26o 24o 24o 24o 190 145 || 135 | 125 | 120 | 12o 115|| 105 || 3975 6– 7 |220 225 || 3oo 25o 26o 275 270 275 26o 26o 25o 25o 200 15o 220 35o 365 325 2 Io 115 5030 7– 8 |200| 28o 33o 300 27o 28o 275 270 265 26o 250 245 || 235 | 1.70 || 410 5oo 460 | 38o 28o | 125 || 5785 8– 9 190 4ool 26o 28o 275 27o 26o 26o 255 25o 25o 245 24o 18o 28o 490 420 285 220 135 | 3445 9–Io 190 200 23o 27o 265 250 24o 25o 24o 24o 245 245 25o 235 220 385 35o 21o 3oo 200 5015 10–11 195| 225 235 || 250 250 245 245 245| 245 245 245 255 26o 26o 250 | 3oo 330 || 385 450 320 T5435 11–12 175 215 235 | 245 25o 26o 26o 26o 26o 255] 250 255 255 26o 25o 275 55o 695 || 560 315|| 662o |. 12–13 175|| 2 Io 24o 26o 3oo 3oo 3oo 290 290 266 || 250 235 230|| 230|| 230 | 200 230 445 405 || 2 15 5295 13–14|17o 290 245 290 300 3oo 3oo 285 265 235 | 215 200 200 200 290 175 | 16o 160 | 210 | 166 4470 14–15 175 180 245 290 330 299| 275 26o 24o 225 225 220 195 || 175 16o 150 150 || 150 | 150 | 95 || 4150 15–16, 176 160 225 26o 285 26o 27o 390 390 366 296 || 245 2ío 170 | 150 | 16o 165 || 150 | 1.35| 76|| 4425 16–17|195| 16o 215 255 310|| 320|| 350 38o 38o 35o 3oo 255 235 | 205 195|| 235 || 235 | 175|| 125 || 70 || 4945 17–18|250 175 225 | 370 385| 375 || 450 57o 565 5oo 425 || 375 35o 31o 256 225 || 266 || 175|| 156 | 160 | 642.5| 18–19|28o 196 || 235 | 370 | 400 | 400 || 48o 550 575 | 530 44o 425 || 375 34o 305 || 3oo 3oo 266 17o 1ool 7025 19–26] 2 Io; 200 || 3oo 365 425 || 525 || 525 55o 535 | 475 || 425 || 425 | 375 4oo || 415 || 350 275 225 | 175 75|| 725° 26–21 175 || 235 | 360 || 45o 6oo 815 9oo 875 | 706 || 475 470 || 450 || 450 425 || 350 28o 225 | 196 176|| 75 8679 21–22 160 3oo 45o 7oo | Ioro Izoo 1299|| 1990 76o 575 530 475 420 345 3oo 26o 200 175 Ioo 75 1045 22–23 16o 325 || 525 | 8 Io|IIoo | Iojo | Io?5 825 625 || 575 530 || 465 || 355 || 425 || 330 25o 190 180 | 200 || 146|| 101.35 23–24|200| 4oo 625 | 825|Ioso | IoI5 IoSo. 750 630 || 525 535 | 525 || 48o || 415 || 335| 285 || 360 || 450 420 || 370 | 11275 24–25 250 | 520 715 925 | 1250 | 1350 | IoAo 780 | 660 | 735 | 756|| 706 || 62o || 510 || 465 456 || 710 || 760 || 510 || 370 || 1389° * - " DETERMINATION OF LOCAL ATTRACTION. 645- From this table we have— tº gº tº º H. — H', - — 1580 H, - H', = – 4375 H, - H', = – 1205 H; – H's = – 22.45 Hs — H's = — 426o H, - H', - – 1230 H6 — H's = – 3390 H, - H', = — 3955 S — S' = — Io.262 IC — K' = — Iooj90 D = 4970 — o”.or 18 x Io.26 – oooz357 x 1808 – ooool 817 × Iooj90 — ‘oooo II.56 × 4970 = – 2"-433 which is the deflection due to the distribution of matter within a circle of nine miles and a half round the Calton Hill. But it is not allowable to terminate the calculation here, as will be seen by continuing it as follows: In Plate XXIV., E is the observatory on the Calton Hill, acegmn the circle just mentioned; the lines ab, cd, ef,gh, mk, n' are each ten miles long, and intersecting in the Station; ab and ml are inclined (N.W. & S.E.) at 40° to the meridian, cd, mk at 14° (N.E. & S.W.), of gh at 65° (N.E. & S.W.) The effect of the matter within the spaces algh and efhl in pro- ducing disturbance may be neglected. The mean height of the space abcd is 420 feet, obtained from the contoured maps. Of the space calefone-sixteenth part is covered with land, and this is at the further boundary of the space; the remaining fifteen parts are covered with sea to the mean depth of 16 fathoms, or 96 feet: if we suppose the sea to be pressed down or replaced by an equal mass of rock throughout, there would remain a hollow of about 60 feet. This quantity we may add to the mean height of the similar and opposite space ghmk, which from the contours is found to be 1060 feet. The mean height of the space mkml, which is similar and opposite to abcd, is IIoo feet. The following table contains the calculation of these disturbances:— Space. J. a' e. 2' r, IDeflection. ghmk 1060 + 60 24; 19: I9' 5 9' 5 – 6.630 mknl IIoo-420 194 140 | 19.5 m 9' 5 — or 5 Io making altogether — I I40. This being added to the quantity — 2.433 previously deter- mined, gives – 3:573 for the total deflection south at the Calton Hill Observatory. ‘. . . Lough Fºyle. To the south of this Station, which is situated in Sheet 9 of Londonderry, the ground rises continuously, attaining a mean height of about a thousand feet at the southern boundary of the county; to the north the country is flat. In the immediate vicinity of the Station the ground. is even, and does not require the calculation of sines. 646 PRINCIPAL TRIANGULATION. LOUGH FOYLE. - North Side. Number of Sector. Number - of Circle. || 1 || 2 || 3 • || || IO II 16 || 17 | 18 2 O I5 1 – 2 Ioo 9o 90 8o 75 75 75 || 75 7o 7o 7o ſo | 70 7o 7o 70 || 75 75|| 85| roo 1555 2–3 || Iool 75 50 6o 5o 5o 5o 5o 5o 5o 5o 6o 6o 6o 7o 7o 76|| 76 75 | Ioo 1270 3–4 9o 75 5o 5o 5o 5o 5o 5o 5o 5o 5o 5o Go || 6o 6o 60 || 7o 7o 75 90 | 12io 4- 5 7o 75 5o 5o 5o 5o 5o 4o 4o 5o 5o 5o 5o 5o 6o 60 || 65|| 65|| 65|| 75 | 11 15 5– 6 5ol 75 5o 50 25 || 3o 30 25 25 30 || 3o 5o 4o 5o 5o 5o 56 || 56|| 75 96 || 925 6– 7 || 5o 5o 25 25 25 || 25 25 || 25 25 || 25 || 25 25 30 4o 5o 50 5o 5o 75 Ioo 795 7- 8 5o 4o 20 20 20 zo 20 20 20 20 25 25 25 3o 4o 5o 5o 5o 75 Ioo | 720 8- 9 || 5o 25 20 | 20 | 20 20 20 20 20 | 20 25 25 || 25 || 3o 3o 5o 5o 5o 75 | Ioo 695 9–Io 5o 25 | 20 | 15 I5 | 15 I5 | 15 I5 I5 20 |25 || 25 25 35 | 50 5o 6o 75 75 64o Io–II 5o 20 | 15 15 15 15 I5 | 15 15 | 15 15 25 25 25 25 | 50 | 5o 6o 75|| 75|| 615 II — I2 3o 20 || To Io Io Io | Io Io | Io | Io I5 20 25 25 || 25 || 25 || 50 | 5o 5o 85 5oo | 12–13 4o Io | Io | Io | Io | Io | Io | Io | Io | Io | Io | I5 20 |25 || 25 25 || 4o 50 | 50 | 85 475 | I3- I4 30 • Io | Io | Io Io | Io | Io 20 |25 || 25 || 25 4o 5o 50 | 85 || 4 Io | I4–15 30 Io Io | Io Io 20 20 || 25 || 25 25 || 25 | 40 | 6o 8o 390 15— 16 25 25 25 35' 2 25 5o 7o 7o 34o 16–17 25 25 || 25 25 25 45 4o 4o 65 315 I7— 18 25 25 || 25 2 25 25 35 4o 75 || 3oo 18–19 25 20 20 25 25 25 35 || 65||75|| 75 | 390 19–20 f 25 | 15 zo 25 || 25 25 || 35 | 65|| 95 90 || 420 2O - 2 I Io 25 25 2 60 | 1.40 | 180 | 1.5o 175 790 2 I - 22 Io 25 25 | 1.5o 62o 96o 75o |370 4oo 3310 22–23 25 || 25 | 24o | Iooo | Ioso | IoIo|7oo | 670 || 5120 23–24 25 || 25 | 6o 4ool 940 | Ioool 730 | 84o 4ozo 24–25 25 25 25 || 330 | 85o || 760 | 720 7oo 3435 LOUGH FOYLE. South Side. Number Number of Sector. of H Circle. Io | II | 12 || 13 14 | 15 16 || 17 | 18 || 19 || 20 I – 2 || IOO || IOO | IOO || ICO || ICO | IOO IOO || IOO || ICO | IOO } 1 OO | IOO || IOO I IO | I IO | 120 I2O I2O | I2O I2O 2 I 2 O | 2– 3 | Ioo | Iool Ioo Ioo too | Ioo Ioo Ioo | Ioo | Ioo too Ioo | Ioo IIo | I to IIo IIo | I ſo too IIo 2060 3– 4|Ioo 1oo | Ioo | Ioo | Ioo too 120 | 120 | 120 Ioo Ioo | Ioo too Ito Ioo | Ioo 11o 125 | Ioo | Ioo 2105 4— 5 || Ioo 125 | Ioo Ioo 13o I Io I4o 14o 15o | I2O | 125 I2O Izo 125 | 125 | I2O | 125 | 120 Ioo | Ioo 2395 5— 6 || 75 | 1.5o | Ioo 12o 15o 150 | 150 | 1.5o 15o || 130 | 125 | 125 | 125 | 125 | 125 | Izo 12o | IIo | Ioo | Ioo 25oo 6— 7 || Ioo 125 | Ioo 130 | 16o 17o 16o 15o I5o I5o I25 I25 || I25 | 125 | 125 | 120 I Io | Ioo | Ioo Ioo 25.5o 7— 8 || 120 | 125 | 125 | 150 | 160 | 160 | 1.5o 15o 150 | 15o | I5o I5o | I25 | 125 | 125 Izo I Io Ioo | Ioo 9o 2635 8– 9 || 120 150 | 1.5o 15o 150 | 18o 190 |200|200|200|200 I75 | I go 15o 15o 12o IIo Ioo | Ioo 90 3035 9–10 || 150 17o 15o 200 190 180 |200|205 |225 |225 |225 200 18o 18o 16o 14o 125 || Ioo Ioo 95 || 34oo Io–II 15o 16o zoo 225 225 || 2 to |200|225 || 25o 250 |250 |225 215 || 2 Io I75 I5o 145 || 120 IIo Ioo || 3795 11–12 180 |200|220 24o 266 |250 |250 |255 275 |28o 275 |265 250 |240 |200|| 175 | 1.5o 14o 125 | Iool 4330 12–13 |200|225 28o 275 || 3oo |300|250 31o |320 31o |300 |300 275 |250 |2 Io 190 | 190 175 150 Ioo || 491o 13–14|220 3oo 31o 3oo 33o 325 320 i 330 || 345 330 325 330 3oo 27o 24o 225 225 | 190 150 | 125 | 5490 | 14–15 25o 310|| 35o 35o 36o |360 |35o 37o 375 375 |350 325|300 |300 25o 25o 225 200 | 185 || 130 5965 15–16 25o 38o 42O || 4 Io 4 Io 415 || 390 || 415 || 43o |425 |4oo 4oo 380 34o 295 || 320 26o 25o | I go | Ioo 6880 16–17 |200|47o 5oo 490 || 48o |47o |470 |490 555 |550|550 |5oo |470 |425 |375|| 34o 315| 275 |200| 90 8215 17–18 18o 5oo 6oo 58o 565 55o 6oo 6co 670 7oo 690 610|55o 470 |4|io || 4oo 370 3 Io 220 I4o 9715 18–19 175 575|68o | 68o 670 750 | Soo |8oo | Soo |800 |750 |68o 6oo 525 |460 4oo 325|| 3oo 175 175||11010 19–26|200|560 |800 820 920 |90o | 890 |75o Soo |75o |690 ||610|555 5oo |455 4oo 3oo 225 |256 | 186||11425 20–21 || 3 Io 530 830 Io8o loSo 8oo 76o |75o 8oo 690 590 470 |435 j41o 406 35o 220 | 34o 325 | 190 | 9560 21–22 |320|55o 820 950 Iozo 850 |68o |76o |85o |770 |600 |460 |360 |300 245 zoo 250 | 325 |275 28o 16865 22–23 |z10 520 |6oo 670 7Io 650 |67o 725 |800 |7Io|58o 390 |290 |230|| 180 21o 240 || 3oo |356 || 560 | 9595 23–24|200|470 |525 | 510 | 6oo |749 |840 ||610|56o 550 |440 |320|275|25 |21o 295 | 400 || 370.|55o 1050 97.32 24–25 |270 |460 |470 575 74o 480 |46o |48o |625 640 |440 |300 |250 |260 |320 560 | 1130 | 64o"|72o 790 IoGro DETERMINATION OF LOCAL ATTRACTION. 647 | From this table we obtain— H, - H', - – 565 H, - H', - – 1280 H, - H', = – 1915 H, - H', = — 790 H; — II's = – 1575 Hs — H's = – 234o H, - H', = – 895 H6 — H's = – 1755 H, - H', = — 2760 .* * - * * * IC — IC’ = IoI265 Giving a deflection to the amount of – o”.oOo.2357 x 1305 — ooool 817 × IoI265 = — 2'". 148 The depth of Lough Foyle is so small that it may safely be neglected; but it is necessary to extend the calculation to a greater distance, which may be done as follows: In Plate XXIV., L is the Station, adhgnmr the circle of nine miles and a half radius; abouqt makes an angle of 65° (N.W. & S.E.) with the meridian, rs makes an angle of 72” with the south meridian, and hklo an angle of 50° with the north meridian ; Ls, Lu, Lv, Lt are each 50 miles. Make ab = be = hk = kl = 6 miles, and describe the circular arcs cgl, bfºk ; de is drawn in the meridian, and fg makes an angle of 15° (N.W.) with the meridian. Draw also mo and mp, each 12 miles long, and making angles 25° (S.W.) and 45° (S.E.) with the south meridian. The effect of the matter within the lines wa, rs, and vh, qt in creating disturbance at L may be taken as insensible. The mean height of the space abde is 600 feet, of the space beſg 410 feet: the space edhk is mostly covered with shallow water, the effect of which may be disregarded; the space gfkl is covered with sea to the mean depth of 27 fathoms; the space ucglu is covered with sea, the mean depth of which may be taken as 40 fathoms. The mean height of the space rmopnqts is 4oo feet, and the mean height of the space mopm is 900 feet. Thé calculation of the disturbances due to each of these spaces is shown in the following table:– Space. h a' &, r’ 7, IDeflection. srqt 400 253 | 11; so-o 9-5 || -1.454 mnpo 5oo 205 I35 2 I 5 9° 5 - * 544 abde 6oo O 295 I5' 5 9° 5 + 314 bef, 4. Io 345 295 2 I 5 I5' 5 -- " Io2 fgkl — 16o 5o 345 || 2 I 5 I5' 5 — ‘oqo culv • –% 5o 295 5o ‘o 2 I 5 - “254. The sum of these partial disturbances is — I".876, which being added to the quantity – 2, 148 previously determined, gives the total deflection south equal to — 4", o24. ICellie Law. This Station is situated in Sheet 19 of Fifeshire. The mean heights of the compartments are given in the following table:— - * * * * * * - **** is • +++ # * * tº sº. # . gº * * * * * * * * * * tº 648 PRINCIPAL TRLANGULATION. KELLIE LAW. North Side. º Number of Sector. Number - of - II | Circle | 1 || 2 || 3 || 4 5 6 || 7 || 8 9 || Io II | 12 || 13 || 14 15 | 16 || 17 | 18 || 19 || 20 1 — 2 |470 || 480 || 470 460 || 450 || 450 460 || 460 46o 470 || 48o 490 5ool 500 500 5oo 5oo 5oo 5ool 500|9600 2— 3 |450 || 45o 470 || 480 || 480 48o 450 || 440 440 || 430 420 || 490 || 41o 4oo 4oo 4oo 420 || 420 450 || 450 |874o 3– 4 |430 || 48o 5oo 5oo 5ool 500 5ool 500 5oo || 480 || 48o 46o 45o 430 || 410 || 4ool 38o 410 || 450 | 400 |916o 4— 5 |43o 48o || 510 || 510 || 510 || 510 || 510 || 510 || 510 || 510 || 510 || 5oo 47o 460 450 || 420 4oo 370 390 || 350 |931o 5– 6|44o 48o 5oo || 510 || 510 || 520 520 520 || 510 || 510 || 510 || 590 499 || 48o 46o 44o 420 || 4oo 360 | 350 |943o 6– 7 |450 || 48o 5oo 510 || 520 53ol 520 520 || 510 || 510 || 5oo 48o 450 || 440 || 440 || 430 430 || 41o 38o 330 |934o 7– 8 |46o 48o 500 || 5 to 53o 540 54o 530 520 || 510 || 490 47o 440 || 420 || 4oo 4oo 4oo 4oo 38o 320 |924o 8- 9 |48o 48o 5oo 530 54o 55o 550 55o 520 || 5 Io 5oo 470 440 || 420 || 4oo 4oo 4oo || 4oo 370 320 | 9330 9–Io |5oo 5oo 520 | 55o 550 560 560 | 570 570 55o 5oo 48o 46o 45o 44o 430 420 || 4oo 36o 320 q690 Io–II |5oo 520 54o 55o 560 58o 580 57o 55o 520 510 || 48o 450 450 450 440 420 4oo 38o 3oo |9750 11–12 |520 550 5éo 550 550' 570 550 540 || 560 || 470 450 || 450 || 440 450 450 440 420 | 400 370 || 325||9555 | 12–13 |55o 56o 570 560 570 580 || 550 500 470 45o 44o 43o 420 || 420 || 41o 420 420 | 400 || 360 || 3oo 9380 13–14|58o 590 58o 58o 570 || 58o 550 | 53o 520 || 48o 470 45o 440 || 43o 4oo | 400 4ool 390 360 | 3oo 9600 I4–15 640 | 6oo 6oo 6oo 560 550 || 48o 480 || 510 || 520 || 510 || 470 43o 4oo 390 38o 37o 390 || 370 275 9525 15— 16|600 6oo 57o 55o 53o 460 || 460 || 450 || 450 || 420 38o 370 || 37o 38o 35o 36o 360 | 360 360 25o |8630 16–17 | 55o 54o 53o 5oo 5co || 490 45o 45o 420 || 4oo 35o 320|| 320 | 35o 35o 350 | 37o 34o || 33o 24o 8150 17–18|54o 58o 560 | 520 5oo || 48o 45o 420 | 38o 360 || 320 | 320 | 3oo 3oo 3 Io 320|| 320|| 320 | 320 220 7840 18–19 |600 62o 55o 520 47o 420 37o 35o 320 | 3oo 28o 26o 28o 25o 290 || 3ool 28o 3oo || 3oo 220 | 7280 19–20 |65o 58o 5oo 5oo 45o 420 4oo 370 || 35o 320 || 3oo || 330 || 3oo 27o 25o 25o 27o 26o 24o 2 Io | 7220 20–21 |6oo 55o 48o 5oo 470 4oo 35o 3oo 3oo 28o 3oo 320 270 240 220 18o 200 zoo 21o 17o 6540 21–22 55o 460 || 460 | 550 || 420 || 320 zoo 16o Izo roo 13o 16o | 1.5o 15o roo IIo | Ioo 12o 130 || 130 4620 22–23 55o 37o 4oo 38o 25o 200 | 12o 5o 20 20 | – 25 – 30 | – 35 | – 4o 20 20 .30 20 | 70 |2520 23–24 |450 26o || 3oo 35o 25o Izo 5o Io — 25 | – 30 — 4o - 5o - 55 - 50 - 5o – 5o – 50 – 30 1790 24-25 || 450 | 200 | 90 7o 7o 20 – 30 – 4o – 50 – 5o - 55 - 55 |- 55 – 55 | – 6o — 70 – 60 900 IXELLIE LAW. South Side. —º Number Number of Sector. - | ...of H Circle. || 1 || 2 3 4. 5 6 7 8 9 || Io II ºf 12 | 13 || 14 || 15 16 || 17 | 18 19 20 I– 2 |470 48ol 50ol 500 490 48o 460 | 45o 430 430 430 430 430 43o 43o 430 || 430 430 440 45o 90° 2 – 3 |450 44o 450 || 450 || 45ol 440 44o 420 || 4 io || 4ool 4oo 4oo 4oo 38o 36o 360 | 360 | 360 35o 370 |809% 3–4|430 390 360 | 3éol 35o 35ol 35o 330 330 | 320|| 320|| 320 320 320 | 320 320 | 320|| 3rol 360 34o 67% 4— 5 |4|io || 35o 34o 310|| 360 290 290 270 27o 26o 26o 26o 26o 27o 28o 290 290 290 28o 300|587° 5– 6 38o 34o 330 | 3oo 270 27o 25o 25o 24o 24o 24o 24o 24o 24o 250 25o 26o 26o 250 28o|537. 6–7 390 360 || 31o 290 26o 25o 25o 25o 24o 24o 24o 24o 24o 240 24o 240 25o 250 | 24o 250 |52% 7–8|460 320 28o 26o 26ol 25o 24o 24o 24o 240 | 24o 24o 230|| 230 230 24o 250 250 || 23ol. 240 |5}: 8– 9 |400|| 3oo 28o 25o 25o 25o 23o 230 23o 230 220 | 200 2 Io 229 220 23o 24o 23o 220 220 4862 9–10 |38o 290 27o 25o 24o 230 230 230 230 220 || 2 Io 200 200 200 || 2 Iol 2 Io 2 Io 2 Io 2 Io 230|46%. 10–11 |360 28o 250 220 230 21o 210 | 200 | 200 | 200 | 200 | 199| 199| 180 | 190 200 | 200 | 200 200 220 [4.33% 11–12 |38o 28o 250 || 2 Iol zoo 200 | 190 190 17o 150 | 16o 16o 160 | 1.5o 150 17o 200 | 200 | 180 | 200|39% 12–13 |4oo 25o 220 | 180 | 1.5o 16o 16o 140 || 130 | 120 12o IIo 12o 12o 12o 12o 14o 160 | 160 180 3462 13–14|400| 26o 200 190 17o 15o 130 Ioo 9o 9o 90 90 | Ioo Ioo 1oo Ioo 12o 140 | 150 180 29. 14–15 |400|| 25o 290 18o 16o 13o | I to Ioo Ioo Ioo | Iool 90 9o 9o 90 90 Ioo | I to 13o 170 27. 15–16|42o 25o 180 12o 90 || 70 7o 7o go Ioo Ioo 90 8o 8o 8o 8o 90 90 go 150 33%. 16–17 |400| 200 | 120 | 9o 7o 7o 7o 7o 8o 7o 6o 7o 7o 70 | 8o 7o 7o 6o 7o 150 23. 17–18|400| 200 100 | 90 90 | 199| 9o go| 6o 6o 5o 5o 4o 4o 30 4o 60 | 70 60 | 120 #. 18–19 |450 | 150 | 8o 6o 6o | 6o | 6o | 8o 6o 20 , * 2O || 2 O | I2O 1:. 19–20 5oo I3o So 4o 4o 6o 4o 3o - 25 - 35 – 50 - 60 - 60 — 55 – 60 |— 30 – 30 – 30 7o %. 20–2 I |450 So 2C) 40 8o 3o – 35 - 50 - 100 – 100 – 110 - 95 – 100 – 85 – 90 – 85 – 6o 2O ſo | 2 I-22 || 4oo 2 O – 30 - 60 - 70 - 90 - 11o 1-115 – 120 – 140 – 145 ||—155 – 150 – 140 – 120 – 90 - 50 #. 22–23 220 | – 20 – 30 – 35 – 60 – 90 – 95 – 11o |–130 – 130 – 150 – 150 – 155 – 160 — 170 — 160 — 170 –160 — 120 – 70 㺠23–24 24o — 30 — 50 – 90 – 95 – 120 - 150 - 150 - 160 – 155 – 150 – 160 – 170 –17o |–16o — 150 – 155 — 155 – 130 - 95 . 24–25 |300 | – 60 – 90 – 110 – 130 – 140 -150 -150 – 170 -150 |–180 – 166 –170 – 175 |—150 – 155 — 150 |–15o |—120 - 11° 3 ** º + DETERMINATION OF LOCAL ATTRACTION. 649 From this table we have— H, - H', = 580 H! – H'. = 3440 H, - H', = 4130 H, - H', - 650 H; — H's = 4060 Hs – H's = 4470 H, - H', = 2400 H6 — H's = 4130 H, - H', = 5030 -- IC — K' = 75640 D – D = — 9150 The deflection therefore is— o"-oooz357 × 2540 + -oooor817 x 75640 + oooor 156 × 9150 = 2".o?8 North. - Monach. This Station is in Sheet Io of the Island of Lewis. The mean heights of the different compartments are shown in the following table:— 4 N o99 "NOILVIſl{}MVISIL IV.IIONIEICI ‘; or £z OIOZ oz8I S/92 $682 o/17 S6SS Syrg ogº.g $599 o269 S694 5694 $864 o988 S478 Sog8 $488 ogoó Sz26 o/#6 |S/66 ozyII og581 op of I olz Sz9. S99 Szg of £ og? S49. og? oo? oo? oo::/ oop oof, Szy Sz? S/? og5 oS9 $49 o/ og I Sz9. Szº of £ o69. oop oo? oo? oof, Szy Szy o947 oo? oof, ogy og5 o49 SS o92 oo? 5 I? $99 S/9 o69. ooy oof, oo? SI+. Szy Szy o947 Szy SI+. $9? SSS 599 ol. Sł, S/ S$z o62 ozº og? 59% 58% oo? ooy Sz? Szy Szy Sz+7 o?? Szy Szy $9? oSS oog S6 o9 OO2 o/z oo: Szº oS9, oq9. #: oop oo:y Szp Sz? Szy Szº og+ oS47 oS47 o/? oSS oog S47 oSI S62 SAz Sz9. oS9. og? oo::/ oo? oop Szy Sz? Szy Szy S$4. oS47 oSp o/7 oSS oog So I O ZZ 992 SI 3 S99 $49, oo:7 oo? SI+7 Sz+ Sz+ Szy o947 off, oS+ 59; o/y oSS oog oS 59 $z I o92 oo: oo: S99 S/9. ooy oo? SI+7 Szy Sz+ Szy S$4. oSp S/? 5/47 S/47 oSS oog S£I oSz oo: SI 3 oS9, S49. oof, oo::/ oit, ozy SIf Szy S$4. oS+ ogy S47 ogy oSS 599 ośg 599 oSS 549 539 oz I oo: oo: oo: or £ oS9. $98. o69. oo? oop oof, oop oo? oo? ooy . Og O II O8 oS S£I OO2 oSz o61 o22 oo: : O §: $49, oo::/ oof, Sz? Szp oS+/ o6 OZ I S9 I OI 2 o82 SI 2 oS9, S49. $49. ooy oo? ooy SI+7 Szy 994, ogy ogy S47 o6 Sz I o/1 OI 2 542 ogz o/z o62 S$9. : o9 SA9. oop § 147 Szy Szp o97 S/? : O . oSS $41 oS I Szz Ozz S472 oo: o6z oSz O32 of £ oS9 o99. $48 ogg og; oš8 $39 $89 oof oo; SI+ $15 Szy Szy oSf opy ogy o94 94% ogy ogy $47 oo:5 oos oSS logs ogz o/z ogz SSz ogz oo:: Sz9. oo:9. $42 oo: oz8. $19. ogz $42 or 9. oS9, o29. S 99. oo: $82 oz8. oS9, og? Sop SI+. Sz? oSf oS+” ogy ogy oo:S SAS ool S8% oz8. ogz o62 of £ S89, oS9, og? oS9. oo:: oo: of £ oq9. #: SI+. Szy S2+ oS47 oS47 o94 5/47 or 5 oog ool. SI+7 oo: o92 $19. S479 : 58 549. oS9, SI 2 S82 Sz9. S/9 o69. oS47 oS47 oS p S£4. S947 oS47 o67 SzS S 19 SI/ S$9. oo: OI 2. ogz or 9. $49. S/2 S/9. oS9. Sz9. oo: S$9. o69. S++ o947 ozy or p opp S/47 SzS oq9. #: 59. # So I §: oSI Soz o92 Sz8. oo: .# $49. oS9, Szº oq8. §: oo? o/* SIS og5 ozg o/9 oo/, oz/ ool oo/ o94 Sz—#2 #z–82 £z—zz || ZZ - I Z IZ - O Z oz–61 61–81 31–41 ; : I – S I #I; #1 — 21 9. I — z1 ZI — II II - O I or —6 –4 –9 —S —W —9. - 2 - I H OZ 61 81 41 9I SI # I 9. I ZI II 9 S |. *10100S Jo Joqun N. ‘oloiſ O Jo Joquin'N “opyS II, noS "HOWNOIN ogs | or SI $922 S6++ SSSS 5919 Sz/9 oS9/. S66/ $418 |5818 o608 SIz8 |S698 S+96 Sogó loo/6 $896 Sz$6 |ooš6 $966 oSzII ogSz1 $9681 OOI oSz So? oS9. S$9. oS9, oS8. $8% SI+7 SI+7 oof, olt, Szp Szy oS+/ S/? SzS 519 O8 SAz ogz SAz o62 oo:: $99 So? SA9. og? ogº oofy Szy Szy Szy oSt. 58? SzS Szg o61 OI 2 $99 o/9 S$9. Szg oS9, : O §: S/9. oo!, oof, oop oof, or p SI+ oziz ogy oo:S oSS Szg op oo: oq9. §: oo? $82 ; 59 $49. S/2 oS9, $8% opy opy olt, oo? oop oo? Szp oof, º: oSS oS9 O8 o62 oS9. $82 oo? oo? So? #: oo? oo? og? S/2 SI+7 oS-7 594, Szp Szy Szp Szy ogy or 5 og5 oS9 o/ o/z ogz S$9. S8% SI+7 ozy ogº S42 ogº oo? oo? S49. 98% $94, SS47 ogy ogy $94, o947 S/47 or S. SAS O99 S91 o4z SAz o49. or p Sop SI+. S49. S/9 oop oo? oo? S/9. ooy S$4. oo:5 or 5 or S. S/? OS+7 S/47 SzS S/S $49 O9I SIz of z oS9, S/? S49. ooy ooy oop or 7 SI+7 oop oof, oo:7 oS47 SzS oSS S$9. or S. S/? $8? SzS o69 549 Sz I 581 581 oz8 S69. $89. oof, oo? Szp Szy Szy oo? SI+ or p oS47 SzS S95 op's or 5 S/? $84. $99 519 589 op o? I OO2 SAz oz8. oof, og? or 7 S$4. oS47 o?? SI+. SI+. SI+. oSp SIS SzS S$S SIS $8? oo:S oSS Szg oo/ $9. I Szz oSz oo: og? oof, ozy oS47 oS47 S 24, or p SI? oS+7 58? SzS o99 SzS SIS 58? oo:S og5 oS9 or 4 S4 I OOZ OC) º º: oop ozy S/47 ogy S$4. or p Szy oof, §: SAS og5 SzS oo:5 oo:S oo:5 #. S. #} Sz S9. I SAI oSz SI 3 S£9. oo? 5/47 ogy S$47 Szp S$47 ogy SzS $89 o/5 or 5 o6? oo!, oo:S oog S/ 9 o89 Sz/ OOI O I Z S472 SAz 582 oit, S/? S/? OS+7 o/? S/? S/? SzS o/S SzS ogy S/47 $8% or S. Szg 589 S$/ O'z I OI 2 59z o6z SI9. S++ S/47 S/7 oSp oS+” oS+7 ogy or 5 SAS oSS oo:5 oo:S oo: of S 519 Sz/ of I 581 oSz Soz ;: ozy ogy oSF oSp ogy S47 oo:S oSS opS oo:5 ogy S/? $8? SIS Szg o69 S2A OOI og I OOZ Ozz oS8. oo? S8% olt, 59; S$4. ogy oo:S ogs oo:S oS+” oS47 S/47 $8? #. Z § oS / o/ of I o91 OOZ oo:: oz8. S/9. oz? oz? SI+. oS47 oS+7 $84. oS47 $94, oS+/ S/47 S/7 SIS Sz §§ oS / OI OOI SAI Szz Szz oSz o82 $99 # 58 Szºp Szy SI+7 Szp oS47 S/? $8? $8? oo:S SzS oog oo/, 594 58 of I OOZ Szz o/z SAz SI? o/8 ogg S$9. S/9. S/2 oof, oSp S/47 oo:S oSS oog ; 9 $49 S$/ 584 Sz—#z #2–22 Cz—zz 22 – I Z. IZ - O2, oz–61 61–81 81 —41 4I-91 91–91 SI —y I +1 –2 I £1–21 2 I - II II - O I or —6 6 —8 –4 –9 —5 —y –8 - Z. - I O'z, 61 8I ZI 9I SI # I 2I 2I I I OI 6 | |. ‘io,00S Jo Joqun N. *oto.110 Jo Joquin N ‘opſ S II].ION "HOWNOIN DETERMINATION OF LOCAL ATTRACTION. 651 On account of the abruptness of the ground in the vicinity of the Station, it is necessary to calculate the corrections (a), page 627, to the quantities H. : they are found to be— For the North side . For the South side . H, - H', - H, - H', = H, -> H', = So that the deflection is— 37o Io90 I225 3O, 4O2 50, 60, 50, 35, 25, 20, 15 45, 9o, IOO, 7.5, 55, 45, 35, 30, 25 These being applied with the positive sign to the quantities H, we get— H, tºmº H', = H. — H'. = H6 º- TI's = 48o I7o 435 IC — K’ = 15555 H, - H', Hs — H's H, - H', o”-oooz3574 × 8or + o”.ooool 817 × 15555 = o”.471 North. Hungry Hill. º: -* 73o Io85 I32O For the more accurate determination of the disturbance at this Station, the ground enclosed by a circle of a mile radius around it has been contoured at vertical intervals of Ioo feet. Beyond the distance of one mile, the mean heights have been obtained from the altitudes found on the 6-inch maps. 4 N 2 652 PRINCIPAL TRIANGULATION. HUNGRY HELL. North Side. : Number of Sector. Number * of H Circle. | 1 2 3 4. 5 6 7 8 9 to II 12 || 13 || 14 15 16 || 17 | 18 19 20 1 — 2 | 195o 2020 2060 |2120 |2 Izo 2150 |216o |216o |216o 21.70 || 218o 2190 2200 |2200 |2200 |22 Iol 2210 |2220 |22zo 217o 43,070 2–3 || 178o 1930 |2000 |2050 |2 too |2 roo 2120 |2120 |2130|2150 |2150 |216o 2150 |2150 |2120 |2070 |2050 |2050 |2050 |1950 |41380 3– 4 || 1790 1840 1910 1950 1970 | 1970 | 1980 |2200 |2250 |2120 |2130|2140|2130 |2120 |21oo |1950 | 1860 1760 1730 1730|39.62o – ;| 1580 | 1690 1790 1850 | 1850 | 1850 | 1840 1850 1890 1950 | 1990 |226o ||2250 |2200 1900 1750 | 16to 1500 1450 | 1560 |35950 § – 6||1360 | 16oo 1730 1750 1750 17oo 16io | 16to 1650 17oo 1750 1800 1820 | 1820 17oo 15oo 1250 | 1zoo 121o 1350 |3|1860 6– 7 || 1zoo 1510 | 1690 1650 155o 1450 1410 || 14oo 1410 1490 155o 16oo 162o 162o 151o 135o 1130 1120 | 1130 | 1230|2862o 7– 8 || 1200 | 1.5oo 1490 1420 1350 | 128o Izoo | f 150 Izoo 1250 | 13 Io 14oo 1520 I520 || 1450 14oo 1320|| 115o 1150 | 1150 26410 8– 9 1390 1390 1290 Izoo IIool IIIo 95o 9ool 91o Iozo II 30 126o I45o I5oo | I520 I55o I45o 13oo | Izoo | Iooo 24530 9–16 || 1180 | 1220 IIool 970 860 760 | 690 690 74o 820 98o 12o.o. 14oo 155o 1640 162o 1540 || 14oo | Io90 8oo 2225o 10–11 1170 | 11oo 90o 77o 7oo 530 || 4oo 4oo 5oo | 660 90o 1150 || 14oo 162o 1730 1730 | 1610 || 14oo 95o 3oo || 19926 11–12 || 1300 || 1 17o 96o 8oo 65o 5oo 38o 38o || 45o 650 95o Izoo 16co 1650 175o 1750 1630 || 135o IIoo 650 |20870 | 12–13 1350 1350 II 30 90o 630 || 7oo 7oo 5oo 4oo 55o 9oo II5o 155o 162o 17oo 17oo 16oo I35o Izoo 7oo |2168o 13–14 135o I 15o 9oo 700 7oo 7oo 45o 200 15o 15o 5Io 86o Ioso | IIoo II.5o 15oo I5oo Izoo | I Ioo 6oo 17020 14–15 14oo IIoo 93o 96o 960 | Iooo | Iooo | Iooo 8oo 55o 35o 3oo 5oo 8oo | 1200 155o 14oo 13oo 9oo | 200 1820o 15–16 16oo 990 IoGo | Izoo 14oo 15oo I5oo 16oo I5oo Iooo 6oo 35o 5oo 6oo 95o 1330 | II5o 8oo 8oo 48o |zog Io 16–17 | 1370 Ioso | 1530 1850 1900 | Iooo | Iooo 16oo 190o Iooo 4oo 3oo 7o Ioo 630 | IIIo 900 || 485 | 8oo 650 | 1964.5 17–18 1750 | 95o 16oo 1920 125o Iooo 420 5oo 5oo 4oo 35o 390 5o | Ioo 62o I 190| 960 5oo 7oo 35o 15410 18–19 15oo 5oo 1420 | 1240 17oo 1715 15oo Io5o 390 25o 33o 36o 25 | 16o 78o II5o Izoo 8oo 3oo 17o 16450 19–26 98o 5oo 1180 90o 990 | 1240 || 14oo 15oo 88o 6oo | I to 95 7o 360 775 Izoo 16oo | Io90 470 330 | 16180 26–21 | 850 490 || 330 | 130 16o 4ool 750 || 65o 45o 3oo | Too Ioo I5o 93o 94o | I 3ro | 1840 || 1450 | 1300|| 490 | 1312o 21–22 62o I2O 8o 45 zo 24o | Ioo 6o 3o 20 9o 14o 200 || 4oo 920 | 76o 1690 | IoSo || 930 || 7545 22–23 28o 220 II5 75 – 70 – 6o 3o 5o | Ioo 3oo 52O 58o | 720 || 34o | IIoo 15oo 15oo 15oo I roo Ioogo 23–24 I4o – 130 – 120 –120 – 130 |—120 – 100 – 70 8o | 200 | 18o 3oo 77o 975 Io:35 | 16oo 17oo Iooo | 8oo 878o 24–25 | 40 – 150 |–140 - 120 30 — 80 — 70 8o 330 || 700 88o 14oo 1270 1040 670 450 | 6890 IIUNGRY HILL. South Side. Number of Sector. Number of H Circle. | 1 2 . , 3 4. 5 6 7 8 9 Io II | 12 || 13 || 14 | 15 16 || 17 | 18 19 20 1 – 2 1960 |2020 |2060 |2190 2140|216o 2180 |218o 2180 |218o 215o 2120 |21 to 21oo 2070 |2040 2040 |2040 |2040 |21oo 41970 2–3 || 1740 1860 1960 |2080 |212o 214o 2180 |2180 |215o 21.5o 2140|212o. 2 Ioo 1970 | 1990 181o 17oo | 1610 | 1610 1750 39270 3– 4 155o 1790 1920 |2050 |2120 |216o 2160 2186|218o 2150 |2160 |2|Iool 2 Ioo 2050 | 1980 | 191o 1730 | 1550 | 1300 || 14oo |38540 4— 5 || 14oo 16oo 1800 1960 1960 190o 1860 1850 | 1850 1850 | 1860 | 188 o' 1940 1950 1930 1780 | 158o 1350 | 1670 || 1 iSo 3455o 5– 6|12o.o. 1350 | 16oo 17oo 1650 | 1690 16oo 16oo 16oo 16oo 16oo | 161o 168o 1760 1760 1660 1410 | 1150 Iooo 12oo 3O330 6– 7 || 95o IIIo 1430 135o 13oo 128o 1290 13oo 128o 1250 | 1300||14ſo I44o 1590 | 1.5oo 1450 | 1220 | Ioso | Ioso | Izoo 25660 7– 8 || 8oo 98o 1290 1960 | Iooo 990 Iooo | 1940 1930 98o | Iooo | IoSo 1190 | 128o 1330 1330 | 12oo Ioro 9oo 112o 21520 8– 9 || 650 9oo 98o 870 78o 8oo 820 | 84o 830 | 830 790 790 9oo | I too | I réo 1180 || 1 150 950 | 71o 9oo I793o 9–1o 520 750 8oo | 68o 64o 65o 670 | 660 | 660 65o 6oo 62o | 720 | 8oo 9oo | Ioso | IIzo 920 | 62o 65o 1468o 10–11 || 520 57o 56o 44o 420 46o 460 48o 48o 470 46o 45o 47o 58o | 730 | 85o 990 920 650 320 TrzSo II — I2 | 75o 360 || 4oo 35o 31o 31o 33o 33o 3oo 3oo 3oo 3oo 3ro || 38o 5oo 62o 75o 820 | 720 320 | 8760 12–13 | Ioso | 3oo 300 26o 200 | 200 zio zio | 200 zoo 200 | 200 | 200 200 25o 3ro 530 650 | 720 320 | 67 Io 13–14 Iojo 420 || 300 18o 15o 150 150 150 | 130 12o Ioo too 12o. 150 | 180 180 200 300|| $50 35o 5610 14–15 950 | 68o 320 299|| 139| 120 Izo roo roo | I5o | I5o 15o 25o 35o 3770 15–16 720 7oo 250 | 139| 75|| 50 8o | Ioo 2O || 5o IIo I45 24.30 | 16–17 | 78o 370 | I5o 35 - 6o |— 70 ||— 80 – 90 – 60 70 I.445 17–18 1220 | 270 | IIo Io 6o 7o 6o — 6o |– 6o – Ioo – 70 — 7o 20 | 1820 18–19 Iooo 200 || 25 2O 2O 45 8o 30|-12o -120 – 140 – 130 - 140 – 140 –120 – 80 – 90 3o I450 19–20 | 54o | I2O 7o 4oo Ioo 3o – 90 - 190 - 140 -150 – 150 -150 -150 |–140 –140 – 140 –100 40 | 1300 2O – 2 I 48o 6o 90 4oo 3oo 7o 8o – 8o – 150 |—160 — 160 — 160 — 160 - I5o -150 – 140 - 130 – 14o |— Izo 3o I5 Io 2 I —22 || 3oo 250 || 650 75 - 80 - 90 - 150 - 180 - 170 – 170 — 160 |–16o |—150 – 150 |–14o |–14o |–150 |–150 20 1295 22–23 35o 30 3oo | Ioo |–1oo -150 – 180 - 180 – 180 – 170 — 12o |— Ioo 4o 6o | Ioo 5o -140 4o 1070 23–24 || 58o 200 —160 |–180 –190|-190 -180 – 180 – 90 | 1.5o 5oo 850 | 750 || 35o 7oo 65o 450 220 54oo 24–25 || 700 250 –100 – 180 – 180 -180 -190 –190 26o 3oo 200 | Ioo | Ioo 4o 8o 240 | 200 || 415 ass :i3|: * DETERMINATION OF LOCAL ATTRACTION. 653 A. On account of the steepness of the ground on all sides of the Station, it is necessary to calculate the corrections (a), page 627; they are found to be— For the North side . . . . . Io, 35, 8o, I75, 360, 5 Io, 560, 560, 635 For the South side . . . . . 55, 140, IoS, 270, 510, 840, 1130, 1345, 1510 After correcting the quantities H. H’ in the table by these quantities applied with the positive sign, we get— - H, - H', - 1055 H, - H', = 1305 H, - H', = 4320 H, - H', = 2005 H; — H'. = 1380 Hs — H's = 5815 H, - H', a 455 H6 — H's = 2630 H, - H', = 6695 R = 232650. - IC’ = 56,135 D = 148o D’ = 10500 The deflection resulting from these quantities is— o-ooo.23574 × 2.272 + o-ooool 817 × 17651.5 + o-ooool 156 × 9ozo which amounts to 3". 847. - - In Plate XXIV., H is the Station on Hungry Hill, adenmr is the circle of 9.5 miles radius within which the attraction has just been determined. With a radius of 28 miles describe the circular arc bopſ, and with a radius of 50 miles the circular arc usy. Draw the following lines: (I), alg making an angle of Io with the meridian, and mp in the same straight line with abg; (2), vu and ay making angles of 35° with the north and south meridians; (3), nqs making an angle of 60° with the meridian, and cd in the same straight line with nqs; (4), hr making an angle of 60° with the south meridian ; (5), ef making an angle of 65° with the north meridian. The mean height of the space abcd is found to be 600 feet, but as the greater height is in the centre of the space, and the ground is low within a mile and a half of the inner limit ad, we shall adopt 450 feet as the effective mean height. The space bguv, consisting of land and water, may be con- sidered to produce no sensible effect. The mean height of the space algeſis to be taken at 4oo feet. The spaces fenqs, nqmp, and cdrh may be neglected as producing no sensible effect. The depth of water in the space pmrh may be taken at 40 fathoms, and the depth of water in the space sqay at 65 fathoms. The space to the west of the lines uvchay being covered with an even depth of sea, requires no further consideration. The calculation of the disturbance up to 50 miles will therefore be as shown in the following table:— Space. h &" q, r’ r Deflection. | abcd 450 13 303 28 9° 5 o"596 hrmp 24o 24o I90 28 9' 5 o “I 35 * | acſ, 4oo 65 Io 5o 9° 5 o' 574. Øsay 390 2 I 5 I2O 5o 28° o O' 244. making altogether I". 549, which has to be added to the quantity 3.847 previously determined. We have thus, by extending the calculation to a distance of 50 miles, obtained a deflection to the amount of 5". 396 to the north at Hungry Hill. s 654 PRINCIPAL TRLANGULATION. This determination cannot be considered so satisfactory as those for the Stations previously considered, as the want of a sufficient number of altitudes on the maps throws some uncertainty upon a few of the estimated mean heights. But the error of the determination can scarcely amount to a quarter of a second. Forth Mountain. This Station is situated in Sheet 42 of the County of Wexford. In the vicinity of the Station there are very few altitudes marked on the map, and the mean heights cannot be well determined within the 5ooo feet circle; there are, however, sufficient altitudes to show that there is little or no disturbance within this circle. The mean heights of the compartments from the Io" to the 24" circle are as follows:— i : DETERMINATION OF LOCAL ATTRACTION. 655 FORTH. North Side. Number | -- Number of Sector. rºof º - - H Circle. | 1 2 3 4. 5 6 7 8 9 Io. II | 12 || 13 || 14 || 15 16 || 17 18 19 20 T--—— -—-ºm- ‘9-11 || 440 295 28o 26o 25o 220 | 200 220 220 25o 290 || 3ro || 350 | 400 || 530 530 || 510 48o 46o 515 7olo II — I2 370 250 25o 24o 23o 215 205 205 || 2 Io 220 || 23o 25o 33o 360 420 5oo 499 || 480 45o 51o 6415 | **-13| 320 |230 2io 220 2ío 216 21o 195 200 200 || 2 to 2io || 25o 275 35o 4oo 420 440 || 420 44o 5626 | 13-14 3oo 25o || 2 oo 200 Igo 18o 190 2 Io 200 290 2 Io 200 | 190 Igo 24o 320 390 45o 35o 320 4980 4-15 330 26o 21o 18o 190 200 21o 225 225 | 18o 185 290 16o 175 200 225 || 25o 3oo 275 28o 4460 *5-16 || 390 265 175 295 215 290 200 18o I4o Izo 16o 16o 130 Izo 15o 175 200 210 225 270 3890 16–17| 28o 185 | 165 185 | 186 165 115 95 90 | 125 | 120 | 11o 165 85 95 | 165 | 120 14o 216 260 2935 2-18, 200 195 | 165 165 175 14o 145 || 115 120 | 120 | 120 30 30 6o go 4o 30 65 235 235 243; 18–19 24o 226 18o 23o 190 | 200 zoo 160 14o 115 6o 30 7o 18o 18o 150 go | 66 186 233 3075 19–26 265 225 23o 26o 2ro 200 230 165 145 | Io; 3o 155 195 195 175 16o 5o 15 35 | 1.5o 319; *9-21 17o 255 290 305 || 320 25o 2Io 17o 215 75 75 165 215 190 | 135 | 135 | 45 3o 3o 328o *1-22 || 135 || 2 15 3oo 320 275 215 16o 185 | 165 9o 55 90 17o 180 | 160 125 | 75 | 15 35 2965 **-23 18o 225 28o 290 195 || 24o 190 | 130 150 | 16o 45 140 | 190 185 18o 155 | 8o 35 | 15 3065 *3-24 17o 34o 375 265 275 23o 18o 175 9o 8o Ioo 190 195 || 2 Io 18o 195 || 145 || 55 | Io 3465 34–25 i *— FORTH. * South Side. *— N Number of Sector. umber of II Circle, | 1 2 3 4. 5 6 7 8 9 || Io II | 12 13 || 14 || 15 16 || 17 | 18 19 20 ~ | ‘9-11 || 530 | 62o 64o 64o 64o 630 | 6oo 54o 5oo 48o 47o 47o 460 45o 430 || 410 || 390 370 38o 45o | Ioroo §-12 440 || 58o 62o 590 530 5ío 500 || $oo 470 420 || 410 || 420 || 420 410 || 4oo 4oo 38o 35o 360 || 41o 9120 :-3 43o 500 540 545 450 || 430 43o 420 || 4to 380 | 38o 4oo 390 | 405 || 4oo 390 35o 325 | 34o 350 | 8265 3-14 || 390 || 415 || 470 || 486 || 430 4oo 360 360 | 365 360 34o 34o 360 | 370 390 390 35o 320 | 320 | 325 7535 *4-15 315 || 345 370 43o 390 || 370 34o 3oo 306 || 290 28o 290 300 320 | 35o 320 || 300 3oo 310 || 3oo 6530 *5-16 || 306 2% 280 || 3:0 34o 3oo 270 230 || 2:30 24o 24o 24o 24o 25o 27o 24o 26o 2.70 || 28o 290 538o 6-17 3oo 265 26o 255 255 235 220 215 2ío 265 200 195 2io || 230 220 220 | 215 2ío 26o 250 || 4630 $7-18 250 246 230 246 23; 230 190 185 195 || 176 17o 166 18o 165 175 185 18o 175 | 16o 200 39.5 $8-19|230 220 235 215 195 195 15o 15o 16o 135 | 120 | 120 | 1zo 13o 135 | 130 12o I2O 75 | 155 3959 ||9-26, 175 150 175 | 196 | 18; 145 | go 95 || 95 | 86 95 || 100 | 90 55 106 || 95 || 7o 90 35 | 79 **59 *9-21 176 14o 125 135 | 156 165 7o 55 | 36|| 6o 76 75 Šo 75 8o 76 65 60 65 4o ... **-22 | 150 | 130 | 120 | 125 115 8; $o 35 | 45 5o 35 | 5o 45 55 6o 75 55 45 || 35 1300 :* -23 135 | 120 95 || 36|| 95 || 56 35 | is #5 20 | #| go 63 | 73 || 70 || 65|| 5 || 4 || 5 #: ; : I [O I 30 IOO 85 35 I5 2O I5 IO 5 55 55 55 55 55 7o 8o 65 35 IO IOOC ~25 tº T- 656 PRINCIPAL TRIANGULATION. From this table we obtain— K = 56790 IG' = 66045 giving a deflection of – o”. Ooool 817 × 9255 = — o”. 168. In Plate XXIV. abod is the 9.5 mile circle. Draw aek, dhl, making angles of 60° with the meridian ; ºf eg, making angles of 40° with the meridian ; and describe the circular arcs epf, Jimg with a radius of 24 miles. Draw also pſ, and mn, making angles of 28° with the meridian, and describe the circular arcs kq, lm with a radius of 50 miles. We may neglect the consideration of all matters to the east of the lines nmge, liſpº, and of all to the west of ak, d!. The effective mean height of the space ealſ is found to be 26o feet. The depth of sea in the corresponding space delig varies from Io to 35 fathoms; the effective mean depth may be taken at 20 fathoms. The effective mean height of the space ekpº is 5Io feet, and the effective mean depth of sea in the corresponding space hlmm is 37 fathoms. Hence the following calculation, in which to the mean heights of the northern spaces have been added ºr of the mean depths of the corresponding southern spaces:— Spaces. h a' o, r" | r, Deflection. calf, cdhg . . 335 4o 63 24 || 9 5 6'552 ekpq, himn . . 65o 28 6o 5o 24°o o' 751 The sum of these quantities is I”. 303. This being applied to the quantity resulting from the conformation of the ground within the 9.5 mile circle, namely, — o”. 168, there results 1”. 135 for the deflection to the north at Forth Mountain. To this should be added the effect within the 5000 feet circle, but this cannot be stated with any precision. It would appear, however, that it is a very small quantity, if at all appreciable. t Feaghmaan. " This Station is in the Island of Valencia, Sheet 78, County of Kerry. As in the preceding case, the data for the calculation are insufficient to determine with accuracy the deflection due to the ground within the 5ooo feet circle. But it is obvious that there is a considerable deflec- tion south, and by interpolating between the given altitudes the quantity — o”. 91 was obtained. The mean heights of the compartments from the Io" to the 25" circles are as follows:— f : DETERMINATION OF LOCAL ATTRACTION. 657 i. FEAGHMAAN. North Side. *— Number Number of Sector. m-º-º-mº. Of C; H. * | 1 || 2 || 3 4. 5 6 || 7 8 || 9 || Io II | 12 13 14 15 16 || 17 | 18 19 20 T---' Io- II - 145 - 145 - 145 – 145 – 90 - 90 – 90 – 90 – 90 – 90 – 90 - 90 – 90 - 90 - 90 – 90 – 90 2O | I IO I3o II - 12 155 I55 I55 I 55 I55 I55 I55 I55 I55 I 55 I IC I IO I IO I [O I [O I IO I IO I5 2 O 35 *~13 180 180 180 180 15o 15o 15o 15o 15o 15o | Izo 12o 12o 12o I2O I2O I2O 40 40 *3-14 180 180 18o 180 | 180 18o I2O ! I2O I 2G I2O | 130 I 30 13o 13o I 30 I3o 13o 3o 4o 7o *4-15 190 190 190 190 | 190 | 190 190 | 190 190 190 | 130 130 | 130 | 130 I 30 13o I 30 90 | 20 ! I Io *5-16 || 21o 210 210 21ol 210 21o 21ol 210 150 I5o | I 5 o I5o I5 o 150 90 90 90 - 9o I5 IO 25 16–17 2 IO 2 Io 2 IO 2 IO 2 IO || 2 10 2 Io 2 IO 2 IO 2 IO I55 I55 I55 155 + I2O + 2 oo + I2 o 5 445 17-18 215 215 215 215 215 215 215 215 18o 18o 18o 180 | 18o 18o 45o 55o |-|- Ioo 5 IIoS 18–19 240 240 240 24o 21o 21o 21o 21o 21o 21o 21o 21o 15o 150 - 150 40 38o I5o 25 I5 61o *9-20 240 240 240 24o 24o 24o 240 24o 24o 240 21o 21o 21o 21o I2O - I2O I3o I55 5o 4o 375 *o-21 27o 270 270 27o 27o 270 270 270 21o 21o 21o 21o 21o 120 I2O I2O IO 12o 25o Ioo 48o **-22 || 270 270 270 27o 27o 270 27o 270 21o 21o 21o 21o 21o 120 I2O I2O 2 OO 460 545 5oo 1705 **~23 2 Io 21o 190 18o I5o I 30 5o 43o 345 255 Io8o *3–24 2 Io 2 Io 190 15o I5o 130 – 120 195 64o 14o 975 *4-25 2 Io 21o 18o 15o I5o I 30 120 540 |I2O5 275 2020 FEAGHMAAN. South Side. § *umber It Number of Sector. of Circle, 6 8 6 8 H I 2 3 4. 5 7 9 IO I I I2 I3 I4. I5 I 17 I I9 20 I - - º *I 30 17o 35o 45o 35o 25o 200 200 zoo 200 18o 15o I5o I 30 I 30 I4o 190 27o 35o 45o 4540 I. : 30 17o 3oo 350 250 200 150 150 15o 140 | 130 Iool 90 99 roo 130 180 250 350 450 |3760 i.T.3 30 17o 3oo 3oo 2 Io 20o 15o Ioo Ioo go go 9o 6o 6o 75 IIo IIo IIo zoo 5oo 3055 ; : 20 | 130 200 zoo 2 Io 200 I2O Ioo 6o 5o 5o 4o 25 I5 IO IO I5 7o I2O 35o 1995 #Tºš 20 Ioo | I5o 200 25o 17o I2O | 5o 5o Io 5o I5o I320 ~ I * I6 Ioo 14o 25o 200 IIo 4o Io Io I5 4o 91.5 i; ; 1oo 14o 15o Ioo | Io Io Io 15 3o 9o 150 | 1.5o 6o 50 | 8o 6o 5 5 I2 I5 išº -180 | 1.5o 12o Io | Io 15 8o ſo | Ioo 15o 3oo 35o 200 I40 I4o 140 7o 30 5o | Io 2145 iglº -215 35o Ioo Io | Ioo 16o 16o 16o 18o 25o 650 6oo 7oo 5oo 6oo 45o 12o 7o 6o 3o 5250 :: * –25o roo Ioo — 150 |–12o 15o 25o 25o 4oo 75o 950 | 9oo 1050 rooo 7oo 65o 250 | 120 | 8o | I5 7715 2.T. -270 -240 - 180 – 180 – 150 – 12o 4oo 7oo 5oo 45o 4oo 35o 35o 5oo 25o 200 || 200 35o 8o 9o 4820 3. *-270 –270 –240 –210 –zio –180 i50 3oo 20|| 360 | 660 | 200 1zo 120 | 120 | 3oo 15o 20o 258o 23. 5o 55o 6oo 3oo I5o 5o 50 | 1.5o 90 450 2495 2: ... Izo 7oo 200 90 I5 5 5 30 Ioo 6oo 1865 25 6oo 350 –100 –160 – 86 || – 76 — so 30 80 450 | 15 ro Yº-l 4 O 658 * PRINCIPAL TRIANGULATION. From this table K = 9205, K' = 45180, D = 37.360, D' = 3835, which gives a deflection equal to — o”.oOool 817 x 3598o – 'ooool 156 x 33530, or – 1".o42. It is unnecessary to extend the calculation further, as the deflection becomes perpendicular to the meridian. Tawnaghmore. This Station will be found in Sheet 5 of the county of Mayo, at a distance of about two miles from the sea. The number of levelled heights marked on the map is not sufficient to enable us to calculate with any exactness the deflection close to the Station, but from the heights that are given it would appear that the disturbance due to the distribution of matter in the immediate vicinity of the Station, though decidedly to the north, cannot be large. We shall therefore neglect the consideration of the matter contained between two parallel lines equidistant from the Station, running east and west, and of which that to the north is a tangent to the coast. The table then will be as follows, the depths being taken from the Admiralty Charts:– W !- t *! DETERMINATION OF LOCAL ATTRACTION. - 659 TAWNAGHMORE. North Side. Number of Sector. Number of - H - Circle. | 1 2 3 4. 5 6 7 8 9 Io II | 12 || 13 || 14 | 15 16 || 17 | 18 19 20 I5–16 – 90 – 11o – 120 – 120 – 120 – 120 – 1 oo - 9o * 87o 16–17 - — Izo | 120 | 1.5o 15o 15o 15o 15o | I5o Izo [-12o -12o 15oo I7 - 18 - I2O i*- I2O 130 I5o I5 o 180 18o 18o 18o 17o 16o I 5o 130 – 120 - 120 2240 18–19 - I2O I3o 130 | 1.5o 16o 16o 185 185 185 185 17o 16o 16o I45 I30 | 125 2480 I9-20 —120 130 145 | 1.5o 16o 175 18o 20o 20o zoo 200 | 180 18o 18o 15o 145 || 130 -120 2.945 2O-2 I * I 3o I45 I55 16o 175 18o 180 21o 210 | 21o 21o 190 18o 18o 16o 150 140 | 125 — 120 | 3210 2 I - 22 150 | 155 17o 175 180 | 18o 190 220 220 220 230 210 190 190 18o 155 || 145 130 I40 || 3430 22–23 18o 17o 18o 190 2 IO 2 IO 2 IO 23o 23o 23o 235 22 O 205 190 18o 17o I5o I4o 145 || 3675 23-24 190 18o 21o 21o 23o 21o 23o 245 24o 24o 24o 23o 21o 190 18o 17o 155 145 || 145 3850 24-25 21o 21o 24o 240 245 25o 26o 26o 26o 26o 24o 240 21o 190 18o 17o 16o 15o 145 || 4120 *— TAWNAGHMORE. * - 1 * ... " - South Side. Number of Sector. Number - of - - | H Circle. | 1 2 3 4. 5 | 6 7 8 9 | Io II | 12 || 13 14 | 15 16 || 17 | 18 19 20 | º I5— 16 Ioo 220 | 200 | 200 | 200 200 18o | I 5o I45o 16–17 18o 25o 18o 18o 18o 160 | 180 | 200 200 | 200 | 180 16o 225o I7— 18 30 Ioo 16o zoo 16o 140 180 140 150 | 1.5o i zoo 35o 490 6oo 48o I5o 3680 18–19 Ioo 7o I5o I70 130 130 150 | 15o 250 28o 300 6oo 8oo | Iooo 6oo 7oo 558o 19–20 7o 9o 55 7o Ioo 12o 14o 18o 250 4oo 5oo 4oo 5oo 5oo 7oo 7oo 9oo 560 6235 2O-2 I 1oo 8o 5o Ioo IIo 16o 16o 3oo 500 650 58o 470 45o 5oo 7oo 7oo 7oo 85o 716o 2 I-22 6o 6o | I to 150 4oo 4oo 4oo 4oo 6oo 65o 6oo 5oo 45o 45o 4oo 46o 55o 85o 200 7690 22–23 75 15o 3oo 4oo 9oo 9oo 8oo 5oo 6oo 520 5oo 5oo 4oo 38o 38o 55o 65o 7oo 250 94.55 *3–24 5o 96 || 14o 230 7oo 8oo 16oo 95o 75o 5oo 4oo 450 360 35o 35o 370 650 | Goo 6oo 350 9690 34-25 | 28o 25o 7o 8o 27o 35o 5oo 64o 560 38o 320 33o 33o 330 370 440 || 48o 65o 430 250 | 73° º | | 4 O 2 66o & PRINCIPAL TRIANGULATION. K = o K = 60500 D = 28320 We have, therefore, the deflection due to the matter with a circle of nine miles and a half, equal to— - ‘oooo.1817 × 60500 — ‘oooo. 156 × 28320 = - 1".426 At the distance of about seven miles from land, proceeding northwards, the depth of the sea is pretty evenly 40 fathoms; it increases gradually and evenly, and at 60 miles it is between 6o and 70 fathoms: the effective mean depth may be taken at 50 fathoms. On the north side of the Station, extend the series of circles already drawn, by eleven more, and produce the radii: then, neglecting all matter to the left of the meridian of Io’ West Longitude (which passes through the north-west corner of Mayo), we find that 160 compartments are covered with a mean depth of 50 fathoms of sea; thus the effect of the sea to the north is to produce a deflection of — o”. OoooII 56 x 160 x 300 = o”. 555. On the south side (Plate XXIV.) draw with a radius of 27 miles the circular arc deſg, and with a radius of 50 miles the circular arc hk: cgk is inclined at 80° to the meridian; iſ at 32°; eh at 27’’; and ad at 36°. The effective mean height of the space abdfis 38o feet, of the space beſg 130 feet, and of the space eligk the effective mean height is 270 feet. Spaces. h a' cº, r’ 7, Deflection. abdf | 38o 21é 148 27 9° 5 o°193 bef, 130 || 148 IOO 27 9° 5 o'oz7 eligk 270 207 IOO 5o 27°o o' Ioa. The sum of these quantities is o'. 324, which added to o”. 555 and I". 426, give 2". 305. for the deflection, to the south, at Tawnaghmore. To this should be added the disturbance due to the configuration of the ground within two miles of the Station. This would diminish the above quantity, but by how much cannot be precisely stated. JBen Hutig. This Station is within a mile and a half or two miles of the sea on the north coast of Suther- landshire. In a south-by-west direction from the hill, runs a ridge of high ground called the Moin. To the west this ground slopes down gradually to Loch Hope, a long and narrow fresh- water lake lying parallel to the ridge, and on the east the ground falls gradually to the Kyle of Tongue, an inlet of the sea, which also lies parallel to the same direction. This ridge extends southwards about ten miles, where its regularity of form is interrupted by the abrupt masses of Ben Hope and Ben Loyal, of which the former exceeds 3000 feet in height. The width of the Moin is about five miles and three quarters; the breadth or base of the eastern slope may be taken at three miles, that of the western at two miles, leaving along the summit a horizontal plane of about three quarters of a mile in width, the height of which is very uniform, and 750 feet above the sea. The regular form of this piece of ground enables us easily to estimate its | DETERMINATION OF LOCAL ATTRACTION. 66I effect upon the plumb-line at Ben Hutig; but it is impossible at present to extend the calcula- tion any further on the south side of the Station. In the immediate vicinity of the Station there is not much irregularity, and within the 5000 feet circle the deflection must be very small: from an examination of the ground, unaided by instruments, it is difficult to say whether it would be to the north or to the South. If a straight line be drawn east and west, at the distance of a mile and a half south from the Station, it may be assumed that the deflection due to the con- figuration of the ground to the north of this line is very nearly zero. By sketching in upon a map the contours of the ridge of ground described above, and drawing a series of circles such that 5 ra. , = 6 r, ,-the radial lines being as in all the preceding cases, we find the following mean heights:— Number of Sector. Number of Circle. 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || Io II | 12 13 || 14 15 16 || 17 | 18 19 2O | 360 5oo 7 Io 700 700 670 650 62o 5oo 270 I – 2 2– 3 3oo 75o 75o 75o 71o 7oo 670 || 65o 61o 58o 55o 530 5oo 220 3- 4 420 | 720 75o 75o 75o 720 7oo 65o 62o 58o 55o 5oo |450 |4oo 35o 150 4- 5 15o 510 | 68o 750 |75o 750 | 720 7oo 65o 6oo 550 |490 |450 38o |320|| 25o 200 | Ioo 5— 6 I5o 38o 6oo 720 |75o 75o 720 690 6oo 55o 5oo 45o 35o 28o 220 150 6— 7 5o 200 45o 630 | 73o 750 720 690 6oo 520 |450 |35o 2 Io I5o roo 7— 8 50 |250 5oo 65o 75o 730 690 6oo 5oo 4oo 2 Io Ioo 8– 9 26o 51o 7oo 75o 710 6oo 460 3oo | 120 9–Io 35o 660 75o 720 6oo 420 200 IO - II 3oo 720 8oo 74o 62o 41o 150 The sum of the heights in this table is 63750, and the corresponding deflection is therefore o"-oooz714 × 6375o × log.: = 1"-37o to the south. - We must next consider the effect of the sea to the north of the Station. The depth of the sea is, at the distance of three quarters of a mile from shore, about 20 fathoms; the line of 30 fathoms depth runs between three and four miles distant from shore. At ten miles north from the Station the depth ranges between 30 and 40 fathoms; and at the same distance north-east the depth is about 45 fathoms. Twenty miles north is the Whiten-head Bank, where the depth is in some parts as small as 25 fathoms. - In Plate XXIV., U is the Station, abed a rectangle having its sides parallel and perpendicular to the meridian : the side ab is 50 miles distant from U, and cd is 5 miles; the lengths of these sides are 36 miles, U being opposite to the middle point of cd. The mean depth of water covered by this rectangle is 35 fathoms. By the formula (3), page 578, we have the attraction of this mass, or rather its defect of attraction— ot 4 = 2 × (1 - 2.75) x 2 Io x log. (#) and the corresponding deflection by (I), page 576– 13:447 × 1.75 × 211 (# q, 5.5 × 528 × 4343 * \cot # 4' cot # 4, > * o".725 logie (### = – 2 X 662 . PRINCIPAL TRIANGULATION." Now the angles b and p' are 15° 30' and 70°, which makes this quantity = – 6".516. A second and smaller rectangle may also be taken into account, covering a mean depth of about 22 fathoms. The outer side of this rectangle coincides with cd; the inner side is parallel to it, and two and a half miles distant from the Station U; thus the meridional dimension of this rectangle is 2.5 miles, and that perpendicular to the meridian is 16 miles. T aking the depth as 130 feet the deflection will be— f / / cot # 4. = — o”.449 logie (#) The angles p and @' are 17° 30' and 32°, which makes this quantity equal to — o'". 121. Adding together the three quantities we have obtained, they amount to 2". ooz ; to this should be added the deflection due to the mass of the county of Sutherland generally; but at present there are not sufficient data. We know, however, that the deflection south must certainly exceed 2". ooz. Cowhythe. It has been shown in the volume of the Ordnance Survey containing the “Observations for Latitude made with Airy's Zenith-Sector” that the deflection observed at Cowhythe is very large, and probably greater than can be accounted for satisfactorily. At present there are no sufficient data for calculating exactly the disturbance, but we may endeavour to ascertain a limit which it cannot be supposed to exceed. . i • *, * - The Station is on a small flat-topped hill, or hillock, the height of which is only 256 feet (by recent levelling) above the sea. To the north, the ground slopes down gradually for 200 yards, and then falls, somewhat abruptly, to the sea, which is within a quarter of a mile from the Station. To the south, east, or west, the ground is flat for about 200 yards round the Station. At about three quarters of a mile south, the ground reaches the level of about 1oo feet above the plane of the sea; the country then rises gradually in a southerly direction, and attains at the visible horizon—about seven miles distant—a height of about 500 feet. In a south-south- west direction the ground does not rise regularly to the visible horizon. At a distance of three miles is a piece of rising ground, in horizontal extent about 15° or 20°, and exceeding Cowhythe in height by something under Ioo feet. In the same direction, and about seven miles distant, the height of the furthest visible ground is about 700 feet; a little to the west of this is Knock Hill, eight miles distant. Although this hill exceeds 14oo feet in height, yet its horizontal extent is so small that it can produce no material effect on the latitude of Cowhythe. In the south-west direction, and between one and two miles from Cowhythe, the ground is from Ioo to 150 feet above the sea; thence it rises gradually, and at the distance of Knock, and imme- diately to the right of it, attains a height of 650 feet. In the south-east direction the ground falls for about three quarters of a mile, then rises, and attains at the distance of a mile and a half a height of 350 or 400 feet; at two and a half or three miles it falls to 150 feet. Alva Hill, about 650 feet high, is six miles distant in this direction. Manor Lee, 770 feet high, is seven miles distant in a south-south-east direction from Cowhythe. DETERMINATION OF LOCAL ATTRACTION. 663 To the north, the line of 20 fathoms depth is about two miles distant from shore, the line of 30 fathoms between three and four miles. Eight miles north or north-east the depth is between 40 and 50 fathoms; this depth continues to the distance of about twenty miles. At a greater distance north or north-west the depths diminish, and are between 20 and 30 fathoms. The effect of the sea to the north of this Station will therefore not be much different from the effect of the sea at Ben Hutig; we may say that probably it will not exceed o”.7. The disturbance produced by the configuration of the ground within a circle of one mile round the Station will be to the south, but cannot exceed o”. 5. - - If we suppose the height of the ground at the distance of one mile from the Station to be Ioo feet, and that it rises regularly in every direction (not to the north) until it attains at the distance of seven miles an altitude of 7oo feet, the deflection calculated on this assumption would exceed the truth, but would not be very far from it. The height h of the country at any distance r would be h = 4; r, and the deflection would be— 5280 iſ ſ”? IOO - //. 2 6”.223 J. iſ. ;:55° 6 d6 dr _ 62”.23 T 528 This quantity probably exceeds the true deflection, that is, what would be obtained from the actual contours of the country between the distances of one and seven miles from the Station. Proceeding in a direct line south from Cowhythe, at the distance often miles the height of the river Deveron is 250 feet above the sea. At Huntly, 17 miles from Cowhythe and a little to the west of south, the height of the same river is 4oo feet, and six miles south of Huntly its height is 500 feet. Thirty miles south, in a direct line from Cowhythe, we come upon the river Don, of which the height is, at that point, 450 feet: following hence the course of the river westward, at five miles its height is 550 feet, at ten miles 750, at fifteen miles its height is Iooo feet. The source of the Don is about forty miles south-west of Cowhythe, and is at the altitude of 1600 feet. The altitude of the Dee, forty miles south of Cowhythe, is about 300 feet; at Castletown of Braemar, fifty miles south-west of Cowhythe, its altitude is over Iooo feet above the level of the sea. In the neighbourhood of Braemar are the highest points of the Grampians, many of them exceeding 4000 feet. ... In general, then, the country rises as we proceed south, but still more in a south-west direction; in the south-east direction there is nothing remarkable in the height of the country: it may not exceed in the mean 400 feet. . In order to make sure of not underrating the probable deflection, let us suppose that between the distances of seven and twenty-five miles from Cowhythe, and between the directions of west and south, the height of the country is 800 feet, and that between the same directions, and between the distances of 25 and 50 miles, the mean height is 2000 feet; the deflection would be—formula (2), page 628– * . . . . . ... *** * * *.*.*, * * * * * * ... . . . . . . ... • -* - F * … --- * * * * * * * * × 2 × 6 = 1”.4 */. 25 //. A o • 38 – //. 2 iſ log; + 5 42 log; = 2 8 664 PRINCIPAL TRLANGULATION. Between the directions of south and east, and between the distances of seven and forty-two miles, suppose the mean height as much as 5oo feet, then we shall have to add to the preceding quantity I-35 log 6 = 1”.o making altogether 3".8. We have also estimated,—for the sea o”.7; for the immediate vicinity up to one mile distance, o”. 5; from one to seven miles, 1". 4; the whole estimate is therefore 6"-4, and this quantity is certainly greater than would be obtained if we had sufficient data; probably it would be found not to exceed 5”.o. Summary. We may sum up the results of this Section in the following table:— º º Distance" to which Stations. Deflection. Calculation is carried. Remarks. Dwnnose . . . – o '54 Twelve miles . Determinations satisfactory. But by extending | Boniface . + 2 °42 33 33 the calculations, each of these deflections would Week Down. . . + 1 '98 33 33 º #. a small + correction due to the mass of Port Valley . + 3 29 tº ſº ngland to the north and the English Channel 33 33 to the south. Clifton . . — o' 9o Eight miles . . . . Determination satisfactory. There are not suffi- cient data for extending the calculations. Burleigh Moor . — 4' 55 Forty-eight miles Determination satisfactory. Calton Hill . – 3'57 Nº and a half | Determination satisfactory. IIlllêS. | Lough Foyle . . – 4:02 || Fifty miles . . . Determination satisfactory. Rellie Law . . + 2 o8 Nine and a half miles | Determination satisfactory. lſomach . . . + o'47 ..... º | | Determination satisfactory. Ben Hwtig t — 2- or | Fifty miles north and | Determination tolerably satisfactory: by extend- ten miles south. ing the calculation the amount would be in- creased. Hungry Hill . + 5° 4o Fifty miles . Determination satisfactory. JForth . tº º + 1 13 33 35 . . . . Determination tolerably satisfactory. Feaghmaam, . . — 1.95 || Nine and a half miles Determination not quite satisfactory. Tawmaghmore – 2:30 | Fifty miles . . Determination not quite satisfactory. Cowlythe . . . '• * * 1 s e s - e. e. Not sufficient data for this calculation, but the deflection may be about — 5"o ; certainly not amounting to — 6"’o. * It is diſficult to know where to stop in these calculations. I have assumed fifty miles as a distance probably sufficient, but in some cases the result would be modified by extending the calculation to a still greater distance. There is, however, some uncertainty as to the propriety of going beyond this, especially when there is sea on the one side and land on the other. The final results in the following Section may, perhaps, throw some light on this question.—A.R.C. ; : ; ; ! :º : i | #.s {# SECTION XII. DETERMINATION OF THE SPHEROID MOST NEARLY REPRESENTING THE SURFACE OF GREAT BRITAIN AND IRELAND. § I. WHEN a number of astronomical observations for latitude have been made at each of a series of Stations, we may deduce the final results by one or the other of two methods: we may either determine the latitude of each Station by means of the observations made at itself, and assumed mean declinations of the stars, without reference to the observations made at the other Stations; or we may obtain differences of latitude which shall be independent of any assumed mean places of the stars, and using these differences, make the absolute latitudes such as will agree best, upon the whole, with the results derived from the former process. Thus, suppose by the former process that we obtain the independent results x, x, x, . . . . A. for the latitudes of the n Stations, and suppose that by the latter we obtain the successive differences of latitude (or amplitudes), a, , o, ø, . . . . 2, , , which are independent of the errors of the assumed mean declinations, and let a, a + cz,, a + cz,, . . . . a + c, -, be the latitudes, then a may be determined by making (a – A, ) + (a + c, - A, ) + (a + c, - A, ) + . . . (a + c, -, - A, ) a minimum. Thus the absolute latitudes will rest upon the whole of the assumed mean declinations, but the differences of latitude will be independent of them altogether. In the first method, if sº, e, e,, . . . . sº be the errors of the assumed declinations of the stars used at a Station, m, n, n.,,. . . . n, the number of times they are observed, respectively; the error in the finally obtained latitude will be— 7, 5, -- m, 52 + m3 =3 −F • * * * *li si m, + n, + n, + . . . . n, or if s be taken as the probable error of an assumed mean declination, the probable error of the latitude will be— Mn,” + n,” + n,” + . . . . ná - -- 7, -i- m, + n, + . . . . n; If we suppose the stars to be observed nearly the same number of times each, then i being the number of stars observed at the Station, the probable error of the latitude will be s -- V 7. In examining the results of the observations for latitude made with Airy's Zenith Sector, it was found that stars north of the zenith generally gave the greatest, and stars south of the zenith the Smallest, resulting latitudes. The cause of this discrepancy appears to have been • 5 4. P 666 PRINCIPAL TRIANGULATION. the pressure of the upper pivot screw upon the revolving frame of the instrument, which, by compression, disturbed the true ratio of the radius to the divided arc. Since the discovery of this source of error, the upper pivot screw has been used with less pressure; and although the same degree of precision is not found in the Zenith Points, yet the difference between the results given by north and south stars has almost entirely vanished. - All zenith distances, (not including those at Arthur's Seat) resulting from observations with this instrument have therefore received a correction of the form + c, z, where a is a quantity constant for each Station, and determined by a comparison of the latitudes given by well known north and south stars. The determinations of these corrections, which vary at the different Stations from o”.038 to o'.308 for each degree of zenith distance, are liable to considerable probable error; but it is to be remarked, that as stars are generally observed equally on both sides of the zenith, the effect of any uncertainty in these quantities will be neutralized in the mean resulting latitudes obtained as in the first process mentioned. § II. Observations made with Ramsden's Zenith Sector. It has been found necessary to revise the calculation of the results of the observations made with Ramsden's Zenith Sector, in consequence of the corrections obtained from a micrometric examination of the divisions of the limb having been applied in the printed volume with a wrong sign. Of the existence of this error, which had been long suspected, no proof sufficiently satisfactory to justify the alterations now effected could be obtained, until it appeared by a communication from Professor Peters, of Altona,” to the Superintendent of the Ordnance Survey, that the corrections determined by the late Professor Schumacher were opposite in sign to those printed in the volume of 1842. * By changing the signs of the corrections, the observations have been in general improved, and discrepancies diminished. The following table of corrections for collimation errors is to be substituted for that given at page 132 of the “Astronomical Observations made with Ramsden's Zenith Sector.” * “According to Professor Schumacher's observations, the signs of corrections given in the table page 2 of the “work “Astronomical Observations made with Ramsden's Zenith Scctor.—London, 1842,' are to be inverted. At the “right hand of the limb, for instance, is, according to Schumacher's measurements, the interval between 4° and 4° 5', “= 5' 5" 55, and between 4° 5' and 4° 10', - 5' 2" 72. The mean value of an interval is 5' 4° 50. Accordingly, the “correction for 4° 5' is nearly 1" of greater than for 4° o', and for 4° 10', nearly 1"'77 less than for 4° 5'. But in the “table above mentioned the corrections are given as follow :— - O f sº #1 4 o, correction — o'o; 4 5 33 — 1 - 17 4 IO 33 + o' 36 “contrary to those found by Professor Schumacher.”—Extract from the letter referred to above. i . GEODETICAL RESULTS. 667 Greenwich, 1802. Clifton Beacon, 1802. Delamere Forest, 1806. Cowhythe, 1813. Dunkirk, 1818. | | | Date. [...] c. Due #: . Date. 5. Date. #: c. Date ºf c. ** ºf ºf Af - *f April. 12 W. 44; 34* July . 20 W 4-3 25 May .. 30 W + 1° 52 | Sept. .. 3 W lºss. October 19 W |+2' 89 13 W i + 4° 34* 21 | E – 3° 36 31 12 – 2° 55 4 W + 2* 83 20 E – 2" 94 15 W |+ 4° 34 22 || W + 3’55 June . 1 E – 2" 79° 5 | E -2°89 ,, . W +3° 23 16 W |+ 3' 67 23 E |–2' 02 ,, . W | + 3’ og ,, . W + 2* 84 21 E – 3' 19 19 W |+ 4° 44 ,, . W. + 3' 66% 2 IX – 2 Io 6 | E – 2'84 22 E – 3' 13 2 I E - 4° 34 26 º -4” 4o 3 E - 3" 24 } | W + 3' oo 3 y W + 2* 94 ,, . W |+3'87 ,, . W +3° 13 ,, . W + 3' 81 7 E – 3’ or 23 E – 3’ II •. 22 E -4° 91 28 E – 3' 81 4 E — I 39 ,, . W. + 2* 95 ,, . W |+ 3’ or 23 E – 3' 89 ,, . W +3° off ,, . W + 1 ° 97 8 E – 2 ° 92 24 I2 -2 ° 93 24 E |–3'87 29 ? -3° 4o 5 | E — I Go ,, . W |+ 2*77 ,, . W |+ 3' 61 ,, . W + 4*83 ,, . W. +3° 9o ,, . W + 2* oz” 9 E – 2 7 25 | E |–3' 13 25 W |+3°77 3o | W +3° 94 6 I2 – 2 ° 45 ,, . W + 3' oo ,, . W |+ 2* 89 26 W |+4' 92 31 | E – 3' 81 ,, . W + 1 '99 Io E – 3’ off 26 E – 3 oz.” ,, . W | + 4° 31 7 | E – 3’ Io 1 1 || W |+ 3' 13 ,, W +3° 16 August 1 I2 – 4° 31 ,, . W + 1 ° 5o 14 E – 3' 85 27 E -2° 79 Dunnose, 1802. ,, . W + 2 7c 9 | E – 1 ° 55 15 W +3° 35 ,, . W | + 2* 8oº 3 F — I 44 ,, . W + 1 ° 28 I6 § — 3’ oS* 28 E – 2" 8o” º: 3 y W + 3' 64 }} W + 2* 82 º W i + 2* 82 * : 3) # -; 4 W |+ 3" Io 18 E – 2 73 29 W |+3° 36 11 E – 3' 19 5 | }. T 3.47 | Burleigh Moor, 1866. 19 W |+2.67 W |+3° 93 ,, . W |+ 3’ oz 20 ! I. –2.87 * | E –3° 56* 7 W |+3° 52 #f ,, . W +3° 21 W + 3' 19 8 E – 3' off July . 4 || W |+ 2* 11° 2 I | E – 3° 21 # I? |–3'46 ,, . W -2° 77° 6 W + 2* II ,, . W |+2" 98 Greenwich, 1836. 14 | E – 3' 79 9 § –2' 77° 7 ; — 2" oz 22 # –3’ 72 * $ 9. + 2* 4 2 — 2" 42 2 + 2* 75 º: i. y *:::: Io W ::::: 1. E – 1 °68 26 W |+2'83 May - 31 W. -1.84 #6 y *::::: ,, . W +3° 59 12 E – 3’55 ,, . W |+ 3'25" 3 w -1.84 .19 13 | B - 2'45 14 W + 2* 58° 28 E – 2" 91 8 IX + 1" 84 3 y W + 3' 85 W * º E 1–2" 9 E |+ 1".84 17 E – 2' 68 33 + 3' 85 15 W + 1" 61 29 2" 73 ſº 20 E – 3' 16* I7 | E – 3' 64 16 || W |+ 2* 52 ,, . W |+3°31 ; #, i.; June . 5 || W + 3' 64 I8 E -2.54 17 | E -3.39 3o W –2.45 à W I.; | 8 : E – 3° 56 ,, . W + 3' 67 18 W |+3.34 Oct. . 2 | f |-3:63 : W + 2* + W |+4:39 19 | E – 3’ 91 19 E – 2' 69 ,, . W + 2* 92* 2O + 2* IO # | E º ,, . W + 2* 54 ,, . W +3° 39 3 E – 2° 22 24 E – 2 Io I I -4.99 º 3 y W. + 3’ 93 25 W + o' 22 , W |+3.69 7 W |+ 3-63* 27 E. –o'22 12 | E –4, 27 Arbury IIill, 1802. IXellie Law, 1813. 8 E – 3' 63” 28 W |+ 2'35 13 | | |−3.49 º 12 | E |–3, 63." 29 | E – 2' 35 3 y w + 3. 84 ff a 33 W | -- 3' 64 July • 4 E -2° 35 14 | E –3.80 Sept. .. 7 | E – 3 of June . 23 E – 2' 65 6 W —3° 51* , W 4-3.32 8 E – 3' of" 25 | W 4-2:58 7 W -3° 51 15 | E T2.33, ,, . W |+ 3' of 26 E -2° 28 8 E +3° 51 ,, . W +3.8; Io E – 3' 85 27 | W + 2* 22 Balta, 1817. 9 I2 |+3° 51 16 | E. –2.91 ,, . W |+ 1 ° 91 28 W |+ 2* 24 ,, . W — 3’51*| ,, . W +2.31 II E — I'91 July . 1 || W +3° 25 f* II W —o' 75 17 | . E. – 2'27 12 E |–2° 24 2 E – 2'32 August 13 W + I 41 12 E + o' 75 ,, . W +3.1; 14 || W |+ 2'47 3 I2 – 2" 92 14 E – I'89 14 W — o' 75 18 E. -3.3% 15 W |+3'85 ,, . W + 2'59 15 | E – 2° 24 15 W —o' 75 , W 4-2:58 16 W |+ 3' 35 4 E – 2' 61 16 E – 2: 31 18 E + o' 75 20 ! E –2.32 18 E – 2'87 7 || W +3° 20 17 | E — I’75 20 | E |+ o' 75 31 w +2.94 ,, . W |+2' 34 8 E – 3" 24 ,, . W + 2* 59 2 I E |+ o' 75 21 | E – 2' 69 19 | E – 2:34 ,, . W + 2'85 18 W + 1 99 23 W — o' 75 ,, . W + 2* 29 ,, . W |+ 2' 67 9 W |+ 2'57 19 W + 1' 76 27 W -2° 52 22 W |+ 2* 72 20 E – 2' 88 11 : E – 2' 66 20 E – 1 99 || August 1 E + 2* 52 21 W |+ 3' 13 ,, . W +3° 23 ,, . W + 2* 93 2 | E |+ 2* 52 22 E |–2' 63 12 E – 3’ 18 21 E – 3’ of 4 W -2° 52 23 W |+ 2*.42 ,, . W +3° 29 ,, . W + 2 '81 8 W -2° 52 24 E |–2'42 13 E |–2' 61 22 E – 2° 57 9 W -2.52 25 | E — I '92 ,, . W +3° 25 ,, . W + 2* 29 19 || 3 |+ 2.52 - , W |+2' 33 17 | E – 2' 62 23 E – 2" 74 16 || || |+ 2.52 26 | E – 2' 66 18 E – 3' 6o ,, . W + 2* 52 17 | 1. -1.84 ,, . W i + ... oG 20 E – 3' 8o" 24 E – 2'55 18 W + 1 ‘84 * - * 27 | W |+ 3' 71 22 W +4' or ,, . W 4-2'89 19 W |+ 1.84 • The quantities marked 28 J2 – 2°81 24 E – 3' 6o 25 2 – 2°83 22 E - 1.84 with an asterisk are in- ,, . W + 2* 8o ,, . W +3°35 26 l? -2° 91 24 || || |+ 2. 11 ferred or interpolated. 29 | E – 2'35 25 | E – 3' 86 27 E – 2" 99 26 W. - 2 II » W + 2* 55 26 E – 3° 41 ,, . W |+3° 18 3o W -2° 11 3O § –2°87° 3 * W + 3' 62 28 y t;.g. 3I W – 2 - 11 53 + 3" I 2 JE i – 2" 29 I2 – 3' 83 October 1 | E –3. ; ſ W I. ; ,, . W +2" 99 2 E – 3 oz 28 W +3°46’ 3 | E – 2" 8o” 29 || W |+ 2* 79 ,, . W Fº 3o | E |–2'79 4 P 2 668 PRINCIPAL TRIANGULATION. RESULTS FOR LATITUDE WITH RAMSDEN'S ZENITH SECTOR. Greenwich, Dunnose, Clifton B - º º * No. fººl" Pºº "ºº"Aºil, Dºrº, Bulºloor. Kolijaw, coºle, º | Duº, c. Namo of Star. 3• Iö13. 1817. 1818. * Lat. No. Lat. |No. Lat No. N Obs. Obs. º Lat. O. Lat. No. Lat. No. No. No. * |Obs. Obs. 6. Lat. 6. Lat. 6. Lat. 6. Lat. Š. Lat. 6. s: 28 sé 3; s: 2; s: 13 © ºf © & O y o , o ,- ſº f O C */ w/ / 53 T 3 54 34 56 I4 57 4 I 6o 44 5 I f 2 Cassi iº f ºf |: º, wº ºf &f " || ||61°47| 7 | " 3 15 Cassiopeiae, k ..... 59°o? | 7 4 18 Qassiopeiae, a ..... 5°24 2 5o'56 || 4 || 8.66 9 || 61.77|| 8 5 249 assiopeiae, m ..... tº 5:3. | 9 || 12:48 || 3 |93:34, 9 |58:43| 5 0. Cassiopeiae......... 17'73 || 2 || 51°52 | 6 || 9-04 || 13 | 62.82 || 7 |57'98 || 7 7 27 Qassiopeiae, Y .... º 61 °36 5 8 3o Cassiopeiae, a .... 15°o.4 || 3 || 51 °os | 3 || 9°94 | 12 61 °66 5 9 || 33 Cassiopeiae, 0 .... 59'86 7 10 | " .................... •. 51 '89 | 1 || II '55 | 11 63-77 | 6 II | 34 Cassiopeiae, p .... 62° 15 4 12 37 Cassiopeiae, 6 .... 61 - 11 || 5 || 58-67 7 13 || 39 Cassiopeiae, x .... 50° 92 || 6 || 9'99 || 1 I 62° 26 || 7 | I 4. i. tº º dº tº º ſº $ tº º ºs º º ſº e º 'º º g g º C & 62 - 66 6 57° 72 7 15 44 Cassiopeiae......... 62°37 || 3 16 54 Andromedae ...... 62-84 || 6 17 | 1 Persei ............ 58-39 || 6 18 || 45 Cassiopeiae, e .... 59°oj | 6 19 || 53 Cassiopeiic......... 5o 72 || 5 || 9°76 11 62°o.4 || 8 20 || 4 Persciº........... 63' 12 4 21 5 Persei, h .......... 59'82 5 22 55 Cassiopeiae......... 57° 77 || 5 23 $ # tº º º ſº e º º 'º º ſº tº t e º sº e º 'º e º 'º 61 “43. 5 34 # & a g : & （ & & ) is a s e º º 'º º sº * * * 62 '99 2 56'86 3 2 º' Cassiopeiae, i...... 63'81 || 3 27 | 13 Persei, 0 .......... 62.81 5 28 15 Persei, m .......... 57°91 5 29 || 23 J’ersci, Y .......... 62-71 || 5 || 58°33 || 5 3o 27 persei, k .......... 59° 29 || 5 3 I Camclopardi...... 6 58°39 4 32 33 l’ersei, a .......... 8° 01 || 2 || 28°8 º º º o°94 3 33 39 l’ersei, 5 .......... 9 7 5 || 26°23 9 19'51 3 || 52-64 || 5 - 57°45 || 4 34 º ... 38 61 - 18 57° 7'o 5 35 | 13 Aurigae, a.......... 38'96 || 3 || 8°7o I • 5 28° º * 18 3 § # tº. 33-#| 3 | " ' 9 || 31 ° 97 55 ; I2 | 19° 5o I 59-81 || 3 37 25 Ursae Majoris, 0 . . 41' of I 38 3. Iſrsac §: p. 38°30 3 39 48 Ursae Majoris, B. * tº º 4o 5o Ursae Mºjoris, C: , 19°92 || 1 49'37 || 3 | 9'56|| 4 |64°ool 1 |58'oz | 8 41 | #2 Ursae Majoris, y. 41 '69 | 6 || 8° 16 3 6o '83 || 1 42 º É. sº X • 7°99 || 4 43 || 64 Ursae Majoris, y. 39°25 * 22 || I 27 ° 30 º º º tº . 44 69 Ursae Majoris, 6. 9 * * * 4 || 27°30 || 1 || 27°57 || 4 || 18°o0 || 4 || 20°o.4 || 1 {...}}| : .#| 4 6'45| 3 |5||9|| } #| || 3:#;: 7' 27 | 1 ##| ||##| ||aces sº 46 || 79 Ursae Majoris, C. 38°36|| 1 || 6’ 64| 11 || 31' 16 || 5 || 27°52 || 4 || 18°85| 8 || 22*21 • 60 8-6 • I 47 || 85 Ursae Majoris, m . º º ſº ſº º Ç I 5o’ og 3 7| 1 |63°ol || 3 || 57. Io 9 # º #. 38-39 || 2 || 6-oš 17 | 30-75 || 5 ||26-97 || 9 || 18.72 | 8 || 22° 26 || 1 || 51 'o6 || 4 |io’ 23 5 60° 6 §§ IO 51 | 17 Boºtis, ".......... * OT | IO tº fº o° 04 2 53 23 Boötis, 9 * * * * * * * g º e ;: I 1 || 32°os H 48°69| 2 62 I 2 Bracºis, • * * * * * * 18-23 7 19°o8 2 49°69 5 9°3o 6 •o8 || 67 || 6 Herculis, v. ....... 7- or | 8 || 3o 63 || 3 18°78 7 2 | UI" Oğ İ 2 68 || 13 Draconis, 9....... 5.o. 98 || 6 || 8*6 6 69 22 Herculis, 7 tº º e º e s e 7'92 | 1.4 31 ° 20 6 29°35 2. 19°69 3 19: 61 2 9 5 2 2*70 I 72 14 Draconis, m ....... 49° 51 8°61 6o" | 73 | 16 Draconis.......... 6° 16 || 1 5o°37 : 4 | Go" 98 || 4 74 17 IDraconiS tº et e º 'º º º tº º 6'96 8 31 65 3 18° 6 º º 77 52 Herculis .…...... 7° 15 | 12 || 31 ° 45 4 1 || 3 | 19' 67 || 8 || 51 ‘83 4 78 19 Draconis, l'...... 6-66 63' os $o 21 Draconis, pi . . . . . . 30" 1 | 6’44 12 || 30°23 || 6 I8° & 2 * º I 81 22 Draconis, K ... .... 8 7o || 5 || 19°37 || 4 || 48°64|| 8 59°74 2 84 || 23 Draconis, 3....... 39'? 4 || 7' 51 | 1.4 3o'76 15 26°8 º & † ... • | 85 24 Draconis, "....... 70 15 7| 14 | 19° 35 | 6 || 20°68 51-65 11 || Io" 24 || 7 61 ° 58-57 || 4 86 || 25 Draconis, *....... ;... 3 87 26 Draconis ......... 8° 6°48 §. 3 88 | 85 #. 1........ 37' 11 || 3 || 7°84 | 5 || 31°oA 8 21 “47 3 48° 55 Io 4 5 |0I*4o | I 58.39 f 90 | 32 Draconis, ; ...... | 61°85| 7 || 58°41 2 GEODETICAL RESULTs. 669 RESULTS FOR LATITUDE WITH RAMSDEN'S ZENITII SECTOR continued. Gregºich, Duºmose, Clifton Beacon, Arbury Hill, Delamore, Burleigh Moor, Kellie Law, cowhythe, Balta, Dunkirk, No. 18oz. 1862. 1802. 1802. 1806. 1806. 1813. 1813. 1817. 1818. | Cº. Namc of Star. N N r y | N No No * |&|*|&| * |&| at |&| at |& is |&||al. Sº, at #| at #|iat à: 0. & º Af O & (). & ū f 0. f tº f {} f º f ſº ºf 51 28 5o 37 53 27 52 I3 53 I3 54 34 56 14 57 41 6o 44|| || 51 I & ºf & ºf ºf f/ J/ &A fy ºf 9| 33 Draconis, Y ...... 38°73 || 5 || 7-11 || 13 || 36- 14|| 15 ||26-49 15 | 18-79 || 6 || 20° 19 || 7 || 5o-66 || 12 9°52 9 57 °53 4 95 36 Draconis ......... 61 °o 5 || 4 90| 39 Draconis, b ...... 48°65| 11 || 7-80 || 8 || 6o. 57 || 4 97 || 42 Draconis ......... 59° 27 5 98|45 Draconis, d ...... 36 73 || 3 || 5'oZ | 6 || 29°41 || 9 |25'34 | 16 | 16.42 || 4 | 18-20 || 4 |49' 11 | Io 7'74 || 8 55 ° 77 || 4 99 || 46 Draconis, c ...... 38' 19 || 1 || 7 of | 5 || 36°35 | 12 |27-43 18 17.44 || 4 || 20-25 || 5 || 56-65 | 9 || 9:39 || 9 |62-og | 6 |58.23 5 *91 || 47 Draconis, o ...... 49° 22 12 || 8* Io || 8 || 61 ° 21 || 8 *93| 48 Draconis ......... 49°76 || 15 8'34 || 9 || 61 - 18 || 6 || 56°36 || 4 194| 49 Draconis ......... + * , - 61 °7o || 3 || 57' 52 || 1 196 51 Draconis ......... 38' 26 || 2 | 6'76 || 5 || 29'54 || 9 || 26'82 17 | 17-87 || 2 | 18° 56 || 5 |50-27 | 13 || 0:46 1o 60-72 || 7 |56-91 4 198| 53 Draconis, n ...... 35° 12 I 7° 19 || 5 17'oz || 4 || 19°31 || 5 || 50° 17 | 13 8-78 Io 61 °45 || 8 |58'13 || 6 *99 || 54 Draconis ......... 57° 25 3 *11 || 57 I)raconis, 5 ...... - Go' 7o 6 **2 || 1 Cygni, k ....... ... 37'23 || 2 || 7' 57 || 5 || 29°87 14 ||26-93 || 17 | 17-81 || 4 || 18°77 || 4 |5o'86 || 14 || 9 79 || 9 || 56°39 || 5 || *13 58 Draconis, tr...... * * 60-70 7 - **4|io Cygni, * ......... 37' 21 || 2 | 6’ 72 || 5 || 3o 18 12 ||26-78 15 18'59 || 4 || 19-30 || 5 |50-65 14 9-44 9 5:19 6 **5 13 Cygni, 0 ......... 3o 66 2 58.2% 5 16 16 Cygni, c ...... 57.9 2 #. i. cºni i"......... 8 8 51 °44 14 || 1 o'o6 II § ; 20 Cygni, d ......... º 2 || 3O" 3 º I o " #|* 3: ...: 7° 78 || 2 || 3o'83 48-79 15 || 6-88 || 11 |60-60 | 8 || 56' 60 | 6 **I | 66 Draconis ......... 60-79 6 *** * ................ º, º 'º - † 6o. 12 || 6 **3| 31 Cygni, on ......... 6'93 || 3 124 | 68 #. º º & ſº ſº tº ſº º tº 9 60° 23 || 6 **5 | 71 Draconis ......... Go' 56 7 **| 43 Cygni, a ........ tº 6°oo | 3 |.30'o6 2 57°5 I 5 **7 46 Cygni, wº......... 6°34 || 2 || 31-40 || 1 $38|| 2 Cephci, 6 ......... 59°84 9 - **9| 50 Cygni, a ........ i. 6' 62 || 2 57-97 || 6 I 30 Cephei, x ......... 7 * 40 || 4 || 29° 7o 2 56.68 || 6 #. 3 Cephei, m ......... 6 61 ° 93 || 8 º;2 ‘gni, f' ......... • 2 I * 2 I 3 133 * §ſ. * † g º ſº tº tº tº 7 4 || 3 49'22 | Io 8: 11 | 18 61 °8o | 8 §4 || 9 Cephei ............ 61 - 2c | 6 # 8o Cygni, "......... § 4. ...; 3 8 I Cygni, ºn 2 tº tº º ſº º ſº tº ſº tº * Ut 4. 29° 9 3 6 ſº I 3 ii. " ......... 1 * 29 5 § 3 ºr ... ...] : $39| 19 Cephei ............ 59.49|. 14o 23 §. 6 * * * * * * * * * ::::: 5 **| 25 Cephei ............ I '59 || 5 8° 2 I *42 | 3 Lacertae, 8........ 7' 12 I 62. 8 5 4. *43| 27 Cephei, 5 ......... 2: 27 • 38 *44|| 7 Lacertae, a ........ 5' 28 || 1 57.3 4 *45 9 Lacerta............. g 57° 21 4 $4%| 36 Cephei ............ º, § : *47| 32 Cephei, ......... * 43 I48 s: §3. $2.63 7 56°53 7 | 19| 2 Cassiopeiae......... 52.93| *59' 34 Cephei, o ......... 60°48 || 7 I § 61 - 3 I | 8 5* | 4 Cassiopeiae......... .3 • 26 || 1 IS2 Cassiopeiae......... 61 °58 7 §§ 5 *53 18 Andromeda ...... º 50°89 # 5 Cassiopeiae, T ... ::::: : #| || Cº. c., , |*| " 157 Cassiopeiae......... - - 1. i. I58 * ë. 8 ... 52-09 || 6 || 10-91 || 8 |62'49 || 9 |58'2"| 7 *---- ºmpºs *=ºmº *mºme, | ** ## JJ &# fy f* ff ". tº º º 86 27O || Jºesulting Latitudes...... 38°51 47 | 7°o? |232 || 36°35 | 157|26'90 152 | 18.55 | 84 19°39 || 7o 56°22 aſs 9-30 |258 61 °55 |382 |57 jo *— 670 PRINCIPAL TRIANGULATION. The results for the latitude of Greenwich, from the observations made by Lieutenant Denison, R.E., in 1836, not included in the foregoing table, are as follows:— GREENWICH, 1836. No. No. No. No. No. - - º N C.º Name of Star. Lat. Obs. dº. Name of Star. Lat. 6. Cº. Name of Star. Lat. Ö. 5í 28 5 * 28 5i 28 45 || 77 Ursae Majoris, e 37.63 I | 66 * . . . . . 3%86 I4 || 94 | * tº º e 38.7 2 I 46 79 Ursae Majoris, |41 57| 2 | 68 13 Draconis, 0 ... 37' 60 | 16 || 96 39 Draconis, b ... 39° 19 || 25 47| 85 Ursae Majoris, |37-64 || 7 || 69 22 Herculis, r ... 39° 14′ 17 | 98 || 45 Draconis, d ... 39'29 22 48 86 Ursae Majoris. 44 '98 || 1 || 70 | * ... 40° 17 | 8 || 99 || 46 Draconis, c. . . 38-69 26 49 | * . 39°37 || 2 || 71 | * ... |40°37 || 1 || Ioo * ... 38' 28 20 52 | 19 Boötis, X ..... |40° 21 || 5 || 73 | 16 Draconis . . . . . 38-42 Io | Io2 I3 Lyrae ... 38°ool 2 I 53 23 Boötis, 0 . . . . . 34°43 || 4 || 75 || 42 Herculis . . . . . 37.79 || 6 || 105 | * ... 37' 6o 2 54 “ . . . . . 38' 12 || 2 || 76 | * . . . . . 39'48 || 13 || Iof 51 Draconis . . . . . 38°74 || 17 55 38 Boötis, h. 34° 34 || 3 || 77 52 Herculis . . . . . 39-46 || 17 | Ioy | * . . . . . 36' 61 | 1 56 | * . . . . . 35' 94 || 4 || 79 | * . . . . . . 40°os 20 | I Io | * . . . . . . 35' 59 I 57| 44 Boötis, i . . . . . 39' 66|| 8 || 82 74. Herculis . . . . . 38-25 || 2 | | II2 | I Cygni, k . . . . . 37° 73 I4. 58 | * . . . . . 4o 33 || 1 || 83 || 77 Herculis, a ... 38' 55 17 | II4 || Io Cygni, ** . . . . . 40' Io 18 59 | * . . . . . 40° 13 || 1 | 84 23 Draconis, 8... 38°74 || 23 || II 5 || 13 Cygni, 0 . . . . . 39°42 | 18 6o | * . . . . . 4o’ og | 1 || 88 85 Herculis, . . . . . 39' 13 23 I 18 18 Cygni, 8 . . . . . 38°og | 19 61 | * . . . . . 35' 70 || 3 | 89 || 3o Draconis . . . . . 39°39 24 * - M. 63 | * . . . . . 35 'o6 || 2 || 9o 32 Draconis, 5 ... 39°og 23 A f 64 | * . . . . . 40° 5o || 7 || 92 | * . . . . 4o 23 18 Resulting Latitude.. 38.81 |586 65 | * . . . . . 38: 11 Io 93 | * ... 38-71 26 If we put the amplitudes— W Dunnose and Greenwich = Š 5. 36 + ær 35 Arbury . . . = I 36 20 + æ, 33 Delamere . . . = 2 36 Io + æ, 53 Clifton . . . . = 2 5o 20 + æ, 33 Burleigh Moor = 3 57 Io + r. we shall have 87 equations for the determination of these five quantities: these equations being treated according to the method of least squares, give— iſ ſ O = - 34.75 + 27.54 a ... a' = + I-26 o = + I-97 + 54, 18 a. - ar, - – O.O.4 o = – 8c.56 + 50-45 as - I'56 rs a; - + I-68 O = - 251.54 + 73-74 wº a", = + 3-4I o = — Io2.73 — I'56 as + 38-56 r, rs = + 2.71 - GEODETICAL RESULTS. 671 So that the required amplitudes are— Dunnose and Greenwich . . . . = 3 5. 3#26 33 Arbury . . . . = i 36 19.96 33 Delamere . . . . = 2 36 II.68 33 ° Clifton 2 5o 23-4. I 33 Burleigh Moor . . = 3 57.12-71 The quantity which has to be applied to these amplitudes, in order to give the latitudes which shall most nearly agree with the independent results in page 669, is easily found to be 50° 37' 6". 96, whence the following latitudes:— JDunnose . . . . . . . . . 53 3% 6.96 Greenwich . . . . . . . . 51 28 38-22 Arbury . . . . . . . . . 52 13 26.92 Delamere . . . . . . . . 53 I3 18-64 Clifton tº gº is tº g º C º º 53 27 30-37 Burleigh Moor . . . . . . . 54 34 19.67 Combining next the observations made from 1813 to 1818 at Kellie Law, Cowhythe, Balta, and Dunkirk, we get 85 equations for determining the three aniplitudes. These equations treated according to the method of least squares, resolve themselves into the following:— o = — 178.22 + 132-52 w; - 40.38 a., - 3I-75 as a; a + 3.90 o = – 72-63 – 4o.38 a., + 99.59 a., aa = + I-90 o = – 264.94 – 31.75 a., + 87.84 as as + + 4-06 Hence the amplitudes— f & f Dunkirk and Kellie Law . . 3. 1% 36 + ær = $ I2 52.90 35 Cowhythe . . . 6 39 Io + æ, a 6 39 II-90 33 Balta . . . . 9 43 o + æs = 9 43 4'o6 The quantity, which has to be applied to these amplitudes, to give those latitudes which shall most nearly agree with the independent results at page 669, is easily found to be 51° 1' 57". 52, whence the following latitudes:— f f/ JDunkirk . . . . . . . . 5i I 57-52 Rellie Law . . . . . . . . 56 I4 50-42 Cowhythe . . . . . . . . 57 4I 9.42 Balta . . . . . . . . . 6o 45 I-58 The amplitudes just deduced are dependent upon and affected with the error of the assumption that the points o' and 7° (Right Limb) are relatively correct with respect to the radius of the divided arc. This assumption is, of course, erroneous, but the error is very small, as a comparison of the results for latitude given by north and south stars does not consistently indicate any error in the angular measures. We must, therefore, allow the assumption to Teſla III, * " * 672 PRINCIPAL TRLANGULATION. The following table contains the corrected results of the observations with Ramsden's Zenith Sector, together with results given in the volume of 1842:— Latitudes. Stations. Stations. I” Method. 24 Method. Vol. : 1842. Latitudes. - I* Method. 2d Method. Vol. : 1842. Dunnose . . . . 563; #97 || 6.96 || 7 os | Clifton: . . . . . 5; 2; 33.35 | 36||37 || 3445 Dunkirk . . . 51 ºr 57.86 57' 52 57° 93 || Burleigh Moor 54 34 19' 39 19' 67 | 19'48 Greenwich . 51 28 38' 51 38-22 || 38-30 || Kellie Law . . 56 14 50-22 || 56'42 56.51 Arbury . 52 13 26'90 26'92 || 27' I4 || Cowhythe . . . . 57 41 9°30 || 9°42 9:74 Delamere 53 13 18:55 | 18-64 | 18.77 | Balta . . . . . 6o 45 I 55 I 58 2 : 31 The results now obtained agree very closely with those given at page 198, which are, however, affected with the wrongly applied corrections for the divisions of the limb. There is some difficulty in deciding whether the results of the first method of reduction contained in the second column of this table, or those of the second method, contained in the third column, are to be preferred as probably nearest the truth. The results in the second column are affected by errors of assumed mean declinations, those in the third column are affected with the error involved in the assumption that the length of the arc from o' to 7” (Right Limb) of Ramsden's Zenith Sector was correct. In all the subsequent calculations in this work the results in the third column have been used, and similarly with respect to the observations made with Airy's Zenith Sector, the quantities used being those in the 6" column of the table, pages 198, 199. But the final results of this Section will be put in such a form as to admit of easily determining the effect of any changes of latitude that may be considered necessary or advisable. Tor the latitude of Greenwich, the quantity 51° 28′ 38”. 3o has been used in all calculations. In the following table the latitudes have, when necessary, received the corrections to reduce them to the Trigonometrical Stations. For Dunnose, Cowhythe, and Balta, the means between the results furnished by the two Zenith Sectors have been used. Stations. Latitudes. Stations. Latitudes. Greenwich 5* 28 38:30 Forth . 5: 18 57'91 St. Agnes . 49 53 33° 93 || Tawnaghmore . 54. I7 4 I 34. Goonhilly . 5o 2 50° of | Lough Foyle . . 55 2 38°74. Hensbarrow 5o 23 I '84. South Berule . . 54 8 56-40 Blackdown 50 41, 8-89 || Ben Lomond . . 56 II 26-27 Dunnose 50 37° 7' 08" | Kellie Law . . 56 I4 51°52 Boniface Down 5o 36 Io'55 || Den Heynish . 56 27 16-88 Week Down . 5o 35 51 '42 Great Stirling 57 27 49' 12 High Port Cliff 5o 35 43°28 Cowhythe . 57 41 8-96 Southampton . 5o 54 46-97 || Monach 58 21 20' 84. Precclly 51 56 45' 18 || Den Hutig 58 33 6'47 Arbury 52 13 26'59 | North Rona 59 7 I5' Ig Delancre . 53 I3 18:61 | Balta . º 6o 45 I '66 Clifton . - 53 27 30°40 || Gerth of Scaw 6o 48 56'43 Burleigh Moor 54 34 I9' 67 || Saxavord . 6o 49 38' 58 Hungry Hill . 5I 4 I Io. 26 Feaghmaan. 5I 55 22 '85 | Dunkirk . . 51 2 8:41 ;| GEODETICAL RESULTS. 673 3. At page I of “Astronomical Observations made with Ramsden's Zenith Sector,” it is stated that the point at which the observations were made was “ 1438 feet S. and IIo4 feet W. of the Flagstaff on the great Church Tower.” On looking back, however, to the original docu- ments, we find that in order to connect the Sector Station with the Tower a small base-line was measured Ioo& 6 feet in length, and at each extremity of this base the Sector Station and the Flagstaff on the Church Tower were observed. By means of these angles the distance of the Sector Station from the Tower is found to be 1813. I feet. From observations taken” on the 14th of October, we find that the Flagstaff reads 44° 46' 6", while the Eastern Elongation of the pole star readst 174° 55' 12". On the following day the Western Elongation of the pole star reads 169° 38' 48", and the Flagstaff on the Tower 44° 45' 58". Hence we infer that the Tower was 52° 29' 2" north-east of the Sector Station; from this bearing and the distance I 813. I feet, it appears that the Zenith Sector was placed IIo4 feet south and I438 feet west of the Flagstaff on the Tower, the numbers being erroneously transposed in the printed volume of Observations. The distance IIo4 corresponds to Io". 89, so that the latitude of Dunkirk Tower is 51° 2' 8". 41. The latitude of Dunkirk here given differs slightly from Delambre's determination, which we find at page 295, tom. II., “Base du Système Métrique” to be 51° 2' 9".7. On examining the observations upon which this result depends, we find that they were taken generally under unfavourable circumstances, and not to the satisfaction of the observer himself (tom. II. pp. 259—262). Two stars only (c. and 6 Ursae Minoris) were observed, and the results furnished by these stars differ by I". By rejecting the observations of 3 Ursae Minoris, which Delambre thinks not improper (tom. III., page 297), the latitude would be slightly increased. At page 548, tom. III., the latitude finally adopted as most probable is 51° 2' 8". 50, but expressly subject to a doubt of o”. 5. The agreement of this with the result with Ramsden's Zenith Sector is very remarkable. If we may judge of the accuracy of the determination resulting from the observations in 1818 by the accordance of those observations among them- selves, or by the accordance of the results furnished by the 53 different stars observed, we find by comparing these different results with their mean, that the mean square of error is 1.091, and the probable error + o”.og5. At the same time that observations were being taken by Major-General Mudge and Major Colby, with Ramsden's Zenith Sector, for the latitude of Dunkirk, the French Astronomers MM. Biot and Arago were engaged in the same determination with the Repeating Circle. In the volume entitled “Recueil d’Observations Géodésiques, &c.—Paris, 1821,” it is stated by M. Biot that the result of their observations agreed perfectly, when reduced to the tower of Dunkirk, with the result furnished by Ramsden's Zenith Sector, and also with Delambre's .* * With Ramsden's large theodolite, placed over the centre of the Zenith Sector Station. f The circle is divided into two semicircles, each reading from o’ to 180°: otherwise the reading of the Flagstaff would be, on the first day 224° 46' 6", and on the second day 224° 45' 58". 4 Q 674 PRINCIPAL TRLANGULATION. determination.” In 1809 M. Biot had made a great number of observations with his Repeating Circle for the latitude of Dunkirk, but the result he obtained was 4" less than Delambre's latitude. This discrepancy he attributes to the constant error of his Repeating Circle. A similar discrepancy is seen in his determination of the latitude of Unst, in the Shetland Isles, when engaged in conjunction with Colonel Mudge and Captain Colby. The point at which his Repeating Circle was placed, was found trigonometrically to be 26". 94 to the north of Balta Station: now the latitude of Balta is 60° 45' 1". 66, hence the latitude of M. Biot's Station must have been 60° 45'28".60, which exceeds his determination by 3". 60 (see page 560 “IRecueil d’Observations Géodésiques, &c."). § III. Calculation of Latitudes, Longitudes, &c. In the treatise on the Figure of the Earth in the Encyclopædia Metropolitana, by the Astronomer Royal, he has assigned the following elements for the elliptic meridian :- a = 209237I3 s b 2085.3810 ... e. = o'coff67c54 These quantities very nearly represent the surface of Great Britainſ but require, the former at least,--to be slightly increased. In the present Section we shall determine small corrections, 3a, 3b, 6(e”), to these elements, such as shall correspond to the surface sought after. The first step in this operation is the calculation of the latitudes and longitudes, and directions of the meridian, at the various points at which Astronomical Observations have been made, using the above values of a and b. Let g and g’ be the principal radii of curvature of the surface of revolution corresponding to this ellipse, and let n = a – b : a + b : then 3 2 3 log (g sin I")- * = log {#; (**) } + 3 M {n cos 2 A. – cos 4 x -- *co. 6 x + - ..] ºr a” b” log (g' sin I")- * = log {º (***) } + M. {ncos 2. A – cos 4 x + ** 6 x + • ..} 7ſ Q.” Now log a = 7.3206387544, log b = 73191834123, log (a + b) = 7.62o.9426870, and the values of the above series are consequently— log (g sin I”)- * = 7-99.45148738 + -oo.21800IIo cos 2 x – “oooool.8237 cos 4 x + -oooooooozo cos 6 x log (g' sin I")- = 7.9930603157 + .oOo.7266703 cos 2 x – oooooooo79 cos 4 x + -ooooooooo7 cos 6 x g being the radius of curvature of the meridian, and g’ that perpendicular to the meridian at latitude = 7. * Page 516, “.... alors notre latitude obtenue par la moyenne des distances zénithales, étant réduite à la tour de “Dunkerque, s'est trouvée parſaitement d'accord avec celle que les savans anglais ont obtenue en même tems par le “grand Socteur de Ramsden ; et ce qui était sur-tout un résultat désirable, cette latitude s'est trouvée exactement la “méme que M. Delambre avait autrefois obtenue.” : : ; : ;i GEODETICAL RESULTS. 675 The following table contains the above quantities for every ten minutes, from A = 49° to 2 = 61°:— - In the Meridian. Perp. to Meridian. | In the Meridian. Perp. to Meridian. * ! 7\ 7. fy I fy. I º | rº I I ſº log p sin 1" IDiff. log p' sin I" . Diff. log p sin I" IDiff. log p' sin I" Diff. 31 7-004211228 * OO2 676 § 16| 7. 87461 ..., | 7'9928o3273 2 O 1881 189 ::::::: 951.3976 ; # 3o 7349851 # 8oo353o #59 3o 17558of #3 $472.Éo #7; 40 7:3.43% ºft 79% #: 4o 1630526. :::::: 943O422 # 5o 71 13289 I 17878 7924676 #; 5o I50537 I *:::: 9388793 || 6 ; 56 o 69954 II II 7603 78.85383 || 3 : 5o o 138o336 I25 # 934.7025 #. IO 6877808 II 7322 7846182 3. IO 1255.426 I249 8 930.5388 #: 3. 2O 6760486 II 7042 7807075 3. 2O 1130648 ::3% 9263796 # 3o 6643444 I 16754 7768061 33 # 3o Ioofloo2 :: ; 92.22247 #: 40 6526690 I 16462 7729I43 #. 4o o881494 ::::: 9180744 § 5o 64. Ioz28 116169 7690323 #. 5o oz;7:3; ; ; 9:39:90 | 1.36 |57 o 3.94%;9|1138% 7;99 || #: 5I o o632.913 ::::: 9097884 # 6 IO 5178187 || 3.6% 7612975 852 IO ojos346 º: . 9056528 ; | 20 6062619 #. 7574.452 ::::: 22 gº º ºsº | ##| 36|| #73; ; ; , ; 3o ºf lºft §73%| #| 42 53344; ºść 74977.4 || 383.1% 4o of 37597 ||...} $33.77% ##|... 59 57.77% |! :::: 745.95% 38.107 5o ool 4 I79 : 889.1639 ; 58 o 5603446 II3998 742. I395 37999 52 of 7.99398953% |: §§3053% . . IO 548944; 33% 73°3393 || # IO 3767&o ||. $83,533 i. 20 537577; 1,334. 73455% #: 2 O 3644970 º? $768% ...; 30 #6:436 |::::: 73°77°5 #670 3o 95.22263 º 87.27667 || 4 3. 4o 5 I494.27 #: : 727Oo35 3 6 #o 3399746 |:::::. $686828 ...}} | jo $ojš, ;. #24%|##. 5o 33%33 |:::::: $546054 ..., |59 'o 49.34426 ºš Žišč #: 53 o 315;295 |...? $63534; ... " to 4812440 |: Žižá|37; IO go33379 |...}. $564%; . . 20 479C865 |::::::: Žiž6;15 |3%. 2O 891 1651 ::::: 85.241.30 40573 3o 458952 | 1.3 : 708342O % % 3o $793:39 |:::::: 8483626 $2524 || 33 447393 |: Żºłł #. 4O 8668841 :::::: 8443193 ::::: 5o 4368o27 :::::: 7oog589 § 5o $547763 ||. $433834 .;3|6o o 4:57.3 |1333; 397.854 || 336: 54 2 #2; ;| $36,533 ||. to +4.9% j ºf #3 IO 8396473 Hºº. 8322337 $º. 2O 4938524 tº 68997.54 36363 2O Ší85874 |::::::: $3823&4 .% 30 3929434 ; §339; #3; 3o 8065706 I ICC) 3 O 82.42148 4oo5 40 382O723 Io8327 6827.154 36 Io9 4o 794;776 |:#; $2:21; . . $o 37.39% |icº £79:3#5 || 3:3: 5o #835%; i. $1622.7 #|61 "o 36043;4 |*7 6755064 55 o #7066;o *944 81.22463 || 39 I4. I 19189 . 3973O The Trigonometrical Station at Chingford was ascertained by careful measurement to be o-454 feet to the west of the meridian plane passing through the centre of the meridian mark at Chingford. This distance subtends at Greenwich an angle of I".62. In the Greenwich Observations for 1842, page xiii, it will be found that the azimuth at Greenwich of the (centre of the) meridian mark is o”.o2 west of north (it is added that “this result may be considered particularly good”); hence the azimuth of Chingford Station at Greenwich is o' o' 1". 64 west. The angle between Chingford and Leith Hill at Greenwich is 4. Q 2 676 8 PRINCIPAL TRLANGULATION. I42° 19 II”.423 (see first triangle, page 498); therefore the azimuth of Leith Hill at Greenwich is 142° 19' 13".o.63. Now let c. = azimuth of Leith Hill at Greenwich. a' = azimuth of Greenwich at Leith Hill. x = colatitude of Greenwich = 90 – A. A’ = latitude of Leith Hill. w = longitude of Leith Hill. s = distance from Greenwich to Leith Hill. Then— cos (x – 6) cos ? (x + 6) sin # (x – 6) sin (x + 6) tan , (c.' + w + š) = cot + c, tan # (a' — a + ') = cot c. *. P ſº 2 X' — A = .S. sin # (c. c. -- ...) I -- #coº ( – ) g sin I" sin # (2' + cz + 3) I2. 2 S. I e” 62 6 = H-7, (1 + 7: . 2 COS” A cos” a) g' Sin I 6 I — e I c3 62 . § = −7; ; cos” A sin 2 c. Sln 4. I – C º It would be practically sufficient to take this small correction & from the table at page 25o; it has, however, been calculated for each required case. - By these formulae we obtain the latitude and longitude of Leith Hill and the bearing of Greenwich. This last angle is found to be 37° 23' 27".755; and by page 498 the angle at Leith Hill between Greenwich and Beachy Head is Ioo” I6' 40". 258, hence the azimuth of Beachy Head at Leith Hill is 137° 40' 8", or 3. Now in the abstract at page 128, Beachy Hill (– 180°) reads 137° 40' 1". 56, to which add the correction (page 387) + o”. 574, making 137° 40' 2". 134 for the abstract reading of Beachy Head at Leith Hill. Therefore it is evident that the reading of the north meridian, if inserted amongst the objects observed at Leith Hill, would be 180° — (8”. or 3 — 2". I 34) = 179° 59' 54". I2 I. Knowing now the latitude and longitude of Leith Hill, with the reading of the meridian in the abstract, we may proceed to determine the same quantities for any other point of which we know the distance and bearing from Leith Hill. The following table contains an abstract of the calculations of latitude, longitude, &c., for those points which are more immediately required for the results in the present Section. The first column contains the name of the Station for which the latitude, &c., are given in the fifth, sixth, and seventh columns; the second column contains the name of the point from which the calculation starts; the third column contains the azimuth of the point in the first column, from the corresponding point in the second, the logarithmic distance, and the value of 0; the fourth column contains log tan (a' + a + 4), log tan 3 (o'— a + š), and the log (distance of parallels). The seventh column contains the calculated reading of the north meridian, found by adding the angle o' to the corresponding corrected “abstract reading,” found between pages 72 and 166, or subtracting it, as the case may require. - - | ſº | GEODETICAL RESULTS. 677 Stations. Obtained from Azimuth Log (Dist.) 6 Logs tan # (a' + a + C) tan + (a’—w + 9) Merid. Dist. Latitude. Longitude. JLEITH ToryER. | Bursen . º BEacow IIILL. DU.NNose . South.A.MPTON. BLAck Dorry. BARRoſy HILL. IIENSBARRoſy . GooxIIILLY PERTINNEY SAINT AGNES J.IGHTIIowsE LUNDY ISLAND. PREcelly. IIIGII WILLIAI's PRECELLY. Greenwich . Leith Tower Butser . JButser . Dunnose Dunnose Black Down Barrow Hill Hensbarrow JHensbarrow Pertinney Hensbarrow Lundy Island . Black Down High Wilhays . 143 16 13. o64 5* I4229329 o 22 45° 184 117 7 7.639 5' 19773428 o 25 5 I Ioo 65 56 5o' 381 5' 27048029 o 3o 33°963 I58 51 33°254 5' 14802983 o 23 3' 376 23 38 38°759 5 ozog'8936 o 19 18° 534 84 55 4' 584 5° 4974O32 I o 5 I 32 °59 I I2 I 39 24.” I4o 5*4984222 I o 51 39°844 77 22 22:286 5' 4295 I547 o 44, 5 II 5 I45 29 Io'961 5' 17326056 o 24, 26. I75 9° 53401869 * 52478814 ‘od.155604 ‘7874591 I ‘777040 15 ‘86oo3794 18928804 * I 7702 I59 ’87576069 ’27196683 26271435 11801869 ;; i '68oo7770 67238850 •o:264761 : O ‘O4O90233 ozo;7416 39779596 ‘749.14607 ‘7285397 I 22.384314 ‘og851 IoI o8 Io9797 * 7542923o '49336734 ‘48368445 ‘os990294 78666084 ‘772484.90 ‘oo44572.7 '80450541 '79272877 '893o8822 . : ::;; • 23475I 16 * 21603605 '45638249 • 39657885 • 37772839 '453.84262 oooo;646 '98390745 ‘749 I5518 o'74683344 o' 71463244 5' 66301646 :: O ? G 51 Io 32 '887 5o 58 sº to 5o 37 5o 50 4. 5o I3 5o 5o 6 49 53 5I Io f f 38. 59° 3 * 54. 47' IO" 58. 45° 22 3o' 233 233 748 226 287. ‘527 8Io •oSI 776 196 51 56 44' 755 5o 4 I 4° 75o 51 56 44' 755 O * JJ o 22 II • OA9 o 58 43' 78o I, 43. I 5' 506 5o 136 7" OS4. 2 32 52 °432 4. I 37° 149 3 5 137 5. Io 38°794 39'961 4o: 633 4 4o 17°983 4. 46.24' 516 4 o 36 Ioo 4 46 24' 515 N. Meridian. 117 16 6. 356 5' 33.879090 o 35 46-427 II 5 7 32-795 5:26078600 o 29 53° 569 6 41 58'912 5'4594o875 o 47 I3 ° 570 4 37 3’563. 5°45527895 o 46 46' 626 89 31 45:297 5' 53015693 o 55 34 836 20 28 43’569 5'6922 IoS9 I 20 43’ I 53 o t. 11 I79 59 54." I2 I 18o o 25' 036 18o o 3 ‘996 18o o 11 o25 I79 59 12 - 217 18o o sºs, 18o o 11:463 18o o 18o o 35' 725 I79 59 58° 702 {Nºis Station. 179 59 44'569 I79 59 44' I44 I79 59 59' 427 179 59 44° 148 678 º|. PRINCIPAL TRLANGULATION. Azimuth tan + Lºgs Stations. Obtained from Log º tan + §: 3 Latitude. Longitude. N. Meridian. | Merid. IDist. 6í 27 58.754 o' 22807935. O M M ſ O f ºf © f ºf mººr } Leith Tower 5.490836+7 22276.1612 51 34 29°856. I-33 57°og8 179 59 45'908 o 5o 46 of 5 5' 16341 190 | 68 4 38' 121 o' 1731 IoS8 i CRADLE JWhitehorse Hill 5' 57766991 o' I478982 I 51 57 5'508. 3 7 16:885 | 18o o 4'971 I 2 o' 193 || 5' 13814190 89 4o 22°788 o'oo;14013 PRECELLY Cradle . . . 5' 57129568 || 9'98oo8733 || 51 56 44°756 4, 46. 24' 517 | 179 59 44° 155 I I 5'906 || 3: 32308415 .., | 18. 36, 3-875 o'787;8297 Annuny HILL. Whitehorse Hill 5' 3984.0001 o' 770899.23 52 13 27-287.| I. I.2-35°o8o I79 59 2 I 592 o 41 2' od 3 5' 37474.244 44 36 41 °861 o° 389748.09 i Ambuny HILL. Greenwich . 5' 58674535 o' 36405782 52 13 27-287.| I. 12 35°ogo 179 59 2f 593 I 3 18°773 5' 43558864 * 743 12 294 | I 17215195 BARD0N HILL. Arbury Hill 5' 25640924 I I5994.672 52 42 50° 754 || I. 19 8 751 | 180 o 6’ of 8 o 29 35' 379 || 5' 2524.1267 -- sº 53 3 26’ 684 o' 30343303 JMorvoopT Bardon Hill 5°38966198 o°28665886 53 6 52-441 || 2 12 41 - 654 || 179 59 58-329 o 40 I2 °858 5' 16494917 69 II 24'407 o' 16208853 DELAMERE Mowcopt 5°o446ooo3 o' 15444049 || 53 13 17:274 2 41 3’562 | 180 o 19° 365 o 18 Io'o.84 || 4° 59136983 9I 37 19°817 | 9'990533.71 SNory DON Mowcopt 5°61266064 9° 96223755 53 4 5' 481 || 4 4 3o'oZ5 180 o 4'208 I 7 12 ‘oor 4'2287on75 n 158 55 50'351 9° 272.46278 r J’RECELLY Snowdon 5'64174764. | 9° 242.238or 51 56 44' 755 || 4 46 24' 516 I79 59 44° 161 I 11 51 283 5:61250768 ſº 17 49 51' 425 o'80732492 SouTII BERULE | Snowdon 5' 61827517 o'778691 33 54 8 57' 597.| 4 40 5°328 18o o 20 787 I 8 4'454 || 5'59631.465 7o 42 34°976 o’ I 5208818 FontLI Precelly 5' 62711621 o' 12.360994 || 52 18 56.829 || 6’ 33 41 °461 | 180 o 2-065 - 1 9 28°719 || 5' 13054873 92 4 54°61o 9'9858.3112 g | JKNocKANAFFRIN | Forth 5°35876256 9'97034988 || 52 17 19° 135 | 7 34 52.941 179 59 57.809 o 37 27' 190 || 3 ‘99590095 | 92 30 37'789 |9-98453331 BAURTREGAUMr Knockamaſſrin . 5’70283559 9'95035443 52 12 24. Io9 - 9 49 44-622 | 180 o 1:366 - I 22 42°648 || 4-47589836 I31 33 9'489 9'6542354o JFEAGLIMAAN. . . Baurtregaum . 5' 19277728 9'64369798 || 51 55 20:297-|Io 20 45' 313 18o o o'808 o 25 33°406 || 5’ or 623367 . : w º :| i3. | GEODETICAL RESULTS. 679 Azimuth Jøgs Stations. Obtained from Log gº #::: 3 Latitude. Longitude. N. Meridian. Merid. Dist. O f #4 O J JJ © f f / O f ff 177 27 46’290 8-34661062 * HUNGRY HILL | Baurtregaum 5°27887967 8° 33376233 51 41 II 474 9.47 31 122 || 179 59 59°796 o 31 9'647 5' 27845865 * - 39 58 51 ° 918 o°442 17618 | KIPPURE . JKnockanaffrin . 5'63ozoig8 o'41326456 53 Io 4o'564 || 6.19 52' 12o 179 59 59:253 I 9 58°363 || 5° 5 II40877 36 59 39°974 o'47960618 JKIPPURE . Precelly. 5-75418108 o'441428oo 53 Io 4o'563 || 6.19.52: 118 || 179 59 59:250 1 33 5' 570 5’ 6530.25oG - 44 48 32 ° 2 II o' 38831434. - SouTH BERULE | Kippure 5'70396709 o' 35334099 || 54 8 57°598 || 4 4o 5' 331 18o o 20.777 I 22 55°346 5° 54983279 41 35 31 o23 o'44206698 + - JKEEPER . JKnockanaffrin . 5' 3554562o o°4067.1257 52 45 4 195 || 8.15.38: 740 || 179 59 58'505 o 37 Io' 15o 5°227479 I7 Io 18 44' 638 I o4837577 CUILCAGH Feeper . 5° 73 Ioo I49 I' or 151916 54 I2 2-877. 7.48 38° 560 179 59 59' off.8 I 28 15 oz.6 5'72368o06 * 4o 3 I5' 754 o'441686.93 CUILCAGIt Rippure 5’ 692 15523 o'40765273 || 54 12 2 '877 7.48 38' 559 || 179 59 59°oyo I 20 41 °851 5° 57.225559 27 14, 3’ offs o' 61938366 NEPIIIN JKeeper . 5’71622.432 o'58376118 || 54 o 47°289 9 22 4° 159 180 o . 4.708 I 25 17: 890 5-66346414 * * 25 31 39°927 o' 64563733 TAIPMAGILMore | Nephin . 5°oš643344 o' 63760970 54 I7 39' 605 || 9 35 51-255 180 . o 7' 617 o 18 40° 132 5’ or 148426 15 19, 23 '856 o'87372521 SLIEVE SNAGIIT Cuilcagh 5: 57672864 o’ 8.4699842 55 II 47° II5 7.2O. o' 253 18o o o' 749 I I 51 '591 5'56060450 i 129 15.5o. 944 9: 67648876 - Lough FoxLE | Slieve Snaght . 4°94653490 9-67007252 55 2 33 '931 || 7 o 25° IoS 18o o . I '872 o 14 29'646 || 4-749 Io'78o o 15 3.786 || 2:66257966 CLIFToM BEacox Arbury Hill 5'65343405 2-63212247 53 27 27 o22 || I. I.3. 7' 668 18o o 15' 343 I 13 49 o'S2 5’ 65342977 4 36 14° 352 I 39768.758 CLIFToM BEAcON. Bardon Hill 5°43504841 1 : 37906519 53 27 27°o22 I. I3 7' 668 18o o 15° 341 sº- o 44, 38' 650 5°43362037 II I4 I5'324 I ‘oog 90458 * i EASINGTON Clifton Beacon . 5'61537072 o' 98.120227 54 33 53° 367 . o. 5o. 24' 132 || 18o o o'913 I 7 37° 142. 5' 60673306 : ſº 9 Io 53°921 | I o9657755 - York MINSTER | Clifton Beacon. 5:27097897 || 1 o83593.16 || 53 57 43.266 || 1 4 49.778 18o o 2'458 o 30 35'813 || 5-26531037 i 68o PRINCIPAL TRLANGULATION. Stations. Obtained from Azimuth Log (Dist.) 0 Logs tan + (a' + o- () tan + (a’—w + () Merid. Dist. Longitude. N. Meridian. Wondeslow . CHEr'IOT . | Sca FELL . Sc4 FELL FIART FELL GoAT FELL SouTH BERULE DIPIs . DITIS . . i SAyns LAiy JURA . BEN NEWIS JBEN JWyj"Is BEN HEYNISII. BEN MoRE, S. U. J2asington . Easington . Cheviot . . South Berule . . Cheviot . . Iſart Fell . Goat Fell . South Berule Slieve Snaght . Cheviot . . Slieve Snaght . Jura . . Ben Nevis’. Jura Ben Heynish •. 45 43 3868 5 ° 2075.2595 o 26 26 - 166 38 49 3' 612 5-63494IIo I Io 43 '887 I48 38 43 ‘843 5'63951494 1 11 28.603 69 44, 26' 592 5' 519365.49 o 54 I2 356 95 6 45°483 5*418384.51 o 42 57° 42 I 77 9 55°436 5' 5791919 I I 2 I2 ° 454. 168 15 16:732 5' 740601.33 I 3o I2 5 Io 59 3 5I '727 5' 52.296532 o 54 39°427 127 7 8. 170 5'54382 II2 o 57 20° 557 38 37 Io' 275 5' 23766058 o 28 20 o49 46 20 22.842 5' 57669069 I I 51 'o63 31 25 56'881 5° 585091.89 I 3 3' 404 14 26 26' 343 5 * 52252507 o 54 35' 631 42 27 32: 651 5'44006639 o 45 9°30I I4 3 42' 661 5°481 15201 o 49 38' of 6 * 33519312 • 323672 oo or 599566 '45599655 '42.5oz 180 ‘52329532 •450984.48 ‘41910561 • 57297.050 * I 5908159 * I 3569226 • OA645578 96.288159 ‘94372.722 ‘4Ioo?644 ;:: :: o' IOOS5575 'o'7286296 ‘90054796 or 576312 ‘97536941 '73 I 749 I5 “24902258 ‘22543849 2270.0631 . : '69.887.703 67348694 3298434o '45656512 *443932Oo 12916926 . : • 37 Io2799 343.64060 *4 II.4O732 : '55312957 * 52470 I52 * 51424O25 ‘8993.1464 ’874I 1937 ‘50823491. ‘41239.458 ' 39.20402 I * 30532732 :: : o'91081.238 o°8881 1354 5 °46764395 O f ſ/ I 25 25-842 2 8 38-127 3 12 36 725 3 12 36.726 3 24 o' 2 I2 5 II 26' 512 4 4o 5°329 2: 656 2’651 2.4o 8' 139 6 o 11'227 5 o 8° 432 4 34 4o '727 6 55 20°981 7 17 38'743 O J f/ I79 59 54°696 I79 59 50 °39 I 18o o 7:217 18o o 7' 219 18o O 13° 769 18o o 8' 555 18o o 20 799 18o o 1' 284 18o o I 273 18o o o' 304 18o o 4' 625 I8o 14' 782 O Latitude. O f f/ 54 5o 56° 160 55 28 42° 372 54. 27 47. 54 27 I4°774 55 24 28'961 55 37 32-899 54 8 57°597 54 36 4o'327 54 36 4o'326 55 50 49°439 55 54 8'90o 56 47 49' 339 57 4o 45° Ioo 56 27 19:638 57 I5 32 ° 205 179 59 53' 164 18o o 1. 367 18o o 7.077 i | ; . GEODETICAL RESULTS. 68 I º Azimuth Lºgs Stations. Obtained from Log (Dist.) i. #::::: Latitude. Longitude, N. Meridian. % Merid. Dist. 8; 56 8.08 495 O f // O f/ O W f/ O 5 °C) o' O495 I49 ScovºxazAP1cII | Ben More, S. U. §§oj” o' or 552482 57 22 Io' 334 5 3 31 679 18o o 12° 24o I 12 43' 608 || 4'60641681 - 28 51 o'919 o' 5912 ooo; * BEN LOMOND . . Goat Fell . 5' 37281477 o' 57388944 56 II 25-26o || 4 37 54° 183 179 59 58'802 o 38 4o 663 5' 31429474 85 37 51 oš6 || o'oj496231 EAST Loyſon D. Ben Lomond . 5'45939307 o' or 352.225 | 56 14, 32°515 || 3 13 II 223 I79 59 53 '951 o 47 12 547 || 4 ° 278750oo - 175 47 35° 218 8: 56566434 CALTON HILL . . E.L. omond 5 oz.2 18968 8' 55782219 55 57 18:042 3 Io 55°592 I79 59 55-472 o 17 15 'o'77 || 5 'oz Io2669 88 26 39'915 o' or 235621 RELLIE LAW . E. Lomond . 4'95283.913 o' ooj6698o 56 I4 53°689 || 2 46 43°752 | 179 59 47'oz 5 o I4 42 312 || 3:332 II581 90 II 17" 763 9-99968,054 BEN CLEUGII . . Ben Lomond 5.24547749 9: 98658077 56 II 8-695 || 3 46 3-873 179 59 59'890 o 28 50'858 || 3:2255oro1 3 31 26' 584 | I 514012oo || BEN MAcDUI . . .Ben Cleugh 5 °5 Io:34.299 I 489905oo 57 4. I4' od 3 || 3 4o 3° 749 I79 59 51 ° 212 o 53 5' I 3o 5° 50950 I53 * - | 67 48 I 4: 203 o' 1744.3125 Scourt.NALAP1c11 || Ben Macdui 5'47207618 o’ I 5.183542 57 22 Io'334 5 3 31-683 18o o 12°277 , o 48 36' 35o 5 'o'383.1537 - 5 o 42 769 || 1 36280698 | BEN MacDUI . . Hart Fell . . 5'78512472 I 31829.316 57 4 I4' od 3 || 3 4o 3-749 || 179 59 51 ° 213 I 39 56'908 || 5'78338734 - - 23 54 23° 513 o' 67739068 BEN MIACDUI . Sayrs Law . 5'69059.228 o:64iigoş5 57 4 14-o.13 || 3 4o 3°749 || 179 59 51 ° 216 I 20 23: 747 5’ 65023965 -- 67 9 45° 141 o' 1800.1544 - DUDIVIck Ben Macdui 3.54%; o: 1534.1963 57 25 50°886 || 2 2 6'952 179 59 49' 199 o 57 12 °433 5' 11927.532 Io3 4 48 or I 9: 9or 14584 MoUNT BATTock Ben Macdui 5' 27887692 9-88666566 56 56 57°814 2.44 25' 376 179 59 45' 302 o 31 9. Io9 4' 64608625 I9 57 49° of 7 o' 75615735 - Christianſ . Ben More, S.U. 5.4384,4003 o. 735 1394.4 57 57 50-561 || 6 48 41-648 179 59 58°856 sº o 44 58 ‘977 5*4 Io9655o 33 52 2'538 o' 51749 II.4. MoMACII . Cleisham . 5-23842308 § 58 21 23'543 6 18 32°931 179 59 55' 396 o 28 22 '809 || 5' 15658744 - 6 5 32° 526 9.95589.298 - - Prs cania. | Monach . . . ºsé"|}}#}|ss 4 7.84 |4 24 33-334 179 s5 53-97. I o 19° 348 || 4 - 64564665 4. R. 682 PRINCIPAL TRIANGULATION. tº º Azimuth anº.9 º * tº sº gº Stations. Obtained from Log gº tank (a’—w +8) Iatitude. Longitude. N. Meridian. Merid. Ilist. o , , iſ O / / / O J / f O M MA tº ſº 16o 49 47' 206 || 9°23020235 : BEN MacDUI . Ben Clibrig 5'65297.290 9° 19489537 57 4 14-043 || 3 4o 3-744 179 59 51 - 130 I 13 42 '927 | 5' 62902369 i. 6o 8 58'903 o°2397.9234 *. Conny HABBIE . . Ben Nevis 5'61442657 o' 20865545 || 57 20 41°415 || 3-11 41.826 179 59 58-971 I 7 27' 589 5°30'129905 | 147 48 38' 209 || 9°46123158 - MoUNT BATTock Corryhabbie 5' 23133844 9'448.15616 56 56 57°813 2 44 25' 371 || 179 59 45-252 o 27 55' 312 5’ I 5976935 67 8 18-786 o' 17957909 Monyſon TII Corryhabbie 5' 39385588 o' 16056812 57 36 Io. 258 2 I 52.860 | 179 59 41 ° 208 o 40 35' 64o 4'97434.578 *- 4o 11 25' 557 o°43767866 | Corwin"TIIE Corryhabbie 5' 2 Io94748 o'42520591 || 57 41 o' 492 || 2 39 32 °726 I79 59 55' 574. o 26 38' Io:3 || 5°og2.43744 * N. * 13 22 50°273 o°93269266 +. ScAnapin . Corryhabbie 5 * 5 I 742.292 o' 90742 1.87 58 13 14° 567 || 3 35 24" 240 179 59 57' 292 o 53 57°279 5° 5oš16967 --- * 2 16 20 291 I '70454339 JBEN FIUTIG . Ben Wyvis 5'50373952 I ‘67983218 58 33 5' 124 - 4 3o 42° 372 179 59 54. 943 o 52 16 751 5' 50338o3.5 - * 49 I5 30-675 o° 34058686 North RoNA . Ben Hutig 5' 50903727 o' 31495285 59 7 17:674 || 5 48 49.941 No Observations. o 52 55' 169 5' 3.1879,034 23 49 58 oz.5 o'67840956 NonTII RoNA . . Cleisham 5'66644395 o°64217299 || 59 7 17' 673 - 5 48 49' 942 | No Observations. I 16 2.333 5' 62631.191 i 46 5 2 207 o°37355oo4. JFITTY HILL Ben Hutig 5' 5934o827 o' 34.241572 59 17 13 ozo. 3 o 3-669 179 59 55'970 | I 4 16°oo8 5°4294,0309 * 34. I4 35 °o8o o°51413438 | IFITTY IIILL JBen Clibrig . 5:67036490 o°47728964 59 17 13 ‘ozo || 3 o 3' 669 || 179 59 55-972 I 1643-644 5° 584.57749 27 49 44'258 o' 60801187 • * Foul...! Fitty Hill 5. 54.914673 o' 57929165 6o 8 26’ 609 || 2 5 38-668 179 59 55-435 * o 58 2 ° 249 || 5 °4942 orog 5o 25 16:360 o' 328471 Io PELL Foula 5' 37153330 o'30890;32 6o 32 49-262 | I 5 12" 594 179 59 56. 139 o 38 33°276 || 5' 17173825 § The following table contains, in continuation, those calculations which, on account of short distances, have been made by the shorter method, page 253. The fourth column contains the azimuth, and under it the quantity log (x, — »); the fifth column contains log w, and under it log v. GEODETICAL RESULTS. 683 Stations. . Obtained from log &–x) #: Latitude. Longitude. N. Meridian. JWROTHAM Leith . º;" ::::::::: s's sº –s º º sº • sº FAIRLIGHT . Wrotham *::::::::::: 3.; so sº 36,494 – 37 378; 79 59 sy49; GADs HILL Wrotham *:::::::::" : ; 51 24 50'o61. –o 27 55-379 179 59 57-669 Southampton. Dunnose *:::::::::3% ::::::::: 5o 54 47' 226 .1 24 7'o';4 º 59 12 - 217 | WEEK Doryn. Dunnose *:::::::::" ::::::::: 5o 35 5o'277 I 14 2 143 18o I 45.759 JBonifacE . Dunnose *::::::::::: ::::::::: 5o 36 9-628 I II, 55-587, 180 ..o 15.237 H. P. CLIFF . . Dunnose . "...:” ::::::::: 5o 35 43' 168 I I I, 30°4I4 . Nil. DUNKERY. High Wilhays . *...:” ::::::: 51 9 44' I 19 || 3 35, 8° 095. 180 o o'5oz DANBURY . . . Gads Hill . . *::::::::” ::::::::: 5, 4, 57.897 -o 34 33-746 iſ 59 35-378 THAXTED . . . Danbury . 3:...}}..." ::::::::: 51 57 13-663 –o 20 36' 183| 179 59 55-604 JBALSIIAyſ . Thaxted . . . :::::::::” ::::::::: 52 7 57'968 |-o 19 II '841, 179 59 53.391 JELY JBalsham . Af Zºº” ::::::::: 52 23 54" o4I -o I5 5I ‘570 180 o 14' 310 "º Ely . . :::::::::” ::::::::: |s. 43 41.884 – 13 27-78, 179 s5 49.437 manos . . . Danny *:::::::::" ::::::::: si si so.136 – 17 23:31: 179 so sz-616 ORFORD CASTLE. Walton . . *:...is...” :#; 52 5 37-411 – 31 57.033 180 59.342 MAUGHToN Danbury *::::::::* ::::::::: 52 6 4' 547 –o 57 II 175 180 o * Sourt Lorius Naughton. o ;....:” ::::::::: 52 23 43°295 -o 59 52.878 I79 59 39'587 Carbridge . . Balsham . *:::::::::7; ::::::::: 52 12 50'821 –o 5 48-99: - Nil. + BURLEIGII Moon Easington tº *::::::::::: .#. 54 34 I5'742 I 2 20-411 179 59 50° 197 BRANDON Wordeslow *:::::::::" :#; 54 45 17°629 i. 40.36.632 179 59 56°oo6 *:::::::}|* . . ; ;"|::::::::: * * * : * * * 4. R. 2 * . . - + j : 684 PRINCIPAL TRIANGULATION. Stations. Obtained from log &–x) ;: Latitude. Longitude. N. Meridian. Horn. * JKippure . . *::::::::::: :#; s i. º g * sº iss & res, %.} IIowth . *:::::::::" ::::::::: 53 I7 32° 559 6 7 51 553 Nil. DUNRICII . Hart Fell . ####" ::::::::: 55 34 I9'95o 3 11 I-472, 179 59 56'249 |*::: *}|Dulwick . . . º.º.º.:” ...; s? 27 33°23' || 48 37.09: 179 sº 49.33, *...*}| Liu, siring . *::::::::::: ::::::::: 57 27 50° 143 | . I 47 16°371. I79 59 II '992 IEoNAs . I’ell . tº *:::::::::* ::::::::: 6o 32 3' 843 || 1 26 37'594. I79 59 54°228 BALT4 Pell *:::::::::” 3.; 6o 45 7. 156 o 47 4242 179 59 57.859 Saxaronſ . Fell . . . *:::::#;" ::::::::: 6o 49 41 ° 992 o 5o 20° 733. I79 59 57°673 GERTII of ScAir Saaravord *::::::::#" ::::::::: 6o 49 I '818 o 46 9' 391] 179 57 37' 295 i GERTII of Scair Balta . . *::::::::” :::::::: 6o 49 I '818 o 46 9:389) 179 57 sº Docking tº {" '}},...} *::::::...” :::::::: i 52 54 2 '956 –o 37 28°456. I79 59 52°426 MoRDINGTON . Sayrs Daw . *:::::::::7; ::::::A; 55 48 28°453 | . 2 4 Io'535, 180 o 7'596 BURNSIrank . . Hart Fell . . *::::::::::: ::::::::: 55 5 42 270 3 16 37' 679, 18o o 2 - 176 Let us now compare the latitude of Saxavord arrived at by these calculations with the distance of the parallels of Dunnose and Saxavord calculated at page 508. Tor this purpose it will suffice to calculate the length of the meridian arc between the latitude 50° 37'3”. 748 (the latitude of Dunnose, see page 677,) and the latitude 60° 49'41". 992. * Ringstown Observatory is fixed from Howth and Poolbeg Lighthouse. All the angles of the triangle Kingstown- Howth-Poolbeg are observed, and Poolbeg is observed from three points, Lyons Hill, Dublin Observatory, and IIowth. This connection gives two cquations of condition, whence we obtain the following corrections— Lyons to Poolbeg + 6-4314 Dublin to Poolbeg – o 'o215 Howth to IGingstown — 5: 2898 Howth to Poolbeg -- o' 2668 to be applied to the observed bearings. From these corrections it is easily found that the angle at Howth between Dublin and Kingstown is 70° 8' 37" o48; IPoolbeg to Howth — dº 6694. Toolbeg to IGingstown -- o'5454. Kingstown to Poolbeg – 3’ or 58 ICingstown to Howth + o' 28o3 and that the log. distance from Howth to Kingstown Observatory is 4' 51 17759. GEODETICAL RESULTS, 685 By page 267 we have this distance S– - 8 a” O’ S-(+y (n + - m, sin & cos 2 x + m, sin 2 + cos 4 × – m, in 3 cos 6x) — ` 9 2 *sm 45 m = 1 + 1 a m, = 3n - # nº – 15 wº – 35 m, = # n m3 = 24 7:3 + In this calculation we must use the same values of a and b as in the calculations of latitudes and longitudes ; namely, a = 20923713, b = 20.853810. These give m = 1. ooooo;2993; m, = oojo 1969; m, = -ooooo;2494; m, = , oooooooo;8; also p = Io° 12' 38”. 244; 2 x = I II* 26'45".74; log 8 a b' (a + b)-3 = 7.31991o25. JFirst Term + Second Term + Third Term — JFourth Term. — 7:31991oz.6 7:31991 og 7:31991 7-3 IQ9 m • -ooooo.274. m, 3.7006768 m, 6.72011 m, 9.8325 & º º: sin p tº 1.2486285 sin 2. p * T-54272 sin 3 § ſº I-7072 sin I” . 6.6855.7487 COS 2 X • 7.5630357 COS 4 × . 1.86489 cos 6 x . I-9549 6.57084262 3-8322513 I-44763 2.81.45 First . . . . . . 37.22567.82 Second . . . . . . -- 6795-97 Third . . . . . . — 28.03 IFourth . . . . . . — •o7 Distance of Parallels . . . . 372.9335.69 which exceeds the quantity calculated at page 508, namely 3729334 oz, by I. 62 feet, or less than 20 inches. This difference must be admitted to be immaterial, when we consider the multitude of figures through which the present distance is obtained. We may apply the same test to the calculated latitudes of Hensbarrow and Ben Hutig and their meridional distance calculated at page 506. The latitudes are 50° 22' 58".8 Io and 58° 33' 5". 124, hence b = 8° 10' 6". 314 and 2 x = IoS’ 56’ 3”. 934: the calculation is as follows:— - JFirst Term + Second Term + Third Term — Ifourth Term — 7.3199 Io.26 7:31991.03 7:31991 7:3199 m . o-ooooo.274. m, 3.7006768 m, 6.72OII ms • 9.8325 ©” . 446844°59 sin 4 i.1525433 sin 24 - 7.44914 sin 3 + . .6178 sin I" 6 68557487 cos 2 × . I-51 (1957 cos 4 x . .89731 cos 6 x , 1,9226 6-47392846 3.6843261 I-38647 2.6928 JFirst . . . . . . 2978025-78 Second . . . • + 4834-22 Third º tº tº tº tº º º 24°35 * Fourth . . . . . . — off Distance of Parallels . . . . 298.2835.60 which differs only ‘og of a foot from the quantity given at page 506. 686 PRINCIPAL TRIANGULATION. § IV. * Pauations of Condition. Latitudes.—Besides the thirty-two points whose latitudes have been determined with Ramsden's or Airy's Zenith Sector in the course of the Ordnance Survey, we may also take account in our equations of condition, without increasing them to an unmanageable number, of the observed latitudes of the Observatories at Cambridge, Durham, and Edinburgh. The latitude of Cambridge Observatory, kindly supplied by Professor Challis to Captain Yolland in 1851, is 52°12' 51".63. A first determination was made by the present Astronomer Royal in 1833, an account of which is given in the volume of the Cambridge Observations of that year, and in the Transactions of the Cambridge Philosophical Society, vol. v. An account of a subsequent determination by Professor Challis, is given in the volume of the Cambridge Observations for 1838, page lyiii. The (weighted) mean of the two determinations is the latitude above stated. ... • The latitude of the Durham Observatory, kindly supplied by Professor Temple Chevallier, is 54° 46' 6". 20. The latitude of the Royal Observatory, Edinburgh, is 55° 57' 23”. 20; kindly supplied by Professor. Piazzi Smyth. Hence the latitude of Calton Hill Trigonometrical Station (which is 6.08 feet more to the south than the Centre of the Dome or of the Altitude and Azimuth Circle) is 55° 57' 23". I4. * - The following table contains the comparison of the astronomical latitudes with those calculated with Airy's elements:— Stations. Observed Latitude. Calculated Latitude. IDiff. - º O f {{ O f #1 JJ Greenwich . . . . 51 28 38° 30 Saint Agnes . . . . . 49 53 33-93 49 53 3o'776 – 3' 154 Goonhilly . . . . . 5o 2 50° of 5o 2 45° 352 — 4'718 Hensbarrow . . . . 5o 23 I '84 5o 22 58 ‘8 Io — 3 oso I}lack Down . . . . 5o 41 8-89 50 41 Io'287 | + 1 - 397 Dunnose . . . . . 5o 37 7 o8 5o 37 3: 748 || – 3-332 Boniface. Down . . . 5o 36 Io' 55 5o 36 9' 628 — o' 922 Week Down . . . . 5o 35 5I '42 5o 35 5o 277 | – I I43 | High Port Cliff . . . 5o 35 43 °28 5o 35 43 168 || – o II2 Southampton . . . . 5o 54 46' 97 5o 54 47' 226 + or 256 Precelly . . . . . 51 56 45' 18 51 56 44°755 — o'425 Arbury Hill . . . . 52 13 26' 59 52 I3 27-287 + o-697 Delamere . . . . . 53 13 18:61 53 I3 17' 274 — I 336 Clifton Beacon . . . 53 27 3o°4o 53 27 27°o22 — 3'378 Burleigh Moor . . . 54 34 19' 67 || 54 34 15' 742 – 3 '928 Hungry Hill . . . . 51 41 Io' 26 51 41 II 474 + 1 .214 Feaghmaan . . . . 51 .. 55 22 '85 || 51 55 20°297 – 2:553 Forth . . . . . . . 52 18 57'91 || 52 18 56'829 — 1.681 Tawnaghmore . . . 54. I7 41' 34 54, 17 39' 605 | – 1.735 Lough Foyle . . . . . . 55. 2 38°74 55, 2 33.931 — 4.869 South Berule . . . . 54 8 56-46 ( 54, 8 57-597 + i. 197 Ben Lomond . . . . 56' II 26-27 | 5é 11 25-266 – 1 of6 º & GEODETICAL RESULTS. 687 Stations. Observed Latitude. Calculated Latitude. IDiff. ICellio Law . . . . . 56 I4 5 I 52 56 14 53*689 + 4. 169 Ben Heynish . . . . 56 2; 16.88 || 56 27 13-638 || -- 2:758 Great Sterling . . . . . 57 27 49' 12 || 57 27 56' 143 | + 1.623 Cowhythe . . . . . . 57 4t 8.96 || 57 41 o°491 – 8.465 Monach . . . . . . 58 21 29 '84 58 21 23'543 + 2 - 703 Ben Hutig . . . . . . 58 33 6'47 58 33 5-124 || – 1:346 North Rona. . . . . 59 7 15' 19 59 7 17:673 | + 2 - 483 Balta. . . . . . . . . . . 6o 45 ºr '66 6o 45 7. 156 + 5°496 Gerth of Scaw . . . 6o 48 56°43 6o 49 i 818 + 5. 388 Saxavord . . . . . 6o 49 38° 58 6o 49 41 ° 992 | + 3 412 º Calton Hill . . . . 55 57 23 I4 55 57 18:042 | – 5’ og8 Durham . . . . . 54 46 6'20 | 54 46 5' 30o — or 90o Cambridge . . . . 52 12 51 - 63 52 I2 5o '82 I – o '809 A careful examination of the differences in the last column of this table will make it clear that the elements used will require modification, as, with some exceptions, we have negative signs in the southern, and positive signs in the northern Station. The required modification will increase the discrepancy at Cowhythe by more than one second; we shall therefore omit this Station in the Equations of Condition. arº Longitudes.—The Astronomical Observations taken at different Stations of the Triangulation during the progress of the Ordnance Survey, do not include any determination of longitude. The longitude of Feaghmaan has, however, been determined by the Astronomer Royal, assisted by Captain Gosset, R.E., and a party of Sappers from the Ordnance Survey. Of these operations an account is given in the volume of the Greenwich Observations for 1845. The arc of longitude from Greenwich to Valentia was subdivided at Kingstown near Dublin, where a temporary observatory was erected. The transit instruments used at Kingstown and Valentia were the property of the late Mr. Sheepshanks, who took an active part in the undertaking; the length of the former was 42 inches, that of the latter 30 inches. For comparison of the transit clocks at the different Stations, thirty pocket chronometers were used, carefully packed in two cases. From Greenwich to Liverpool the chronometers were transmitted by railway, thence by steamer to Kingstown, thence by railway to Dublin, and thence by mail coach to Limerick. From Limerick to Tralee the chronometers were transmitted by mail coach, under charge of a Sapper, and thence under another Sapper to Cahirsaveen Ferry. The chronometers left Greenwich the first time on the morning of June 27, 1844, and reached Kingstown the last time on the morning of July 27, having made nine journeys the one way and eight the other: they then left Kingstown for Liverpool Observatory on the evening of July 27, and were returned to Kingstown the last time on the morning of August 4th, having made four journeys each way: they then left Ringstown for Feaghmaan on the evening of August 5, and were returned to Kingstown the last time on the morning of September 14, having made ten journeys each way. 688 PRINCIPAL TRIANGULATION. * For all the details respecting the reduction of the observations, determinations of clock errors, corrections for personal equations, &c., the reader is referred to the Greenwich Observations for 1845, where every point is very fully treated. The final results, page coxxiii, are:— ??, S Liverpool Observatory, West of Greenwich . . . . 12 o'o.5 Ringstown 33 35 32 • 24, 3I-2O Feaghmaan 33 55 53 • . . 4I 23.23 The longitude of Cambridge Observatory, as finally determined by Professor Challis, from Observations of Galvanic Signals, is 22°. 689 East of Greenwich. This determination will be found in the Monthly Notices of the Royal Astronomical Society, vol. xiv, May 1854. The previously adopted longitude was 23°. 54, determined by transits of chronometers between Greenwich and Cambridge in 1828, of which an account is given in vol. iii, of the Transactions of the Cambridge Philosophical Society. The dome being 45.4 feet east of the transit instru- ment, its eastern longitude is greater by o”. 729 or o’.o.49. The longitude of the dome is therefore 22°.738. The longitude of the Durham Observatory is 6” 19”. 75. The dome being 12.5 feet west of the transit instrument, its longitude is greater by o”. 213 or o' or 4; hence the longitude of the dome is 6” 19”. 764. - - The longitude of the Royal Observatory, Edinburgh, is 12" 43°. oo; that of the Trigonome- trical Station is greater by o”. OS6 or o'-oo.4. , Stations. Obsd, Longitude, Calc. Longitude. IDiff. D x cos A. O f ſ/ O f f | Calton Hill . . . 3 Io 45° off 3 Io 53.59. — 1 o' 532 — 5'896 Durham . . . . . I 34 56°46 I 35 4° 4oo – 7'94o – 4° 580 Cambridge . . . . – o 5 41-66 – o 5 48-991 | + 7.931 + 4-859 IGingstown . . . . 6 7 48°oo 6 7 51.553 – 3:553 – 2 - 123 | Feaghmaan . . . . Io 20 48'45 Io 20 45' 313 + 3 - 137 -- I '935 Azimuths.-Pages 167 to 196 contain observations for the determination of absolute azimuth at thirty Stations: page 197 contains an abstract of the results of similar observations at thirty-one additional Stations, which being less accurate or less important from their position in the triangulation, it was not considered necessary to print in full. The calculated probable error is given, which will show the amount of dependence that may be placed on each. Obser- vations for azimuth have been also taken at a few other Stations, but have been cancelled, having been taken either under very unfavorable circumstances, or by men under instruction, or merely for practice. The sixty-one results given in this volume are more than sufficient for the deter- mination of the absolute azimuth of the triangulation as a whole. It would swell the number of equations of condition to an unnecessary amount were all these 61 results included; it has been considered sufficient to take the first thirty (given in full) together with the azimuths at Docking, Orford Castle, Walpole St. Peters, Sayrs Law, and Scournalapich. | - GEODETICAL RESULTS. 689 For the comparison of the observed and calculated azimuths, let P be a Station at which these quantities have to be compared. 4 = Abstract Reading of Q at P (pages 72–166) If = 33 99 Referring Object at P R = Observed azimuth of , 32 , (pages 166–197) C = Calculated correction to A (pages 372–41 3) – E = Calculated reading of North Meridian at P ºr At fº azimuth of Q = A + C + E Observed azimuth of Q = A + C + R' — R ... (Calc. – obsd.) azimuth = E + R – It’ 180° In the following table the calculated and observed azimuths at thirty-five Stations are contrasted. The sixth column contains the required difference. Abstract Reading Observed Azimuth - 77° -1. T. Stations. of *~ of I? - R' IE I? — I?’ + E S x cot A. Referring Object. Referring Object. - :- d & J. f {{ If 4 / JJ f f Blackdown . . . 316 31 58-96 316 32 I 55 — 2 '59 || – 5'854 – 8'444 – 6'915 Dunnose . . . 339 12 19: 99 || 339 12 12° 59 + 7' 40 – II '925 – 3' 625 | – 2 976 Precelly . 2 II 58 30°og 21 1 58 46' 38 — 16'29 + 15-851 – o '439 — o' 344 Cowhythe . . 66 27 31 '99 || 66 27 36'91 — 4'92 | + 4*426 — o'494 — o' 312 Wrotham . 274 56 45 - 11 274 56 37' 5o + 7' 61 – 5° 566 + 2 o44 + I 637 Gads Hill . 307 II 50° of 307 II 48' 95 || + 1 . I2 + 2* 33 I + 3 ° 45 I | + 2 754 Fairlight º . 276 5 8° 93 276 5 II • 57 – 2 64 + 6' 505 || + 3 '865 + 3 144 Orford Castle . . 68 51 29°77 | 68 49 23.65 + 126-12 — I 19° 342 | + 6-778 + 5.278 I3alsham . . . . 15o 59 14°94 15o 59 12" 77 | + 2 - 17 | + 6'609 || + 8.779 || + 6-826 Walpole, St. Peter's . 194 47 29°96 || 194 47 31 '91 | – I '95 | + Io' 543 + 8:593 + 6' 539 Docking . . . . 4o 47 29.’ Io 4o 47 21 ° 26 || – I 16 + 7' 574 + 6-414 | + 4-851 South Lopham . . 190 II 6'82 190 II 2 '68 + 4* 14 | + o-413 + 4-553 || + 3 - 567 Ieith Hill . . 22 I 32 45°os 22 I 32 53' 17 | – 8: 12 + 5°879 || – 2 - 241 — I '8o3 JButser . . . IoS II 14'96 || Io8 io 54-92 + 20°od – 25 'o';6|| – 4: 996 || – 4: o39 IBeacon Hill . 212 52 57: 12 212 52 55 o8 + 2 o4 – 3 ‘996 || – I '956 — I 574 Darrow Hill . 352 32 29.98 || 352 32 27-79 + 2 - 19 – II 463 – 9:273 || – 7'718 Lundy Island . . . 194 2.5 50.99 194 26 4'99 || – 14' oo + 15°43 I + I ‘431 + 1 . I52 Dunkery . . . ... 84 41 9.98 || 84 41 14-46 — 4-48 || – o'502 || – 4: 982 – 4 or I Mowcopt . . . . 28o 37 6.87 286 37 2'55 + 4'32 |-|- I 671 + 5°991 + 4*496 York Minster . . 26o 26 25: o3 26o 26 26'63 | – I'69 - 2'458 – 4: o38 – 2 '952 Basington . . . . 128 38 55' of 128 38 60'49 — 5:46 – o '913 – 6' 373 – 4' 535 Wordeslow . . . . . 57 51 4'98 || 57 51 18-off – 13 'oZ + 5' 394 – 7'766 — 5:468 Hart, Fell º . 35o 20 29-89 350 20 11 - 11 + 1878 - 13-769 + 5’ or I + 3:456 Cheviot º 246 9 15 'o'; 246 9 30' 63 – 15'58 + 9'609 || – 5'971 – 4: Io'7 Dunrich . . . 242 28 42 - 12 242 28 56'85 – 14° 73 + 3 751 — Io'979 || – 7' 525 Goat Fell , * 233 2 2-31 || 233 I 57'98 || + 4°33 - 8' 555 – 4-225 | – 2 '899 Sayrs Ilaw . º 113 5o 20 oo 113 50 21 '61 — I 61 – or 3o4 — I '914 — I 298 Mordington º 148 27 44'92 | 1.48 27 4o. 51 | + 4*41 – 7.596 – 3’ 186 || – 2 - 165 Burnswark . . . 204 52 12-04 || 204 52 7:20 | + 4:84 || – 2 - 176 + 2*664 + 1 ‘859 Den More, S. Uist . 305 41 44-45 305 41 4t '70 + 2.75 – 7'o'77! — 4.327 | – 2 782 Ben Macdui 161 48 21 '98 || 161 48 29.96 – 7'98 || + 8-786 + o-'806 | + or 522 I}en Nevis . 81 52 46 oz 81 52 22:51 | + 23: 56 – 14-782 | + 8-778 + 5’745 Scournalapich . 351 58 3999 || 351 58 35' 14 || + 4-85 — 12 240 | – 7° 390 - 4'73% Mount Battock 238 28 2 I 5o 238 28 44'26 – 22.76 + 14' 698 || – 8.062 | – 5 246 Mormonth . 84. 55 I 7'oz 84 55 47° 19 – 30° 17 | + 18: 792 —II : 378 — 7 - 220 4 S 690 PRINCIPAL TRIANGULATION. Equations of Condition—If the sides a, b, and the included angle C of a spherical triangle receive increments da, db, and dC, the corresponding variations of the other parts are given by the following equations:— Sin C dA = sin B da – cos c sin A db – sin a cos B do Sinc dB = sin A db — cos o sin B da — sin b cos A dC do = cos B da + cos A db + sin b sin A dC These are without much trouble transformed into the equations (18), page 62o. If in the latter we put— IOO (1– c’)” ico; = p , p = } cos ?) (A + 3 x') h and also for y and s, write w(arc Ioo") and v(arc Ioo") respectively, then— Q e = p.’ (X' – X) sin I”. v — 80 = Ioo 6 sin I". w -- Ioog 9 sin I”. v # sin 2X 1 – c' sin “A Where g is a constant quantity, namely the value of for the latitude of Greenwich; = o' 307299 = log - I.4875618. Divide each of the three equations by sin 1", and the second and third by — sec x' and tan x' respectively; they will then assume the form— *" = k + a, § -- b, n + c, w -- e, v m. - * = k + a, § -- b, n + c, w -- e, v * = k + as š + b, n + c, w -- e, v The values of the absolute terms are— k, = (calculated – observed) latitude k, - (observed — calculated) longitude x cos x' k, = (calculated — observed) azimuth x cot x' The values of the coefficients are— a, = COS w b. = sin A sin w # * c. - p. 6 cos &’ e, - tº g 6 cos &’ + p.’ (x’ — A ) . in x' si Ö cos x' sin 6 cos &’ - - = 81E1 CE) := -- sºme --→ . c, - Ioo 6 sin a' e, as Ioog 6 sin c.' sin w sin A cos w 0.3 = — —-, b, = —-7– SIIl A Sln. A c, - Ioo 6 sin &’ e, as Ioog 6 sin c.' f. º,| GEODETICAL RESULTS. 691 The following table contains the logarithms of p. sin I" and p sin I":— X/ Log p sin I" | Log uſ sin 1" A x'' Log usin 1" | Log H'sin 1" A 49 .. º ### 46 55 .. 6.6%; ...; ; 4o 77. 3.; 4.50 4O | . # 3. 530 5o o 6-68676. :::::::: § 56 o 6'68654 6°21043 ; 2O - tº º * 40 # | ###| #: . . ; ; ; ; ; ; 5I o 6-68672. 6'28575 ; 57 o 6'686.50 6' 19408 # : | . . . . ; ; ; ; . . . . . ; #; ; 52 o | 6’ 68669 || 6’27149 #. 58 o 6'68647 6' 17726 ; - : % || 3:; #3 | . # ### #; 53 o 6'68665. 6' 25685 492 59 o 6-68643 6’ I 5996 582 2O 64. 6' 25188 497 2O 42 6' 15408 | 588 4o & 6:24686 . 4o 41 6' 14814 || 334 54 o 6'68661 6' 24.180 ; 6o o | 6’ 68639 || 6’ 14215 ; : ..., | #| || | | | | | | | | #; ; 55 'o 6.686;7 | 6’22633 || 5 61 "o | 6,686% 6.12% | * ; In the application of the equations (18), page 620, to the different points in the triangulation at which astronomical observations have been taken, it is to be observed that 9 corresponds to the distance of any such point from Greenwich, and 2' is the azimuth of Greenwich from that point. All azimuths are measured from north by east, and longitudes westward. It is immaterial that the latitude, longitude, and direction of the meridian at any point have been arrived at, not by means of the direct distance from Greenwich in one step, but by several steps. The quantities 6 and o' are required for every point entering into the equations of condition; their values, computed from the latitudes and longitudes, are as follows:— Stations. {} a’ Stations. {} a’ Arbury . . . I 3 IQ 134 26 13 Cowhythe 6 22 51 164 55 42 Balsham . . . o 40 59 196 57 44 Cheviot 4 II 26 I61 24, 23 IBarrow Hill . 2 38 37 6o 26 50 Corryhabbie . 6 8 31 I6I 4 5 Bardon I 28 34 I46 Io 38 Cambridge o 44. I5 1844I 49 Butser o 47 24 5o 29 16 || Cradle I 59 27 Io2 30 55 Ben Lomond. 5 26 I4. I47 56 34 Dunnose . I 8 27 40 49 2. Ben Hutig 7 3o 55 I58 o o Delamcro. * - ſº 2 23 26 135 38 12 Ben Heynish 6 25 5 I37 48 20 Dunkery . . . . . 2 I 5 45 8o 37 9 Beacon Hill . . . . I 6 53 74 3 55 Dunrich . tº º q 4 3o 6 I53 5 I I Ben More, South Uist . 7 9 25 I4o 36 14 Durham . 3 25 5 163 I2 32 Ben Macdui . . 5 58 33 I 57 29 52 Ditchling. . O 34 42 6 33 28 Ben Nevis 6 3 36 I49 2 22 Dunstablo o 3o 30 I39 4 22 Black Down . I 47 4 62 46 I9 Docking . I 28 16 195 20 2.I 1 Boniface Down . I 9 9 40 22. 52 Easington . . . . 3 7 17 17o 20 48 Burleigh Moor . 3 8 48 168 7 46 Edinburgh Observatory I55 5o 51 Burnswark 4. 6 I9 I5o Io 50 (Calton Hill). º 4 50 49 Balta. . . . 9 I6 3 I76 57 42 Feaghmaan . º 6 25 20 89 53 8 Beachy Head o 45 II 347 5I 27 || Forth Mountain. 4. 7 59 99 4 30 Bunwell . I I3 4o 215 o 29 Fairlight. o 42 5 I 327 I4 30 Clifton . 2 6 37 I58 54 51 Frittenfield . o 35 I 297 47 26 | 4 S 2 692 PRINCIPAL TRIANGULATION. Stations. 9 a’ Stations. 6) a’ O f f/ O f J/ Q J & O * f f Goonhilly 3 34 18 64 27 25 | Orford Castle . . I 7 46 237 38 2 I Gorth of Scaw 9 I9 57 I77 2 29 II. P. Cliff • * I 9 20 39 59 I3 Gad’s Hill o I7 49 282 28 50 IPrecelly . tº ſº 2 59 38 97 5 54. Goat Fell. 5 9 3 I I4I I I 4o Pertinny . tº ſº. 3 49 II 66 5 I 30 IHensbarrow . 3 I3 34 68 22 II l'aracombe . 2 25 48 8I 22 28 IIungry Hill. 6 5 I 88 7 11 IRyder's IIill . 2 37 59 66 54 o IIart Foll 4. 24. 46 I5 I 18 33 Scournalapich 6 34 15 I5I Ig 7 Inkpen o. 55 I6 8I. 37 5 I Sayrs Law 4 38 I4. I58 58 40 Ringstown 4. 9 20 II 3 22 4. Saint Agnes . iſ . 4. I9 4. 66 5 36 IXellie Law 5 2. I I59 52 I7 South Berule i. 3 52 49 I 3 I 29 32 Great Stirling . 6 3 48 169 2 3 47 Saxavord. • - 9 20 46 I 76 46 49 Leith Hill O 22 45 37 23 28 Slicve Donard . . . 4, 28 36 I24 37 18 Lough Foyle. 5 29 35 127 28 7 Southampton. tº I 2 36 56 48 59 Lundy Island . 2 56 8 82 7 2 South Lopham I 6 II 2I4. I7 36 Lumsden tº 4 36 29 I62 38 59 Tharſiclal Tower. . o 32 19 177 47 50 Laxfield Tower . I Io 42 226 18 2 Tofts Tower . Ç I 24, 29 224 9 I2 Mormonth º 6 I 3 28 168 I5 5 Tawnaghmore tº 6 25 49 III 59 54 Mount 13attock . 5 4 I 24 162 31 18 Week Dówn . . . I Io 18 4o 59 55 Morrick . 4 3 I 23 I42 2 9 Wrotham. ſº O I4. 25 3 I2 3 9 Monach . * . 7 45 23 I49 31 36 Wordeslow 3 28 22 165 I 5 Mowcopt . 2 7 I3 I39 29 I5 Wingreen . . . I 24 27 68 45 13 Mordington . 4 29 27 163 18 28 Walpole, St. Peter's , I I5 I9 186 23 30 Mendip I 36 33 79 45 46 York Minster s 2 33 49 164 46 33 North Rona . 8 18 34 I54 6 55 - EQUATIONS or CONDITION Greenwich Saint Agnes Goonhilly Hensbarrow IBlack Down Dunnose IBoniface Down Week Down H. P. Cliff Southampton IPrecelly Arbury Delarnere Clifton Burleigh Moor Hungry Hill Feagllmaan Forth Tawnaghmore Lough Foyle South Berulo IBen Lomond ICellic Law Ben IIeynish Great Stirling Monach Ben Hutig North Rona IBalta Gerth of Scaw Saxavord Ldinburgh Durham Cambridge Cowhythe 5. 8, 8. $, 5; $6 8, 8s $io $1. $1. $13 $14 $is $16 $.6 Bas $19 $o $3. $3. às (£) DERIVED FROM OBSERVED LATITUDES. i --- = : + -º- : -º- -:– itº- i 7 8 -: “O23 ‘703 346 '483 '496 388 3°412 5°ogg o' 9oo — o'809 i : = — 8°469 + I O O O : O O •oooo { ‘9939 & ‘9959 5 ‘9965 : '9990 5 ‘9998 : ‘9998 : ‘9998 : '9998 : ‘9997 : ‘9965 : ‘9998 : o' 9989 : O O O O O O O O O O O O O O O O O O O O I O ‘9998 : ‘9998 : 9854 & '9837 : ‘9935 & '9860 : ‘9925 & '9967 : '9967 : '9988 : '9927 & ‘9995 : ‘9939 5 9969 : ‘9949 } 9999 : ‘9999 : ‘9999 : ‘9985 § '9996 : “oooo & '9989 : + OO O'OO'O "O'O'OO O *O "OO O I 6 6 i -* H. : : * OOOO 7& 'o623 w '6952 w oS II at '4287 w ‘5 Io9 at 5361 tº * 5475 ºt * 5494. At ‘9993 u '6473 w ‘2927 at ‘9903 tº *4447 ºt ‘3873 w * 3492 at * O2 2.4L 7. 1406 at 2138 w '8460 at *4975 at c605 w 2669 w 3184 tº Io'4233 at II • I2 ° 13. I6 • I6. I6. 7. 5 * I • IO" 6910 at 1860 at of 3o wº 1815 w 2960 w 3154 tº 7362 w 7248 w 2860 at 7758 at : + O' * OOOO ty zoo.7 v • 1975 v 1364 v • I I I 8 v 1406 v 1438 v * I442 v 1445 v o862 v • II63 v º IoI 5 73 2072 v 2091 v “2492 v “2495 v 3070 v 2076 v '4563 v • 3616 v • 2877 v 258o v * 222 I ºf * 304 I • Io89 o8or ‘oo30 ‘oj95 '485 I ‘5012 * 5040 2440 • 26 Io • 1486 o909 v EQUATIONS or CONDITION DERIVED FROM OBSERVED LONGITUDES AND AZIMUTIIs. + + = i : = - {º : : # = n -- Greenwich "To Edinburgh 71 Durham 72 Cambridge 73 Ringstown 714 Feaghmaan 75 Blackdown 716 Dunnoso 77 IPrecelly 718 Cowhy the 79 Wrotham % ſo Gad's Hill 7 II Fairlight 7/12 Orford Castlo 713 Balsham 7/14 Walpole, St. Peter's mis Docking 7, 16 South Lopham 717 Leith IIill 718 Rutscr]Hill 719 Beacon Hill 712o I3arrow Hill 7/21 Lundy Island %22 Dunkery 7/23 Mowcopt 7124 York Minster 725 Easington 7/26 Wordeslow , 727 Hart Foll = tºº E – : i O" OOO 5'896 4' 58o 4-859 2 : I.23 I ‘935 6'915 '976 * 344 "312 2 ‘754 Hºmº oooo : o460 & o226 & ‘ool 3 & o856 : • I413 8. ‘o;75 : •o270 & • Io;7 : oš49 & •oo64 § 'oro4 & ‘og39 5 •oo71 ; ‘oo49 : 'or 37 & o220 ºf •oo83 : 'oz20 & of 85 Å o838 : • Io46 : o8o3 : •og&3 : ‘o233 & or 8o : •ogo8 & o?20 : oA.54 * 'o673 : • Io96 : •o263 & o437 & 'o697 : * 1509 5 o;62 : • Ioa 2 & • Io47 & ‘os?o § •o420 # of 40 & + o' 94.44. + o- 9302 + o' 93.14. + or 92.54 + o' 93.23 + o' 9260 : = "OOOO 7. • 4614 w ‘7234 ºt * Ioj4 w 6575 w • 2087 w ‘7685 u * 30 I4 tº 1853 w '8958 w ‘3 II4 w ‘5059 tº 6744 w • 6653 w * 3478 it 2439 tº '6793 w o847 w '4019 w 'o639 at '8707 w or 37 w 'oZ47 at '8960 u '4040 at * 1749 at '9135 at 5670 u '6975 w 332 I w *4619 at • 6426 w ‘9034 tº • 2513 tº 3° 5630 u 7'9278 w 3'9916 w ° 44 II w * 5040 at '9826 w * 2 I2O 70 : I I 2 – * OOOO ºf •oj88 v 5296 v of 24 v * O459 v ° 4445 v '8507 v * 3999 v * 5934 v ‘8899 v •og57 v * I 555 v *2073 v 5117 v • IoG9 v 'oZ5o v 2087 * 3333 ‘I 235 3269 • 5748 * 23.34. * 5595 • 1972 '7387 3611 • 2807 '4815 • 1362 ‘7166 'o641 ‘734o •8926 '69.18 ‘og49 ‘4362 • 2266 6720 '6914 v o'9166 v o'6798 v 728 F Cheviot %29 Dunrich *130 Goat Foll 731 Sayrs Law *132 Mordington 7133 Burnswark *134 B. More, S. Uist was B. Macdui "136 IB. Nevis 737 Scournalapich 738 Mount Battock *139 Mormonth 740 º : GEODETICAL RESULTS. 695 . . . § V. Solution of the Equations. We have in the preceding equations all the requisite data for determining the elements of that spheroid which most nearly coincides with the surface of Great Britain and Ireland. These elements are— - Semiaxis major = 20923713 + 10144. u Square of excent. = •ood 67054 + -ooo.4848 v The quantities u and v, together with the quantities é and n for Greenwich, have to be deter- mined so that the é's and j's for all the stations shall be in the aggregate the least possible. The equations for latitude must be considered much more important than those for observed longitudes or azimuths, inasmuch as the probable error of an observed latitude is much smaller than the probable error either of a determination of longitude or of the direction of the meridian. Were all three classes of observations equally to be depended on, we might determine à wo by making > (É") + 3 ("") a minimum. This will, indeed, give us that surface which best repre- sents the whole of the observations, but we must allow an advantage to the latitude equations, and a disadvantage to the others, in order to obtain that surface which should be considered as the best representation of the whole; that is, we must make 3 (#") + w > (*) a minimum where w is a quantity less than unity. Let à, a m + ač + bi + cu + eu be the type of a latitude equation: ", = n + a'é + b'm + c'u + e'v, the type of an equation derived from an observed longitude or azimuth, then 3 m, u v are to be determined so as to make a minimum the quantity— S (m -- aft + bi + cu + ev) + w S (n + a'; + b'm + c'u + e'v)” This gives the four equations— . . . o = (am) + w(a'n) + [a”] : + [all] n + [ac) u + [ae] v o = (bm) + w(b'n) + [al] : + [bº] n + [be] w + [be] v o = (cm) + w(c'n) + [ac) # + [be] n + [c'] u + [ce] v o = (em) + w(e'n) + [ae] : + [be] q + [ce] u + [e] v where [a] = (a") + w(a”) : [ab) = (ab) + w(a'b'), &c. 1. In the first instance, we shall determine those values of 3 m w w which make S (#) + 3 ("") a minimum, the value of w being unity. . From actual multiplications the following values are found— (a”) = 33.7768 (ab) = 1.6788 (ac) = - 147:8547 * (ae) = 1.2083 (b’) = o-1356 (bc) = – 6.6372 (be) = 0.2341 - (c’) = 1814.0613 (ce) = 2.5Ioo (e) = 2. II.46 (a”) - o. 1676 (a'b') := - I-78.44 (a'c') = – 9.4035 (a'e') = — 2.8895 (5°) = 38.9743 (5'c') = IOO. I245 (Ye') = 3o. 7643 (c") F 548.8328 (c'e') = 168.64II (e”) = 51.8189 696 PRINCIPAL TRLANGULATION. If we put A = ma + m, a, + m, a, + • na' + n,a,’ + . . . . I} = mb + m, b, + m, b, + . . . . nb' + n,b,’ + . . . . C = me + m, c. 4 m, c, + . . . . mc' + n,c,’ + . . . . D = me + m, e, + m, e, + . . . . ne' + n,e,’ + . . . . We get - o = A + 33:9444 # – o'Io 56 m – 151.2582 u – 1,6812 v o = B – o Io56 # + 39. IIo8 m + 93-4873 u + 30.9984 v o = C – 157.2582 # + 93-4873 m + 2362.894I u + 171.1511 v o = D — I-6812 # + 30.998.4 m + 17I. I5II u + 52.9335 v I'rom these we find the values of § 7) w and v in terms of A B C D, as follows:— = — ‘o.471729 A + -oorooA31 B — oo393545 C + 'oroa:4Ioo D + ooloo.43 A — oA701 Ioo B — oooo.4.228 C + .oz718515 D w = — ‘oo39354. A — oooo.4228 B — ooo&7818 C + "oozó8843 D v = + ,oio.4410 A + .oz718515 B + 'ooz68843 C – o42372Io D ; -: By substituting the values of A B C and D, we have finally £ u v in terms of the observed quantities m 'm, . . . n n, . . . with numerical coefficients. Suppose à = & A + 3 B + y C + 6 D, then by substitution # = (&a + 6b + ye -- ?e) m + (&a, + 6b, + ye, + &e) m, + . . . . Let also &a + 3b + ye + 3e = A &a, + 3b, + ye, + 6e, = x, ca, + 3b, + ye. + 8e, = x, and so on. Multiply these cquations by x x . . . . . and add, then we have A* + 2\,” + . . . . . equal to & S (Aa) + 3 S (Ab) + y S. (Ac) + 3 S (Ae) Now multiply the original equations— #, = m, + a, § -- 0, n + c, w -- e, v # = m -- a # -- b y + c u + e v }* #, = m, + a, § -- b, n + c, u + c, v by 7, 7..., x, . . . . and take their sum, then of necessity 7.5 + 2, 3, + 2, #, + . . . = o, and since & = &m + x, m, + x, m, -- . . . we have identically S (Aa) = — I ; S. (ab) = o? > (Ac) = os S (Ac) = of consequently the sum of the squares of the coefficients of the observed quantities in the expression for ś is— * X*. -- X,* + x2 + . . . . = – c. Similarly, the sum of the squares of the coefficients of the observed quantities in the expression for n is the coefficient of B taken with an opposite sign (that is, -o-;701 Io), and similarly for w and v. - * GEODETICAL RESULTS. 697 ă = By substitution of A B C D in the linear expressions for # n w v, we get, after the necessary multiplications, the following values:— – ‘oa/I72 mo ‘os474. I m? “O23345 mrå " or 2537 mar “or 1460 m28 ‘ooooo; m, "ooz2 II mg ‘ooog33 mis ‘oo225 I maz ‘ool 399 m29 ‘oor 627 nad * “oo Ioo.4 mo ‘oo3771 m, ‘oo7339 ºn 14 ‘oo5384 mal * OI2OO2 77128 or 82.18 m, "Oo3554. 778 oA8245 mis ‘oo4982 m.a. ‘o25272 m29 'oroß30 m36 ‘oo3935 m. ‘oo5682 m, ‘oor 466 mi, ‘oo3847 mal ‘oo897 I mas °oooo;4 m. ‘oooºo; ns ‘oooo48 mis ‘ooo IOS 7.2.2 ‘oooo I7 mag "Ooooš3 m36 ‘olo44. I mo 'oz 1166 m, 'oiá218 mis 'ozo&77 mar ‘ol 22 17 m28 – ‘oo897o n, – ‘o27763 ms + ‘ozg3oz mig — ‘oz6316 na: + °ool 228 mag — ‘oió751 m36 tºmº * – 'o60944 m, – ‘oj4752 mg – o451 18 mis – "oi 2224 maa + or I 742 map + ‘ooo815 m, + ‘ooI4I4 no + ‘ooo833 m, 6 + ‘ool 962 m23 + oor 612 nso + °ool.895 m37 — ‘oo8654 m, — ‘oo3756 ms + °oo I 5oo mis + ‘oo5609 mas — of 2426 map — ‘og261 I m, — org461 no – ‘os 1744 mić — ‘ol 4823 na; — or 5806 mso + ‘ool 333 m37 – “oo7.I.44 m, — ‘oo5685 m3 – ‘Oo352O mis + Oo3925 maa + oogo28 mag – "Oooo.43 m, + oooo.26 m, — ooooºo n,6 + oooo7I mas + oooo.46 mso + ‘oooo&8 msn + o294.65 m, + o2 II 70 ms + “oo4274 mis – “ozo I'77 maa — or 1848 mag + oogo35 m, – ’oos354 no + ‘og3826 m, 6 – "oi 3842 mas - 'oro?39 mso - 'o61986 ns) . : : : : ‘oj9576 m. ‘os IQ71 mo "O43 I44 m 16 ‘oro821 mas “or I 790 m30 ‘ooro I9 ms "Ooog3 I 7-lo "Ooo 743 mi, ‘ool 5 I2 ma; oozo I 7 m3r •ool 867 m38 ‘oo78o2 m, ‘oo2279 mo 'ooz728 mió ‘oo5183 mas ‘oi 2548 mga oA7881 ns ‘O4970I ??io of 54.12 min 'oz6017 m, ‘oo24. I2 m3r ‘oo2 I 39 m38 ‘oob820 m, *Oo3O44 mg ‘oo3072 mió ‘oo42 I2 mas ‘oogo37 m3o "Oooo.42 m3 ‘OOOOSI mio "Oooo72 min "Oooo.24 ma; ‘oooog8 m3, ‘oooo&6 m38 ‘O2.7932 m2 “or 72.96 mo °ool I42 mió ‘o22320 m23 ‘ol I 755 m30 'oz8285 ns * O30533 7tro ‘og8279 mln ‘ool 230 ma; 'o63785 ms: 'o62807 mss i . : . : ‘oj6555 m, "O43 I 75 mtro *oqor IQ miº ‘oo4966 ma; ‘oiáoß4 mg. ‘oool 99 m, ‘ooo882 m, , “oo I Io8 m,8 ‘oo I2 I7 mas ‘oooo&3 m3. ‘oo I457 m39 ‘oo5884 m, “oo II.4.3 mio ‘oo2487 min ‘oo3258 mas ‘oo5923 m31 ‘oo8437 m, ‘OSI244. 7-11 o43876 n.8 'o6573o 772; 'ozo281 m3. or 9094 *39 ‘oo61 19 m, * Oo3O42 2nro !oo2354 miº “oo55I2 ma; ‘oo3518 m3; ‘oooo; I nº ooooš7 2711 ‘oooo.3 I mig ‘oooo Io mas oooo&6 m3, *Oooo3O 7.30 ‘o23565 ms ‘oo5485 mio *Ooog4I mi? o2 1537 ma; ‘ol 95.32 m3r o42613 m, "O32544 7/11 "O23059 7.18 ‘ol 391 I mas ‘oo4617 m3; ‘oočoyo ngo ‘os3878 m, "OAO999 mir - ‘O25033 mis + i : . i ‘oooo48 mas o2 1876 m, ‘ooo.488 mg ‘ooo34.2 mra ‘oo I275 mio oo II 49 2.26 ‘oo I374 2,33 ‘oo I3O4 zºo ‘oo373.2 m; ‘oo3O42 mir ‘oo7443 mis ‘ooo373 mas ‘oo7326 m3. ‘OA6487 ng * OS2999 7112 ‘og8516 no o27561 nºg 'oz 5772 m33 ‘o25187 mio ‘oo5488 m, ‘oo2527 mr1 "Oo IO4. I am 18 ‘oof 567 ma; ‘ool. 794 m32 ooooog n; ‘ooooo; mra ‘ooool I mio "Oooor 7 mag ‘oooo IS m33 ‘ooool I mio ‘ol 99.53 m; * Oo3 III mir or 6823 m,8 o22 Io9 mas ‘ol 5426 m3. 'ogo.382 ns “O3453O 7112 of 6152 mio ‘oi6474 mas ‘ool.981 na: ‘ool 877 m to Hºmº . : -- iſºmº, i ‘o;4560 mg ‘O33I52 mra ° or 99.40 mio "Oolo25 mag ‘o43661 m3; “oo I714 mg ‘oooºo.7 m, ‘ool.464 m.o ‘ooI274 may ‘oor 654 na; ‘oo3648 mg "Oo3O42 mra ‘ooč585 mio ‘OOL293 ºn 26 ‘oo3O42 m33 o24.539 7.6 'o60404 m,3 of 1677 mao 'o61974 man or 52.29 m34 ‘oo5640 mg "Ooo750 mra ‘oo2 196 mio ‘ooë784 m,6 ‘oo3206 m3s oooo.39 mg ‘oooo.89 m,3 "Oooo II 712o oooool may "Oooo49 m3; ozogo1 mg "OOS394 m 12 ‘oi So?9 mio ‘ozo808 mas 'or 33.16 mss “oo 1741 mg ‘O44-505 7113 ‘oo7557 nao ‘oog492 7.27 or 1651 m3; — ‘oj4693 m3 — of 1406 mis — o262.49 mao + °oo3975 m2.7 + oo IOO4. 7to + “oo 1344. 777 + ooog I.3 mrå + oozo;6 mat + “oor 661 mas + 'ooz282 m3; – ‘oo374.1 mg + oogoş4 m,3 + oogo1.8 mao – "Oo3794 ma; — oA-701 I no — of 6786 m, – ‘OA9472 mit ..— ‘ol 4477 mar - * or 394o mas + °oz2369 m3; — ‘oo5671 mg – ‘ooo348 m,3 + ooo798 mao + °oo74oz may – ‘oooo.42 mo – ‘ooooo.4 m, – ‘oooo;2 mri + oooo.78 mar + "Oooo; I mas + “ood I42 m3; + o2 IIo? mé – ‘oo7231 m, 3 - ‘ol 2 I43 mao — ozoo.81 man + o27185 no + or 3784 m, + 'ogodog nºt — or 473 I mar — or 3164 mas — oš8408 mss 4. T 698 PRINCIPAL TRIANGULATION. By putting the final values of 3 m w w in this form, we can at sight estimate the effect that would be produced in them by an alteration of any of the observed latitudes. When the numerical values of the observed quantities ºn, m, &c., are supplied in these expressions, there results— - &/ # = + I-479 m = - O'4O4. gº 7t = + O.2433 v = + o-8918 By substituting these in the Equations of Condition we get the following values:– Name. ; Name. # Name. * | Name. y r {{ fº Jº f/ Greenwich . . [+1-479 || Tawnaghmore . —6'948 || Greenwich . . |-o'404 || Barrow Hill . —6' 176 St. Agnes . . -I IS3 || Lough Foyle . —4°48o || Edinburgh . . —4° 58o Lundy Island . -- 3: 218 Goonhilly . . -2 °794 || South Berule . -- I '808 || Durham . . . -4° 125 || Dunkerry . . -2° 519 | Hensbarrow . —I 198 || Ben Lomond . —I 292 || Cambridge . . --4-402 || Mowcopt . . --5°273 I}lack Down . -- 3: Io8 || Kellie Law . . [+ I '818 || Kingstown . . [+o '792 || York Minster . |–2 '769 Dunnose . . —I 618 || Ren Heynish . --2'435 | Feaghmaari . . -- 7" I25 | Easington . . -4°477 Boniface . . [+o 796 || Great Stirling . --o' osz | Black Down . . |—5'976 || Wordeslow . . -5 °o89 Week Down . --o' 577 || Monach . . . -- I 365 | Dunnosc . . . —2°751 || Hart Fell . . [+4'879 Port Valley. . --1-608 || Ben Hutig . . ]-2-858 | Precelly . . . -- I '782 || Cheviot . . . -3°351 Southampton . -- I '893 || North Rona . --o' 689 Cowhythe . . --o'731 || Dunrich. . . -6° 216 IPrecelly. . . [+o'969 || Balta. . . . . [+2' 601 || Wrotham . . ]+ I o8o || Goat Fell . . —o. 514 Arbury . . . -- I ‘945 || Gerth of Scaw . [+2'451 Gad's Hill . . [+2 Io:3 || Sayrs Law . . -o- 216 Delamere . . ;-o'416 || Saxavord . . |+o 467 || Fairlight . . . --2'408 || Mordington . —I '447 Clifton . . . . -2 °558 || Edinburgh . . |–5:303 || Orford Castle . --4'o66 || Burnswark . . |+3° 214 Burleigh Moor. -3°543 || Durham . . . —o. 596 || Balsham . . . [+6-256 || Ben More . . [+o '723 Hungry Hill . --2 '925 || Cambridge . . ]+o. 443 Walpole, St.Peter's-i-6 oz.3 || Ben Macdui . --2 : o38 Teaghmaan. . –o '876 Docking . . . --4 124 || Ben Nevis . . --8°o29 Forth . . . --o' 26o South Lopham . |+2 579 || Scournalapich . —2:413 Leith Hill . . –2 or 3 || Mount Battock. —4° 164 F- Butser . . . |–3 ° 938 || Mormonth . . ]-6' 512 Cowhythe (#) = — 9"" 548 Beacon Hill . . -I:069 | The system of quantities é º contained in this table have this property, that the sum of their squares is less than that of any other system that can be obtained in reference to any spheroidal surface whatever. They are therefore to be understood as the actual inclinations of the surface (north or cast) to that of the spheroid we have above determined. They are, however, affected with errors of observation, more especially the quantities 7, ; for it is clear that their mean value should not exceed the mean value of the quantities #, whereas it is nearly double. Since this spheroid so nearly agrees with the observed quantities, it might be expected, with some probability, that the corresponding inclinations would agree in some measure with those derived from calculations based upon a knowledge of the magnitude and position of disturbing : : : | ; GEODETICAL RESULTs. 699 masses in the vicinity; namely, the quantities given at page 664. The comparison of these is given in the following table:– º From the By. * From the By. º Names. eodetical | Difference. Names. -- eodetical | Difference. Groni ||. é. . J/ º # iſ ** f f f DunnoSC — o' 54 — I 62 — I o8 || Forth . tº + 1 . I3 | + o- 26 || – &87 Poniface . + 2 °42 + o-'80 — I 62 Tawnaghmore . – 2:30 | – o '95 + I-35 Week Down + I '98 || + or 58 — I 40 || Lough Foyle – 4'oz – 4:48 — o'46 Port Valley. + 3 '29 |’ + I 61 | – I '68 || Kellie Law . + 2 o8 + 1 '82 — o' 26 Clifton . . . — o' 90 – 2 56 || – I '66 || Monach. * + o'47 + I 36 | + o-'89 | Burleigh Moor'. – 4: 55 – 3’54 || + I or || Ben Hutig. . . . . . - 2' or – 2 '86 — o'85 | Hungry Hill + 5-40 | + 2 '92 || – 2:48 || Calton Hill, Edinburgh - 3’57 | – 5:30 | – 1.73 || Feaghmaan. — 1 '95 — o'88 + 1 oz (Cowhythe) . . . . (– 5") – 9'55 — 4-55 If we disregard signs in this table, the average amount (omitting Cowhythe) of the deflec- tions accounted for by the ground is 2". 44, while the average of the corresponding deflections, as inferred from the connection of geodetical and astronomical observations, is 2". Io. The average amount of the differences in the third column is 1". 23. The agreement between the quantities in the second and third columns is not, perhaps, so close as might have been anticipated, and shows that the deflections cannot be entirely accounted for by the inequalities of the surface. In the Isle of Wight, for instance, we have a second and a half to the south which cannot be accounted for; and here it must be remembered that the attraction of the nearer parts of the mass of England have not been taken into account in assigning the deflections at page 664: this attraction, if included, would increase the discrepancy to at least 2". - At Hungry Hill also there is apparently 2”. 5 unaccounted for, as though the attractive power of the mountains had been overrated; while, on the other hand, at the Calton Hill, Edinburgh, there are nearly two seconds to the south unaccounted for, as if the attractive power of the mountains had been underrated. . . . * . . . . . . - ~ :- At Cowhythe the ground will only account for half the disturbanče observed, aid leaves four or five seconds unaccounted for. At Lough Foyle and Kellie Law the ground seems to account satisfactorily for the observed deflections. *.*.*. - The hypothesis of the Astronomer Royal respecting the influence of masses of high land upon the plumb-line (pages 572-3) makes it very doubtful to what distance from any given point their apparent attraction should be taken into account. We shall therefore divide our ground deflections into two systems: the first, which for convenience we shall call A, results from the consideration of the irregularities of the ground more immediately in the neighbourhood of the Station; that is, excluding all masses at a distance greater than nine or ten miles (in the Isle of Wight Stations, three miles). In the second system, which we shall designate B, the action of more distant masses is generally included. This system is the one we have just been considering. - 4 T 2 7oo PRINCIPAL TRIANGULATION. Let us next'éompåre the system of deflections A with those resulting from the surface which renders X (ā’) + 3 ("") a minimum :— º Names. *. the Geºlia IDifference. Names. From the gºal Difference. round. | infºrence. Ground. tº j DunnoSO – “oz – #62 — 3.60 Forth ºmº & 17 -H. 3.26 & 43 IBonifaco + 1 ‘94 | + o-80 | – I 14 || Tawnaghmore . - I ‘43 — o' 95 + o-48 Week Down + I 50 | + or 58 — o'92 || Lough Foyle – 2 15 – 4' 48 || – 2 33 Port Valley. + 2 '81 | + 1 61 — I 20 ! IXellie Law . + 2 o? | + 1 - 82 * - tº Clifton . º – or 90 – 2 56 ... Monach . + o'47 + 1:36 tº tº º Burleigh Moor . – 3: o3 — 3’54 — o' 51 || Ben Hutig ._; . . . - I '63 – 2 '86 — I 23 Hungry Hill + 3 '85 | + 2 + 92 — or 93 || Calton Hill, Edinburgh - 2'43 – 5:30 – 2 '87 Teaghmaan. – I'95 || – o'88 ... (Cowhythe). . (– 2") – 9° 55 — 7' 55 It appears from this, that by omitting the deflection apparently due to distant masses, the two systems are brought to more close agreement in eight cases, and in four cases are rendered more discordant. In the remaining four cases, it is uncertain what would be the effect of extending the calculation over a greater extent of country. The average amount of the quan- tities in the second column is now I".82. - f f The equatorial radius of the spheroid we are considering is— a = 20923713 + IoI44 w = 209.26181 feet. It will be convenient to use a symbol 2 s for the square of the eccentricity: and for the compression, let - a — b (! ; Then we shall have— I *-* # = 1 - V 1 - 2 = 4 + i + . . . . Now, s = o'oo333527 -- v . arc 50", therefore in the present instance s = Oo355145, and : = •oo355775 ..". C = 281.08 If w and v be liable to errors ºw and ºv, then a will be liable to the error IOI.44 Su, and to find the error of the quantity c resulting from ºv we have— - - ds - – ; # = (1 + ) # = (1 + ) are 52" Hence, with sufficient precision— 8c = – c’. arc 5o” . ºv In the expression for u, page 697, the sum of the squares of the coefficients of the m's is o. ooo378, and the sum of the squares of the coefficients of the n's is o-ooooool . . . . In the | * * º.l *f *: GEODETICAL RESULTS. 701 expression for v these quantities are o-olo2 and o.o.322 respectively. The mean square of the quantities é is 4:49, and the mean square of the quantities º is 16. 13; hence— Probable error of u = + 674 y (oooº;8 × 4.49 + . . . . . . ) = + .o.A:2 . . . Probable error of v = + ,674 wº (oloz × 4:49 + “og22 × 16:13) = + 507 . a = 20.926.181 + 430 c = 281.08 + 9.75 It is to be observed that these probable errors are not to be regarded as results of errors of observation: they are the probable errors of these quantities as representatives of an irregular surface. The probable error of a depending upon the errors of observed latitudes would not perhaps exceed # 50 feet. 2 There is no general principle by which we can assign to the equations derived from longitudes and azimuths their value relative to the equations derived from observed latitudes. The probable error of a determination of either longitude or azimuth is considerably greater than that of a latitude, but their ratio cannot be generally assigned. In consequence of this difficulty, the equations themselves have been made to contribute to the determination of a relative weight; for the quantities º are much greater than the quantities à in the table, page 698, whereas they should not be, but for errors of observation. Let a' and y” be the mean squares of these systems of quantities, and put v = i + cz + c,”, y' = i + 3 + 3”, where i is the mean value of a deflection, c. the error due to the astronomical determination of the latitude, o' the error due to the corresponding geodetical determinations; and let 3 and 3’ be the errors of the astronomical and geodetical determinations of azimuth or longitude. The quantity gº (16. 13) is nearly four times wº (4.49), but 3 + 3” is considerably more than four times o:* -- c.”. After due consideration, the quantity was chosen as the representative of the weight that should attach to the equations derived from longitudes and azimuths in obtaining any final conclusions. We proceed to determine that spheroid which makes X (#) + + 3 (m) a minimum. If in the equations at page 695 we make w = } and substitute the numerical values of (a") (ab) . . . . they become— * o = A + 33-8047 : + I-3814 | – I49.42.19 w -- o'7267 v o = B -- I-3814 § -- 6.6322 m + Io-ošo2 u + 5-3615 v o = C – 149.4219 8 + Io.o.5oz n + 1905-5334 u + 30.6168 v o = D + o-'7267 : + 5.3615 m + 30.6168 u + Io. 751 I v 702 PRINCIPAL TRLANGULATION. Where the values of A B C D are— * * A = ma + m, a, + m, a, + . . . + + (na' + n, a,' + n, a,' + . . IB = mb + m, b, + m, b, + . . . + (nb' + n, b,' + n, b,' + . . C = me + m, c, -i- m, c, -- . . . . 4- 4 (ne' + n, c.” -- n, c,’ + . D = me + m, e, + m, e, + . . . 4- ), (ne' + n, e.' -- n, e.' -- . . º &gºº . By elimination we obtain— # = - 04751080 A + ·oo703928 B – ‘oo393806 C + orogi 570 D * = + -oo703928. A – 25463240 B – oool.4427 C + .1269,185o D w = — oog.93806 A – oool 4427 B — ooo&7846 C + "ooz83978 D v = + orogi.570 A + 1269.1850 B + .oO283978 C – 16513200 D Tinally, by substituting the values of A B C and D, we get the values of § 7) w v in terms of the observed quantities m, m, m, . . . m, n, n, . . . . The values are as follows:— GEODETICAL RESULTS, 703 # = — ‘oA75 II mo — ‘os SoSI m/ — 'oz 3466 mid — ‘ol 235o 7mar + orogg3 mas + °ool 187 m, H. “ooI494. 778 + °ool 138 mis + °ooI509 maz + °ooI246 map + “oor 306 na: + “oo/o39 mo — or 5765 m, + °o:5827 mit + o24831 mat – “oj4920 m28 — ‘ol 9996 m, — ‘oo8562 ns - ‘o433or mis — ‘oog738 ma. – ‘o2522I mag – "oi 37.15 m36 – ‘oo3938 mo — ‘oo5708 m, + ‘oor 500 mi; + ‘oo?879 mar + °oo8898 m28 + "Ooooo I m, + °oooo.41 mg – ’oooo.27 mis + °oooo.4o man + °ooooo.5 nao + °oooo.24 m36 + orogi 6 mo + oAI252 m, - o43734 mi, - o46593 mai + “o 16426 mas $ºmº ‘ood 524 221 – “ozoö48 ms i 'o60862 m, ‘ossoffs ms ‘O44532 m is ‘ol 2207 maz of I271 mao ‘oor 182 m, ‘ool.238 no ‘ool Io9 n,6 ‘ool.433 2-23 ‘ooi 308 mga ‘oor 388 msn : - ‘oj9589 m.a. — 'o';2238 m, - ‘o42484 mić - 'oro422 mas + “ol I.324 mso + °ooII.73 m, , + °ool I55 mio +" oologo nin + °ool.295 ma; + "ool.427 m3; + °oor 379 m38 – ‘oj6422 m, — ‘oo89 II mg + °o IOI IO mió + °oz2772 m23 – ‘oš7503 m30 — o43 II6 m3 – ’oº-A546 mio — od 3902 nº — o25968 m2; – ‘oo3647 m3. - ‘oo3750 m38 — ‘ooë860 m, — ‘oošoë2 m, – ‘oo3O42 mió + ‘oo4248 mas + ‘oo8962 mss — ‘oooo.25 m3 — oooo.28 mio – ‘oooo.37 m, , + ooooof mas + “oooo.44 m31 + °oooo.41 m38 * +'o60099 7722 + ‘ojo409 m, — ‘ozzoöz mig * ‘osio;5 ºn 23 + 'o';9269 mga + o2 1995 m, + o23700 mis + o29586.m, + °ooI394 na; — oz.5283 ms: 'oz4561 was i i : – = : 'oj6566 ms o43062 mio ‘oj9815 mi, ‘oo5079 ma; or 4005 m3; ‘ool 198 m, °ool I4I 7-11 *ool. 205 7.18 “ooI2O5 mas ‘oo Io:34 m32 ‘ool.255 m39 ‘o2732.7 m3 ‘oo5356 mio “o Io'742 min 'oï6148 ma; 'oz8062 mat ‘ooo756 m; o45738 m, , ° O40O24 7/18 ‘og3468 na; “O2 I299 7.32 'ozo.3 I5 7-39 ‘oof I49 m3 *Oo3O33 ºn to ‘oo2334 ºn 17 ‘oo5526 ma; ‘oo3550 m3r oooo.26 m; ‘oooo3O mir ‘oooo.I.9 mig ‘ooooog mas ooooos ng, ‘oooo 12 m39 ‘947650 m; ‘ool 986 m,e of 5329 mi? ‘o33576 mas o45854 mg. ‘og2248 m, 'oz5229 nº ‘ol.8ol.8 mis “or Io97 mas ‘oo3263 mga ‘oo41.98 mao — ‘oj4063 m, — o41186 m, , - ‘o24.353 ºn 18 + oooz98 mas — o2 1946 m3. + ‘ool 190 mg + “oor 138 mia + °ool.252 mio + °ool 180 mag + °ool.236 m33 + °ool.204 m to — or 62.24 m, + ° or 5905 mri + °o32257 mis - ‘oo3O49 mas + of 5488 mga + °ojo416 m; — ‘od/148 mra — o?5868 nig – ‘oj4851 m.5 – ‘o25589 mgs – ‘O25oz I at to – ‘ooš51 I m, — ‘oo2516 mi, + ‘oorogó mis + ‘oof 571 ma; + °oo 1831 m3. + oooo;8 mg – “oooo.33 mia — ‘oooo II mio — ooool.2 mag + °ooooo4 m3; + ooooo.3 mio + o?7839 m, – ‘oo7424 mil — 'o60oo3 m,8 — o24663 mas - ‘O45704 m32 — 'o68812 mg + o26742 mra + of 2766 mio + of 2983 mag + °oo 1942 m33 ..+ °ool 849 m to * *…* c” Awar: ***istaſ a tº — ‘oj487.1 mg – ‘og3163 mia – ‘ol 9513 mio + °ool og I mag — ‘o.14060 mss + ‘ool 371 mé + °oološ7 mis + °ool. 3 oo mao + °ool 2 I4 man + °oor 323 m3; – or 51.75 mg + °o2444. I mira + o294O7 mio – ‘ooë504 mas – “o I 1966 mss — o25ol I mé – ‘o;2809 m,3 – ‘O30527 avao – ‘ogo48 I may — of 7426 m3; — ‘oo5666 ms – ‘ooo724 mia + ‘oo224o mig + ‘ooë779 m25 – ’oo?231 m33 +-oooor 1 ns - "Oooo.44. 7-13 — " OOOOOI ?lao – ‘ooooo.4 may + °oooo Ig m3; + oAo490 mg – ‘o271.58 m, a - ‘os3359 mio – or 64.14 mag + o?1967 m3; — ooo&38 mg + °og4323 m is + °ooô227 mao + ‘oo7667 ma; — ‘oo8428 alsº + o22755 mis - * or 95.35 maa + “oo I37.I nao — of 233 I m36 * *oqog44 mir or 5676 77.8 ‘oo4661 mis o26761 maa ‘osé896 m, ‘o:312 I5 m2 'ozoś57 n, o46olo n,6 “or 74O4 mas 'or 7843 mss ‘oo44.13 m37 •oo?186 m, °oo 571 I mg ‘oo3498 mis * Oo3954. 77,22 ‘oo8953 20129 *ooool I n, oooo II no "Oooo32 m, 6 ‘oooo.25 ma: ‘oooo.18 mga ‘oooo41 m3; 'o63666 m, '641244 ms of 2560 mi; ‘oº!A4o ma, o48734 m.o. ‘oo7308 n, ‘oo3659 719 'oz6196 n,6 'oroo48 mas ‘oo7738 nse ‘o23929 man tº . • * * - * - ... t →... .º.º.º ir w \dº tºº . * ~ * * *** ***.*.*.*.*.*.*.*.*.*.**** * * * * * *...* "sº ºf t. * *** *** *** , " . " # * * * * * * *...* * * *** * * * * * * . : -H s : + : oš5ooš mé 'o.31536 m;3 o26054 mao ‘ooA. I22 maſ 'ool 173 mo ‘ooI274 m, “ool I4o 2114 •ool.465 mat “oo I323 mas ‘ool 506 m3s or 56Io mé 'oz.9847 m: * O27959 ºn 20 or 8855 ma: *oq.2439 7lo ‘o:34552 777 “O443o I ºn 14 of 72 I4. 7tar of 6401 mas or 201 I m35 ‘oo5697 mé ooo320 mi; ‘ooo834 mao ‘oo7386 may “oooo.24 alo ooooo3 m7 ‘oooo.28 mit ' oooo.27 mar * OOOO2 I ??28 oooofig näs ‘od. I IO3 mé ‘og I 291 m,3 o41316 mao ‘ooô375 m2, oz II 53 2-o •orogó7 m, ‘oz3753 2/14 or of II 712; oog583 mas 'o. 4056 m3s 704 PRINCIPAL TRLANGULATION. Substituting the numerical values of the m's and n's from the Equations of Condition at pages 693, 694, the values of § 7) w and v are found to be— These quantities do not differ materially, with the exception of the value of v, from those # = m = 20, E Q) = Af +. I-49I — o-888 + o-2479 + I-5397 which render the sum of the squares of all a minimum. The system of corrections resulting from these values are as in the following table:– Names. : Names. # Names. y Names. y) ! J/ JJ f/ Greenwich . + #49 I || Forth +o. 358 || Greenwich . —o. 888 || Barrow Hill . —5'851 St. Agnes . —I 299 || Tawnaghmore . –o'723 || Edinburgh . –4° 361 || Lundy Island +3°766 Goonhilly –2 ° 932 || Lough Foyle –4° 306 | Durham . . —4'257 || Dunkery . — 2 ° 2 I 2 IHensbarrow — I 297 || South Berule + I '955 Cambridge . +3°897 || Mowcopt . . + 5°290 Black Down +3° of 8 || Ben Lomond — 1 181 || ICingstown . + 1 . 666 || York Minster —2 998 Dunnose . |—I '698 || Kellie Law . + 1 '917 | Feaghmaan. +8'928 || Easington —4-756 Boniface Down. |+o 714 Ben Heynish +2 560 | Black Down —5'902 || Wordeslow –5' 233 Week Down +o 494 || Great Stirling . -i-o-o/5 | Dunnose . |–2 977 || Hart Fell + 5° 172 | IH. P. Cliſt . + I 526 Monach. . |+ 1 334 || Precelly. . |+2' 358 || Cheviot –3' 336 Southampton + I '845 || Ben Hutig . –2 - 931 || Cowhythe . +o '873 || Dunrich . —5'970 | Precelly. +-I oz2 || North Rona. +o. 564 || Wrotham, . +o 532 || Goat Fell. +o 177 Arbury . +2' oog || Balta . . 4-2-219 || Gad's Hill . +1:516 || Sayrs Law —o' o?2 Delamere —o. 301 || Gerth of Scaw. |+2 os:8 || Fairlight Down |+ I '783 || Mordington . — I 446 Clifton . . |–2 °434 || Saxavord . +o-o;2 Orford Castle +3° 248 || Burnswark . . [+3° 479 Burleigh Moor. —3'402 || Edinburgh . —5' 190 | Balsham . . . --5'706 || Ben More, S. U.. --I'890 IIungry Hill +3° of 6 || Durham —o. 446 Walpole, S. P. . --5'497 || Ben Macdui . +2' 461 Feaghmaan. —o'733 || Cambridge . +o. 51 1 || Docking . . . [+3° 511 || Ben Nevis +8. 686 South Lopham . -- I '881 || Scournalapich — I '741 Ileith Hill . —2 °417 || Mount lattock . –4: * f. Dutser Hill . . [–4. 20 Mormonth – O " tº IO Courhythe (#) = — 9"' 543 Deacon Hill –4. I ; 5 The comparison of these quantities with the deflections A and B, is as follows:— By Geod. IDefl. Defl. iff. IDiff. Names. #: A i. P B Dunnose º — I '70 || – fºoz | – o' 54 || – 3.68 – #16 IBoniface . . . + o' 71 || + I '94 | + 2 '42 || – I 23 — I ‘7 I Week Down tº + o' 49 + 1 50 | + I '98 || – I or | – I'49 Port Valley º + 1 53 + 2 '81 + 3°29 — I 28 — I '76 Clifton . * — 2 °43 | – o 9o tº º º - I 53 ... Burleigh Moor . – 3:40 – 3 of – 4' 55 — o'37 | + I 15 IIungry Hill . . + 3 o4 || + 3 '85 + 5°40 || – o '81 – 2:36 Feaghmaan º — or 73 | – I '95 tº tº tº + I "22 º º is Forth . © + o' 36 – o' 17 | + 1 13 | + or 53 — o'77 Tawnaghmore . – o'72 | – I ‘43 – 2:30 + or 71 | + 1 : 58 Lough Foyle . . . – 4’31 | – 2 15 – 4'oz – 2 16 — or 29 Kellie Law + I '92 || + 2 o8 — o' 16 • * * Monach tº º + 1 33 + o-47 tº tº º + o '86 - C - Ben Hutig. . . . . . – 2 '93 || – I'63 | – 2 or | – I 30 — or 92 Calton Hill, Edinburgh . – 5' 19 – 2:43 – 3:57 – 2.76 – 1-62 (Cowhythe) * – 9' 54 (– 2") (– 5") – 7' 54 – 4:54 | | ! : ; w: f ! . GEODETICAL RESULTS, 705 It appears, therefore, that, as in the case of the spheroid that renders S. (#) + 3 ("") a minimum, the deflections A agree with the quantities in the first column more closely in eight cases, and less closely in four cases, than the deflections B. If we neglect Cowhythe, the average amount (independent of sign) of the differences A is 1". II, while the average of the differences B is 1"-35. If we include Cowhythe, the average of the differences A will still be less than the average of the differences B. The elements of this spheroid are— a = 209237I3 + IoI44. . w = 209.26228 e = •oog33527 -- are 5o". v = •oog70850 c = 269. I5 -- The sum of the squares of the 34 quantities à corresponding to this spheroid is I.46.86, and the sum of the squares of the 41 quantities m is 68o. 41. The sum of the squares of the coefficients of the m's in the expression for u, page 703, is .oOo.878, and the sum of the squares of the coefficients of the n's may be called zero. The corresponding quantities with reference to v are -oj28 and .org/. Therefore, for the probable errors of w and v we have— Probable error of u = 674 W (oooº;8 × 4'32 + . . . . ) = + “O42 - - - Probable error of u = 674 Y (oš28 × 4.32 + or 87 × 1660) = + 495 . . . a = 20.926.228 + 422 c = 269-15 + 8.69 3. We have now determined two spheroids which represent the actual surface of Great Britain and Ireland with some precision. Of these, the former represents the whole of the Astronomical Observations with the greatest exactness, without distinguishing between determinations of latitude and longitude or azimuth. In the latter spheroid allowance is made—but necessarily in a somewhat arbitrary manner—for the greater exactness of the latitude determinations. The major axes of these spheroids are very nearly identical, but the minor axis of the latter is considerably less than that of the former. * In Section XI. we have determined for several Stations the apparent effects of the irregu- larities of the distribution of matter on the surface of the adjacent country, and by making use of these quantities we may obtain the latitudes that would belong to those points, supposing the hills and valleys to be cut down on every side to one level plane. If it were proved by obser- vation that latitudes observed in perfectly flat countries presented no discrepancies when geodetically compared, it might be assumed as probable that latitudes corrected for the effect of external irregularities would coincide with the mean figure of the earth. But inasmuch as 4. U 706 - PRINCIPAL TRIANGULATION. latitudes observed in flat countries have not been found free from discrepancies when geodetically compared, it must be assumed that every latitude is affected by two distinct sources of dis- turbance; namely, superincumbent irregularly-disposed masses, and irregularities in the distribution of matter below the surface. Of the amount of error attributable to the latter source we must be in every case totally ignorant, but it is always possible to make an estimate of the effect due to the former. By thus removing one of these sources of error we shall in all probability arrive at a result more near the mean latitude than is the immediately observed value. . . . . . . * - : , * - If we take any three of the equations at page 693, and put m = o, a spheroid will be determined which will have its surface parallel to the actual surface at those points (that is, in a northerly direction). This spheroid will, however, be restricted to having its surface at Greenwich parallel to the actual surface in an east and west direction: this, however, is no material restriction, for we have seen already that ris a very small quantity, and, moreover, it has little effect in the latitude equations. * . I. Let us first examine the points Dunnose, Clifton, and Burleigh Moor. Leaving the absolute term symbolical, the equations are— - o = m, + o-9998 : + 1.5Io9 u — or 1406 v O = m, + o-9998 # – 3:4447 u + o-2091 v o = m, 4- o-9998 # – 5:3873 u + o-2492 v Whence— # = - o'5579 m. - o'7928 m, + o-3504 m, w = + o-o834 m. – o-8IIo m, + o-'7276 m, i w = + 4'O4I9 m, - I4.3527 m, + Io.3 Io9 m, The system of deflections A makes— I. .* ' m, = — 2.312 m, = — 2.478 m, = – o 898 which give— - # = + 2'-94 w = + 1.1635 v = + 16.96 The system of deflections B makes— - - m, = – 2.792 m, = – 2.478 m, = + o-622 which give— # = + 3”.74 t = + 2.2294 w = + 30.69 2. Take now the points Boniface Down, Kellie Law, Monach. If we put m, m, m, for the absolute terms, we find— * # = — o'7306 m, - o'5885 m, + o-320.1 m, w = — o-oš32 m, - o'o642 m, + o-1381 m, v = + 1.3069 m, - 4.99 Io m, + 3.70.10 m, By using the system A of deflections, we get— # = + 2".75 u = + o-4530 v = + 4.08 .*.ºt . i- : :: # |º GEODETICAL RESULTS. 707 The system of deflections B gives— # = + 3”. Io w = + o-4785. u = + 3°45 3. The three points Week Down, Burleigh Moor, Calton Hill, treated in like manner, give— * - º, * - . - – o-6387 m, - o'7682 m, + o-407.2 m, = - o'oošI m, - o-4038 m, + o-4095 m, v = + 2.4518 m, - 9-6607 m, + 7.2179 m, , Using the system A of deflections, we have— * ; # = +1”.29 u = — o-7163 . v = - 17.06 The system of deflections B gives— * - - - - : . . # = + o”.89 2. E - .8609 v = – 24.69 4. The points High Port Cliff, Lough Foyle, and Monach, treated in like manner, give— # # = — o'7475 m, - o'3112 m, 4- o-oš66 m, u = - o'o656 m, -o-o-;45 m, + o-roo.4 m, v = + 1.1519 m, - 2.6303 m, + 1.4679 m, By using the system A of deflections, we have— g . . . # = + 3”. I4 w = + o-3off I v = + 6.91 The system B of deflections gives— # = + 2'-91 u = + o-4486 v = + I-43 The elements of these eight spheroids are shown concisely in the following table:– Deflections A Deflections B Spheroids. * w § 70, ty f w. 7) . . . 4, 4.94 | + i. 16 | +16:96 | + 374 + 2.23 || 4:30-69 2 + 2.75 + o-45 + 4 oš + 3 Io + o-48 || + 3°45 3 - || -- 1:29 – o '72 — 17'o6 | + o-'89 | – o '86 —24'69 4 - || + 3-14 | + o- 50 | + 6'91 + 2 '91. + o'45 + I “43 In examining and comparing these results, it must be borne in mind that each quantity is liable to considerable probable error, resulting from the probable errors of the astronomical determinations of latitude, on account of the magnitude of the coefficients of the quantities m, especially in 1 and 3. Giving due weight to this consideration, it is a fair conclusion that the points we have considered do not lay upon the surface of any one spheroid, whether we use the deflections A or the deflections B. The results produced by the former system are, however, less discordant than those produced by the latter. - - : 4. U 2 708 PRINCIPAL TRLANGULATION. 5. Let us next determine the spheroid which best represents the latitudes of the firs thirteen points in the table at page 664, when corrected for calculated deflection. If a be the sum of the squares of the thirteen quantities à for these points, then we must make a* + š + n’ a minimum, otherwise m will come out a large quantity altogether beyond the truth, and 3 will be similarly affected, though only slightly. - If we correct the thirteen latitudes for the system of deflections A, the thirteen absolute terms become— - m; = - 2.312 mis = – 2.478 mio = - 2,659 mg = — 2.862 m, , = — o'898 maa = + o-o&9 m, = - 2,643 m;; = – 2,636 ma: = + 2.233 mg = - 2.922 mix = - o'9II 7m 26 F + o-284 m, = — 2.668 † The equations are found to be— o = - 20-3264 + 13.917o # -- or 6393 || - 49,0302 w -- I'244I v = — o'8196 + o-6393 : + I'o609 m - 3.0501 u + o-IIoo v + 2.8677 – 49,0302 # – 3.0501 m + 499.2936 u - 9.9034 v – 1.4616 + 1.2441 # + o-11oo n - 99034 u + o-5395 v O O O From which by elimination— + 2. I32 – o'o.40 + o-25I2 + 2-4I24. : := Substituting these in the equations from which they were derived, we have the following system— Greenwich - - - - -- 3.1 32 Hungry Hill . . . . -- & I49 Lunnose . . . . . – O. I4. I JForth .. • . . . . -- I-418 Boniface Down . . . – o 692 Lough Foyle . . . . — I. I.43 Week Lown . . . . – O.47 I Rellie Law . . . . . -- o'675 H. P. Cliff . . . . . — o-751 Monach . . . . . . -- I-605 Clifton . . . . . – o'707 Ben Hutig . . . . . — o-647 # Burleigh Moor . . . -- o-48.I Edinburgh . . . . . . — 1.896 The sum of the squares of these quantities, together with that of m, is 16.94 . . . . whence the mean error— gº I6-94 -- r '/ ſº- º immºmºmºsºme -: --- I • 2 I If we apply these values of # u v to the northern portions of the arc, we get for Saxavord + o-226, which is not much out of the way. But when we apply them to the longitude of Feaghmaan, we get for that point n = + 12.719. i - : |i ! * GEODETICAL RESULTS, 709 6. If we had used the system B of deflections, we should have obtained a different system of quantities. In this case— mg = — 2.792 mºs = – 2.478 mo = — o'789 m3 = - 3.342 m, = + o-622 m, = + o-o89 m, = - 3.123 m;; = — 4, 186 mas - + 2.233 ! ms = - 3-402 m, = — 2.21 I mas - + o-664 mar = — I'528 And the equations are— o = – 20-1721 + 13.917o # -- o'6393 m - 49,0302 u + I-2441 v o = — o-90.Io + o-6393 : + I'o609 m - 3-050I w -- or IIoo v o = — 31.7Io4 – 49-0302 # - 3-05oI n + 499.2936 w - 9.9034 v o = — o'5088 + 1 .244I # + o-IIoo n - 9.9034 u + o-5395 v From these by elimination— # = + 2.513 * = + o-171 w = + o-3372 v = + I-302I Substituting these in the equations from which they are derived, we have for Greenwich - - - - -- 45. 3 Hungry Hill . . . . — #444 Dunnose . . . . . -- o-ošo Forth . . . . . . 4- o. 187 Boniface Down . . . – o 496 Lough Foyle . . . . -- o-221 Week Down . . . . — o-274 Jºellie Law . • + o-Io'7 A. P. Cliff • • — o' 552 º Monach . • * + o:908 Clifton . . . . . — o-852 Ben Hutig . . . . . — o'925 Burleigh Moor . . . -- 1.645 JEdinburgh . . . . . — 1.302 The sum of the squares of these quantities, together with that of m, is 15.42 . . . . whence the mean error— V; – † 118, I5 - 4 which is rather smaller than the corresponding quantity from the system A of deflections. If we apply the present values of 3 m w w to the extremities of the Triangulation, namely, Feaghmaan and Saxavord, we obtain for the latter # = — o'. 230, and for the former + II". 175. These are nearer the probable truth than the corresponding quantities derived in the last article by using the deflections A. 1. 7. It appears, then, that whether we use the system A or B of deflections, the corrected latitudes will still present discrepancies greater than the probable errors of observation, and of which the mean amount is + 1". 2. A comparison of the results in the last two articles is in favour of the second system of deflections. 7Io PRINCIPAL TRIANGULATION. 4. The values of 3 m u v which make 3 (3) + + 3 ("") a minimum, as given at page 703, being in terms of the observations explicitly, we can easily find the modifications the quantities already obtained will undergo from the correction of the observed latitudes by calculated deflections; and in the first place we shall use the deflections A. If A, be the coefficient of m, in the expression for 3, then the value of g at page 704, namely, I-491, will receive the increment— - - 1-024, - 1944 – 1.5o 4. – 2.81 As + o-904, + 3:03 A., - 3.85 A. + o-I? 4, -- 2:15 49 – 2.08 A, – o:47 A.: + I-63 A,6 + 2.43 4, By actual multiplication the value of this quantity is found to be + o-3o4. In the same manner the quantities r . . .-- " ' " ' 4. *- + o-268 + o-očo 4. — o-48oo are obtained for the increments to the values of 7, it v at page 704. Thus we have— * + 1,491 – 0.888 . . 4 o'2479 + 1,5397. + O.304 + o-268 + o-oGo.4 — o-48oo # = + I-795 : M = — d;62o : w = + o-3083 3, 25 st + ..I.O.597 The substitution of these quantities in the Equations of Condition—the absolute terms being corrected for the deflections A–furnishes the results shown in the following table — Stations. # Stations. # Stations. " ' || Stations. m J f fº J/ ji Greenwich . . ]+ 1 .795 || Forth . . . -i-o- 685 || Greenwich . . –o 629 || Barrow Hill. ... —; '953 St. Agnes . . -o- 692 || Tawnaghmore . —o'861 || Edinburgh . . -4°406 || Lundy Island . +3° 561 Goonhilly . . [−2 °353 || Lough Foyle . |–2' 356 | Durham. . . -4° 147 | Dunkery. . . —2:306 Hensbarrow . —o'785 || South Berule . [+ 1.865 | Cambridge . . [+4' 175 || Mowcopt. . . --5. 327 Blackdown . . [+3°490 || Ben Lomond . . ;-1 472 Kingstown . . |+ I 327 || York Minster . |–2. 849 Dunnose . . [-o' 21 1 || ICellie Law . . ]-o'455 | Feaghmaan . . [+8. I75 | Easington . . –4° 583 Boniface Down. —o' 756 || Ben Heynish . |+2 239 Black Down . —5'889 || Wordeslow . . [- 5 I23 Week Down . -o- 535 || Great Stirling . —o. 296 | Dunnose . . [−2°827 || Hart Fell . . [+5.083 H. P. Cliff . . [-o'813 || Monach . . . [+o'444 || Precelly . . [+2 140 || Cheviot . . . —3.298 Southampton . 4-2-255 || Ben Hutig . . —I '718 Cowhythe . . . [+o'852 | Dunrich... . . —6-o:8 Precelly" . . [+1'248 || North Rona . --o' 126 ||Wratham, . . [+o'830 || Goat Fell . . —o-o;4 Arbury . . . |+2' 191 || Balta . . . . [+1.781 || Gad's Hill . . H-I '831 || Shyrs Law . . —o-ość Delamere . . –o 268 || Gerth of Scaw. |+1-621 | Fairlight : . |+2' 116 || Mordington . . |–1.40% Clifton . . . . -I 534 || Saxavord . . |—o. 364 Orford Castle . -- 3:668 || Burnswark . . +3° 4oz Burleigh Moor. -o-569 || Edinburgh . . —3'929 | Bºlsham . . . . |+6°oo4 || Ben More, S. U.. |+1-4oz Hungry Hill . –o 578 || Durham. . . —o'607 Walpole, S. P. . |+5'783 || Ben Macdui . . 4-2. 339 Feaghmaan . . [-o'542 || Cambridge . . [+o'69; Docking . . . . [+3°837 || Ben Nevis . . |+8 ° 430 South Lopham . |+2 247 Scournalapich . –2 °ood. Leith Hill . . |–2 186 || Mount Battock . –4°og5 cºlle (9 = – 9.9ss |#. in -;|* : * –$4% * a H* *i . : .3.º8. . .i* ... GEODETICAL RESULTS. 71 I The elements of the spheroid under consideration are— a = 20923713 + IoI44. I u = 20926840 # = 'oog33527 -- arc 5o”. v = •oo359215 c = 277.88 * The sums of the squares of the quantities #, n, are 74.81 ... and 669. oo ... respectively: hence— * ) = + •674 wº (oš28 × 2.20 + or 87 x 1632) = + 3 = Probable error of u = 674 wº (oooº;8 × 2.20 + . . . . •o3O . . . Probable error of v = •437 . . . . . . a = 20926840 + 3oo c = 277.88 + 8.20 pº J. If A, be the coefficient of m, in the expression for 3 at page 703, then if we correct the latitudes observed, for the calculated deflections B, we shall have— # = + 1.491 + o-54 4. – 2:42 A6 – 1.98 A, - 3.29 As + o:90 4; 4 4.554, – 5-40 4; – I. I3 4, + 4-O2 49 — 2-o8 4. — o'47 4.5 + 2 -OI 4.6 + 3-57 4. Performing these multiplications, and similar for w w and v, we have finally— + I-49.I — o-888 + o-2479 + I-5397 + O.443 + o-416 + o-og29 - O-744I # = + 1.934 : * = – o 472 : u = + o-3408 : v = + o-7956 The substitution of these quantities in the Equations of Condition—the absolute terms being corrected for the deflections B–furnishes the results shown in the following table:— Stations. # Stations. # Stations. 7| Stations. y Greenwich . ++934 | Forth –6. 555 || Greenwich . —o'472 || Barrow Hill. –6'oro St. Agnes . . [-o' 389 || Tawnaghmore . —o'963 || Edinburgh . –4°433 || Lundy Island +3° 44.7 Goonhilly . –2'o64 || Lough Foyle —o. 619 | Durham. —4' o86 || Dunkery. -2' 359 IHensbarrow —o: 533 || South Berule + 1-791 || Cambridge . +4' 328 || Mowcopt. + 5° 348 Black Down +3°7I1 || Ben Lomond . |–1-654 || Kingstown . + 1 138 || York Minster –2 766 Dunnose —o-463 || Kellie Law . . ]-o-638 Feaghmaan . . 4-7'755 | Easington –4' 488 Boniface Down. —I 'ooz || Ben Heynish 2-oxo Black Down —5'883 || Wordeslow —5 'o62 Week Down —o'785 || Great Stirling . —o. 521 | Dunnose –2 744 || Hart Fell + 5°og3 H. P. Cliff . —I 'o63 || Monach. . . . . [+o 194 : Precelly. +2' or 9 || Cheviot . —3° 278 | Southampton +2'452 || Ben Hutig . . . —I 588 || Cowhythe +o ‘840 || Dunrich . . —6 oz.6 Precelly. + 1 344 || North Rona —o. 133 Wrotham +o '994 || Goat Fell . |-o" 245 Arbury. +2 263 || Balta . |+ 1 : 524 || Gad's Hill. . +2' oot || Sayrs Law —o’ og5 Delamere —o. 276 || Gerth of Scaw. |+1.364 Fairlight Down |+2' 300 || Mordington . — I 378 Clifton -. — I 560 || Saxavord -o-62; Orford Castle . |+3.901 || Burnswark . . [+3°360 Burleigh Moor. |+o. 911 || Edinburgh . . |–2'o60 | Balsham . . . |+6' 169 || Ben More, S. U. . |-Fi 131 Hungry Hill –2 o26 || Durham —o. 720 Walpole, S. P. . |+5'942 || Ben Macdui . . [+2 272 Feaghmaan. -o-465 || Cambridge . +o 763 Docking . . . [+4' or 7 || Ben Nevis. +8°288 South Lopham . --2'449 || Scournalapichi - -2° 150 -- T-I Leith Hill . —2 oš8 #. * ſº TÉ. * * * f / - Bu ill . . [- 3 * Mormonth .. - I - O " Cowhythe (#) = — Io". 155 #... . If .# 444 712 PRINCIPAL TRLANGULATION. The elements of this spheroid are— The sums of the squares of the quantities 5, 7, are 70 hence— 0. E C Probable error of u = Probable error of v = Either of the last two spheroids may be taken as a very close representative of the actual surface of Great Britain between the latitudes of 49° and 61°, and for 12° of longitude. We = 2.0923713 + IoI44. I u = 20927170 = 'oog33527 -- arc 5o”. v = •oo352813 = 282-94 •674 y (ooos,8 × 2-o'7 + . . . . •674. W (oš28 x 2.07 -- or 87 × 1622) - a = 20927170 + 291 c = 282-94 + 8:41 6. shall adopt the mean of the two sets of values, namely— These values of § 7) u v being substituted in the original Equations of Condition, page 693, # = + 1 . 864 * = — or 546 w = + O. 32.45 v = + o- 9276 a = 20927OO5 + 295 c = 280.4 + 8.3 32 . . . and 665. OI . . . + ) = + •O29 tº ſº tº °433 tº . . . we obtain the following results for the probable deflections at the different Stations — respectively: Unexplained. *. Unexplained. Stations. # - Stations. # Defi. A Defl. B Defi. A Defl. B f/ J/ */ JJ Aft JJ Greenwich . + 1 - 864 Forth + o- 545 + o' 715 — o' 585 St. Agnes — o' 54. I Tawnaghmore . — o' 912 | Goonhilly — 2 209 Lough Foyle — 4' 573 - 2'423 - o' 553 Hensbarrow — o' 660 South IBerulo -- I '828 Blackdown . + 3 6oo Ben Lomond — I 563 Dunnose — 1 - 117 — o' og7 — o'577 | Kellie Law . + I 533 - o' 547 Boniface Down + 1 .298 || – o 642 | – I 122 || Ben Heynish . + 2* I4o Week Down + 1 o8o — or 420 — o' 9oo || Great Stirling . — o' 409 H. P. Cliff . + 2 - 111 | — o' 699 — I 179 || Monach . + o' 789 || + o' 319 | Southampton + 2 + 353 Ben Hutig . – 3:473 || – I '843 || – I'463 Precelly. + I 295 North Rona. — o' oo3 Arbury . + 2 - 226 Balta + I 653 Delamere .. — o' 272 Gerth of Scaw . + I 493 Clifton . . . - 2'447 — I 547 Saxavord . – o '492 Burleigh Moor. - 3'589 |- o'559 |+ o'961 || Edinburgh . – 5' 545 – 3' I 15 — I ‘975 Hungry Hill . . . + 3'323 – o' 527 | – 2 oz7 | Durham. — o' 664. Feaghmaan. — o' 504 Cambridge . + o' 727 '..:i-: - * -*- GEODETICAL RESULTS, 7I3 '.. :t In this table, the figures in the third column are the apparent errors of latitude unaccounted for by the external irregularities of ground, not considering the effect of disturbing masses above nine miles distant. The figures in the fourth column are apparent errors of latitude unac- counted for after including the attractions of more distant masses. It appears, therefore, that in the Isle of Wight there is (as compared with any spheroidal surface that nearly represents the actual surface of Great Britain) a general southward deflection, whereas from the mass of England to the north we might have anticipated a general northward deflection at the four Zenith Sector Stations. At Burleigh Moor it would appear from the fourth column that the calculation of local attraction has been extended too far, and the same at Hungry Hill. At Feaghmaan the com- puted deflection, — I’’. 95, is apparently too great, but the determination of this quantity was not very satisfactory. º, At Lough Foyle the ground within ten miles will only account for half the probable deflec- tion: the same observation applies to Ben Hutig and Edinburgh. At these three Stations it seems probable that the plumb-line is drawn southward by dense subterranean masses. The largest remaining deflection is 3".60, at Blackdown. This is the highest point of a range of low hills in Dorsetshire: to the north of the Station the country is considerably higher than to the south, but from the very undulating nature of the surface it is impossible, without contours, to cstimate the amount of the deflection. It may amount to 2", but it seems impro- bable that the ground would account for a larger quantity than this. At Southampton there appears to be a deflection of 2". 35 to the north. From the Sector Station the country rises as we proceed northwards, but falls to the south ; the sea being distant from half a mile to a mile and a half. This inequality of ground would account for 1" or perhaps I”. 5 to the north, but not for the whole amount of 2". 35. - At Greenwich we have seen that all our calculations have assigned a positive value to #, and yet the ground will not account for any such positive value, but rather the opposite At Balta and Gerth of Scaw all our calculations have indicated a northerly deflection, which the ground will scarcely account for. These Stations, together with Saxavord, were visited by the Astronomer Royal in 1849, who has expressed his opinion that all three are fairly good as far as the form of the country is concerned; that Balta is the best, but that Gerth of Scaw is also a good Station, and that it was impossible to say on which side, north or south, there is any preponderance of attraction: however, nearly three miles north from Balta, and two miles south from the Gerth of Scaw, lies Nive Hill, rising to the height of about 516 feet, so that if any local deflection of the plumb-line exists at these Stations, it might be expected to be in opposite directions. Saxavord he considered to be more exceptionable than the others, on account of the steepness of the declivity on the north and west sides, as compared with that on the south and cast. At Cowhythe there is a deflection amounting to nearly, if not quite, Io" to the south, the greater part of which is certainly due to dense masses below the surface. 4 X. 7I4. PRINCIPAL TRIANGULATION. 7. It is important to remember, with respect to the probable errors of the adopted values of a and c, that they do not belong to the figure of the earth, but merely to a very small portion of its surface. The precision of the surface obtained will be better comprehended if viewed in another light. At Durham Observatory, for instance (being nearly a central point in respect of latitude), we have à = — o”.664, n = — 4". 117: these quantities give the actual position, or direction rather, of the tangent plane to the surface. In this tangent plane, through the point of contact, suppose the meridian and the perpendicular to it, traced; take these lines as axes of co-ordinates a, y, then the surface will be defined by a third co-ordinate 2 measured vertically downwards from the point whose co-ordinates are ar, y; the probable error of 2 will give the best idea of the precision of the adopted surface. 'The equation of a spheroid whose semi-axes are a and b when the co-ordinates originate at the centre, is— a’? + y” 2/2 #– + F = 1 Transfer the origin of co-ordinates to a point on the surface in the plane of a 2 whose latitude is A, and let the axes of w and y be tangents to the surface, the former pointing northwards, the latter eastwards; let 2 be measured vertically downwards. If h k be the distances of this new origin on the surface from the axis of revolution and from the plane of the equator respectively, and if we put p = 2 cos x + a sin A, q = 2 sin A — a cos A, then— h = z' + p tº k = 2 + 7 Also y = y', whence by substitution— (1 – e’) y' + (1 – e’) (h – p) + (k - 6) – b = o Now if n be the normal, h = n cos x, k = n (I – e’) sin A, consequently - * (I – e’) h’ + k” — tº - o Also (1 – e’) hp + kg = n (1 – e’) (p cos x + q sin x) = m2 (1 – e'); so that the equation is reduced to *. (1 – e’) y' + (1 – e’) p” + q’ – 2 m2 (1 – e’) = o Now (I – e’) p” + q = ~" (I — e” sin” x) + 2* (I – e’ cos’ x) – e' we sin 2 x; conse- quently the equation of the surface is finally * % a ( – ’) = - (1 – e' sin” x); T In this equation, suppose w, y, and a constant, and a, e, 2 variable, then— dq, dq # a + i e + #3: = o 2 q = (1 – e’) y' + x' (1 – c' sin’ A) + z” (I – e' cos’ x) – e' wa sin 2 x — O d. &|i*; : f.i d:*} GEODETICAL RESULTS. 7I5 * By differentiating we get— d4 – - 2 (I – e’) da T (1 − 27 sin;Tx), I d * . * — l 2\ ,-3-2 |a ; = – a sin’ x − y – 2 cos’ x – we sin 2 x + 2 az # (1 + e”) sin’ A q, # = 2 (I – c’ cos A) — e” a sin X cos x — In forming the value of (I — e” sin” x); a (I - *) (I — e” sin” x) dº dº da de 32. * = 7. 3a ſºmº, 7. 3e d2. dº it is clear that, 6a and be being very small, it will suffice to retain the principal terms of the three differential coefficients, and reject those that are comparatively small. Now from the equation of the surface we have— a' + y' = 2 az – 2 + terms in e” wº, e y” . . . Let v' = r" cos’ a, y' = r" sin” cº, then— dº — da T d tº 3C . d? = 0 7” (cos a cos x — , sin” A — — sin 2 x) de sº 2 (1. * T tºmº ºr ſº *- * tº (E (, 7.2 7.2 ſº 7° * . 32 = — ; a +- a; (cos a cos’. — , sin” A — ; cosa cos a sin x) ae. Če Suppose r = 400 miles, the greatest distance to which our surface refers, then the probable error of z, corresponding to the estimated probable error of a (viz. # 295 feet), will amount to only + 3 -ofeet. Again, taking x = 55° and o. = o, we have— ar cos’ x – # sin’ A = — o'ooč5 — # sin 2 x = — o'4698 ae &e = aºs = 5072 ºv So that the error 8v will produce an error 82 = — (-ooooo; + .oOo.47) 5072 v = – 27 ºv Therefore the probable error of 2, as depending upon that of v or c, will barely exceed one foot. It will, however, be greater in the direction perpendicular to the meridian ; and for the same value of r, equal to * 82 = – 35 -: * ſº # ae șe 17.7 ºv which, taking 6v = + , 43, will amount to + 7.7 feet. If, however, we take our origin at a point centrally situated with respect to longitude, we shall not require to assume such a large 4 X 2. 716 PRINCIPAL TRLANGULATION. value of r as the maximum, but 200 miles will be sufficient, and thus, instead of + 7.7 feet, we should have + I 9 feet. Jºqualion of the Surface. - Taking Durham Observatory as the origin; the tangent plane to the surface (determined by § = — o”.664, m = — 4". I 17), as the plane of X and Y, the former measured northwards, and z measured vertically downwards, the equation to the surface is— º •99524953 X* + .99288oo5 Y” + .99763052 Z” – “ood? Ioog X Z – 41655ozo Z = o .: .*: h .. -.,f- *. | ; .3. º | S E C T I O N XIII. LATITUDES AND LONGITUDES OF THE STATIONS, LENGTH OF THE DEGREE, &c. \ § I. Having determined in the preceding Section the axes of that spheroid which corresponds most nearly with the surface of Great Britain, we proceed to develop the expression for the radius of curvature in and perpendicular to the meridian, the length of a degree in and perpendicular to the meridian, &c. By page 267 it appears that the radius of curvature of the meridian is— * = a (, – 2 m, cos 2 x + 2 m, cos 4 x + . . .) (1) In which expression— a' = a (1 — n) (I — n°) _ a ~ * .* n = Ti, 9 ...a o = I - * º 77 +: " 4 n, – 3 n + 3–3–3 m + . tº º 2. 2 - 4 - 2 n, a 3–3 r + . . {º 2 * .4. I. If s be the length of a meridian arc between the latitudes of x1 and Ås, and if we put x, — A = p ; \; -- A1 = 2 * we shall have— *A + 4 ºp S = gda A — 4 p s = aſ (m. 2 – 2 n, sin p cos 2 x + n, sin 2 % cos 4 x + . . . .) (2) The whole perimeter is therefore 2 7 a' no, and hence, tra' no 18O Mean degree = 718 PRINCIPAL TRLANGULATION. 2. If w and y be the coordinates (originating at the centre, and measured parallel to the directions of a and b respectively) of the point whose latitude is A, then since ds = gda, da: = — ds sin A = – g sin a da dy = ds cos x = g cos x da Also— Ç * * 2 COS 2.x sin A = sin 3-2. — sin a 2 cos 4 × sin x = sin 5 × — sin 32. 2 cos 2 A cos A = COS 3 A + cos A 2 cos 4A coS X = COS 5 x + cos 32. Multiplying the value of g by sin A and cos A, we have— * E - a'ſ (G. + n,) sin X – (n, + n,) sin 3 x + n, sin 52) da 3/ = a'ſ (G. – nº coax - (-, -n) cos 3x + n, cossº) dź. / / a = a' (no + n,) cos A – ; (n, + n,) cos 3 x + #n, cos 5 Å (3) / 3/ = *G. – no in – ; (; – ) in 32 + #1, in sº (4) 3. Let g’ be the radius of curvature perpendicular to the meridian in the latitude A, then— - g’ cos x = x: Assume g’ = a, + 2 a, cos 2 x + 2 a, cos 4 x, then— g' cos x = (e. + a) cos x + (a, + a.) cos 3 x + a, cos 5 x Comparing this with the value of w in equation (3)— as + a, = a' (no + n) * as = a' (no + n,) + a' (n, + n,) + a' 7la º - | 3. 5 — 3 (a, + a,) = a' (n, + n,)} . . . a, = – “. (n, + n,) — 2. 7ta * . . . . " 3 ; 5 a, - a n, . a = * : ". Therefore the value of the radius of curvature g’ is— * — »” £6 * , — (26. 2 a. as g = a' (ne + n,) + #(º, + n) + ; ". (*: (n, + n,) + 5 n) cos 2 + + n, cos 4x (5) 4. For finding the spherical excess of a triangle we require the logarithm of the quantity 2 g g sin I". Referring to page 229 we have— — — ... — A' = —& a 7 - a aGEF) T â(IFE) I - = |ſ) ſº :-- ~ // 2 gigſ sin 1” T log 2 b" sin I" + 4 log A ... log 2 - - log (2 a’ (I º nº) sin 1) + 4 M (a COS 2. A — # COS 4x) (6) where M is the quantity o. 434.29448 . . . . .*s º LATITUDES AND LONGITUDES, &c. 7I9 5. Let us now determine the area contained between any given meridians and parallels. Let dA be the area of an indefinitely small rectangle on the surface, of which two sides are formed by the parallels of the latitudes x and x + dā, and the other two sides by meridians. whose difference of longitude is day; the length of either of the two first sides is gala, and that of either of the latter is g’ cos x day. ... dA = g g’ cos x dº do ... A = a” (I – e’) ſiſ A-4 cos x da dw I ‘d in X (1 ., SIIl T; a. s , ſº I = abw ſ 4. 72 2 ºmº * 2 ( (1 + n)” SIIl x) Now we have— da: r 3: a da: - z—- = 1. . --— l. ſº; + 3 H + , ſº which applied to the preceding value of A gives— abw sin A º COS X. A = − (I — nº ( 2. ( ) T+ 27, cos 2XTºi ºf TT2 ..., x. Tº dº But— I — ” 2 º - - - mº X tº dº ſº H=HE = 1 - 2n cos 2 x + 2n cos 4A – 2 nº cos 6 x + This quantity multiplied by sin A and cos A, becomes the following— (1 + n) (sin A — n sin 3 x + n’ sin 5 x + . . .) (1 — n) (cos A – n cos 3 x + n’ cos 5 x + . . .) If we substitute these in the expression for A, the general expression for the "term is— abw *(G + n) sin (2i – 1) x + ++ sin (2 : – 1) x) (– :) - º — - i – I = al., it'ſ I) m sin (; ; – ) ... (- ) 2 : — I Hence we have, making i = 1, 2, 3, &c.— A = ab: in x – “(2 sin 3 A nº + 2 n) sin 5 x . . . (700) (in 3 (2 + n) sin 3 A + 5 (3 m) sin 5 ) (7) the integral being taken from the equator to the latitude x. The area between the limits 7 – 3 p and x -H \, g is— A = abw 4. (?, cos x - m (2 + n) 4, cos 3 x + n’ (3 + 2 m) @g cos 5 × – ...) (8) sin - © q. 720 PRINCIPAL TRLANGULATION. Numerical Values. At page 712 it will be seen that the elliptic elements which most nearly represent the meridian curve of Great Britain are— a = 20927005 * = 279.4 a 28o. 4 b = 20852372 n =– T 559.8 From these quantities we get the following— a' = 20889555 a' me = 20889.705 n. = I. ooooo/18 a' m, = 55974 ºn, = o 'oozó7954 a' m, = I 25 n, - O -ooooo;98 These values being substituted in the values of g g’, &c. given in the preceding paragraphs, we get— I.—Radius of Curvature of the Meridian, = 20889.705 – I I IQ49 cos 2 x + 250 cos 47. 2.—Radius of Curvature perpendicular to the Meridian, = 2.0964.404 – 37450 cos 2 x + 50 cos 47. 3.—IRadius of Parallel, = 20.945679 cos ? – 18700 cos 3 x + 25 cos 5 Å 4.—Length of a Meridian Arc whose amplitude is p, and mean latitude A, = 20889.705 b – 11 1949 sin & cos 2 x + 125 sin 2 + cos 4 x 5.—Length of a Degree of the Meridian, = 364594. I — 1953.8 cos 2 x + 4-4 cos 4 × 6.—Length of a Degree of Longitude, — 365571 "o cos ? – 326.4 cos 3 x + o-4 cos 5 x i LATITUDES AND LONGITUDES, &c. 72 I il ſ For converting distances in the meridian and perpendicular to it into seconds of arc, we have— Log &º ſº = 7.994.4959375 + .oO23274088 cos 2 A — ooooozo'788 cos 4 x + -ooooooooz4 cos 6 x Og zºº = 7-9929429442 + ooo7758029 cos 2 x – oooooooº.29 cos 4 x + oºooooooo8 cos 6 \ And for computing the spherical excesses of triangles— –F–F–F, - º º *f A. * @ og 3 ggſ sin I” o:3719838 + -oo:3Io92 cos 2 oooooz8 COS 4 Å. Length of a Degree, Minute, and Second in Latitude and Longitude. Minute of Second of Minute of Second of Degree of Latitude. Latitude. Latitude. Degree of Longitude. Longitude. Longitude. Lat. Lat. Fect. Miles. Milcs. Fect. IFoet. Miles. Miles. Rect. 45 364861-8 69' 103 || 1: 1517 | 101 3505 || 2401997 || 45-475 o'7579 | 66-6972 43 5o 364929'2 | 69' 115 || 1 - 1519 || 1 or '3693 235267°o 44' 558 o' 7426 || 65' 3520 56 5I 364996'3 69' 128 I I 52 I IoI 3879 23O352 “o 43' 627 o' 7271 63'9867 51 52 365062 9 69' 141 I " I S.23 IoI ‘4064. 225.366. I 42 683 o' 7114 | 62-6017 | 52 53 || 365.128'9 69' 153 I 1526 IOI '4247 22031 o’8 - || 41 '726 o' 6954 61' 1975 53 54 || 365194-3 69' 166 I 1528 IoI ‘4429 || 2 15187° 7 || 4o 755 o'6793 59' 7744 54 55 || 365259°o 69' 178 I ‘ I 530 IoI 4608 209998-2 39 °772 o:6629 58° 3328 55 56 365322 8 69' 190 I ‘ I 532 IoI '4786 2O4744 °o 38.777 o “6463 56'8734 56 57 || 365385-8 69' 202 I “I 534. IoI '4961 1994.26'7 37: 770 o' 6295 55' 3963 57 58 || 365447 9 || 69° 214 | I 1536 || IoI 5133 ::::::...? 36 751 o' 6125 53-9022 || 58 59 || 3655o8'9 69'225 I I 538 IoI '5303 188609'? 35° 72 I o' 5954 52 °39'14 || 59 60 365568-8 69'237 I " I 539 IoI 5469 183112 - 1 34°68o o' 578o 5o '8645 6o 61 365627' 5 69'248 I " I 54 I IoI 5632 I77558' 5 33°629 o' 5605 || 49°3218 6I | The following table contains the logarithms of I I I g sin I" g' sin I" 2 g g'sin l' 4 Y 722 PRINCIPAL TRIANGULATION. WALUES OF # I - I # I *- wº Log (, sin F.) 3 Log (; sin in) 3. Log (: g g’ sin 7) For THE SURFACE OF GREAT BRITAIN. Log -- Log I º I tº tº * I * I tº § ** (#P) ºr ºs (; ) biºlºr|*|*GP) ºr “G) ºr (ºr) ºr 40° 7'994.1740. ..., |7-99.88564 ... lo'sſiss; ... les' 7-993705 |..., |7-99.678.4 |, | o'379925 | . Io' 416061 #. 831.17 447 537 ; Io' 7. 9 368879 ... 67389 ; 908 : 2O 4. I4.722 #. 82670 #% 519 18 20 367609 : 66966 : 891 : 3o 41.3383 #3 82224 #: 52T | 18 || 30 366342 ; 66544 ;: 874. Ž 40 4. I2O45 #. 81778 44 483 || 3 || 4o 365078 1262 66122 42O : 857 17 5o 410735 | *33 81333 445 465 5o 363816 65702 84o 50 I335 8o888 445 I8 56° 7' 0.036 I259 6528 420 sal' ° 7'994O9374 7'9928o o' 371447 ° 7'99362557 7'99265282 o' 370823 Io' 408041 #3 80443 445 43O : Io' 36.1302 :::: 64864 #: 807 º 22 || 4267: | #: 79% | #: #2 | #|32 || 36:49 |: §44; #: 79% | } 3O 42337; 13; 7255% | #3 394 | 18 || 30 358799 || 2:6 £423° iá 773 16 4o 494.24% | #3; Z3.3 |AA; 376 || 7 || 49 35Z553 | 1244 £39.4 i. 757 || 17 5o 402720 78670 359 5o 356309 632 oo 740 1326 8228 442 18 57° 6 I24o 62786 4. I4. 17 51° | 7'994or 394 7 '9927822 o' 37 I34. I 7°993.550b9 7'992027 o' 370723 #|”;|# #3 |: 323 ; 10| " ":#834 ||. 62374 #: #3}| 2O 398747 | #: ZŽº 440 393 || 4 || 20 #58 # 51%. #. 696 || 3 3o 33% tº 1319 76905 O 288 . . 30 35.1367 ::: 61552 # 974 || 3 4o 396106 išić 76465 44 271 # 4o 35o I4o ... 61143 : 658 . . 5o 394788 7662é 439 253 5o #39;6|***4 6073; 4 641 | *7 1316 439 18 I 2.2 I 60228 4O7 6 I6 52°| 7'993.93472 7'99275587 o' 37 I235 58° 7'99347695 7°992bo328 o' 370625 Io' 392 I58 #: 75 I49 438 37 218 # Io' 7 *:::::: #. 59922 #: 609 : 2O #2846 || 3:. $47: #. *32 || 17 | * #5264 ... §3 ||3: 593 | 16 3o 3:2535 | #3; 74.75 || 3:6 #3 #| 39 344:54 | 1207 53.5 | io; #7 17 40 388228 3. 73836 | #3 166 || 4 || 4o 342847 2. 5$712 | . 56o || 6 5o 386922 | "3 73434 435 148 5o #1644 | *3 $84.11 || 4 544 53° 8-618 | * ge 435 '. Iso I IQ9 7 399 || 70528 I6 7°99385b I 7°992729b.9 o' 37 II.3.I ° 7'9934o445 7. 99257912 o° 37052 ro" " "::4316 || 3. #233; #34 #| || 3 *:::::: ; #7;13 || 333 #: ||. 2 O 383017 : 721.3% #33 og6. : 2 O 338o37 #: 571 16 % 497 # 3o 381719 ... 71670 4.32 o?9 : 3o 33.6869 I 18 56720 39 481 | 16 4o 38o324 :::: 71.238 #. o61 | ..., | 40 335685 ; 56325 395 465 I6 5o 379; 32 | **9 jošč7 43 oqā | *7 || $o 334.504 #5331 || 394 449 || | | || sai | ** 430 I7 | I 177 392 I5 54°| 7'993.77841 7°992703 o' 37 Io27 60° 7' 99.333327 7'992 55539 o' 370434. | |*|7%; : #|429 |**". #| 10' ' '333i:; #. *#: 3. *# : 2 O ###| #: 㺠|| 3 || 0-370994 | #|3: ãºgă #: $4758 |3: 432 || 1 3o 373985 23; §gí | }. 976 || 4 || 30 32.3821 || 3: $4379 |3: 387 | # 4o 372704 1278 68665 #: 959 # 40 328660 II 56 53983 3. 37} | 1 55° 7'99370151 7'99267814 o' 370925 61° 7'99326351 7'992532 I4. o' 37034. I LATITUDES AND LONGITUDES. º 723 § II. - Latitudes and Longitudes. The following table contains the latitudes and longitudes of the principal points of the triangulation, calculated from the approximate values, # = I". 40, n ='o, w = o' 2500, and Q) = O :- - Names of Stations. Latitude. Longitude W. North Meridian. Acklam Wold....................................... 54 3 I '98 o 47 o' 32. 186 & 17:52 Arbury Hill ....................................... 52 13 28°36 I 12 34°58. I79 59 2 I 22 Arrenig ............................................. 52 55 I'32 3 44 39°42 tº º ſº. Axedge ---------------------------------............ 53 I3 56°78 I 56 50° 25 18o o II '82 Back Tor ................ tº º 'º º is º e º is º is a s is e s is e e s a s n e s a 53 24 54 ° 90 I 42 8-70 • * * Baconsthorpe Tower.............................. 52 53 I2 '98 | – I 9 43’56 18o o 1' 35 Ballycreen .......................................... 52 55 6' 16 6 2.1 53.68 I79 59 50 °29 Balsham Tower ...... * * * * * * * * * * * * * * * * * * * * * * * * * * * * * s 52 7 59' os – o 19 II '71 I79 59 53°49 Balta ................................................ 6o 45 4°51 o 47 3' 84 I79 59 57° 52 Banstead............................................. 5I Ig I 31 o 12 46' 58 18o o 4'94 t Bardon Hill ....................................... 52 42 51 62. I 19 8' 2.0 18o o 5’ 62 8 Barrow Hill ....................................... 5o I3 40 °49 3 41 35' 69 18o o 10-40 Bauriregaum ....................................... 52 I2 25°34 9 49 40 ° 59 I79 59 58' 34 Beachy Head ....................................... 5o 44, 23-66 | – o 15 15:43 | 186 6 2.57 Beacon Hill ....................................... 51 II o' 77 I 43 I4'81 | 180 o 3-48 Beacon Hill, Trescow ........................... 49 57 38' 7o 6 20 22 '86 180 6 52-73 Ben Cheilt ..................................... ..... 58 I9 I5'44 3 22 37° 72 I79 59 55 ° 4o Ben Clºugh.......................................... 56 11 8 o'7 3 46 2 - 17 I79 59 58°53 Ben Clibrig.......................................... 58 I4 6' 33 4 24 33°43 I79 59 5 I 34. Ben Corr.:::......................................... 53 3o 23 °43 9 47 25 °og I79 59 53° 41 Ben Heynish ....................................... 56 27 18:95 6 55 17: 83 I79 59 58' 84 Ben Hutig .......................................... 58 33 3:47 4. 30 4o 20 I79 59 53° I2 Ben Lawers ....................‘s e e s = • * * * * * * * & C tº e º ſº 56 32 41 °42 4 13 8-61 18o o 30-65 Ben Lomond ....................................... 56 II 24' 64 4 37 52 “og I79 59 57* I2 Ben Macdui ....................................... 57 4. I3 °o3 3 4o 2 °os I79 59 49'84. Ben More, Mull.................................... 56 25 29' 20 6 o 44' oo I79 59 57° 77 Ben More, S. Uist................................. 57 15 31 18 7 I7 35' 35 18o o 4'32 Ben Nevis ...... *P* is tº e º ºs e s ∈ tº e º 'º º e º 'º t e º is e s s e s s e e s tº e s we 56 47 48’46 5 o 6' 13 18o o 12 93 Ben Tartovil ....................................... 55 43 32°38 6 26 32° 55 18o o 1-77 Ben Wyvis .......................................... 57 4o 43 ‘83 4 34 38°57 I79 59 5 I '40 Berkhampstead .................................... 5I 45 23'58 o 7 25 'o'; 179 59 56-47 Black Comb ....................................... 54. I5 27°52 3 19 37' off 18o o 12-96 Blackdown ......... * * * * * * * * * * * * * * * * * * * * * * g º 'º e º º ſº s g º e 5o 41 I2 “O4. 2 32 5 I 4 I 18o o 5’ Io º Blackheddon ....................................... 55 38 18° 52 I 55 38°39 180 o 24' 50 : Blue Hill............................................. 57 5 40' os 2 7 3o 4o I79 59 44'42 . Boniface Down .................................... 5o 36 II '41 I I I 55° II 18o o 20-63 : Boniface, S.E. .................................... 5o 36 7' 21 I I I 59'44 18o o 46.45 # Boston Church Tower ........................... 52 58 42° 13 o I 26' 57 I79 59 30°29 º Botton Head ....................................... 54. 24, 22 °4 I I 5 3° of I79 59 55' 60 . Brandon, Suffolk ................................. 52 24 20-82 – o 37 20-78 18o o 16° 59 Brandon Down, Durham ........................ 54 45 17: 61 I 4o 35°89 I79 59 55°42 : Brandon, Kerry.................................... 52 I4 6°43 Io I5 Io'os I79 59 59°99 s Brassa.........................“.............. 6o 7 47 '79 I 5 4o 61 I79 59 57'71 ; Brimmond .......................................... 57 Io 20 15 2 I4 II '85 179 59 48-96 | Broadway Tower ................................. 52 1 26-8o I 5o 2 '81 179 59 53°40 : i - # 4 Y 2 724 PRINCIPAL TRIANGULATION. Names of Stations. Iatitude. Longitude W. North Meridian. Brown Willy ....................................... 5o 35 25 ° 95 4 36 4' II I79 59 50 *oq. Duckminster Spire................................. 52 47 52 '68 o 4 I 45 ° 43 . . . . Bunwell Church Tower ........................ 52 29 28°46 — 1 7 51 - 1 18o 2 52 '79 Burleigh Moor .................................... 54 34 I5'8o I 2 1996 I79 59 49°84 Burnswark .......................................... 55 5 42 II 3 16 36' 24 18o o I o4. i Butser Hill...... tº . . . . . . . . e. g. ſº ſº º tº tº º ſº ºn tº E tº ſº ſº º 'º º g tº dº ſº º ſº º 5o 58 39°85 o 58 43°39 18o o 24' 75 Cader Idris.......................................... 52 4I 58' 31 3 54. 25 °7o tº . . Caherbarnagh....................................... 52 I 5 I 67 9 Io 36° 51 I79 59 54°4 I Calton Hill.......................................... 55 57 I?’ 5 I 3 Io 54° 16 || 179 59 54°33 Carrigfadda.......................................... 51 38 7-88 9 5 36 II | 179 59 59. Io Cheviot ............................................. 55 28 42°og 2 8 37' I7 179 59 49' 64 Chingford “........................................ 5 I 38 Io' 19 O O O" OI I79 59 55 °8o Cleisham.................. tº $ tº ſº º 0 tº $ tº º e º 'º e º s tº e º e s tº e º e º 'º 57 57 49' 2 I 6 48 38'42 179 59 56' 21 Clifton Beacon .................................... 53 27 27°56 I 13 7° 15 18o o I4. 95 Cnoc Ghiubhais.................................... 58 35 3'86 4 58 55'73 I79 59 52 °43 Collier Law.......................................... 54 46 I5' 56 I 58 28°35 179 59 42 62 Coringdon ........... tº e º 'º º tº G & º 'º º t e º e º 'º º ſº º 'º e º 'º º is e º 'º º º 5o 37 49' os 1 59 16-78 18o o 2 6o Corryhabbie ............... tº º ſº º ſº I tº ſº ºn L & º º ſº tº . . . . . . . 57 20 4o 27 3 II 4o'34 179 59 57'76 Cowhytho .......................................... 57 4o 59' 20 2 39 31 °47 I79 59 54' 55 Cradle.................................... tº º tº dº º dº ſº º ſº º is tº 51 57 6'72 3 7 15: 61 18o o 4° or Crittel ................................................ 54 56 26' 38 3 37 37° 16 18o o 13' 65 Croghan ............................................. 53 20 46° 37 7 16 36' 51 I79 59 57°83 Cross Fell ................ tº $ tº a s & ſº tº t e º 'º e º 'º e º is sº º sº º s º a tº 54 42 Io'76 2 29 6'73 18o o 17' 58 Crowborough ....................................... 5 I 3 19° 37 – o 9 2 I o9 179 59 56-64 Crowle Beacon .................................... 53 36 37°45 o 49 29' ob 18o o 29° 13 Cuileagh............................................. 54. I2 3' IQ 7 48 35°20 179 59 56-46 Cundtham ..............................------------ 55 II 2 °7 I 7 7 27° 40 I79 59 57° 73 Cyrn-y-Brain......... ---------------............... 53 2 17-61 3 Io 20° 97 I79 59 49' 17 | Danbury Church Spiro ........................... 5 I 42 57" IQ | – o 34 32° 52 I79 59 35' 55 | Deadman.......... * * * * * * * * * * * * * * * s e º 'º e s a s a c e s e s sº e º a s 5o I3 I7 "22 | 4 48 o' 21 18o o 1 '90 Dean Hill “........................................ 5 I I 49' 7I I 39 5'59 18o o 28°40 | Deerness......... * * * * * * * * * * * * * s e s e s e s s a e º e s see e s a e s a s 58 57 5-22 2 44 56°26 I79 59 55' 30 Pºlamore............................................. 53 I 3 I7 ° 93 2 4 I 2 °43 18o o 18° 50 Pitchling............................................. 5o 54 5’ 69 o 6 21 '8o 18o o 6 oz Pivis ................................................ 54 36 40'42 6 I o' o4. I79 59 59° 24 Docking Church Tower ........................ 52 54 3: 74 || – o 37 28' 20 179 59 52 '63 Doolieve ............................................. 5I 47 22 ° 92 8 27 24' 65 179 59 56° 18 Drung Point ....................................... 55 9 II 36 7 8 53° 34 179 59 58°53 | Dublin Observatory Dome ..................... 53 23 I4 ° 2 I 6 20 13 ‘od. I79 59 58°os Pudwick......... ................................... 57 25 49' 69 2 2 6' oo 179 59 48' 39 Dunkery Beacon .................................. 51 9 45'68 3 35 6' 65 I79 59 59' 42 Dunnet Head............ C & tº º º is º º in s is a ſº s is e º e º e º is is a 58 4o 8° 25 3 22 II ‘43 I79 59 55 ° 92 Dunnose ............................................. 5o 37 5" 53 1 II 49' 66 18o o Io'67 Dunrich ......... tº C tº dº ſº º 'º e* - - - - - - - - - - - - - - - - - - - - - - - - - - - 55 34 I9'58 3 II o' os ‘I 79 59 55 “I2 Dunstable .......................................... 5I 5 I 5o '79 o 32 5’ og 18o o 2'48 Tasington .......................................... 54 33 53° 42 o 5o 23°77 18o o o' 63 East Lomond ..................... • - - - - - - - - - - - - - - - - - 56 I4 31 '85 3 13 9-76 179 59 52 '78 Easton Church Tower ........................... 52 37 50 °65 o 3o 21 96 I79 59 29' 15 By Minster ....................................... 52 23 55'94 | – o 15 51-46 18o o 14' 39 £Pping Cupola .................................... 5I 42 I5'89 o 7 28’ og 18o o 3° 56 Fair. Isle ........................... § - ºg º 'º dº ſº tº º – º – º ſº º ſº tº ſº 59 32 45° O4. I 37 50°23 I79 59 54 '73 Fairlight................. * * * * * * * s is º 'º e s m ſº tº e º s º ºs e º º ſº tº s tº 59 52 38' I6 –o 37 13 '54 I79 59 53°68 Tashvon “.................................... 58 33 42 74 4 53 55°48 I79 59 54 '70 Feaghmann “.................................... 5 I 55 2 I 68 Io 20 4 I og I79 59 57-64 Tetlar ......” “............................... 6o 37 12.71 o 51 43 '82 I79 59 56' 96 Fitty Hill “.................................. tº º e º 'º º 59 17 II : o3 3 o 2 Ig I79 59 54*72 Porth Mountain .................................... 52 18 57'93 6 33 38.76 18o o o 'oz Foula ......... tº e s tº a sº tº º tº e º 'º e º is tº e º e s is e is a s e º is e º g s tº $ tº º ſº a 6o 8 24.24 2 5 37' 61 179 59 54°56 h. } ;-:Y. i LATITUDES AND LONGITUDES. 725 Names of Stations. Latitude. Longitude W. North Meridian. Four Milo Stone.............................. tº dº ſº º ſº º 5í 7 #48 f 5í 1755 183 & 13-oo Frittenfield ........ * † ºn tº a tº g g tº * * * * * * * * * * * * * * * * * * * * * * * * * 51 12 19' 60 | – o 50 Io' 62 I79 59 32 °47 Gad's Hill ....... * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 5 I 24 51 °49 – o 27 55' IQ 179 59 57°81 Galtymore ........ * * * * * * * * * * * * * * s • e e s e s e e s e e s e s a e s a e 52 2 I 57° 4. I 8 Io 38: 93 * , º, Garforth Cliff........................... tº dº º is . . . . . tº º ſº tº 53 46 55-54 I 22 7' 40 I79 59 46'46 Garreg......... # tº tº ſº tº a s ſº e s º º * * * * * * * * * * * * * * * * * * * g e º s º is a e 53 I7 38' 55 3 17 58' I9 18o o 22 '81 Glashmeal ........ tº ſº º º ſº dº º º ºs e º 'º e º 'º e º ºs º is a s g º ºr s is s tº a tº º is ſº 56 52 22:76 3 2 I 59° 23 I79 59 55 ° 29 Gorth of Scaw .................................... 6o 48 59' 15 o 46 8 '99 179 57 36' 96 Goat Fell.................................... tº gº tº tº º º ſº º 55 37 32 °54 5 II 24 ° 20 18o o 6.72 Goonhilly ........................... tº tº a g º a tº º is is is tº º s º 5o 2 47 ° 42 5 Io 36'76 18o o 34° 24 Gorleston Church Tower ........................ 52 34 43 ‘ I 3 || – I 43 33° 39 179 59 36' 90 Great Sterling ........... & e s e s e e s is s e s is e º a s s a º ºs s = * 57 27 48 ° 94. I 47 I 5" 53 I79 59 II 29 Great Whernside ........... * & tº º e º is ºn tº s º º tº º ſº tº dº e º 'º º 54. 9 39 OA. I 59 48' o4. 179 59 56'85 Gringley .....................--------------- tº tº * * * * * tº ſº 53 24 3o 47 o 53 3' 66 I79 59 57' 52 Gwaunysgaer......... ... º. º. º. º. º. º. ºº e º 'º º 'º º º tº º tº º ſº º ......... 53 19 18°6o 3 23 4o'65 I79 59 40 °2 Hampton Poorhouse .............................. 5I 25 34'86 o 2 I 50-83 ſº Hanger Hill Tower .......... * & º 'º º 'º $ $ tº º tº t t tº e º e º 'º 51 31 23 36 o 17 50 '98 I79 59 48'96 Hanslope Spire .................................... 52 6 46: o3 o 49 33°63 tº º is IIappisburgh Church Tower......... tº º º 'º e º 'º, º is º º ſº. 2 49 30°42 | – I 31 56° 18 180 o zo'70 Hart Fell......... tº e º ſº tº º º ſº, º is ſº tº tº tº º is tº a n e º a º º g º ºs e º e ...... [ 55 24 28’ 67 3 23 58° 7o 18o o 12 57 Hensbarrow ....................................... 5o 23 o' 73 4 49 3 ° 23 18o o 2-83 High Port Cliff .................................... 5o 35 44 ° 95 I II 29° 94. 18o o 49' 38 High Wilhays................. tº º is ºn s : º ſº º ſº º ſº º 'º - tº * G - sº tº it 5o 4 I 6' 52 4 o 34° 41 I79 59 58' 25 Hingham Church Tower ........................ 52 34: 45 ‘ I 5 - O 59 I 54 18o 1 17:21 Holme Moss ...... § tº º ſº tº ſº ſº tº $ ſº º º ſº º º ºs º º º 'º e º ſº tº º ſº e * @ º is 53 32 I9' I4. I 52 54 ° 55 18o o 10-85 Horton's Gazebo.................. tº t tº º 'º º tº a tº e º ſº is is is ſº tº º 50 51 36° 37 1 57 23 '66 tº º ſº Howth Hill......... tº . . . . . . . . . . . tº e º 'º º is º ºs e º 'º º ſº t t e º is tº e º is ſº º 53 22 23 76 6 4 3'54 I79 59 59° I 3 'l Hungry Hill ................................. • . . . . . 5 I 4 I I2 ° 94. 9 47 27' I4. I79 59 56'82 Ingleborough .................. •: - - - - - - - - - - - - - - - - - - - 54 9 58° 73 2 23 45'87 * . . . . | Inkpen Beacon .................. tº ſº tº dº tº ſº tº º tº e º E t e º 'º a º 5 I 2 r 8' 54. I 27 48° 57 I79 59 58' 23 Jura North Pap.............................. º tº º º 55 54 8°43 6 o 8° 53 18o o 2'48 Rarnbonellis ................. ſº e º is sº tº º * † º º ſº tº tº ſº º ſº tº º is 5o Io 56° 56 5 I3 38° 56 I79 59 58-76 ICarn Galver ..... & tº e s m is a º º is is tº tº º º is tº $ ſº tº s h tº ſº dº º is tº tº ſº ſº tº º º 5o 9 54°67 5 36 41 '91 18o o 7-96 Karnminnis...... tº e º 'º e º s tº a º ºs s is tº it is a 4 tº º 'º e º ºs s is a tº ſº tº tº it ºn tº a g 5o II 41 °oo 5 31 56° 38 I79 59 57°84. ICeeper......... tº ſº ºn g c tº e º ºr tº º is tº sº º is tº a tº e º ºs e º sº e º is sº º ºs & Cº º ſº º ſº. 52 45 5’ I 5 8 I5 35' 30 I79 59 55' 89 Rollic Law .................................... tº º ſº it ſº º 56 I4. 53 'oz 2 46 42 °49 I79 59 46 oz Reysoe Spire .................... tº $ tº tº º º is tº ſº ſº tº e º ºs º ºs e º 'º 52 I4 59'81 o 25 36'74 18o o 2 - 20 Ring's Arbour ............ ſº tº ſº tº ſº º º º ſº, º is nº º ſº º is ſº tº º tº e º ſº. 51 28 46-89 o 26 55-27 I79 59 48°69 Kippure .............. tº tº º ſº º ſº º is ºn tº ſº I tº it is tº ſº tº ſº ſº g { } tº C is ſº ſº º ſº ſº. 53 Io 4 I 29 6 19 49°46 I79 59 57°2 I Inock.................................... * ... tº ſº tº º ſº tº ºi e º º 57 35 2' 60 2 46 25° 36 I79 59 5 I '93 Knockalongy ....................................... 54 II 39° o2 8 45 3o 95 I79 59 56' 17 Inockanaffrin............................... tº º ſº º º ſº tº ſº 52 17 20:28 7 34 49'82 I79 59 55 ° 45 Knocklayd ............. tº G & º $ tº º ſº tº dº ſº e º is ſº º is ſº tº º ſº tº tº tº ſº º 55 9 43° 43 6 I4.57°42 I79 59 57' 54. Inockmealdown................... tº º ſº tº dº ſº ſº ſº tº . . . . . 52 I 3 40° 23 7 54 5 I Io tº . . . Inocknadober .................................... 5 I 59 35 “I2 Io Io 24'84 I79 59 59° 35 ICnocknagante............................... * º 'º ſº 5I 53 37°2 I 9 56 3 ‘oo 180 (41' 31 ICnockmaskeagh .......... tº º º ºs º º ſº tº º ſº º 'º e º 'º tº e º is º g º e º º 52 6 25' 57 8 25 55' 25 I79 59 53° 54. Lawshall Church Tower ........ tº ſº ºn tº ſº º ſº, º g º º ſº tº E tº º 52 9 I7 - 94 – o 43 3 I 25 18o o 29.96 Laxfield Church Tower ........................ 52 18 6' 65 — I 22 3'91 I79 59 50 °23 | Layton Hill.......................................... 57 16 49'o6 2 . I 29' os I79 59 47° OA. Leith Hill Tower ................................. 5I Io 34°42 o 22 Io 90 I79 59 54" or Lincoln Minster.................................... 53 I4. 3' oo o 32 4° 46 179 59 35' 60 Little Sterling .................................... 57 27 32 °o2 I 48 36' 24 179 59 48°64 Littletown Down ......... * * * * * * * * * * * * * * * * c e s e e s a e 5o 35 59 °2 I I I2 4° 4 I 179 59 13 '9/ Planelian................... tº º º º e º 'º e º 'º e º is e • “ . . . . . . . . . 53 I 5 20°81 3 43 46' 13 179 59 45'91 Longmount Pole........ sº e º e s tº e º 'º s is a tº a tº º e º º ºs e is a e º º z º. 52 32 4 o' 39 2 5 I 43°77 179 59 52°45 Lough Foyle Base, North End.................. 55 9 5'96 6 56 5o 58 179 59 58° 73 Lough Foyle Base, South End.................. 55 2 33 '86 7 o 22 : o3 179 59 59°45 726 PRINCIPAL TRLANGULATION. Names of Stations. Latitude. Longitude W. North Meridian. Lumsden............................................. 55 54. 26' 64 # 12 16-22 I79 59 53° 09 Lundy Island ....................................... 51 Io 1 '77 4 4o 16” Io I79 59 43 “ I” Lynn Old Tower .......................... tº º º ºs e º ſº 52 45 4' 48 o 24, 2 °29 I79 59 42 " I 5 Lyons Hill .......................................... 53 I7 25' 30 6 32 2 42 I79 59 54°75 | Maker Church Tower ........................... 5o 20 49' 9o 4 I I I 19 18o o 4' 50 Malvern ............................................. 52 6 16-95 2 20 I4 ° 25 18o o 6'72 Mamºuil ................. tº dº ſº º O & C º º tº e s tº w is a ſº e º 'º is is is tº t t e º 57 16 47' 65 5 7 8'98 18o o 13' 67 Mendip ............................................. 51 13 6' 39 2 32 35 °52 I79 59 45 ‘I 5 Merrick ............................................. 55 8 2 I os 4. 27 59° 9 I I79 59 54 79 Morrington Church .............................. 54 40 38°75 I 35 35 ° 23 I79 31 22 °48 Mickfield Church Tower ........................ 52 I2 43 '97 | – I 7 29' 37 I79 59 47 'o6 Milk Hill .......................................... 5I 22 34° 33 I 5o 57'75 I79 59 54'88 Misterton Carr Base, North End............... 53 31 45' 60 o 54. I4'64 I8o I 4° 31 Misterton Carr Base, South End............... 53 27 29 “O2 o 55 22 I/ 18o I 57' 69 Moclfre Issa ....................................... 53 I4 48 ° 91 3 34. I7' Io 179 59 44'26 Monach ............................................. 58 21 22 or 6 18 29 91 179 59 52 '81 Mordington......................................... . 55 48 27 97 2 4 9' 61 180 o 6'87 Mormonth .......................................... 57 36 8'99 2 I 5 I '91 I79 59 40°43 Mount Battock .................................... 56 56 56'84 2 44, 24.” II I79 59 44 ° 28 Mount Léinster .................................... 52 37 5 ° 22 6 46 43° 36 * † tº Mount Sandy....................................... 55 Io 54°8o 6 55 51 67 I79 59 57° 93 Mowcopt............................................. 53 6 53° 13 2 I2 4o '72 179 59 57°62 Naseby Church Tower ......... ſº º ſº tº C tº º is º º ſº ºn e º e º 'º º 52 23 48°42 o 59 I4. 92 180 o I 69 Naughton Church Tower ........................ 52 6 5'68 || – o 57 Io'78 I8o o 2 '88 Nephin .............................. ............... 54 o 47° 73 9 22 o’ I 5 18o o I 6o Nive Hill .......................................... 6o 47 33° 36 o 46 56-66 I79 59 47 ° oz Nodes Beacon............................----------- 5o 4o o 'oZ I 32 24 °og 18o o o' 75 North Rona ............... -----------------------. 59 7 I5'8o 5 48 47 Io North Ronaldshay Lighthouso.................. 59 23 3’ I 5 2 22 9°os : Norwich Spiro ............................. tº tº ſº tº e º 'º 52 37 54°44 || – I 18 Io' 37 18o 2 I ‘O4. Norwood...... • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 24 50' 63 – o 5o 6’ II I79 59 47° II Old Lodge .......................................... 51 8 3 '71 I 38 45'87 18o o 8-79 Old Sarum Castle ................................. 51 5 35°31 I 48 I 3 '49 179 59 28'90 . Old Sarum Gun.................................... 5I 5 43 70 I 47 48° 36 18o o 11:38 Orme's Head ....................................... 53 19 58-76 3 51 6'89 Ł tº ſº, Orford Castle ....................................... 52 5 38' 54 — I 3 I 56'42 18o I 59'82 Otley Church Tower.............................. 52 8 54'90 | – I 13 17°46 179 59 48°74 Over Hill .......................................... 57 I5 18'91 2 6 20- 15 I79 59 49' 90 Paddlesworth ....................................... 51 6 48' 95 — I 8 23:38 I79 59 25 ° 99 Paracombo .......................................... 51 Io 32° 17 3 5 I 33 ° 99 179 59 50°76 Pendle Hill .......................................... 53 52 6'43 2 17 48°68 18o o I2 53 Peninnis Windmill................................. 49 54. 28'96 6 18 12-84 179 59 58' I4 Pertinny............................................. 5o 6 24° 13 5 38 37' 74 179 59 57 oš Peterhead Old Windmill ........................ 57 3o 43°78 I 47 3I '94. 179 59 2 '66 Pillesdon ............................................. 5o 48 24°37 2 49 55 ° 49 18o o 27° 45 Plynlimmon ....................................... 52 28 o'74 3 46 53°os tº º º Precelly ............................................. 51 56 45'99 4. 46 22 56 I79 59 42 '69 Reform Monument................................. 57 29 30 '87 I 47 49 'oZ is tº ſº. Rhuddlan Base, East End........................ 53 I7 II '83 3 28 13.65 18o 37 48° 5o Rhuddlan Base, West End ..................... 53 I7 4 I ‘OS 3 34. 54 II 18o 43 12 7o Ronas ---------....................................... 6o 32 I 30 1 26 36.86 179 59 55' 61 Ru Rea -::::......................................... | 57 5o 8 o'7 5 45 53° 21 18o o II 2 I Ryder's Hill “..................................... 5o 3o 21 ° 27 3 53 23 ‘ I 7 18o o 13 '8o St. Agnos Beacon ................................. 5o 18 24-28 5 I2 56°4I I79 59 57°89 St. Agnes Lighthouse * † tº ſº tº tº º º is º G is # * G - ſº º is ſº tº # 49 53 32 ° 93 6 20 38° 14 tº . . . St. Ann's Hill......................... ...-----... ... 5I 23 5o '98 o 31 22 64 I79 43 27 ° 91 St. Martin's Head ................................. 49 57 59° 53 6 I5 53 Io I79 59 56° 04 St. Paul's Cathedral .............................. 5I 3o 49° 14' o 5 48° 32 179 59 5 I I4. *- *- * i LATITUDES AND LONGITUDEs. 727 Names of Stations. Latitude. Longitude W. North Meridian. St. Peter's Church Tower ..................... 51°21 3455 tºº 1°2; I2 * 22 175 59 49' 6o Sºwel “....................................... 54 49 Io'82 7 2 I5'83 18o o 1 : 58 S**word............................................. 6o 49 39°31 o 5o zoº 3o I79 59 57° 30 Sºº's Law .......................................... 55 50 48'94 2 4o 6'94 | 179 59 59' 35 Sº Fell ............................................. 54 27 I4'89 3 I2 35 ° 34. 18o o 6' 14 *in “........................................... 58 13 1.3' os 3 35 22 ° 53 I79 59 55'88 Seournalapich....................................... 57 22 9'2 I 5 3 29° 32 18o o 10:36 Severndroog ....................................... 5I 27 59' 49 || – o 3' 4 I "59 18o o 7:32 Shanklin Down .................................... 5o 37 5' 59 I I2. 2 I 34. 18o o 29° 73 Slieve Donard....................................... 54. Io 48° 56 5 55 9'51 || 179 59 53' 67 Slieve League....................................... 54 39 4' 50 8 42. I9' 12 18o o o' 14. Slieve More ....................................... 54 o 35 °oo | Io 3 26° 32 I 79 59 50 ° 33 Slieve Snaght....................................... 55 II 46' 98 7 19 57 oz I79 59 58' 20 Snowdon ............................................. 53 4, 6' 2 I 4 4. 28' 37 18o o 2 '91 Southampton ....................................... 5o 54 48' 88 I 24 6'49 I79 59 II '8o South Borule ....................................... 54 8 57 '87 4 4o 3° 32 18o o 19°23 South Lopham Church Tower.................. 52 23 44' 30 – o 59 52 '46 I79 59 59° 90 South Ronaldshay ................................. 58 46 54°84 2 56 30 II I79 59 55 ° 23 Southwold Church Tower........................ 52 I9 41 ° of — I 40 48' oo I79 59 55 °oo Start Lighthouse ................................. 59 16 39' 6o 2 22 28' 86 tº . . Stoko Church Tower.............................. 51 59 2 I 30 — o 53 33° 35 18o o 18- 15 Stoko Hill .......................................... 51 16 18-73 2 3 4o '71 I79 59 57° 22 Storr “.............................................. 57 3o 25° 38 6 Io 52 48 18o o 12'35 Stronsay ............................................. 59 5 37' 60 2 32 34’ 16 || 179 59 55' 51 Swaffham Church Spire ........................ 52 38 52 '84 || – o 4L 29' of 18o o 19'42 SWyre Barrow .................................... 5o 36 20-63 2 5 34° 35 18o o or of Tara .............................. tº $ tº $ tº º ſº º 'º e º ſº º 'º it is ſº * 52 41 56°41 6 12 58' or I79 59 53'48 Tarbathy............................................. 57 I2 42 og 2 4 6'34 I79 59 49'90 Tºur ................................................ 52 I4 17’ 69 9 7 27-61 I79 59 53 '72 Tawnaghmore .................................... 54 I 7 39 ° 93 9 35 47° I2 18o o 4'40 Telegraph Tower ................................. 49 55 43°62 6 18 7" 53 179 59 58°36 Tharfield............................................. 52 I 2 °43 o I 59' 66 I79 59 5 I ‘o: Thaxted Church Spire........................... 51 57 14'86 || – o 20 36°oa. I79 59 55 ° 71 Tilton ................................................ 52 38 43' 19 o 5 I 56' og 179 59 46.67 Tofts Church Tower.............................. 52 30 3 '96 || – I 34 29° 24 179 59 38' 67 . Trevose Head....................................... 5o 32 54." 39 5 I 52 '73 180 o 7° 32 Trostan ...... $ tº $ tº $ tº º ſº º t tº º º is º º it tº g º 'º º is is tº ſº tº º is º º ſº g º s a g º º 55 2 44 ° 4 I 6 9 IS ‘O4. I79 59 58°33 Upcot Down ....................................... 51 28 44° 19 I 48 20° 93 18o o I2 - 68 Vicars Carn ....................................... 54. I7 53 ‘7 I 6 35 42 38 I79 59 55 °42 Walpole, St. Peter's Church Tower............ 52 43 42 74 – o 13 27°69 I79 59 49' 53 Walton Church Tower ........................... 5 I 5 I 5 I 37 — I I7 22 '79 I79 59 58' or Wart Hill Hoy .................................... 58 54 I '98 3 20 18-73 I79 59 54.’ I 5 Water Crag ....................................... 54 26 12' 47 2 6 32 '98 || 179 59 57'85 Week Down .................. tº tº C tº º ſº º 'º tº º ſº e º is a tº º º ºs º º 5o 35 52 'o6 I 14, 1 '66 18o I 45' 40 Westbury Down................... * ... º. is tº º ſº tº dº ſº tº e º tº º tº 51 I5 36' 5o 2 8 3o '74. I79 59 38' 34 Whitehorse Hill.................................... 5 I 34 31 ° 22 I 33 56'40 I79 59 45 ° 44. Whittio ............................................. 53 39 59' 66 2 15 52' 68 .18o o 1.27 Wingreen .......................................... 5o 59 6' 36 2 6 23' 89 I79 59 54." I3 Wisp ..... “.......--------------.................. 55 I7 3° 5o 2 57 56-78 I79 59 56' 24 Wolf Rock .......................................... 49 56 43°38 5 48 27° 4o * † : Wordeslow .......................................... 54 50 56°og I 25 25 ° 2 I ..I 79 59 54°2O Wrotham ...........................---------...... 51 19 o' 18 – o 17 II o4 18o o 5’ 65 Wroxall ............................................. 5o 36 7' 53 I 12 23.78 18o o 39:92 *"................................................... 6o 32 46'71 1 5 12'o4 . . .179 59 55’ 67 York Minster....................................... 53 57 43°58 1 4 49' 32 . . .18o o 2 " II 728 PRINCIPAL TRIANGULATION. Positions of Observatories. Observatory. Latitude. Longitude W. Q Af f/ ſ ff Armagh Observatory............ tº ſº tº ſº tº º & © tº t e º 'º g g g is tº e º s º º º 54 2 I 1 o' 56 é 38 53 '71 Brisbane 33 tº º 0 & 0 e º e º º ſº º is tº e º e º e º 'º tº º Q tº º tº C tº º tº e º & © tº 55 49 I '82 4, 5 I 33’ I 5 Sºmbridge , .................................... 52 I2 5I '90 | – o 5 48° 95 Edinburgh , ..... tº tº e º 'º º tº º G & º º tº tº tº º tº º ſº e º 'º Q tº º º C & G tº e 55 57 17' 57 3 Io 54." Io Durham 3? tº $ tº G & © tº º 'º º º ſº tº tº tº ſº tº ſº tº º ſº tº º tº g g g g º ºs e º 0 º º 54 46 5-27 I 35 3 ‘7 I Dublin 33 e < * * * * * * * * * * * * * * * * * * * º, tº e º ºs e º 'º ºf p * tº º tº º 53 23 I4 ° 2 I 6 20 13 o4. Liverpool ?? - e s se e s • * * * * * * * * * * tº tº e º e t t e º e º is ſº tº tº º º º 53 24 47'o6 3 o 3-88 Markree 33 e º e º sº e < e < e < e < e < e < e < * * * * * * * se e s • * * * * 54. Io 30°5 I 8 27 21 - 30 Oxford 33 e < * * * * * * * tº º C tº C C C C tº e p is e e º e e s e º se e s • * * 51 45 38° 56 I 15 43' 69 If we suppose a spheroid whose semiaxes area = 20926249 and b = 20856337 feet, so placed with its minor axis parallel to that of the earth's revolution, that there shall be at Greenwich an apparent deflection of 1".40 to the north, and no deflection in the direction perpendicular to the meridian ; and if we suppose all the points of the triangulation to be projected upon this regular surface, the latitudes and longitudes of these projected points, together with the directions of the meridians, will be as given in the preceding table. The surface just named, as also its position, were obtained from the approximate solution of the equations at pages 693, 694; if the final values of § 7) u and v at page 712 had been used, we should have obtained quantities differing slightly, but immaterially, from those calculated with the first approximation to the nearest spheroid. The comparison of the different observed azimuths with the transferred azimuth of the § III. Comparison of observed Azimuths. meridian mark at Greenwich, is shown in the following table :- . Abstract Reading Observed Azimuth 180° – Stations. - of of Diff. N. Merid. Iºrror. (Err.)” IReferring Object. IReferring Object. O º Af O f fi f f il ſº J/ Arbury IIill . . . 185 7 I 3 '94 185 7 50-69 — 36.75 + 38.78 + 2 : o3 4." I2 IBalsham . . . . I5o 59 I4 ° 94. I5o 59 12 77 | + 2 - 17 | + 6' 51 | + 8.68 75°34 IBardon IIill 2 I 3 4.7 I2 °42 213 47 Io' I 3 | + 2 - 29 – 5' 62 – 3:33 II og IBarrow Hill 352 32 29'98 352 32 27'79 | + 2 - 19 || – Io' 39 — 8' 20 67 24 IBeacon Hill º 212 52 57* I2 212 52 55°oS + 2 'od | – 3-48 || – I'44 2 o? Ben More, South Uist 305 4: I 44 ° 45 395 41 41 ° 79 | + 2 75 | – 4'32 | – I ‘57 2 °46 Den Macdui 161 48 21 '98 161 48 29'96 – 7'98 || + 16-16 | + 2 - 18 4 * 75 IBen Nevis . 81 52 46' of 81 52 22:51 + 23.56 — 12 '93 || + Io'63 || 113: oo Blackdown . . . 316 31 58'96 316 32 1 '55 – 2:59 || – 5' 11 || – 7.76 59 °29 Brandon (Suffolk). 126 I5 30 *oq. 126 15 II 35 | + 18-69 || – 16'59 || + 2 to 4. "4 I IBunwell Tower . 183 23 3o'oo 183 20 28.23 | + 181: 77 | – 172 '79 || + 8.9 8o. 64 Durnswark . . 2O4. 52 I2 "O.A. 2O4 52 7'20 | + 4'84 - I o4 || + 3 '8 I4. "44 Butser . . . Io8 II I4'96 IoS Io 54'92 | + 2.0°oq | – 24” 75 | – 4'7 22 I 8 COMPARISON OF OBSERVED AZIMUTHS. g 729 i#. : i Abstract Reading Observed Azimuth Stations. of O Diff. 180°- Error. (Err.)” Referring Object. Referring Object. | N. Merid. O * // C) & fif Af f/ Af Aſ Clifton Beacon . . . . 2 I 34 35 °89 21 34 22° 58 + 13:31 || – 14-95 || – I 64 2.69 Cheviot . . . . . . . . . 246 9 15 'o'; 246 9 30-63 | – 15'58 + Io' 36 – 5' 22 27' 25 Corryhabbie . . . . . 204 46 ro'96 204 4o 1 '59 + 9°37 + 2 - 24 | + II ‘61 | 134°79 Cowhy the . . . . . 66 27 31: 99 66 27 36'91 — 4'92 | + 5°45 | + o' 53 o “28 Cradle . . . . . . 13o 5o 37.98 13o 5o 37' 59 | + o' 39 – 4 or - 3-62 13 Io Ditchling . . . . . . 274 23 17-16 || 274 23 10-65 | + 7. 11 | – 6:02 | + i. og I 19 Docking . . . . . 4o 47 20° Io 4o 47 21 26 — I 16 + 7'37 + 6' 21 38: 56 Dunkery . . . . . 84. 41 9' 98 84 41 14-46 – 4:48 + o' 58 – 3 '90 I5 °2 I Dunnose . . . . . 339 i2 1999 339 12 12 59 || + 7-40 || – Io'67 || - 3 °27 Io 69 Dunrich . . . . . . . . 242 28 42 - 12 242 28 56.85 | – 14-73 + 4'88 || – 9 '85 97' o2 Easington . . . . . I28 38 55 °o: 128 38 62:49 — 5:46 — or 63 | – 6 og 37 °og Epping Poorhouse . . . 342 3o 4-97 || 342 29 56°23 + 8°74 - 3’56 || -- 5' 18 26-83 Fairlight . . . . . . . 276 5 8: 93 276 5 II • 57 – 2 '64 | + 6'32 + 3 '68 13 54 Frittenfield . . . . . 231 8 Io. II 231 8 35° 44 - 25°33 || + 27' 53 -H 2 - 2 o 4. 84. Gad's Hill . . . . . . 207 II 50-67 307 II 48'95 + 1 . I2 | + 2 - 19 || -- 3:31 Io'96 Goonhilly . . . . . 342 58 II '99 || 342 57 35-14 + 36'85 — 34" 24 | + 2*61 6-8 I | Goat Fell . . . . . . 233 2 2 - 31 233 I 57'98 || + 4* 33 – 6'72 - 2 - 39 5: 71 Happisburgh . . . . . I45 27 59' 61 I45 27 39:70 + 19 91 — 20 7o – o '79 o “62 IIart Fell . . . . . 359 20 2.9-8.9 35o 20 11 11 || + 18.78 – 12:57 | + 6' 21 38: 56 Hensbarrow . . . . 78 25 55' or 78 25 49'82 + 5° 19 — 2.83 + 2 - 36 5 * 57 Inkpen . . . . . . 319 9 39'94 || 319 9 45-78 – 5'84 || + 1.77 — 4'67 16:56 Laxfield Tower . . . . I45 54 30' of I45 54 34’ og – 4'o6 + 9.77 | + 5: 71 32' 60 Leith Hill Tower . . . . 221 32 45° off 221 32 53' 17 | – 8 I2 | + 5°99 || – 2 13 4 * 54 Lumsden . . . . . . I44 53 47 '86 144 53 59'95 || – 12 ‘og + 6'91 || – 5' 18 26-83 Lundy Island . . . . . 194 25 5o'99 194 26 4.99 || – 14' oo + 16-83 | + 2 -83 8 or Mendip . º II4 54. Io 'o6 114 54 24-91 || – 14'85 | + I4'85 O * OO O "OO Merrick * * * * 71 27 o' 36 71 27 6-48 || – 6' 12 | + 5° 21 - o'91 o'83 Mordington . . . . . 148 27 44-92 148 27 40-51 | + 4'41 | – 6'87 | - 2'46 6 off Mormonth . . . . . 84. 55 17 oz 84 55 47' 19 || – 30° 17 | + 19.57 –Io' 60 | 112'36 Mount Battock . . . . 238 28 21 : 50 238 28 44'26 – 22 '76 | + 15.72 | – 7 of 49' 56 Mowcopt . . . . . . 280 37 6.87 28o 37 2 55 | + 4'32 | + 2 - 38 | + 6'70 44'89 Orford Castle . . . . 68 51 29-77 68 49 23.65 +126' 12 | – 119-82 | + 6. 30 39' 69 | Paracombe . . . . . 87 45 7'o6 87 45 I 1 - 24 — 4° 18 + 9 24 + 5 'o6 25' 60 Pertinny . . . . . . 31 2 I 4o oz 31 21 43.70 || – 3 '68 + 2 '92 || - or 76 o' 58 Precelly . . . . . . . 2 II 58 3o’ og 211 58 46.38 || – 16:29 + 17-31 || + I o2 I o4. Ryder's Hill . . . . 31o o 44-97 31o o 36' 12 || + 8'85 – 13 '80 – 4: 95 24' 50 Sayrs Law. . . . . . . I 13 59 zo'oo 113 50 21.61 | – I 61 + o' 65 — o'96 o' 92 Scournalapich . . . . 351 58 39°99 351 58 35' 14 + 4*85 | – Io:36: - 5' 51 30°36 Slieve Donard . . . . . . 130 5 13° off 130 5 23: oy | – Io' or | + 6' 33 – 3: 68 I3° 54 South Lopham . . . . 190 II 6'82 190 II 2 '68 + 4* 14 | + o' lo + 4*24 17.98 Stoke Tower . . . . . . 272 34 49' 95 272 34. 28' 67 | + 2 I 28 — 18 15 + 3 13 9'8o | Tharfield . . . . . 111 38 29.96 III 38 39'58 || – 9' 62 + 8'97 — o' 65 o “42 Tofts Tower . . . . . . 273 34 59-98 273 35 14-96 || – 14-98 || + 2 I 33 | + 6' 35 40° 32 Walpole, St. Peter's . . . 194 47 29.96 19447 31 '91 — I '95 + Io'47 | + 8° 52 72°59 Wingreen . . . . . 85 58 34-88 85 58 44'84 || – 9'96 + 5'87 | – 4’ og 16.73 Wordeslow . . . . . 57 51 4° 98 57 51 18' os — 13° of + 5'8o – 7' 27 52 '85 Wrotham . . . . . . 274 56 45' 11 274 56 37' 5o + 7' 61 | – 5’ 65 + I 96 3 ‘84 York Minster . . . . . 266 26 35-03 260 26 26.63 — I 6o – 2 II | – 3 '71 13.76 1619 o9 The sum of the positive errors is + 135.41, and the sum of the negative is — 127. 69, which shows that the observed azimuth of the Chingford mark at Greenwich is very exact. The sum of the squares of the 61 errors is 1619-09, whence the mean square of error is 26:54, and the probable error + 3”.47. In the comparison of azimuths observed at two different Stations we have seven independent sources of error: at the one Station, (1), the error s, of the 4. Z 73o T'RINCIPAL TRIANGULATION. astronomical determination of the angle between the meridian and the terrestrial object observed in connection; (2), the error s, in the bearing of this point relatively to all the Stations around; (3), the error s, due to local attraction; (4), (5), (6), or s,’s,' s,ſ, are the corresponding errors at the other Station; and (7), the error se of transference due to errors in the intermediate triangulation. But as we have not the means of separating these different sources of error, we shall suppose the error of comparison due to : (1), errors of observation; (2) and (3), the local deflections at the two Stations whose azimuthal determinations are to be compared. In comparing the different observed azimuths with that at Greenwich, we may suppose the influence of local attraction at Greenwich upon the azimuth as zero, so that the comparison will be affected by : (1), errors of observation (every kind combined); (2), the effect of local attraction at the Station under consideration. Now it will be seen in the Section on the Tigure of the Earth that the probable value of the disturbance of the plumb-line due to accidental local attraction amounts to + 1".75; and therefore the probable error of an observed azimuth due to local attraction is + 1".75 tan A. Let r be the mean value of tan” x for Great Britain, then 3 oé2 + will be the square of the probable error at any Station. From A, to x, the value of r is, - * * r * I A2 T = tan” X da *2 – X, A1 ...tan x, — tan X, T = - I Aa - A, Taking x, - 50°, 2, - 60°, we have: = 2 - og 6, ... 3 o62 r = 6.418.; hence the probable error of a comparison of observed azimuths, separated from the effect of local attraction, is + W3.47° – 6.418 = + 2"-37 Of this the greater part is doubtless due to the astronomical determinations. . . . . : The probable error of " (page 712) is + o”. 55, consequently the probable error of the absolute azimuth of the whole triangulation is + o”.69. . . . . - § IV. Distances of Parallels. The logarithmic values of the distânces of parallels will be found from page 677 to page 682. They are, however, necessarily dependent, within small limits, upon the assumed figure of the earth, and must receive corrections corresponding to the quantities 3 m w v, page 712. Let s be the distance of any Station from Greenwich, o, its azimuth, and 0 the angle subtended by s at the point where the normal at Greenwich intersects the axis of revolution: let x be the latitude of Greenwich, and 90° — p the third side of a spherical triangle of which 90 – A, 0, and a are two sides and the included angle; then by spherical trigonometry— sin p = sin A cos 3 + cos x sin 6 cos & cos w cos ? = COS X cos ( — sin a sin 3 cos & cos &’ cos ? = sin a sin 6 — cos x cos 0 cos & LISTANCES OF PARALLELS. 73 I ... Differentiate the first of these equations, and we have— cos ? dº – cos x cos 3 da – sin a sin 6 cos a da - sin a sin 3 d5 +-cos x cos 3 cos & dº — cos x sin 6 sin & do. ‘. . ~ = cos w cos p da — cos &’ cos. p d5 – cos A sin à sin a da by reason of the second and third equations; ...— . . . dº. = cos a da - cos 2' dº — sin–0 sin a' d', which might have been deduced directly from the expression for dc, page 690. If S be the distance of parallels, we have by page 248— * * * * * * * * * s = sº-Hº as – sºde - tº . ( = 8) & 6* = — ; ((; — cos w) dx + (t + A. -H COS 2) d} + sin 6 sin &' da) f i Also— . . - - * * * * 8 0 T sin # (2' + &) . . . cos 2 + +* = cot A (2 + 2) in a * = # a sin # (p + x) sin a' ... nearly. which may be taken as the coefficient of d. Again, .2 s being put for the square of the excentricity— - - . . . . * ** 3 = ; * * * VI – 2 s sin” A Taking the logarithmic differential— dº sin” x , da + = - I-2Tsimſ, as - 7 | the values of § 7) u v are— • # = dx # = + 1,864 tan A. q = dx # = — o'546 arc Ioo”. w = º u = + o:3245 il - º arc Ioo”. v = 2 d: v = + o-'9276 Remembering that azimuths are to be counted from the north round by east, south, and west, and longitudes measured westwards, we have for dS, by putting s = aſ in the common factor, and substituting for 6 sin o' sin (p + x) its approximate value , a sin 2 ×, dS = a sin " (— (1 — cos w) # + (1 — cos oj (u + gu) 50 sin 2 x + n sin a sin w) : *: where, as in page 690, g = .3073. Substituting the numerical values of é º w v, there results finally— - * * - - -- * † - - - - -- . . .d.S = 2824. (I - cos w) — 43.3 sin w 4 Z 2 732 PRINCIPAL TRLANGULATION. with the values corrected to the true spheroidal figure. Distances of Parallels. The following table contains the distances of the parallels as derived from pages 677–682, Stations. On Approximate Spheroid. Corrections. | Final Results. SAINT AgNEs . O - O + o 'o - O - O | GooMIIILLY 562 Io. 9 – 4: 9 56206. o JHENspannoſy . I792 Io. 2 – 6. I 1792O4. I HIGII Pont CLIFF 256691.2 — 12.8 256678.4 WEEK Don'N . 2574II - 9 — I2.7 257399. 2 Boniface DoIPN . º 2.59373 - 5 — 12.7 259360.8 DUNNose . . . . .264859 .7 — I2.8 . 264846.9 BLAck Dojº's . 289851.4 — II .6 289839.8 SouTHAMPTON . 372666 .8 — 12.6 372654. 2. Greenivicii 578576.6 — I2 - 4 578564. 2 FIUNGRY HILL 654938. 3 + 2 I o 654959.3 FEAGHMAAN 74Iooo. 7 + 25.3 74Io26. O PRECELLY . 749564. I — - 6 • 3 749557. 8 CAMBridge º 8475.18 '4 – I2 - 5 847505 9 Annuity HiLL , * 85.1216.0 — 12.8 85.1203.2 ForTII. 884631 -o + 1 .o 884632.0 DELAMERE. . 12 15262.6 — II 4 I2 I525I-2 CLIFToM BEAcon . I3OI44I 2 — 12.7 I3OI428.5 SouTII BERULE . I554O46.6 – 6.6 || I554O4o-o TAWNAGILyſore I 606994 .7 + I9. 6 1607014 • 3 BURLEIGII Moon . 1708o38 • I | — 12.8 I708025.3 DURIIAM . . . . . 178ooI5. o — I2.6 I78o002.4 Lough Foyle BASE . 188o3O4.8 + 3.3 188o308. I CALTON HILL . 22O3487.7 — Io. 5 22O3477-2 BEN LoMoMD . 2299448.6 – 6.7 229944I 9 | KELLIE LAir . 232O596.8 - I I • 2 232O585.6 BEN HEYNISII 2396286.2 + 2.8 2396289. o GREAT STIRLING . 2764699 • I – I2 - 4 2764686.7 CoIPIIITHE • , 2844909. O – I I 4 2844897.6 MoNACII . 3090834-7 || – or 2 3090834-5 BEN HuTIG . 3162O45.8 — 7. I 3.162038.7 NonTII RoNA . 337O394 - 2 – 2 - 4. 3370391 .. 8 BALT4 . 3966289.3 — 12.8 3966276.5 GERTII of ScAIP . 3990I I6. 3 — 12.8 3990IO3 - 5 SAXAPORD . 3994 IQ5' 5 — I2.8 3994.1827. r |: SECTION XIV. FIGURE OF THE EARTH. IT is proved in the mechanical theory of the Figure of the Earth that, neglecting small quantities of the second order, the generating meridian is an ellipse. When the investigation is pushed to include quantities of the order of the square of the ellipticity,” a second parameter or constant is introduced, the value of which can only be obtained from observation. The determination of the Figure of the Earth from geodetical operations is virtually the deter- mination of that curve, generally assumed elliptic, which will bring the different measured arcs into the best accordance with their observed terminal latitudes: this curve may be said to represent the real Figure of the Earth with the greatest measure of probability. § I. Previous Determinations. The attention of many eminent writers has been turned to this problem, and it may be instructive to compare some of their results. The results arrived at by Laplace in the Mécanique Céleste were very unsatisfactory, owing entirely to the very imperfect state of geodetical measures at that time. In Bowditch's notest to that work, Vol. II., page 453, we find the following expression for the length of an arc of the meridian between latitudes o and J, in feet— ar s = IoI-259564 º’ – 5ozog.2 sin 2 J – 6o-o sin 44 where y' is the latitude expressed in seconds. This result is deduced from the arcs in Peru, India, France, England, and Sweden. The curve is not restricted to the elliptic form, but differs very slightly from it; the axes are— a = 20919768 2 – 3riº b = 20.852822 a T 3.12.2 The curve is depressed below an ellipse of the same axes, but the maximum depression is only 58.8 feet, which takes place at the latitude of 45°. * ºm * Phil. Trans. 1826, page 548; and Phil. Trans. 1841, page 75. f MâcANIQUE CELESTE, by the MARQUIS DE LAPLACE, translated, with a Commentary, by NATHANIEL Bowditch, LL.D.—Boston, 1832. * 734 PRINCIPAL TRLANGULATION. The most celebrated determinations of the Tigure of the Earth are those by Professors Airy and Bessel. The former is given in the Encyclopædia Metropolitana (Art. Figure of the Earth), being based upon the discussion of fourteen meridian arcs and four arcs of parallel: the resulting quantities are— a = 20923713 * 298.33 b = 20.8538 Io a T 299-33 Bessel's determination will be found in Nos. 333 and 438 of the Astronomische Nachrichten. The results contained in No. 333 were subsequently found to be vitiated by an error in the geodetic distance of the parallels of Mountjoy and Mola. The corrected values were found to be a = 3272077. I4 toises; b = 3261139-33 toises; or, - : a = 209236Oo 9 – 298.15 -- b = 20853656 a T. 299-15 ... The probable error of the determination of the mean degree of the meridian is + 1.916 toises, or + 12.25 feet; and the probable error of the quantity 299. I5 is it 3. I5. . . . The agreement of these two sets of results, with one another is very remarkable, but must perhaps be considered rather in the light of a singular coincidence than as a proof of their accuracy. * In Colonel Everest's “Account of the Measurement of Two Sections of the Meridional Arc of India between the Parallels of 18° 3' and 29° 30',” he has, by the consideration of twelve meridian arcs, deduced the following values— *... . . . . . . . . . . a = 20920902 b 3Io-o4 b = 20853642 a T 3.11.04 in which the value of a is considerably less than in the two preceding determinations. In the Philosophical Transactions for 1856 there is a paper containing a new determination of the Figure of the Earth founded upon the same arcs as used by Bessel, but including the extensions of the Indian and English arcs. The sum of all the total arcs amounts to 63° 21', the whole distance, measured geodetically, being about twenty-three millions of feet, or a tenth part greater than the radius of the earth: the number of Astronomical Latitudes employed is 38. The results of this calculation are— * , a = 20924933 & 297-07 b = 20.854731 a 298.o? The probable errors assigned to a and b are + 539 and + 408 feet respectively, and that of the denominator of the fraction representing the compression (298.07) is + 1.82. Of the accuracy of these estimates there may be a question; they were obtained as follows: Using the notation of that paper, the quantities p q are such as render a minimum the quantity (m, + v)” + (m, H- a, p + b, q + ar)” + (m, +- a, p + b, q + æ)* + . . . . -- (m.' + æ')" + (m,' + a, p + b,' q + æ") + (m,' + a, p + b,' q + æ") + . . . ., where a w'a" . . . . are the corrections to the initial points of the several arcs. Suppose p finally expressed thus, X. m., + x, m, + . . . . -- ?... m.' -- ?,’ m,' + . . . . , then the weight of p was taken as equal to * FIGURE OF THE EARTII. 735 the reciprocal of x. + x." -- . . . . -- A,” + x,” + . . . . ; for the quantities m, m. m." . . . . are zero. By including the sum of the squares of x, x' . . . . the probable errors of a and b would be # 626 and # 503, and that of the denominator of the fraction representing the compression would be + 2 - 37. - 4. - By omitting the point Evaua in the French arc from the data, on account of the extraordinary deflection at that point, we should have obtained— * a = 20.925I74 2 296.72 b = 20.854914. a 297.72 and for the mean value of the corrections to the latitudes + 2". OS. If with the data employed in the paper just noticed, omitting Evaux in the French arc, we determine the meridian curve without restricting it to the elliptic form, we get the followingº expression for the length of an arc of the meridian from o to 9, * * * - - s = IoI-285925 º' – 5416o sin 2 || -- 765 sin 4 J, and the values of the axes— 0. b 20927623 b 287.8o 208554Io a T 288.8o = This curve is more protuberant in middle latitudes than the ellipse of the same axes: the maximum elevation above the elliptic curve, which takes place at the latitude of 45°, amounts to 377 feet. The mean degree of the meridian is 364,629 feet. The mean value of the corrections to the latitudes necessary to bring them into accordance with this curve is + 1". 97. Although this curve does not differ in form but by a very minute quantity from an ellipse," yet the comparison of the axes with those of the ellipse best representing the same observations, shows a difference of about 2450 feet in the equatorial radius. Such a difference is very remarkable when we remember that the sum of the measured arcs employed amounts to more. than the sixth part of the circumference of the earth. . . . . . . . - For the surface of Great Britain we have found a = 20927605, and the denominator of the fraction representing the compression c = 280.4 + 8.3. Comparing these with the two last-mentioned determinations of the Figure of the Earth, we infer that the surface of Great Britain does not present any anomaly with respect to the general figure, as from its insular position might perhaps have been expected. . . . . . . . . Since the publication.of the last-mentioned determination of the Figure of the Earth, the data of the problem have received a most important increase by the completion of the Russian: Arc of Meridian, which extends from Ismail, in latitude 45° 20', to Fuglenaes in the Island of Qual-oe, in latitude 70° 40';--an arc of 25°20'. - -* 736 PRINCIPAL TRIANGULATION. § II. Method of Calculation. Let g be the radius of curvature of the meridian at the point of which the latitude is x, and put g = 4 + 2 B cos 2 x + 2 C cos 4 x (1) The Figure of the Earth will be known by the determination of the quantities A, B, C. The distance s, measured along the meridian, of two points whose latitudes are 2. — ; © and x + y p, is § s = A 4 + 2 B sin q cos 2 x + C sin 2 + cos 4A Suppose now ar, ar, are the requisite corrections to the two observed terminal latitudes, and 3y the correction to the length as actually measured, then— - s + y = A (4 + c, - a.) + 2 B sin (4 + æ, - a,) cos 2 x + C sin 2 (4 + æ, - a.) cos 4 × where s, x – } {p, x + 3 p, are the actual results of measurement and observation. The effects of ar, and ar, upon the mean latitude of the arc may be safely neglected; we may also neglect a, and v, in the term in C, and thus by transformation, neglecting the squares and products of the very small quantities ar, we have— o = A + — s — y + (A + 2 B cos 2 a cos ?) (a, - c.) + 2 B sin & cos 2 x + C sin 2 + cos 4x or, putting A + 2 B cos 2 a cos p = A p , A (*, - a.) – P. y = (s – A 4) p. – 2 B P sin & cos 2 x – C P sin 2 + cos 4x But for the errors ar, w, y, each pair of corresponding quantities s p would give an accurate relation between A, B, C, and three arcs would therefore determine the Figure of the Earth. But the relation is affected by various sources of error: the latitudes observed are affected by errors of observation and accidental local attraction, and the measured length is affected by errors in the geodetical operations and the error of the assumed relation of the measuring unit of length to the standard or reference unit. Suppose that the probable amount of local attraction is + 1".75, which is not far from the truth, and that the probable error of the astronomical determination of latitude is + o”. 25; then the probable error of an observed amplitude is + V2 (I-75 -Fo:25) = + 2". 50; this quantity multiplied by A, or the radius of the earth, is equivalent to about + 253 feet. The probable error of the actual length of the arc depends entirely upon the accuracy of the different operations, and must be much larger in the earlier arcs than in the modern. The probable error of the Russian arc of 25°20' is less than + 40 feet; the probable error of the partial arc of about 11° from the southern point to Jacobstadt is + 24.9 feet. The probable error of the English arc cannot at most exceed this quantity; but in the southern portion of the great Indian arc, the first Indian arc, and the Peruvian arc, the uncertainty is doubtless much greater. Still, even in these earlier measures, there can be no doubt º- .:--- *, º..!- FIGURE OF THE EARTH. 737 which may be put in the form— that the errors in the equations will be due principally to the latitudes. From this it follows that the correct method of calculation is to make the sum of the squares of the corrections to the observed latitudes a minimum, remembering that the corrections so obtained will be affected with the errors of the different terrestrial measures. Omitting, then, the quantity y, we have— S B º * 22 – ar, - # - e) º – 2 #2 in cos 28 – 2 in a cos 4x Assume three unknown quantities w w 2 such that I * — * Tocco A T 20890ooo 2 B — 1 7) A T 200 ' Ioooo - (2) C 2. A T Ioooo * Put 20890000 sin I", which is the approximate mean second of latitude = a, then, expressing a', a, and p in seconds, we have— I S SQM, sin & cos 2 x , sin 4 cos 2 x sin 2 + cos 4 × + (x, — a.) = + + — q + ſº // - A/ º // ſº O IOOOO . Or 2CO SIIl I IOOOO Slſl I IOOOO S111 I w, - a, = m + au + by + cz (3) where the values of m, a, b, c are as follows:— 777 – (. — q + ###). Or 20o sin I" C. E. S. T Toooo... * b = sin q cos 2 A *- º 77 ſº IOOOO SII]. I C E sin 2 @ cos 4A T Ioooo sin I’ º = I + I cos p coS 2 A M = 2OO If a measured arc have only the latitudes of the two extremities observed, there will result from this arc only one equation between the quantities u v 2 and the two corrections w, and v, ; and in general if there be i observed latitudes, or i – 2 intermediate Stations, there will be i – I equations of the form * = m + æ + au + bu + cz = m' + a + a'u + 'bv.-- c'z a." 5 A 738 . PRINCIPAL TRLANGULATION. If 2 U. be the sum of the squares of the corrections of the observed latitudes in one meridian arc, 2 U, the same quantity with reference to another arc; and so on; w, w, v, being the corrections to thé initial points of the different total arcs, then— 2 # * * * ". is r ** # " * 2 U. = x,” + (m. + æ, + a,w -- b.v + cº) + (m/+ a!, H- a,'u + b,'v + cº) + (m." + ar. -- . . .) + . . . 2 U2 = a,” + (m. ++, + a u + b.v + cº) + (m/ + ar, -- a,'u + b,'v.-- cº)" + (m." + æ, -ī- • ..) + . . . 2. R 2 U. = a,” + (m. + æ, -- a, u + bau + cº) + (m/+ as + ayu + b,'v + cº) + (m." + as + . . J'4. tº º ſº The values of u v 2, w, v, w, . . . . which render the quantity U = U, +- U, + U, + . . . a minimum, are the most probable values of those quantities. They are obtained as follows :— dU d'U, , dū, , dū =4 - Sº f .2 iſ " T.I. + 7. # + . . . = S (am) + S (a") u + 3 (ab) v + S (ac) z + (a|) r, + (a,) ar, + (a) r, + . . . = o # = # ++++ + ... = sºn) + s (a) u + s () + 3 (º) = + (b.) ar, -- (b.) wa '-- ~. (b) as + • * : * = O . • = S (cm) + S (ac) w + S (bc).v + 3 (cº) 2 . . . . . . + (c.) w; + (c.) r, + (c.) a, + . . . = o # =#4 #4 #4 - = (n) + i = + (), (), 4 ()= - 0 dU dU, dU, dU, gº º - - º # =#####4 ... = (m) + i +, + (a) u + (), 4 () = ′ = a and so on, in which for abbreviation— - . - - S (a b) = (a, b,) + (a, b,) + (a, b,) + . . . I'rom the last equations we have— – , = (#2+ $2n + ºr +% I - ºf = @ + (42, 4.9%), 4 (£), 2 22 22 22 2 2 – , = (#) + (g) u +% + º- - ſº 23 *3 *3 *3 : and so on. Substituting these values in the first equations, we have for the determination of w v and 2 the following equations: (4) . . . . . . . . . . * O E > ((am) mº ©go) + > (@) — (? ) 2t + X ((ab) ſº @9) v -i- ((a) * 09). O E s (on) –%) —H· s(a)-99) w + 3 (Qº) – (). ) ty + *@-99). O E x (cm)—º) -- > (a)-99) 2. -- s (Qº) –%9) 1) + > (@) – %)- r | * FIGURE OF THE EARTH. 739 . Probable Errors.-Having thus obtained u v 2, the next step is to determine their probable errors, or that of the quantity au + 8v -- 72. For this purpose suppose p unknown quantities u v z y & . . . to be contained in q (> p) equations— o = n, + a u + b v + c, z + e, y + . . . o = n, + a, u + b, v + c, z + , y + .. iº O = m, + a. * + b, v + c, a -H c., + . . . Then for the determination of u v z y . . . we have— o = (an) + (a’) 20 + (ab) v -- (ac) 2. + tº tº O E (bn) + (ab)u + (5°) ty + (bc) 2 + . . . (a) o = (cm) + (ac) u + (bc) v + (cº) 2. + . . . 3. * and so on. From these we have, by eliminating w v 2, = u + xas (an) + æ (bm) + xas (cm) + . . . * + ** (an) + æ (bn) + & (cm) + . . . * (b) 2 + xas (an) + Are (bm) + ^ca (cm) + . . . = y + *a. (an) + xi. (bn) + . . . . . . * : == Multiply these equations by a 3 y . . ., and put . * tº A = x^2 + 3xas -- yºae + . . . B = 2x2 + 3x3 + y^* + . . . (c) C = ax + 3 + 2 + . . . and so on; then o = cºw + 3v + y2 + . . . + (Aa, + Bl, + Cº. + . . .) n, + (Aa, + Bl, + Co. + . . ) 7ta + (Aa, + Bb, + Co. -- . . .) n, The sum of the squares of the coefficients of m is A (A(r) + B (a) + c (a) + . . ) + B (A (a) + B (º) + c (º) + . . ) + . . . () 5 A 2 74o PRINCIPAL TRLANGULATION. If in equations (a) we substitute the equations (b), the results must be identically zero, or the different coefficients of (an) (bn) (cm) . . . . must vanish; hence we have— I = (6') *, + (ab) x + (ac) x. + . . . I = (ab) was -- (0°) A, -ī- (bc) A. I = (ac) *a- + (bc) as -- (c) x, o = (a”) was -- (ab) Aya -- (ac) x. o = (a”) was -- (ab) A. -- (ac) A. : and so on. By help of these relations, and the equations (c), q a = A (a") + B (ab) + C (ac) + . . . g 6 = A (ab) + B (bº) + C (bc) + . . . 'y = A (ac) + B (ch) + C (c") + . . . Therefore the sum of the squares of the eoefficients of the quantities n in the expression for aw -- Øv + y2 + . . . . is Acz + B3 + Cy + . . . ., and consequently if W be the weight of the determination of au + 3v + y2 + . . . ., we have by equations (c), # = A2 + B3 + Cy 4. . . . ..". W = (2. Aa2 + 6° At 2 + y” Aca + 2 & 3 *ab + 2 &y ^ae + 2 3) *te + . . )" By means of this theorem it may be proved that if the resolution of the equations (4) give # o = u + f\ + g|B + HC o = v + gA + i B + jQ * (5) o = 2 + h^ -- jB + kC where A, B, C represent the absolute terms of the three equations (4), then the weight of the resulting value of any quantity cºw + 3v + y2 is the reciprocal of fa” -- i3* + ky” + 2 gag + 2 hay + 2j6 y (6) * * Aves of the Curve, 30–After obtaining u v 2, we get finally through equations (2) the value of g given in equation (1). The axes of the curve are determined as follows: If a y be the co-ordinates (measured from the centre of the curve) of the point whose latitude is A, I 1 - * 2: E – ſº inxes - (A - B) ºx +;(B-C) co, 3 + c co, sº . 3/ = ſecº da = (A + B) in x + i (B + C) sin 3 * * : C in sº | sº FIGURE OF THE EARTH. 74I By taking the integral from A = o to x = }, ºr we have, a and b being the semi-axes— a = A – B + i (B – C) + + C = A – B – # C \ 3 5 3 I5 I I 2. 2. (7) b = A + B — it (B + C) + + C = A + + B — it. ;(B + C) +: + gº – i. Taking the sums and differences— 3 a + b = 2 A – # C I5 _ a + b 2. A = 2 +; C — b B = — a 3– Whence by substitution— b g = (+. + 2. c) – ; a – b ) cos 2 x + 2 C cos 4 × 2T T is _ /a + b , 3 2. a – " ... C. C = (++++}( – ) + , c) ºx 4. +.) co, sº 4 co, sº a + b 2. {} a — b º C . y = ( 2. –3(a – ) +; c) in x- 4. – a an 3x + i ºn 5.x The curve will be an ellipse if — 45 (* ~ bN a C = (; TÉ) a Consequently if a.' y' be the co-ordinates of a point whose latitude is x in an ellipse whose axes are a and b, - - - - ſo – 5 (-ºl (e.… — ; I * - 2 = {c # (#)'a) (; cox ; cos 38 + cossº) " — ” — _ 15 (a - "Y" 3 si # si # si 3/ y = {C # (H)a} (; in x + in 3 x + i in 52) Suppose the curve (1) to be actually described, and also on the same axes an ellipse: Let P be the point whose latitude is a on the ellipse, and Q the point whose latitude is a on the curve (1). The points P and Q would coincide if C were equal to # n° a (putting n = a – b : a + b), otherwise they depart from each other in proportion as C increases or diminishes. Measure PS along the curve of the ellipse and SQ perpendicular to it, put PS = 6s and SQ = 3r, then— e 3s = - (< − 2) sin x + (y – y') cos a 3r = (x - 2') cos x + (y – y) sin a t * : * * 742 PRINCIPAL TRIANGULATION. Substituting the values of a - aſ and y – y' in these expressions, and reducing, we get— - 8 c a — UN " * 8s = # C – (#) a} in 4. A 8 a — b 2 — J. * * =º *=mºmº-º. * * ... * * = {#c (; #) a} in 2. A which again are equivalent to the following— * =#|{6%-5%)- - * =: 6 x 5 Raj sin 48 8 *r = ** 6%-5%}ir ax w (8) 45 A. A” This last quantity measures the protuberance of the curve (1) above the ellipse on the same axes in any given latitude. The semiaxes a and b in terms of u v and 2 are obtained by substituting (2) in (7); thus we find— a = 2092.4817 – 2092-5 u + 696.3 v + 278.5 z ſq) b = 20855183 – 2085-5 u – 696.3 v + 278.5 z J. * * * — 2 N v YT' - * a - b T (300 + #) ( -- 5oz. . . “. . . . . . or = — 29 or — 1.16 v – 557-67 z *** *…* * * * * + * * * - sº -- - - - - § III. Data of the Calculation, and Corrections in terms of u v 2, &c. 1. The English triangulation differs essentially from the other meridian measures, first, in the extent of the triangulation across the meridian; and secondly, in the great number of astrono- mically determined latitudes. In general it is objectionable that the triangulation for deter- mining the meridional distance of two points should be oblique to the meridian, on account of the influence of uncertain errors in the observed azimuths upon the calculated result; but in the present instance the number of observed azimuths at different points, and their sufficiently satisfactory agreement, preclude any doubt as to the true azimuth of the whole network. The number of points having astronomical latitudes is so great that we may dispense with some of them without fear of lessening the accuracy of the final results. We shall therefore omit Cowhythe, Calton Hill (Royal Observatory, Edinburgh), and all the Irish points. With respect to the observed latitudes, we shall make use of the quantities given at page 664,-the influence of superincumbent masses upon the observed latitudes at certain points. There can be little or no doubt that the latitudes so corrected will be more probably true, or be more TIGURE OF THE EARTII. | 743 near the mean latitudes, than the direct astronomical results. But as this point may be questioned, the results will be given in such a form that the influence of the calculated corrections upon the Figure of the Earth may be ascertained by a very short computation. English Arc. Stations. Latitudes. Amplitudes. Distances o J JA O ºf & M. Feet. St. Agnes . . . 49 53 33 '93 | . . . . . . . . . .” --- • --------. O "O Goonhilly . 5o 2 5o" of o 9 16' 14. 56206'o Hensbarrow . . . . . 5o 23 I '84 o 29 27 ° 91 I7920.4.” I High Port Cliff . 5o 35 46' 57 o 42 I2 64 256678.4. Week Down . . 5o 35 53°40 o 42 IQ 47 257399 2 Boniface Down . 5o 36 12 97 o 42 39 “OA. 259360-8 | Dunnose . tº 5o 37 6' 54. o 43 32°61 264846' 9 IBlack Down * 5o 41 8-89 o 47 34’ 96 289839'8 Southampton . tº 5o 54 46-97 I I I 3 'O4. 372654'2 Greenwich i. 51 28 38' 30 I 35 4° 37 578564° 2 IPrecelly º 51 56 45' 18 2 3 II • 25 7495.57°8 Cambridge * 52 12 51 63 2 19 17 7o 847505'9 | Arbury ſº 52 13 26*59 2 19 52' 66 85.1203 °2 Delamere . wº 53 13 18: 61 3 19 44' 68 12 15251 2 Clifton . . s 53 27 29° 50 3 33 55' 57 | Igor.428' 5 South Berule . º 54 8 56'40 4. I5 22 °47 1554O4·o “o Burleigh Moor 54. 34. I5 I2 4 4o 41 ° 19 1708025' 3 Durham 54. 46 6' 20 4 52 32'27 | 178ooo2'4 Ben Lomond . 56 II 26-27 6 I7 52' 34 229944I '9 ‘. . Rellic Law 56 I4. 53 '60 6 21 19-67 2320585'6 Ben Heynish . 56 27 16-88 || 6 33 42 '95 || 2396289°o Great Stirling. 57 27 49' 12 7 34 15-19 2764686-7 Monach 58 2 I 2 I 31 8 27.47° 38' - 3090834' 5 | Ben Hutig. 58 33 4-46, 8, 39 30°53 || 3162038.7 North Rona . 59 7 I 5 Ig 9 I3 41 ° 26 3370391 .. 8 Balta . . . 6o 45 I '66 Io 5 I 27° 73 || 3966276' 5 Gerth of Scaw 6o 48 56°43 Io 55 22 ° 5o 3990 Io.3 ° 5 | Saxavord . 6o 49 38° 58 Io 56 4' 65 3994.182 '7 If v, be the correction to the latitude of St. Agnes, the corrections to the other points will be as follows:– Goonhilly . . . . – 1,649 + o-o554 u – o'oog6 v – o Io.45 z + r. Hensbarrow . . . . – o'o62 + o-1768 u — o'o.315 v – o 3308 z + r. High Port Cliff . . . — o'537 + o-2532 u – o'o.16o v – o 4719 z + r. Week Down . . . . — o-258 + o-2539 u — o'o.462 v – o'4734 z + æ, Boniface Down . . . — o'478 + o-2559 u – o'o.465 v – o'4769 z + æ, Dunnose . . . . . -- o'o66 + o-2613 u – o'o.476 v – o'4873 z + æ, Black Down . . . . 4- 4.251 + o-2859 u — o'o 524 v – o'5319 z + r. * Southampton . . . . -- 3-047 4 o'3676 u — o'o688 v – o 6822 z + æ, Greenwich . . . . -- 2.663 + o-5707 u – or 1123 v — 1.0506 z + r. Precelly . . . . . 4. 2.192 + o-7393 u — o-1514 v — 1.3513 z + 1, Cambridge . . . . -- 1:685 + o-8360 u — or 1751 v — 1.5212 z + æ, Arbury . . . . . 4- 3.187 -- o.8396 w – o 1759 v — 1.5273 z + 4, 744 PRINCIPAL TRLANGULATION. Delamere . . . . . -- o'943 + I. 1986 u — o'2715 v — 2.1429 z + æ, Clifton . . . . . . – o'266 + 1.2835 u — o-2959 v — 2.2849 z + æ, South Berule . . . -- 3:319 + 1 .5325 u — o-37Io v — 2.6905 z + æ, Durleigh Moor . . . -- 2:583 + I-6845 u — o-4198 v — 2.93.20 z + æ, Durham ' ' ' ' ' -- I'o26 + I-7553 u — o'4432 v — 3-0421 z + æ, Ben Lomond . . . . 4 o'670 + 2.2673 w — o-626o v — 3.8023 z + æ, Kellie Law . . . . 4. I-717 + 2.2882 u — o'6338 v — 3.8314 z + r. Ben Heynish . . . 4- 4.479 + 2.3628 w – o-6625 v — 3.9358 z + æ, Great Stirling . . . -- 2:384 + 2.7258 u — o'8095 v – 4:4223 z + æ, Monach . . . . . -- 3:534 + 3-0471 u – o'9491 v — 4.8200 z + r. ſłen Hutig . . . . -- 1:850 + 3.1173 u — o'981o v – 4:9031 z + r. North Rona . . . . -- 3.607 -- 3:3225 u – I-o/59 v — 5:1355 2 + æ, Balta . . . . . . 4- 6.2O3 + 3.9.095 u – I-3674 v – 5-7247 z + æ, Gerth of Scaw . . . -- 6.083 + 3.933o u – I-3797 v — 5:7459 z + æ, Saxavord . . . . . -- 4:1 oA + 3-9370 u – I-3819 v — 5:7496 z + æ, 2. The latitudes and distances of parallels of the points in the French arc will be found at pages 548, 549 of the Base du Système Métrique Décimal. We shall, however, omit the point Evaux, for although there is no reason to doubt the accuracy of the astronomical determination of the latitude, yet there is certainly a very unusual amount of local disturbance at that point, amounting probably to — 8" (Phil. Trans. 1856, Part II. page 625). There appears, however, no reason for excluding the point Barcelona from the data; the determination of the latitude was considered by Delambre as in itself unexceptionable, but some doubt was thrown upon it from its presenting a discrepancy of 3" with the transferred latitude of Mountjoy, the two Stations being only Io94 toises apart. The distance of the parallels of Mountjoy and Formentera given in the Base du Syst. Met, is erroneous; in Number 438 of the Astronomische Nºchrichten will be found an elaborate recalculation of the distance of parallels by Bessel. The data for Barcelona are given in the second volume of the Base du Syst. Met, pages 565 and 615. JFrench Arc. Stations. Latitudes. Amplitudes. Distances. * o / # / O J fº Toises. Formentera. . . . 38 39 56' II • * * . . • * * Montjouy . . . . . 4.1 2 I 44 ° 96 2 41 48' 85 153673-61 Barcelona . . . . . 41 22 47'90 2 42 5 I '79 154616-74 Carcassonne . . . 43 I2 54 ° 30 4 32 58' 19 259172 61 Pantheon . . . . 48 5o. 49' 37 Io Io 53° 26 58o312 °41 Dunkirk . . . . 51 2 8° 41 I2 22 12' 30 . 705257' 21 dº º -. *+* y{ -- FIGURE OF THE EARTH. 745 The correction to the observed latitude of Formentera being called a, , the corrections to the latitudes of the other points will be as follows:– Montjouy . . . . . -- 2.321 + o-97 II u + o-1682 v — 1.8242 z + æ, Barcelona . . . . — 1.034 + o-9771 u + o-1690 v — 1.8364 z + r. Carcassonne . . . . – 2.793 + 1.6375 u + o-2312 v – 3-134o z + r. Pantheon . . . . . -- 5.125 + 3-6648 w + o-1583 v — 7.1518 z + r. Dunkirk . . . . . – 2.061 + 4,4530 u + o-o230 v — 8-6320 z + æ, In obtaining these equations, the toise has been taken as equal to 6. 394.54378 feet of O,. This quantity was obtained in the following manner: A series of 54 comparisons was made by the late Lieutenant Murphy, R.E., in the summer of 1834, between the Ordnance Standard O, and two lengths of the Royal Astronomical Society's 5-feet Brass Scale; these comparisons are given in detail at pages.[29] and [30] of the Account of the Measurement of the Lough Foyle Base. The result was— O, = 2 A – ‘oorg5o inch, “Lough Foyle Base,” p. 85; but O, = O. — -oooog4 inch, and A = 59-999712 mean inches of centre yard of A, (Mem. R. A. Soc., vol. 9, page 100), whence O. = I 19.997.508 mean inches of centre yard of A. In the months of May, June, and December of the following year, Mr. Baily compared the mêtre à traits, which had been previously compared in. I 818 by Captain Kater with Sir George Shuckburgh's Scale,_with the Royal Astronomical Society's Scale. The mean of Io2 comparisons gave this result— - Standard mêtre = 39-369678 mean inches of centre yard of A. Combining these two results we have— - Mètre = 3-28087463 feet of O, log = o'5159896351 Toise = 6.394.54378 feet of O, log = o-8058095651 It appears from later observations on the Royal Astronomical Society's Scale that it has undergone an alteration in length. This makes it necessary to remark that the interval between the two comparisons just quoted was only from one year to a year and a half; during the whole of this period the scale was in Mr. Baily's hands and under examination, and had any change in length been going on at that time it could not have escaped his observation. 3. If we apply the corrections given at page 624 of the Philosophical Transactions for 1856 to the latitudes of Dunkirk and Greenwich, and thence deduce the distance of the parallels of . those points, it will be found to be about 161,142 feet, being less than Delambre's determination by about 260 feet. From this it is evidently necessary that the geodetical connection of Greenwich and Dunkirk should be taken into consideration in the Figure of the Earth, forming 5 B 746 PRINCIPAL TRLANGULATION. an entire arc of 22° Io' from Formentera to Saxavord. The connection of Nôtre Dame, Calais, and Blancnez with the English triangulation is unexceptionable, and Colonel Blondel (le Directeur du Dépôt de la Guerre) has kindly supplied the new triangulation connecting these points and Dunkirk. The data supplied by him is contained in the first three columns of the following tables; the fourth column contains the inferred spherical angles; the fifth contains the seconds of the sexagesimal angles corresponding to the angles in the second column. The second part of the table contains the calculation of the direct distance of Dunkirk and Blancnez, the computed angles being marked with an asterisk. - * † Noms des Stations. Angles Moyens. **. sºRise iº: Log. Sines. Log. Distances. G. f M. C & J J . JJ -- |, Watten, tour signalée 82 74.22 4 27458 6o 74 28 5- 26 4'86 9°983.8432 4'4386784. Cassel, clocher tº º 72 4628°7 25486'52 || 63 24 6o Io 59' 7o 9'9514754 || 4:4063io6 Dunkerque, tour du pavillon 46 7948-9 19112'42 42 6 55-83 || 55'44 9-8264864 4:28.13156 - * = 1 19 - Gravelines, tour du beffroi . 96 o492 I 25486'52 || 86 26 39:73 || 39°44 9-999.1633 4'4063 Ioff Watton 5I 1219 o 18371 ‘83 46 o 35' 25 || 34’ 96 9° 8570051 || 4 - 2641524 Dunkerque 52 8288’ 9 1884 o’ 72 || 47 32 45'89 || 45' 60 9°86795oz 4 ° 2750975 - s = o' 87° * | Hondrecoutre, signal 61. 6295. I 1884o'72 55 27 59'87 59' 61 9° 9158194, 4°2750975 Watten . . . . 86 I61 o' I 22332 ° 37 77 32 41 ° 93, 41 67 9'9896568 || 4:3489349 ‘ Gravelines . 52 2094.8 16723°40 || 46 59 º: 1872 9 8640464 4'2233245 s = o' 7 Calais, grande flèche 78 2112' 6 22332' 37 || 7o 23 24-78 24.48 9°974o508 4'3489349 | Hondrecoutre 61 1640°5 19431-27 | 55 2 5i '82 || 51-52 || 3:31.36172 4'2885013 Gravelines 6o 6246'9 1931.5' 51 || 54 33 44-30 || 44°oo 9-91 to221 4'2859062 s = o' 9o - Fiennes, signal . 62. 1836' 9 22332° 37 || 55 57 55' 37 || 55' 16 || 9 9183968 || 4:3489349 Hondrecoutro IIo 5938-8 26576-57 99 32 4° 37 4° 17 9°993.9588 4'4244969 Gravelines 27 2224’3 II 175' 58 24 30 o' 88 o'67 9' 61773ol. 4’ o482682 * = o' 62 Fiennes . 49 91.97° 3 19431 27 || 44 55 40° 14 39'92 || 9'8489367 4'2885013 Gravelines 33 4013-3 || 13782 '78 || 3o 3 4o'53 | 40°31 9-6997724 .4° 1393370 Calais II6 6789'4 || 26575-77 || Ios" o 33% 3977 9°98492.13 || 4'4244859 - & E O “ Fiennes I 12 1042 7 | 1931.5' 51 || Ioo 53 37'96 || 37°84 || 9:992 Io22 + 4* 2859062 Hondrecoutre 49 4272-7 || 13783’ og 44, 29 4' 48 4." 35 9 8455.425 4' 1393465 Calais 38 4684-6 || 11175' 58 || 34 37 17: 94 17 81 9°7544662 4' o482702 s = o' 38 Blancncz . 6o 4347-4 | 1931.5'51 || 54 23 28°73 28'56 9'91oo969 || 4-2859062 Hondrecoutro 29 $468.3 | 16632 '93 || 26 35 12°46 || 12:29 9' 6508437 4’ o266530 Calais . IIo o244' 3 || 23464’ o4 99 I 19° 32 | 19. I5 9° 9945935 | 4° 3704028 - : * = o' 51 jº | Blanchez. . . . 77 ogo.5:3 || 13782 '94 | 69 22 53'43 || 53° 32 9-97.12507 4:1393418 Riennes . {} & 51 3539-3 || 10632°og 46 13 6-84 6.73 9'8585275 || 4 ozóół86 Calais . . . . . . 71 5555'4 13280°58 || 64. 23 6o'o6 59'95 9'9551259 || 4: 123217o | * º: s = O' 33 +& - FIGURE OF THE EARTII. 747 Calculation of the Distance Dwmkirk—Blancmez. º Noms des Stations. Angles Moyens. * º snºe. iº Log. Sines. . Log. Distances. º | - - º M. O d {{ A f IIond recoutre 25486'52 || 34 34 50°35 | 56°os 9:7540152 || 4:4063ro5 Dunkerque 16723°40 || 21 5 I 53° 37 53° of 9'571o291 || 4 2233245 Watten . . . . 123.33. 17° 18 16'88 9 92.08320 4' 5731274. - * e = o' 9o ºt - - - Hondrecoutre 18371 ‘83 || 26 53 9's. - 9-27 9:55,0695 4.264154 Dunkerque 22332 °37 25 4o 52 '52 || 52'27 | 9'6368520 | 4:3489349 | Gravelines . . . . I 33 25 58' 71 || 58° 46 9'86 Io443 4' 5731272 s = o' 75 t - - º - : Blancnez . . . . . 49 9 41 ° 9o 41 18 9'8788496 4' 5731273 | Dunkerque 23464’ og 28 19 6'46 5’74 9'6761161 4° 3704028 Hondrecoutre . . . . Io2 3 I I 3 '80 || 13 o8 9°9895474 4' 683834I t = 2 * 16 - Calais . . . . 74 16 32' 39 || 31 ‘8o 9'9834.35o 4' 5731273 Dunkerque * 1931.5' 51 || - 29 47 28' od 27°45 9' 6962 I39 || 4°2859062 Hondrecoutre . . . . 75 56 I 34 o' 75 9-9867782 4' 5764705 * = 1 - 77 - The following table contains the triangulation from Greenwich to Blancnez, Calais, and Montlambert; the second part contains the calculation of the direct distance of Blancmez from Greenwich :— Stations. Angles. - Bºr º: Log. Sines. Log. Sides. sides in Fect. Wrotham. 5& 5 43°39 – 6.93| 33-66 || 9.8848531 5:1392655 || 137741-70 Tairlight . . . 31 56 4'44 3 * 51 9 : 7234I 18 4'9776242 94978' 26 Stede Hill 97 58 17.77 * | 16'83 9:9957833 5' 24.99957 177826, 17 2 * 8o * = 3 'o6 Wrotham. º 93 16.48° 5o — o'74 47'77 9°9992880. 5' 1516375 I41787° 35 Crowborough tº 41 58 20° 52 1978 9.8252764 || 4'9776259 94978*63. Stede Hill 4. 44. 44 53° 19 52'45 9°8475657 || 4: 9999.152 9998o'47 2 * 2 I - * = 2 24 Fairlight. º 6; a 36-06 |- 1 is 34.9 9'9574-76 5° 1516362 141786-93 Crowborough º 61 44 2-81 I • 66 9°944.8560 | 5' 1390646 13774I '37 Stede Hill {} 53 L3 24' 58 23'43 9'9036182 5’ og78268 125264° 14 3 ° 45 of -- * = 3: 70 Fairlight. IIo 3o 3o '76 — o' O “ 9. 9715637 5:3286260 . . . 213120'90 Crowborough º 36 5 23 ° or 39 3. .# 9 : 7701521 - 5: I.272 I44 134033°83 Tolsford . . . 33 24 7°40 7 or 9°7407645 §:0978268 125264° 14 1 - 17 * = 3 °7o 5 B 2. 748 PRINCIPAL TRIANGULATION. -je. Seconds of * = 2 *32 Stations. Angles. ; red. Ang. Log. sines. Log. Sides. Sides in Feet. Tairlight. 43 27 54." 7o — 1467 53-03 9'8529792 5 oz I5083 Iošo'77' I5 Stodo Hill 65 24 11-67 IO " OO 9°9586853 5* I272 I54. I34034.” I 3 Tolsford . 69 7 58: 65 56'97 || 9°9705359 5* I 39.0650 I3774 I 54. 5 * oz s = 3 * 1 I Crowborough 25 38 39'8o – 2 Io 37-70 9'6362623 5 “O2 I 5 Io9 105077-78 Stede Hill I 18 37 36' 25 34 I5 9 ° 9433779 5°3286265 213121 : 13 Tolsford . 35 43 50° 25 48° 15 9: 7663882 5' 1516368 141787° 14 6' 30 s = 3 °og Fairlight. 6 go 15' 35 | + o-55 | 15.90 9:0757592 || 4'4306515 || 26955-76 Tolsford . 136 51 46’ 63 47° 17 9°8348934 5' 1897857 I548os' 25 Folkstone 36 17 56° 38 56° 93 9°7723226 5* I272 I49 . I34034°oo | — 1 °64 - - ſº s = o' 58° | Fairlight. 51 18 58'89 — o'78 58: II 9°892.4322 5' 28490oo I92705" 53 Tolsford . 95 48 I '68 o' 91. 9°9977708 5' 3902378 245605'34 Montlambert. 32 53 I '76 o' 98 9° 73474.71 5* I272 I49 . I34034 °oo - 2 * 33 wº * = 6' of Fairlight. 44 28 43’54 — or 90 42 64 9°8454982 5 * 2387842 173294° 26 Eolkstone 96 46 26°44. 25' 54 9°996.9578 5 °39024.38 245608 75 Montlambert. 38 44 5:. 51 '82 | 9°7964997 5' 1897857 I548o3'25 2 * 9 * = 6'29 Fairlight . . 33 39 33°72 | – I of 32' 65 9° 74.37057 5' 2027355 I 59490°74. Tolsford . . I 18 34 49'o6 47 '98 9°9435687 5 * 4025995 252696.67 IBlancnez . 27 45 4o "44 39°37 9'668.1841 5* I272 I49 I34034°oo 3 * 22 & F 4'44 Fairlight. 26 49 18' 37 — o'77 17' 60 | 9'6543819 5' 1276314. . 134162 '60 Folkstone 12 I 48 I2 ° 92 I2 I5 9°9293482 5'4025977 252695-61 IBlancmez . 31 22 31 °oz 3o° 25 9° 7165362 5' 1897857 I548o3'25 2 * 31 ; e = 4° 17 - Tolsford . 22 46 47° 38 — o'44 46'94 9° 587923o 4'8853604 76799-86 Montlambert. 53 31 9°36 8'92 || 9 '9052861 5' 20272.35 159486°34 Blancnez . Io3 42 4° 59 4. "I4. 9'9874626 5' 28490oo . . . I927oS’ 53 I "33 e = 2 * 81 Fairlight. 17 39 25' 17 | — o' 15 25' 02 9'4818970 4'8853473 76797'54 Montlambert. 86 24 II 12 Io '98 9°9991436 5 * 4025939 252693 °4o Blancnez. 75 56 24’ I 5 24" oo 9°9867905 5' 39024.08 245607'os $ o "44 * = 4 ° 45 Folkstone 25 I 46-48 || – o 'o2 || 46'46 9' 6264288 4.8853546 76798.82 Montlambert. 47 39 18° 41 18° 39 9-8687052 5' 12763 Io 134162 °47 Blancnez. Io'7 18 #. 55'. I 5 9° 97.98584 5' 2387842 173294° 26 O "O FIGURE OF THE EARTH. 749 Stations. Angles. ; ‘.... Log sines. Log. Sides. Sides in Feet, | Tolsford . 4f 3. 44.95 + *43 43.38 9°8174882 5' 2387783 I73291 '91 Montlambert 5 5I 5o 95 51 38 9°oog333o 4'4306231 26953 '99 IFolkstone I33 4. 22 '82 |. 23 ° 24. 9'8636099 5°28490oo I92.705'53 - I - 28 a F o' 8o | Tolsford . 18 16 57' 57 | + o-'85 58:42 9°4965270 5' 1276.151 I34.157° 55 Blancnez. 3 36 5o'5 51 °43 8: 7996.118 4°4306999 26958-76 Folkstone 158 6 9:30 Io I5 9° 5.716416 5 ° 2027295 I59488'54 – 2 ° 55 - s = o' 32 Tolsford . I7 39 I5'54 | – o '91 I4°63 9°4782396 4*779.1956 6or 44'46 Montlambert . 87 58 48.88 47 '97 || 9 '99973oo 5:30.06860 19984 I 65 Fiennes . * | 74 30 58°30 | 57°4o 9°98394.40 5°28490oo I927.05" 53 e = 2 * 72 :- Tolsford . 5 16 31 ‘84 || – o' 24 || 31 '60 8'9635224 4'6392529 4357.6° 56 I}lancnez . . . I55 3 36'66 36°43 9' 6249697 5' 3007002 199848- 16 | Fiennes . * | 19 39 52 ° 2 I 5I ‘97 9° 526.9990 5' 2027295 I 59488'54 s = o '71 4. Montlambert 34 27 39°52 — o'21 39-31 | 9'7526967 4' 6392.077 43572 °o2 Blancnez. . 5 I 2 I 32 °o'7 31 '86 9'8926912 4*7792022 60145 ' 37 Fiennes . * | 94. Io 49°o:3 48°83 9°9988.431 4'8853541 76798: 74 s = o “62 Tolsford . 7 32 41.70 || – o°30 || 4 I "4o 9' I 182553 4' 542.5591 34878.60 Blanchez. . . I35 33 29°47 || – o' 31 || 29° 16 9 8452132 5:26.9517o 186001 '75 Calais * | 36 53 49°75 49°44 || 9 '77842.57 5' 2027295 I59488'54 s = o '92 * Folkstone 9 2 5 2 I '83 — o' 27 | 21 : 56 9° 2 IIo353 4' 5426184. 34883 : 37 Blancnez. . 131 56 38-89 38°42 9°8714548 5 ° 2030379 15960I '8o Calais * | 38 4r 60. Io 59'82 9'7960481 5' 1276312 I34162 53 s = o '82. Blancncz (1). 69 22 53'43 | – or 11 53° 32 9° 97.125oz 4' 6553325 4522 o' 20 | Fiennes . 46 13 6'84 6'73 9'8585275 4' 5426093 34882 '64 Calais 64 23 6o'o6 59°95 || 9 '955 I:259 4' 6392.077 43572 “O2 s = o' 33 g (l) The observed value of this angle by Captain Kater is 69° 22' 53”87. 750 PRINCIPAL TRIANGULATION. Calculation of the Distance Greenwich–Blanchez. * * * ~ *-* + Stations. "Angles. . º Iog. Sines. Log. Sides. side in rest Severndroog. 145 33 35'74ol-gºo/Al 33,696 || 9.7055413 || 4944077; 87917°85. Wrotham 4, 5o 14°812 14. 768 8'9259765 4°1647.123 1461.2 °og Greenwich 25 39 9'579 | 9° 536 9'63640.18 4'8751376 75oI3 .I.9 s = o' 131 Epping 33 35 54°8 II –o'555 | 54°256 9°743or 43 4°944O77o 87917°83' Wrotham 33 24 II '841 II 286 9:7407781 ::::::::: * • §: Greenwich * | II2 59 55 “OI3 54'458 9° 96403 Io 5' 1650937 . . . 1462.49°27 s = 1 '665 w Wrotham . . . . . . 157 45 32° 185| —o'464 || 31 '721 9'5780731 5*4171897 261330'24. Fairlight . . . . . . 7 18 57°464 57: ooo 9: Ioagóo4 4-9440770 87917°83, Greenwich . . . . . 14 55 31 '743 31-279 9-416879; 5°2499.957 177826, 17. * = I 392 - # tº Beachy Head . . . . . 71 22 16-870 | –2 or 5 || 14-855 | 9-9766277 5*4171897 261330'24. Greenwich . . . . . . 20 54 1898o I6'966 || 9' 55.24429 4'993oo49 98492'22 Fairlight . . . . . . . 87 43 3; 28° 179 || 9°9996574 5 °44O2 I94. 275562 oA. s = b oA4. - . . . . . Fairlight . . . . . . . . I 18 22 30°32 —4:56 || 25' 76 9.944164 5-644926. t 441489-19 Greenwich . . . . . 3o 14 25:09 r 2O '54 , 9° 7020933 5*4025970 252695'32 Blancnez . . . . . . 31 23 18:26 13:70. ... 9.7166860 5:41.71897 261330'24. s = 13 '67. * * * " ſº At Greenwich the observed azimuth of Chingford is 359° 59' 58%. 360. This has to be corrected by the quantity " tan x = — o”.686, which gives the azimuth of Chingford finally 359° 59'57".674. From the preceding table, . - + w The angle Chingford—Greenwich—Severndroog = 106 16 3 3.365 ... Azimuth of Severndroog . = Ioé Io 33-039 The angle Severndroog—Greenwich—Wrotham . . . = 25 39 9. 579 ..". Azimuth of Wrotham . = I31 49 42-618 The angle Wrotham—Greenwich—Fairlight - • = I4 55 31-743 ... Azimuth of Fairlight . . . . . = I46 45. I4.361 The angle Fairlight—Greenwich—Blanchez = 30 I4. 25.og ..". Azimuth of Blancnez . tº tº II6 3o 49-27 Taking the latitude of Greenwich 51°28'38">30 + 1".864; by means-of-the distance and bearing of Blancnez we find for the distance of parallels of . - Greenwich—Blancnez = 201693. I feet. Also, the back azimuth of Greenwich at Blancnez is 2.97° 50' 53”.888. If from this we subtract the angle Greenwich—Blancnez—Fairlight, or 31°23' 18". 26, we have 266° 27' 35".628 for the azimuth of Fairlight at Blancnez. This agrees satisfactorily with the result of Captain Kater's observations of the Pole Star at Blancnez; he obtained 266° 27'33".40 (Philosophical Transactions, 1828, page 233). FIGURE OF THE EARTII. 75 I To find the azimuth of Dunkirk at Blancnez we have— The angle Calais—Blancnez—Fairlight . . . . . . . = 16; 13 991 33 Calais–Blanchez—Dunkirk . . . . . . . = 5 I3 46.83 Azimuth of Fairlight at Blancnez . . . . . . = 266 27 35-63 * 53 Dunkirk at Blancnez . . . . . . = 75 o 32-37 The log. distance of Dunkirk—Blancnez is 4.6838341 :, if to this we add the logarithm of a mêtre expressed in feet, namely or 51598.96, we find 5. 1998237 as the log. distance of Dunkirk and Blancnez in feet.….This distance, together with the above bearing, gives the distance of parallels of . , * - -- . . . Dlancnez—Dunkirk = 40289.7 feet. This quantity subtracted from the meridional distance of Greenwich and Blancnez gives the Distance of Parallels of Greenwich and Dunkirk = 161403.4 feet. The quantity used by Delambre was (Base du Syst. Met., III. 192) 25241.9 toises, which is equivalent to 1614Io. 5 feet of the Ordnance Standard o, . so that the present determination differs seven feet from that of Delambre. By Delambre's observations for azimuth at Watten, he found, after transferring the azimuth geodetically to Dunkirk, that the azimuth of Watten at Dunkirk was 205°19'42", 14 (III. 14); if from this we deduct the angle Watten—Dunkirk— Cassel, viz. 42° 6' 9".73 (II. 800), we get 163° 13' 32”.41 as the azimuth of Cassel at Dunkirk. From the preceding table of triangles we get— Blanchez—Dunkirk—Hondrecoutre . . . . . . . = 28 19 -: 646. Hondrecoutre—Dunkirk—Watten . . . . . . . = 21 5.I., 53°37 Watten—Dunkirk—Cassel . . . . . . . . . = 42 6 55-83 Now the back azimuth of Blancnez from Dunkirk, as obtained in the same calculation which gave the distance of parallels above (40289.7), is found 255° 31' 31".98. By subtracting from this the sum of the three angles specified above, namely 92° 17' 55". 66, we have 163° 13' 36”. 32 as the azimuth of Cassel at-Dunkirk. The difference between this and Delambre's determination is only 3”. 91. - - - We are now able to assign an equation between the corrections to the latitudes of Formentera and St. Agnes, and thus to eliminate the former quantity w, ... the equation is— a', -a, - – 2,788 + 4.0415 u + o-Ioro v - 7:8692 2. ' Thus the corrections to the different points of the French arc become— IFormentera . . . -- 2.788 – 4:0415 u — or IoIo v + 7.8692 z + r. * Montjouy . . . -- 5. Io9 — 3.07.04 u + o-oG7I v + 6-oA5oz + r. Barcelona ' ' -- I-754 – 3.0644 u + o-oé79 v + 6.0328 z -- 2:1 Carcassonne : " - o-oo:5 – 2.4040 u + o-1301 v 4- 4.7352 2 + r. Pantheon . . . – 2.337 – o:3767 u + o-oš72 v -- o-71742 + ºr Dunkirk . . . . -- o'727 -- o:4115 w — o-o/81 v – o,7628 z + æ, 752 PRINCIPAL TRLANGULATION. where w, is the correction to the latitude of St. Agnes. These equations are now to be treated in one group with those of the English Triangulation. - º º 4. Professor Struve of Pulkowa has kindly furnished this department with the first two / 22 sections of the account of the Russian “Meridian Arc of 25° 20',” containing the whole of the geodetical operations, but only part of the astronomical. The observations and calculations of 1. this magnificent work have been conducted in such a systematic and masterly manner, that we find in connexion with every measured base-line or calculated quantity its probable error, and these probable errors are carried through to the final results, the distances of the parallels, an advantage which no other arc possesses. The possibility of assigning the probable errors of the final distances arises from the nature of the triangulation, which is very simple and direct, and presents very few equations of condition other than those resulting from the sum of the three angles of the different triangles. The sum of the lengths of the ten measured bases is 29,863 toises, or 190,960 feet, so that the average length of a base-line is 19,096 feet: in the British Triangulation the total length of measured base-lines is 183,001 feet, and the average length of a base 30,500 feet. The length of the total arc is 1753 miles, with a probable error of + 39.8 feet. The following table contains the data of this arc. The latitudes are not final, but the probable errors of the quantities stated are less than half a second. That we may have a correct idea of the influence of this uncertainty, suppose the probable error due to local attraction to be + 1".75, then the uncertainty of the astronomical determination, assumed as + o-50, will raise the probable error of the adopted latitudes in the proportion I-75 : V I 75* + o- 5o’ = Ioo : Ioa. Russian Arc. Stations. Latitudes. Amplitudes. Distances. +. O / WW O / WW Toises. Staro-Nekrassowka . 4520 2. ‘8 | ......... . ............... o + o Wodolui . . . . . 47 1 25°2 I 4 I 22 °4. 964.15° 136 + o' 651 SSuprunkowzi . . . . 48 45 3' I 3 25 o' 3 194973° 124 + 1.646 IKremenetz . . . 5o 5 50 °o 4. 4.5 47".2 27I724' 51o -f- 2 °og.9 Delin . . . . . 52 2 42 2 6 42 39°4 382943’521 + 2 - 611 Nemesch . . . . 54 39 5'9 9 19 3' I 531753° 042 + 3 °453 Jacobstadt . . . 56 36 4'8 I I Io 2 'Q 637483. 921 + 3 '893 Dorpat . . . . 58 22 47' 6 || 13 2 44°8 || 744764-484 -E 4: 177 IHogland . . . . 6o 5 Io' I I4 45 7'3 842303 Io2 + 4° 372 I(ilpi-Maki . . . . 62 38 5’o 17 18 2-2 988016.669 + 4' 502 Tornea . . . . ; 65 49 44' 7 20 29 41 ° 9 || 11708 Io'973 + 4*957 Stuor-Oivi . . . . 68 4o 58° 4 || 23 20 55'6 1334032 '877 -E 5: 539 Fuglenoes . . . 7o 4o II 3 || 25 20 8' 5 || 1447786'783 + 6' 226 FIGURE OF THE EARTH. 753 If w, be the correction to the latitude of Staro-Nekrassowka, the corrections to the other points will be as follows:— Wodolui + 3.883 + o-6086 u — o-o250 v — 1.2114 z + æ, SSuprunkowzi + 5.686 + I-2306 u — o-o875 v – 2:4285 z + ar, Kremenetz - + 1-oš1 + 1.7148 u — o-I62o v – 3.3509 z + æ, Belin . + 3.7 Io + 2.4163 u — o'3094 v — 4,6269 z + æ, Nemesch + 2.188 + 3-3546 w — o'5786 v – 6.1893 z + æ, Jacobstadt . + 6.989 + 4 ozog w — o-81.85 v — 7. 1716 z + æ, Dorpat . + 3.534 + 4.6969 u – I-1025 v – 8.0426 z + r. Hogland . + 4.866 -- 5.3114 u – I-3948 v — 8-7106 z + æ, Kilpi Maki . + 5-353 + 6.2290 w – I-8895 v – 9.4695 z + æ, Tornea + II.306 + 7.3799 u – 2-6029 v – 9.9857 z + æ, Stuor Oivi. . + 7.247 -- 8.4072 u – 3.32 Io v — Io-oi 88 z + r. Fuglenoes + 9-497 -- 9-1231 w – 3.8622 v – 9.8or 8 z + r. 5. There is some little uncertainty relative to the unit of measure in the earlier geodetical operations in India. In Volume VIII. of Asiatic Researches, page 138, it is stated by Colonel Lambton that his Standard Chain, made by Ramsden, was measured off “ by the Standard in London when the temperature was 50° by Fahrenheit's thermometer.” It is not stated whether the Standard was Ramsden's Bar or his Brass Scale: the former supposition has in itself the greater probability, as the Bar was constructed from the Brass Scale expressly for the laying off of the Ioo-feet chains used in the English Base Lines. In the Philosophical Transactions, 1823, page 28, Colonel Lambton states, in reference to this same Standard Chain, that it “was laid off from Ramsden's Bar at the temperature of 52°.” This temperature (52°) is probably a mistake, as Colonel Everest, at page 51 of his first volume,” states that the chain was “ set off at the temperature of 50° Fahrenheit from his (Mr. Ramsden's) Bar.” These three statements all differ, but upon the whole it would seem probable that the chain was measured from Ramsden's Bar at the temperature of 50°, which is in fact Colonel Everest's statement. But on examining the “Reduction to the Temperature of 62°” in Colonel Lambton's different bases, we find that he has supposed the chain to have been laid off from the Brass Standard at 50°: for if r be the mean temperature in which the base was measured, he has applied the correction IX C. ow ‘o ox ‘OI2 IOO I2 -* * “An Account of the Measurement of an Arc of the Meridian between the Parallels of 18° 3' and 24° 7' &c. By Captain George Everest.”—London, 1830. s 5 C 754 PRINCIPAL TRIANGULATION. where B is the length of the base, and -oo74 and -ot 237 are the expansions (in inches) of Ioo feet of iron and Ioo feet of brass for each degree of Fahrenheit. This correction is erroneous if, as seems most probable, the chain was laid off from Ramsden's Bar; but it would scarcely be prudent to alter Colonel Lambton’s reductions for temperature at this distance of time; we shall therefore consider his first bases, as he himself has done, to be expressed in terms of Ramsden's Brass Scale at 62°Fahrenheit. The northern part of his arc is in terms of his own Standard. - Now from Captain Kater's comparison of this Standard with the others mentioned, page 61 of the Philosophical Transactions for 1821, it appears that Ramsden's Brass Scale exceeded Colonel Lambton's in the proportion of º: 36-oo3147 : 36-oooooo = 1-oooo&74. Therefore to reduce his latter distances to the same standard as the earlier, namely Ramsden's Brass Scale, they must be divided by I. oooo&74. Again, the factor for reducing measures in terms of Ramsden's Brass Scale at 62° to the Ordnance Standard O, (see page 212) is (I -oooo.328) (I -oooo.383) = 1 -oooo/II. The distances in this arc are as follows:– | Col. Lambton. Factor. Corr. Punnae to Putchapolliam . . . . . . . io291oo.5 | + ·odoo/11 | + 73.2 Putchapolliam to Dodagoontall . . . . 727334-6 + -oooo.7.11 + 51.7 Dodagoontall to Yerracondah - . . . . 332662.3 || + -oooo711 + 23.7 : ". . Yerracondah to Namthabad . . . . . . 429I34'3 – “ooool 61 – 6.9 “Namthabad to Daumergida . . . . . . . Io'73428.2 — -ooool.61 – 17.3 Hence in terms of O, the distances from Punnos are— Punnoe to Putchapolliam . . . . . . . Ioz9173.7 , Dodagoontah . . . . . . . 175656o-o 33 Namthabad . . . . . . . . 25.18373-4 35 Daumergida . . . . . . . , 35.91784.3 A small portion of the northern part, of this arc was revised by Colonel Everest, who found a sensible difference between the lengths of sides as determined by Colonel Lambton and himself. Unfortunately, but few of Colonel Lambton's Stations could be refound, and from those that were identified it appears that Colonel Lambton's distances were short in proportion of about o-99993 : I -ooooo. If we suppose this error to have accumulated gradually during the work, it would indicate an error of — 126 feet in the arc between Punno, and Daumergida. It seems more probable that the discrepancy is due to his base-line II].CàSUITCS. - º The Station Takal Khera is omitted in Colonel Everest's second volume; its meridional position in the new work may be found as follows:— ; FIGURE OF THE EARTH. 755 Let MN be the points in which the meridian of Takal Khera cuts the sides Ashti-Ner and Ashti-Badali; then, by Colonel Everest's first work, putting A for Ashti, which is the same as the South End of the Takal Khera base, and T for Takal Khera— M AM = 4879.4 , AN = 5972.2 TM = 17397.8 , TN = 22888.o The points in which the meridian of Kalianpur cuts the same two sides being designated by M'N', we have by Colonel Everest's second volume”— AM’ = IoI88.03 AN’ = 12469-62 AM/N’ = 70° 2/ 487 # AN/M/ '- 5o° “Io' 23” From these quantities we have MM’ = 5 308.6 feet, NN' = 6497.4, and the difference of parallels of Takal Khera and M' = 15586.o Takal Khera and N’ = 27049.2 Now by page 53 of Colonel Everest's work the distance Kalianpur to M' is III2955.7, to which must be added the proportional part of the correction II .87 at the foot of the page; thus we get— - Kalianpur – M' = 1112961-7 Kalianpur – N’ = II 24424.8 The first of these, with the meridional distance of Takal Khera and M', gives the distance of Kalianpur and Takal Khera = Io97375.7; the second, with the meridional distance of Takal Khera and N', gives Io97375. 6. tº The measurements given by Colonel Everest in his last volume are expressed partly in terms of his Io-feet Standard A and his 6-inch Brass Scale A, twenty parts of any result being in terms of the former and one part in terms of the latter. He has also given at the end of the same volume the results of comparisons made between his 10-feet Standards A and B, and also between the 6-inch Brass Scales A and B; and in Lieutenant-Colonel Yolland's Account of the Measurement of the Lough Foyle Base we have the comparisons of the two Indian Standards B with the Ordnance Standards. Let * - = a foot of the Ordnance Standard O, ten feet. ºf 3y = 25 33 Odin, six inch. a' = a foot of the Indian Standard A ten feet. a’’ := 33 :3 B ten feet. 3y' = 3, " : * > * * A six inch. *- 3)” = 23 ° - * >5 * * I} six inch. * “An Account of the Measurement of Two Sections of the Méridional Arc of India, &c. &c. By Lieut.-Colonel JEverest, F.R.S., &c.”—London, 1847. - tº - 5 C 2 756 PRINCIPAL TRLANGULATION. At page [40] Appendix VI. of the Measurement of the Lough Foyle Baše we find the result of 60 comparisons between the Ordnance 6-inch Scale and the Indian 6-inch Scale B, giving # y – # y” = + -ooor 51 inch. And at page IoI of the same volume— Io w” – Io a = — oooo721 foot. # y – ?, a = - -ooooz22 , At pages 436 and 437 of the Account of the Indian Arc— Io w” – Ioa' = + -oooo.459 inch. # y” – # y' = — -ooo Ioo& , From these equations we have the following:— 3) — y” = + -oooo.252 foot. 3y - a = - -oooo.444. , Ay’ — y' = — -oooo.168 , a" — a = — -ooooo.72 I , a" — aſ a + -oooooog8 , a’ = z — -ooooo7.59 3y' = a – oooo.528o f *# / = z – ooooog74 Consequently, in order to reduce the Indian measures to feet of the Ordnance Standard, they have to be multiplied by I — o-ooooog74. The actual corrections will be as follows:— Col. Everest. Daumergida to Takal Khera . . . . . . IIoš550-6 , Kalianpur . . . . . . . . .2202926-2 35 Kaliana . . . . . . . . 4164083.3 Corr. — Io.8 – 21.5 – 40.6 Reduced to O, IIoš539.8 22O2904-7 4164042-7 In Numbers 334, 335 of the Astronomische Nachrichten will be found a discussion of the earlier zenith sector observations of this arc by Bessel. The latitudes he obtains, dependent upon assumed declinations, are— O f JPunnos . . . . . . . . 8 9 IPutchapolliam • • Io 59 Dodagoontah - . . . . . I2 59 Namthabad . . . . . . 15 5 Daumergida . . . . . . 18 Takal Khera . . . . . . 21 Ralianpur . . . . . . . 24 : w 3I. I32 42.276 52-165 53-562 I6-245 51,532 II .860 - - . FIGURE OF THE EARTH. 757 By eliminating the declinations of the stars, he obtains the following amplitudes:— O f/ Punnoc, Putchapolliam 2 50 Io-985 Putchapolliam, Dodagoontah . 2 o IO-530 Dodagoontah, Namthabad 2. o,788 Namthabad, Daumergida . . . 2 57 22.532 ,a Daumergida, Takal Khera . 3 2. 35'95o Takal Khera, Kalianpur 3 I 20-392 These amplitudes do not agree precisely with the differences of the previously determined latitudes. Of the two sets of results, however, the former hāve the greater weight, and are therefore entitled to the preference. , - ſº * The latitudes of Daumergida and Kalianpur have been redetermined by Colonel Everest in his later operations in India, together with that of the present northern terminus, Kaliana. At pages lxx and lxxi we find the amplitudes of Daumergida and Kalianpur = 6° 3' 55".97, and of Kalianpur and Kaliana = 5° 23' 37". O6. At page clxxiii the latitude of Kalianpur is given as 24° 7' II". 262. In consequence of the small uncertainty in the absolute distances south of Daumergida, we shall arrange the equations in such a manner that the two portions can be separated if necessary. This will be effected by making Daumergida the initial point, and measuring southwards and northwards from that point. Indian Arc. Stations. Latitudes. Amplitudes. Distances. P * * t § & M.J. o J/ 6. Feet. 8 Ul Illſloº . . . . 9 31 ° 132 - 9 53 44" Ibo - 35917.84° 3 Putchapolliam . . . Io 59 42: 276 | – 7 3 33° or 6 — 2562610-6 Dodagoontah . . ; I2 59 52 165 | – 5 3 23° 127 | – 1835.224".3 Namthabad. . . . I5 5 53° 562 — 2 57 21 '730 – 10734Io'9 Daumergida . . 18 3 15°292 || “................... . ............ O * O Takal Khera . . . 2.1 5 51 - 532 3 2 36' 240 IIoš539°8 | Kalianpur . . . . 24 7 11:262 6 3 55'970 22O2904*7 Kaliana. . . . . 29 30 48' 322 II 27 33 °oso || 4164042 °7 wº If a, be the correction to the latitude of Daumergida, the corrections to the other latitudes will be as follows:– : Punno - . . . . 4- o-402 – 3:5622 u – 3:1942 v – 4,2775 z + æ, Putchapolliam . . . – o 629 – 2:5413 u – 22256 v – 2.6704 z + æ, Dodagoontah . . . 4. 4.538 — 1.8198 u – I-564I v — 1.7017 z + r. Namthabad ' ' ' ' - 1.5oG – 1.0643 w – o 8943 v — 0.8574 z + r. Takal Khera ' ' ' ' -- 2:168 + 1-og58 u + o-8525 v + o-4451 z + æ, Kalianpur . . . . — 4.063 + 2.1831 u + 1.6212 v -- o'4285 2 + r. Kaliana . . . . . 4- o-365 + 4-1251 u + 2.7741 v – o'7213 z + æ, 758 PRINCIPAL TRIANGULATION. Of Colonel Lambton's first arc in Southern India the particulars will be found in the eighth volume of the Asiatic Researches. The data are as follows:— Indian Arc. tations. Latitudes. Amplitude. Distance. - o 4 ſh Feet. Trivandeporum . . II 44 52° 590 Paulree . . . . . 13 1949'ois 1 34 56'428 574327°9 If a, be the correction to the latitude of Trivandeporum, that to Paudree will be— ... . . . Paudree . . . . . . 4- or 197 + o-5697 u + o-5182 v + o-7329 2 + w; 6. - The account of the Prussian Arc by Bessel will be found in the work entitled Gradmessung in Ostpreussen, &c.—Berlin, 1838. The latitudes of the three Astronomical Stations are finally. deduced at page 419, and the distances of the parallels at page 448. - - Prussian Arc. Stations. . . Latitudes. ' || Amplitudes. Distances. → O M M & Toises. Trunz . . . . . . 54 13 1#466 Königsberg . . . . 54 42 50:500 o 29 39-034 28211-629 Memel . . . . . . 55 43 40-446 || 1 30 28'98o 86176.975 If a, be the correction to the observed latitude of Trunz, the corrections for the other points will be— Königsberg • . . . — o-671 + o- 1778 u — o-oš76 v — o-2804 z + æs Memel . . . . . -- 2.865 + 0.5432 u — o-1849 v – o'8312 z + æs The astronomical observations for the determination of the latitudes of the extreme points of the Peruvian arc have been recomputed by Delambre' (Base du Syst. Met., III. pages 112–133), and also by the Baron Von Zach (Mon Corresp., XXVI. page 52). The amplitudes assigned by these differ by o”.67; the mean value is 3°7'3”.455. The latitudes found by Delambre are— -- + - Tarqui a tº e º is a e 3. 4. 3#90 S. Cotchesqui O 2. 31'22. N. .- - *:*** *- FIGURE OF THE EARTH. 7.59 The difference of these differs by o”. 335 from the mean amplitude just stated: by adding o”. 168 to the latitude of Tarqui and o”. 167 to that of Cotchesqui, we get for the latitude of Tarqui 3° 4'32".o68, and for that of Cotchesqui o 2' 31". 387: these are the values used by Bessel. The mean of the two values of the distance of parallels assigned by Delambre and Von Zach is 176875.5 toises. The determinations in this arc cannot be considered as very accurate, which is much to be regretted, as the position of the measurement on the surface of the earth otherwise renders it most valuable. - The data for the Hanoverian and Danish arcs are taken from the Astronomische Nach- richten, Number 333. § Peruvian Arc. Stations. Latitudes. Amplitude. Distance. C & f/ Toises. Tarqui * * * * –3 4 32 offs Cotchesqui . . . o 2 31 387 s 7 3:455 176875' 5 If r, be the correction to the latitude of Tarqui, that of Cotchesqui will be— Cotchesqui . . . . . o.262 + 1.1223 u + 1.1258 v + 2.2388 z + r. JHanoverian Arc. * } Stations. Latitudes. Amplitude. “ Listance. © ºf f* Toises. Göttingen . . . . 5I 31 47 '85 Altona . . . . . . . 53 32 45° 27 2 o 57°42 II5163’ 725 If a, be the correction to the latitude of Göttingen, that of Altona will be— Altona . . . . -- 4:436 + o-7262 u – o 1885 v — 1.2524 z + æ, IDanish Arc. Stations. Latitudes. Amplitude. | Distance. o f iſ O f { / Toises. Lauenburg . . . 53 22 17°o46 Lysabbell . . . . 54 54 Io. 352 I 31 53° 306 87436-538 - If as be the correction to the latitude of Lauenburg, that of Lysabbell will be— Lysabbell . . . . . – I-310 + o-5512 u — o. 1726 v — o-884o 2 + æs 760 PRINCIPAL TRLANGULATION. § IV. Determination of u v 2, w, . . . . as, &c. By making the sums of the squares of the 66 corrections a minimum, the following equa- tions are arrived at— - - - * = + 64.389 + 34-oooo w, + 30.715o u – 12:4884 v - 45.5355 2 = +460-6524 +F, (w, w, ...) + 539-916o u – III-2099 v – 694,3329 2 – 172-7428 +T, (r, ar,...) – III-2099 u + 83. IoI6 v -- 229.4756 2. = —668.9672 +F,(r, x, ...) —694,3329 u +229:4756 v +1134,0821 2 O o = + 65.310 + 13-oooo r, + 54,4933 w - 16:1539 v - 81.00762 o = + 1.275 + 8-oooo r, — 1.5836 u – 2-6304 v - 9.3547 & o = + o- 197 + 2-oooo r, + o-5697 w -- o'5182 v 4 o'73292 o = + 2.194 + 3-oooo r, + o-7210 u – o 2425 v — 1.11162 o = + o-262 + 2-oooo as + 1, 1223 w -- I. 1258 v + 2.2388 z s o = + 4,436 + 2-oooo r, + o-7262 u — o.1885 v - I. 2524. 2. o = — I-31o + 2-oooo as + o-5512 u — or 1726 v — o-88.40 z O g O O In which the values of F, F, F, are— F = + 30.715oz. -- 544933 a. — 1.5836 r, + o-5697 r, + o-72 Io r, + I. 1223 as + o-7262 r, + o-5512 as F. = – 12:4884 a., - 16. 1539 a., - 2-6304 a., + o-5182 *. – o'24.25 as + I-1258 as — or 1885 a., - o- 1726 as F, = - 45.5355 w; - 81.0076 r, – 9.3547 w, + o-7329 r, – I-III6 as + 2.2388 as — I-2524 a., - o'884o as º - From the first eight 'equations obtain the eight quantities a in terms of u v 2; substitute these values in F, F, F, , and we have finally— o = + 126-9908 + 282-0495 u – 33-34oo v - 315.9814 z — 67.2347 – 33-34oo u + 56-7563 v -- Io'7.2795 z (w) o = — 171.6256 – 315.9814 u + io'7.2795 v -- 553.oroo z O which is the final equation for the determination of u v and 2. For convenience of future reference the details of the multiplications for the different arcs are contained in the following table:– f - {...} * * * 761 E EARTH, &+ * * IGURE OF TH T * * ooſo. £559994. 95S6#0. zgzS64z. Zo1 + | +1 96.919 – Į ooyº. 99– | 95 z9. I / I — | Zººz. 49 — || 8066.9zI + 306$. o6 VI o. o615 I. o£92o.o -+ | Zºz. o — | 54*o. o — | 064$.o + | o£ 1 ſ.o + | ¡ 198.0 - | * * * usțuvCI z†34. oZA I o. o4892. o1ği I. o + | 3+5+.. o — | 939o. o — | 3444. z — | 131 º. o — | 4949. I + | ~ uuſ Joaout H 1905. zZ$$9. o86z9. ozðgz. 1 + | $99 z. I + | 3ī£9. o + | $9.62.o + | SZYI. o + | 94 ºg -o + | ~ ~ uuſando I 949$. o64 Io.o#89 I. oooğo.o + | ºſºz. o — | ſzºo. o — | $ogº. 1 — | gº 19. o — | 4696. o + | ~ ~ ugļssnā） 5392. oziyº I. oºz91. o66ğ1. o ' + | Zgoz. o + | 94:VI. o + |zzZo. o + | II So. o + | 195o. O + | * * 'I ſuuſpuI Izz9.61 + | z38$. 32 + | 519 z.gf + |zzĚo.61 + | gšz9. zż + | 93 zz. 98 + | 961 o. 9 — | zz†6. 8 — | {{zz. II - | * * 'II ‘uuſpuI ſoºſ. 151 + | 39 I 5. oz-+ | z 261.Žor + | SZºo. Z† --+ | Šğ96. I z 1 — | ŠŽg8.5† - || 1996.56 — | #414.39 - | †465.33 + | ~ ~ uu!$$n?I foº.º. 349 + | 6598.9 + | 461$. Zzi + | $9.gſ. 69 + | 1ğgo. 91 z— | 1 ző4.†z- || 95õý.99 — | 3#5 1.61 — | 195z. 47 + | ~ oſlluſ)-Oſſºuw zOz8I•Y{0{IĶOV{IVĶOJŲ{II\[VIŲ*sory Œ Izſo. I 35$$$$.gzķ$998. 45 z1961. zz1 + | S 159.349– | 6698. ZA – į 91+9.46† - || 1905. So I –9199.99£ +· 496$. o6ýro, o čº | 61$ 1.0ºg/o.o + | 9€yz. o — | 94 #0. o — || o64$. o + | 1911.o + | 919$. o– || • • • qëĮudoſ ". Q| 3430.9tº || 489 z. ooğ11.o + | Ž#5$. o — | #890. o — | 3444. z — | 1917. o — | 4949. i + | ~ ſuuſtoa ouvÉI， 1905. z49.99.0 || 9679. ozõgz. I , + | 999 z. I + | 4ī£9, o + | 296 z. o + | SĀĻI. o + | 94 #1.0 + | ~ | ° uuțAntoài 61 I #7. o96 Io, o $ | $$Zī. og6ğo.o -+ | 179z. o — | $3$.o. o — | 6z 19. o — | 944 I. o — | $425. O + | ~ ~ ugļssniðI 9899, o į | $$$ 1.9 % | 9291. oš6ğ1.o + | 99óz. o + | 9.o + |zzZŐ.o + | oſ So. o + | {9$.o.o + | ~ º 'I ſituſpuſ 8386.91 _+ | 6ț98.0 + || 591$.o + | g9|Žo. £ + | ğřSg. I ） + | Zozş.o + | 606#. I — | z61*... o — | Vz52.9 || — | * * 'IŤ ‘uuſpuI | 9484-†95 + | oĘZ9.ęz+ | 9țzț. Șzz+ | ğogg.oo i + | č/gš.699– | 38 14.49– | 4696. goº- | (+5.1. 18 - || 9994. ºſz+ | ~ | ¡ ¿ ugļķiļºſ 4*86.09 + | 1485, † + | +4+4.Žz + | $5%ž.91 + | ogĚ1. rº — | 519«. 11— | sſz.gs — | #os9. ºž - || 6491.85 + | ~ | ¡¡II，0-giã ſv. –º–-*-| --??? .—{?——- “S3)）; z(o)z(q)z(p)(o) (q) ！(9) (p)(q) (p)(5) (ū)(Q) (uu)(ſo) (mu)y i zgo. #9 II || 91 or . $3o916.695954+.6zz + | 6zºº..#69– | 66oz. I 11—| zł96.999– | sz†4. z41 - | †z$9.99£ + 5 I 34. o36zo. Ogºoº..o9zŞ I. o + | €4.gſ. o — | 156o.o. –| 039 r. 1 + | 19zz. o +izzº.o- | * * * qsſuuq $895. I599 o. o†AzŞ. o199 z. o + | 5656. o — || 69$ 1. o —| 955$. 5 — | zgºg. o — || vſ z.z. º + | ~ uuſio Aout-H z z Io. 9†49z. I965z. I†óz$. z + | 9z 19. z + | $$9z. I +| 9999. o + | oŚ6ż.o + | oțóz. O + j * * uuſAnd@I | 5694. o54% o. o49zº.o3691. o -ſ- | † 105. o — | ZoÍ 1. o —| žĚŠI. z — | 116$. o — | 049 V. I + | ~ ~ ugļssnů） 1499. o589.z. o9ýz€.oğ67$. o + | S/ I w. o + | zº6z.o +| www.i. o + | Izo I. o + |zzy I. o + | * * 'I ſuuſpuI | 6996.6z + | 1 $5$.6z + | 5945. gº + | ögor. zz + | gogy. Vz + | 96#/. 99 +| zo 19. Z — | $199.6 - | $44#. I 1 _ — | * * ''I [‘uuſpuſ $4$ I. 99.9+ | 399$. off-ſ- | g195.599 + | 1ğ69. Zł 1 + | Šºž9. ogſ- | $1o1.ŠI I —| 9996. zoŞ– |\1 z^3.611 — | #89$. z99 + | * * * utſsºnſI 1519.6% W+ | 5$žy. I 1 + | IZgo. SS 1 + | gőrz. 99 + | 1 zzz.6Śz— | 69Zo. 99 – † 1ț9. z$1— | zŚoğ. z† — | oſzy. So I + | ~ oſituſ)-otºuw (zo)(eº)(rp)(0%)(oo)(qv)(ou)(qui)(ou)' *sory 762 PRINCIPAL TRIANGULATION. If we write P Q R for the three absolute terms of the equations (a), and then express w v z in terms of PQ R, the result is— a- o = u + or 25381 P - oog752I Q + ·oogoş59 R o = v – oog7521 P + 'o654,054 Q — or 24.405 R (w') o = 2 + oogo.559 P – or 24.405 Q + ·oog3960 R The weight of au + 3v + y2 is the reciprocal of + or 2538 &” + “og5405 3' + “oog296 y” – "oig BoA. 23 + or 8112 ay – “O24881 3) The numerical values of u v z are— w = — o-6937 v = + 1.4838 2 = + o-3739 Suppose that the correction to the latitude of the r" Station in the n” arc is represented ** by - [n rl + air u + bar v + c, z + r. When r designates the point taken as initial, this all vanishes except a...: in general, for the initial point r = 1, but in the Anglo-Gallic arc r = 7 (St. Agnes): in the Indian r = 5 (Daumergida). So that in general [n. I] = 0, but in the first and third arcs [1.7] = o and [3-5] = o. The following expression is the value of ou + 3v + y2 in terms of the observed latitudes:— -- Anglo-Gallic ............ * + (– : on 8796 a. + (– : or 2812 & •oj691o 8 — ‘og8431 y) [1-1] of 7731 8 'oz7992 y) [1-2] : + (– : or 2769 & + og7609 B — 'oz7922 y) [1°3]. + (– ’oo&691 & 'oz 5705 8 — ozog36 y) [1'4] + (+ °ool 564 & •ool 927 8 — "ooz451 y) [1-5] p + (+ ‘oo?767 a - 'ooz865 g + 'ooz636 y) [1°6] + (+ ooz78o c. – ’oo;153 8 + ooor 67 y) [1-7] + (+ ooz938 & — ‘oo5573 8 + ooo;27 y) [18] + (+ ‘oo3252 & — ‘oo64298 + °ool.282 y) [19] + (+ °oo;430 a. - 'oofig26 8 + °ool 735 y) [1’ 10] + (+’ ‘oo34.33 a – ’oogg31 8 + °ool 741 y) [1-11] + (+ °oo?437 c. – ’oof,944 8 + °ool 752 y) [1°12] + (+ °oo3453 & – ’oobg82 8 + 'ool 787 y) [1-13] + (+ °oo35or a – ’oo?I27 8 + °oorg23 y) [1°14] + (+ •oo3678 & — ‘oo7619 8 + ooz392 y) [1'15] + (+ °oo4044 & — ‘oo8682 8 + °oo?473 y) [1-16] + (+ ‘ooA272 a - 'oog394 8 + "ooq2857) [1-17] - * * * * + (+. ‘oo4367 a - “cog725.8 + "ooq/II.Y).[1-18]... . . . . . ... . FIGURE OF THE EARTH, JRussian ............ Indian, II. .......... tº º ſº º º Indian, I......... e e s be e s we Prussian................... Peruvian... • * * * * * * * * * * * * * > JHanoverian............... Danish.... tº ſº tº ſº º dº e º 'º º 'º º ſº e º is + (+ + (+ + (+ + (+ + (– . --- (+ + (– ... + (+ . --- (+ + (— . + (+ + (– + (– + (+ . -- (+ + (– Anglo-Gallic—(continued) *4 (+ ‘ooł369 & ‘oo45IO c. ‘OO4494 a. “oo43 I3 & “oo41 18 oz ‘oo3999 a •oo2681 a. 'oozóo.7 a. "ooz337 a. •ooo758 & *ooro51 & “ool 469 a. "ooz863 a. ‘oo7730 & “oo7952 a. “oo7990 a. ‘oo8244 & * OTI34o a “or 3954 a. * or 55 Io c. ‘oló832 a. ‘ol 6591 a. ‘ol 4793 a or 1436 C. •ooë93o c. °oo2527 & - "org239 & •og8823 & * OS5O42 & o42385 & “o24477 c. * or 3 Io9 & “oo2523 & •oog865 & “org 321 a. “O25307 & ‘o28ooo & ‘oo4363 C. ‘oo436.3 c. ooo446 & ‘oool 94 & ooofláo a or 1683 a or 1683 a. ‘oool 99 a. “oool 99 & “ooo.294 & ‘oooz94 a + : &rº sº. nº. 2- * : * * * * ** * * * * * * * **** ***** * **, *, *-*** **** . . vs - a. * * , " ºr * * , * * * *- : *w 3. *+ *** oog7388 •oro51o 8 ‘ološ85 8 ‘ološ44 5 'o Io938 8 'oro.89 8 •oo8181 B •oo8063 B •oo7618 8 . ‘oo4926 8 •oor 798 B •ooto17 8 “oo L453 8 •ororó88 ‘ološ69 8 ‘oloé4o 8 . “oo7353 8 'or 5603 B o22466 6 •o26581 g : 'o60395 8 ‘og II51 8. o28379 8 •o22568 8 * or 4536 8. oozá86 8 . •og2546 8 'o67578 3 •og6420 B . '629975 B o25630 8. 'oz 1297 8 'ois3548 ‘ooA836 8. ‘oog123 8 'oz5942 3 'o62127 8. •oor837 8. ‘oor&37 8. ooo;96 8. ‘ooo311 g : •ooogo7 8 •ooo;31 8. ooo;31 8 •ooog12 8 •ooog12 B ‘ooo244 8 ‘ooo244 8 ... sº, e -r-, *** * * * * * * * * : º º : : •oo4725 y) [. •ooôo69.)) [1 ‘ooô331 y) [1 ‘oofig53 y) [1 ‘oo7238 y) [1 ‘oo7341 y) [1 ‘oo7573 y) [1 •oo756o y) [1 •oo7508 y) [1 ‘oo6963 y) [1 ‘oo6054 y) [1 •oo;8oz 'y) [I'30] ‘oo4947 y) [1' 31] “ooI541 y) [1°32] ‘ool 374 y) [I'33] ‘ool 345 y) [1°34] ‘oo5131 y) [2 1] ‘ooo.429 y) [2.2] ‘oo5455 y) [2°3] •oo881o y) [2 ‘orz613 y) [2 or 5447 y) [2 or 5658 y) [2 'oï4187 y) [2 'or 1263 y) [2 ‘oo3929 y) Dz 'oro518 y) [2 'oz84447) [2 ‘o43699 y) [2 'oz4024 y) [3- or 1728 y) [3' ‘oo4322 y) [3' ‘coz Izo y) [3' •oo86897) [3. of 2189 y) [3' ‘oi2317 y) [3' ‘oo4757 y) [3' 'ooz799 y) [4. ‘doz799 y) [4 ‘oooz99 y) [5 ‘ooooo3 y) [5 ‘doo291 y) [5 ‘oo8597 y) [6 •oo8597 y) [6 •ooI423 y) [7 •oolá237) [7 •ooo.584 y) [8 •ooo.584 y) [8 • 19] ‘zo] “21] 22] • 23] ‘24] ’25]. •26] ’27] • 28] *29] '4] ‘5] '6] ‘7] •8] '9] • Iol • 11] • 12] 13] 1] 1] ’2] 1] ’2] •3] • 1] •2]. • 1] ’2] • 1] •2] 5 D 2 764 PRINCIPAL TRIANGULATION. By inspection of this formula we see at a glance the influence of each observed latitude upon the final result. The points which have the greatest influence are the extremities of the Indian arc, the south point of the Anglo-Gallic, and the north point of the Russian arc. An error of a second at Formentera would affect the major semiaxis by 69 feet, and the minor by only 11; an error at Saxavord of the same amount would affect the axes by smaller quantities, viz. 25 and 9 feet; at Fuglences an error of one second affects the semiaxis major by 170 feet, and the minor by 35; at Punno an error of a second affects the major semiaxis by 60 feet, and the minor by Io2; at Kaliana the same amount of error would affect the axes by 14 and Ioo feet respectively. The small arcs have very little influence at all. Corrections to the Latitudes. By substituting the values of u v and 2 which we have found in the expressions for the corrections to the different latitudes, we get the results given in the following table:– ... rv Stations. f Correction. [.. . . . . . Stations. Correction. Eormentera . . . -- #.276 Staro-Nekrassowka . — 2' 602 Montjouy . + 3' 855 || Wodolui . . . . + I 274 Barcelona. . . + o' 502 || Ssuprunkowzi º + 3 oo3 Carcassonne — 1 - 138 || ICremenetz tº — 1 728 Pantheon . . . — 3-482 Belin tº ſº tº + o- 703 Dunkirk . . — o' 612 | Nemesch . . . . — I 286 - Jacobstadt . . . + 3'o65 St. Agnes . - I 223 || Dorpat . . © — O'955 Goonhilly . — 2-886 || Hogland . { } — o' 233 Hensbarrow..... . — 1 321 || Kilpi-Maki nº – o '833 High Port Cliff — I '827 || Tornea. & + 3 °456 | Week Down . — I 549 || Studr-Oivi º — 2 369 Doniface Down — I '769 Fuglenocs . e — I 5oo Dunnose . . — 1 227 . . T}lack Down . + 2 ° 951 | Punnoc . . {º} — o' 513 Southampton . + 1 . 722 | Putchapolliam º — I 416 Greenwich + 1 270 | Dodagoontall . º + 3 '870 Precclly + o' 737 || Namthabad º - 2 "O2O Cambridge + o' 191 Daumcrgida . . — or 246 Arbury + 1 - 692 || Takal Khera . + 2 - 26o Delamere . – or 713 || Kalianpur . . . — 3' 578 Clifton — I 964 || ICaliana + 1 - 643 South Borule . . + I 488 Burleigh Moor . + o' 665 | Trivandeporium e — o' 148 Durham . . . — o' 935 | Paudree . . . . . + o' 148 Ben Lomond . — I 633 - IXellie Law. . . — o' 601 | Trunz . . . . – o' 583 Ben Heynish . . + 2 - 106 || Königsberg . — I 358 Great Stirling . — or 277 || Memel . . . . . + I '941 Monach : + o' 591 ||, … . Ben Hutig — I 158 Tarqui . . . . — o' 158 North Rona + o'403' | Cotchesqui . . . + o' 158 Balta. . . . . + 2 - 38o - Gerth of Scaw + 2 °233 || Göttingen . . . . . – 2 o60. Saxavord . . + o' 249 || Altona . º + 2 oôo - Lauenburg . . . . . +.6:809 Lysabbel . . . . — o'809 ſ : : FIGURE OF THE EARTH. 765 The sum of the squares of these 66.corrections is 208.486; consequently the probable error of a latitude is * 22., . . / 208.486 . … + 6743 &/# = + 1".313 This, however, is not to be taken as the probable error of an observed latitude, as some of the points in the English arc have received corrections for the apparent effects of the irregular distribution of attractive matter in their vicinity. The corrections to the actually observed latitudes at these points are as follows:— High Port Cliff . , 4 (463 | Dunnose . . . . . . – #767 Kallie Law . . . . 4. ‘A’9 Week Down . . . 4- or 431 Clifton . . . . – 2.864 || Monach . . . . . 4- 1.061 Boniface Down . . . .-- o'651 Burleigh . . . . – 3.885 Ben Hutig . . . . . . . — 3-168 The sum of the squares of these nine quantities is 42. 5173; and the sum of the squares of the corresponding quantities in the table is 16.7232. Hence the sum of the squares of the corrections to the 66 observed latitudes is 208.486 -- 42. 517 – 16.723, and the probable error of an observed latitude, in consequence, = + 6745 */*** = + I”.392 55 Values of the Aves, &c. Substituting the values of u v z in the expressions for a and b, we have— , a = 20927I97 b = 20855493 a : b = 291.86 : 290.86 With respect to the weights of the determinations— - a involves . . . . – 2092-5 u + 696.3 v + 278.5 z - - b involves . . . . – 2085-5 u – 696.3 v + 278.5 z a : b involves . . . . – 6 v + -3. v” + +–2 25 259 From these we easily find— • * * - . - * $ - - - Probable error of a = ′ = 2092.5 (oi260) I'313 = + 385 feet. * , b = + 2085.5 (co883) I.313 = + 257 feet. In estimating the probable error of the denominator (291.86) of the fraction representing the compression, we may neglect the small uncertainty due to the quantity 2, then— Probable error of 291.86 = + (6 * #v) (og543) 1313 = +...+39 766 PRINCIPAL TRIANGULATION. The quantity &r by which the curve is more protuberant than an ellipse of the same axes is— * - * * * ** –twº ºra, w ºr = (1775 + 70.9) sin” 2 x This last quantity is remarkably well determined, and shows decisively that the figure of the earth does not differ sensibly from the eract elliptic form. . s - For the radius of curvature of the meridian, and the length of an arc. of amplitude b, WC have— - - ...” g = 208.91449 – Io/557 cos 2 x + 1562 cos 4A - - # s = 208.91449 4 – Io'7557 sin. © cos 2 x + 781 sin 2 + cos 4 × . The meridional quadrant = (364624.58 + 5.36) x 90 = 32816212 + 482 feet; conse- quently the métre = 39-3794544 +...oOo.5784 inches. . . . . . . . . . . . . . " * • ? " * , ºn Y. -: * * - * - - t - - - r º * - * - • , - * - r - - * * * - ſº f - - - - - - - - - , Determination of the Ellipse most nearly representing the Observations. The curve g = A + 2 B cos 2 x + 2 C cos 4 x becomes an ellipse if 6 A C – 5 B = of that is, if neglecting the square of v, * — -º- * - - 2 E - - - - 96 T 386 * * * *-- *. … s. If we substitute this value of 2 in the expressions for the corrections to the latitudes of the different points, they become, on the elliptic hypothesis, as follows:— Tormentera ........ tº º ſº tº º E tº dº ſº º + 2: 378 – 4°oºrs w – o' I 175 v -- ar, Montjouy..................... + 4*794 – 3:6704 u + o-d;45 v 4 x, * Barcelona ..................... + I'44o – 3 'o644 u , -- o'o653 v -- a, Carcassonne ............ tº tº º 'º tº dº – o' 252 – 2 °4040 u + o' 1202 v -- ar, Pantheon ......... … — 2-374 - o:3767 u + o' os-S7 v + æ, Dunkirk ..................... + of 767. -- of 4115 tº — o'oZ65 v -- 2, St. Agnes ...... … o? O " C * + acr Goonhilly......... & © tº º ſº tº º ..... — I'644 + o-oš54 w – o'oog4 v. H. a. . . . . . Hensbarrow .................. — o'og5 + o- 1768 w — o'ojoš v + æ, High Pört Cliff=............ – o'512 : +3 of 2532 u : - o'o.45o v -- a. Week Down.................. – o' 233 + o-2539 u - oroá52 v -- e. Boniface Down!..............”— of 453 - + o-2559 tº – o'o455 v -- a. Dunnose ........ ............. + o-ogi + o-2613 u — o'o.166 v + r. ... . . . . Blackdown. ....................+, 4:279. H. o'.2859 u — o'o;13 v -- a-, ... . . . . . . . . Southampton................... + 3:083, 4 o'3676 u , — o'o674 v + æ, f Tº Greenwich ".................. + 2*718 + 'o'5707 u — or rior v. + r. . . . r ... Precelly ..........…......:” --,2:262 +...o:7393 u — o' 1486 v. 4. r. º. *Cambridge .................. + 1 .764 + o-'8360 w – o' 1719 v + æ, ; i;- --;: !;; : . . |* : . * * . ; : .: FIGURE OF THE EARTH. 767 — o' 1727 v. — or 2670 v — o' 291 I v — o' 3654 v – o'4137 v — o' 4369 v — of 618 r v — or 6258 v — o' 6543 v — or 8oo3 v – of 9391 v – o '9708 v — I'o652 v – 1:3555 v — I’3677 v — I 3699 v `... O – or oz25 v . — or oS24 v – or 1556 v - o' 2998 v — o' 5657 v — o'8036 v tºmº 1:0857 v — I 3767 v T– 1:8698 v – 2:5821 v — 3'30.or v – 3' 84.18 v — 3’ 1853 v - 2 ° 22 OO 27 — I 5606 v — o'8925 v o: * + o:8516 v + I 6203 v + 2:7756 v O " . + or 5167 v O ş . . — o'os 70 v — o' 1832 v o: + i. 1211 v o' — o' 1859 v O" - o' 1708 v Arbury ........................ + 3:267 + o-8396 u Pelamere...................... + . I of 5 + 1 1986 w Clifton......................... — o' 147 -- 1:2835 u South Berule * * g º e º 'º g tº tº º is tº º & + 3 ° 459 -- I'5325 u Burleigh Moor............... + 2 736 -- I -6845 w Durham........................ + r. 184 + 1-7553 u Ben Lomond..........“..... + o'868 + 2.2673 u Rellie Law ............ ...... + I '917 -- 2: 2882 u Ben Heynish.................. + 4*684 + 2 - 3628 w Great Stirling ............ ... + 2 - 614 + 2*7258 tº Monach ........................ + 3 + 785 + 3 'o.47 I w Ben Hutig.......... tº G & © tº tº º G & º º + 2* Io; + 3 II 73 w North Rona ................. + 3 '874 + 3° 3225 w Balta...... tº º 0 & 0 ºr tº ſº º ſº º is º º ºs e º tº e º 'º + 6' 501 + 3’9095 w Gerth of Scaw............... + 6' 382 + 3'933o w Saxavord .............. ....... + 4'403 + 3 ° 9370 ºt Staro-Nekrassowka ......... O " . O * Wodolui ..................... + 3-946 + o-'6086 u SSuprunkowzi • * * * * * * * * * * * * * * + 5°813 + I 2306 w Kremenetz................... ... + 1 ° 226 + 1 : 7148 w Belin ..................... Q & © tº º º + 3’ 951 + 2* 4163 vº Nemesch ..................... + 2* 510 + 3° 3546 w Jacobstadt................... ... + 7° 363 + 4 ozog w Dorpat ......... * * * * * * * * * * * * * * * + 3'953 + 4*6969 it Hogland...................... ... + 5°32'o " + -5° 3 II.4 u. Rilpi Maki .................. + 5'846 -- 6°2290 w Tornea .................. ...... + II '826 + 7.3799 2& "Stuor Oivi..................... + 7.769 + 8:4072 w" Fuglenoes ..................... + Io'oo8 + 9°12'31"w Punnae .................. Q tº ºn tº º gº + o' 625 – 3’5622 w - Putchapolliam ............... — o' 490 – 2 °5413 w Dodagoontah........ dº º º º G & © tº º º + 4-627 —..I '8198 u Namthabad .................. — I 461 — I'o643 w Daumergida ..... e e º e º e º 'º º º see O o' Takal Khera.................. + 2* I45 +. I ‘og58 w Ralianpur............. ſº tº º tº º ſº tº º ºn – 4 o'S5 + 2 - 1831 w Kaliana ........................ + o' 403 + 4*1251 tº Trivandeporum.......... tº º & º º O - O" - Paudree........................ + or 159 + or 5697 tº . Trunz .......................... O " ... - O " . Königsberg.............. ..... — or 656 + o' 1778 u Memel ........................ + 2 '908 + o'5432 tº Tarqui ............ tº tº º e º e º 'º º e º g O" O* - Cotchesqui .................."+ o: 145 + 1 : 1223 u Göttingen ...........“........ o. o' + Altona ....................... + 4'501 + o-'7262 u Lauenburg .................. O" O * . . Lysabbel ..... ................ - I’264- -- 'o' 5512 u + i ſ 3CI 302 302 768 PRINCIPAL TRIANGULATION. The following table contains the results of the multiplications for the different arcs in order to render the sum of the squares of these corrections a minimum :— Arcs. (ma) (mb) (a”) (a) (52) | Anglo-Gallic + 118'9207 - 45° 3653 +155.067 – 35 °5339 + 11 1906 Russian . +386'3623 — 126:4488 335' 5318 || – 1 12" I421 39° 9745 Indian, II. . — 12 7516 – Io'4936 46' 5750 + 36'6984 29' 3612 Indian, I. + o'ogoó + o 'o622 o' 3246 + o' 2944 o: 2670 IPrussian . . . . . + I 4630 - o'4953 o' 3267 — o' 1096 o: o368 Peruvian . . + o- 1627 + o- 1626 I 2596 + I 2582 1 ° 2569 Hanoverian . + 3 2686 — o'8367 o° 5274 — 'o' 1350 o og46 Danish . . — or 6967 + o' 21.59 o' 3038 — o' og41 o'oz'92 +496'8196 || -183° 1790 | +5.39°916o –Io9'7637 + 82 - 1508 Arcs. — (m) (a) — (m) (9) (a): — (a)(b) — (b): § i. & t * t Anglo-Gallic — 60' 3098 + 24. 3352 – 27.7474 + 11 1962 — 4' 5177 Russian . . . . . -29 I 45 II + 85*4950 –228'4246 + 67'oofió — 19 6559 Indian, II. . . + o' 3492 -H o' 5757 – o' 3135 — o' 51.68 — or 852 I Indian, I. i. – o 'o453 — o' oA.II — ... o' 1623 – o 1472 – o' 1335 Prussian . – o' 54.12 + o' 18o3 – o 1733 + o' os-77 — o' or 92 Peruvian i. * — or oSI4. — o' oº 13 — 'o' 6298 — o' b291 — o' 6284 | Hanoverian . . . – 1 6343 + o'4183 – or 2637 + o-oG75 — o' or 73 Danish . . . . + o' 3483 — o' Io'79 – o' 1519 + o' o471 — o' or 46 –353° 3656 +IIo'7742 —257.8665 + 77'o62o — 25'8387 Arcs. MA. MB A. AB B2 Anglo-Gallic + 58-6109 – 21 of or + 127°31.97 – 24°3377 + 6’ 6729 Russian . + 94 '91 I2 – 4o '9538 Io'7' Io'72 - 45° I 355 20'3186 Indian, II. . - I2 °4024 – 9: 91.79 46’2615 + 36' 1816 28' 5091 Indian, I. + o' o453 + o' o4II o' 1623 || + , o' 1472 o “I335 Prussian + o' 92.18 – o' 31.5o o' I 534. – o' of 19 o' or 76 Peruvian + o'o613 + o'o613 o' 6298 + o' 6291 o' 6285 Hanoverian + I 6343 – o' 41.84 o' 2637 — o'o675 o' or 73 Danish . – or 3484 || + o- 1080 o’ I 519 — or oqºzo o “ol.46 + I43°454o — 72'4048 +282 o495. – 32°6817 + 56' 3121 Trom this it appea following:— * rs that the final equation for the determination of u and v is the O O = + 143.4540 + 282-0495 u – 32.6817 v = – 72.4048 – 32.6817 u + 56.3121 v If we write PQ for the absolute terms of this equation, it becomes by transformation— o = u + -oo.38or I P + ,oo22060 Q .... o = w -- 'ooz206o P + zorgog85 Q FIGURE OF THE EARTH. 769 * Whence it follows that the weight of the determination of au + 8v is the reciprocal of •oo38or &” + “oo4412 aft + or 9038 6° * The actual values of u and v are— 7& E — o-3856 v = + I of 20 We may, as in the preceding Section, obtain an expression for the value of cºw + 8v in terms of the observations. Adopting the same notation, the value will be as follows:– Anglo-Gallic”-- (+ or 8251 & -- ‘oof 206 B) [1, 1] Russian... * + (+ or 3221 c. – "oiá1638) [2-1] + (+ ‘oiá180 & -- ooo789 £) [1-2] + (+ ‘olog57 c. – "oi 5077 3) [2.2] + (+ or 4156 a + ' ooo76o 8) [1' 31 + (+ ‘oo8725 & – or 5309 8) [2.3] + (+ or 1502 a - “ool.932 B) [1-4] + (+ ‘oo7045 a - 'oïq995 8) [2.4] + (+ ‘oo3939 & — ‘oo5 1768) ſt's] + (+ ‘ooq698 & — or 37868) [2.5] -- (+ °ool 234 & — ‘oo4398 3) [1.6] + (+ °ool 718 & — ‘oio/93 3) [2.6] + (+ oozó30 c. – ‘oo4947 8) [I'7] + (– : oooz90 & – ’oo/734 3) [2-7] + (+ 'ooz440 & — "ooq890 8) [1-8] + (– 'ooz237 a - ‘oo3854 8) [2.8] + (+ 'oozozó 2 – “ooA751 3) [19] + (– : oo3931 a -- 'ooo;3o 3) [2.9] + (+ ‘ool 767 a - "ooq649 6) [1-10] + (– ‘ooff&31 a + 'ooz694 3) [2.10) + (+ °oor 764 & — ‘oo4647 8) [1-11] + (– : oog135 a + 'oï8716 8) [2.11] + (+ °ool 757 a - ‘oo4645 B) [1-12] + (– : or 1456 a + 'ogo119 8) [2-12] + (+ ‘oo1739 & – "ooq636 8) [1' 13] + (– : on 2982 a + 'o;8853 B) [2-13] + (+ ‘ooi656 a – ’oo!6or 3) [1-14] | Indian, II, * + (+ 'orgog; a + 'o61851 g) [3-1] + (+ ool 381 c, - ‘oo4475 B) [1'15] + (+ 'or 3085 * + oA:1221 B) [3.2] + (+ ooo703 & — ‘oo411o 3) [1' 16] + (+ ‘oo8888 a + 'oz7076 g) [3-3] + (+ oool 47 c. – ’oo3749 8) [1' 17] + (+ oo4542 a + 'oï 2690 3) [3-4] + (– : ooor 69 a - ‘oo3519 8) [1-18] + (– 'ooiá72 a - ‘ooô65o 8) [3-5] + (– : oool 81 a - ‘ooš511 B) [1' 19] + (– ’oo7516 a – 'oz 5281 3) [3-6] + (– ’ool 337 & – 'ooz 508 B) [1-20) + (– : or 3345 x – o42314 3) [37] + (– •ooléoy a - 'ooz2368) [12] + (– : o33275 a - 'o68593 B) [3-8] + (– : ooz389 & — ‘ool 371 B) [1'22] Indian, I...* + (+ °ool 653 & 4- ‘oo;547 8) [4 II + (— 'ooz861 & – ’ooo787 3) [1°23] + (- ‘ool 653 & – ’oo;547 8) [4.2] + (– :oo3079 a - 'ooo;or 3) [124] | Prussian... " + (+ ooo737 a - ‘ooog94 3) [3-1] + (– : oO1625 a + 'ool 819 8) [1°25] + (+ oool 87 c. – ’ooo.301 B) [5.2] + (– ’oo-1687 a + 'ool 920 8) [1'26] . + (– : ooog24 a + 'ool.295 8) [5'3] + (– :oo.1908 a + 'ooz298 B) [1-27] Peruvian...* + (+ ‘oo3370 a + 'oï 1910 B) [6-1] + (– ’ooš966 a + 'ooA276 8) [1-28] + (– : cos370 & — or 1910 8) [6'2] + (– : oof 881 a + 'oof,210 3) [1'29] IIanoverian" + (+ ‘ool 175 & – ooogó9 8) [7. II + (– ’oo7078 a + ‘ooğ659 8) [1:30] + (– ’ool 175 & + ooog69 8) [72] + (– ’oo?65o c. + •oo8oo3 3) [131] Danish ... * + (+ ooo359 & — ooloi & 3) [3-1] + (– : oog24o a + 'of 2235 B) [1'32] + (– : ooo359 & + ‘ool or 88) [8'2] + (– : oog 303 & 4- or 2416 8) [I'33] + (– ’oog 313 a + 'or 2449 B) [1-34] 5 E 770 PRINCIPAL TRLANGULATION. a latitude Corrections to the Latitudes. Stations. Corrections. Stations. Corrections. Formentera + 2 - 584 | Staro-Nekrassowka . — 4. 426 Montjouy . + 4'808 || Wodolui . * * + 1 - 261 Barcelona . + 1 .452 | SSuprunkowzi º ... + 2 - 825 Carcassonne — o°425 || Kremenetz lº — 2 oz.6 I’antheon . . — 3° 398 || Belin . . . & + or 275 Dunkirk — o' 7on I Nemesch . * > — I '81 I Jacobstadt * + 2 °533 St. Agnes . . — I 228 || Dorpat. . . ; : - I 437 Goonhilly . — 2 903 || Hogland . . — o' 616 Hensbarrow . – I 364 || Kilpi Maki Ç – o '968 High Port Cliff — I '885 || Tornea . tº + 3 '812 Week Down — 1 - 607 || Stuor Oivi tº ſº - I '404 Boniface Down — I '828 Fuglences . . . . — o' or 6 Dunnose tº — I 287 Blackdown * . + 2 - 886 | Punnoc ſº – I 334 Southampton . * + I 642 | Putchapolliam. ſº — I '818 Greenwich * + I I53 || Dodagoontah . ſº + 3’ 72 I Precelly tº + o' 591 || Namthabad º – I 949 Cambridge ſº + o- og I Daumergida tº -- o' offo Arbury tº + 1 - 532 || Takal Khcra . rº + 2 - 677 Delamero . : ; — o' 919 || Kalianpur . iº — 3 * 156 Clifton. tº i. – 2 - 179 IXaliana † + I 8 Io South Borule . º + I 252 Iłurleigh Moor tº + o'419 Trivandeporum — o' 244. . Durham t — I 185 || Paudree . . + o' 244. Ben Lomond . ſº — I '891 Rollie Law 4. — o'858 || Trunz. — o' 573 Ben Heynish . . . -- I '850 || Königsberg — I 358 | Great Stirling . . — o' 515 || Memel . . . + I '931 Monach . . . . -- o' 385 Ben Hutig. . . . . — I 356 || Tarqui . . . — o' 451 North Rona . tº ſº. + o' 234 || Cotchesqui + o' 4.5I Balta. . . . . . -i- 2'326 - Gerth of Scaw . . . . -- 2 - 185 Göttingen. º - 2 * O I2 Saxavord . tº º + o' 202 || Altona. . . . + 2* or 2 Lauenburg + o' 829 Lysabbel . — o'829 If in the expressions for the corrections to the latitudes we substitute the numerical values of u and v just obtained, we get the following system of corrections:— The sum of the squares of these 66 corrections is 219. 360, and hence the probable error of 2IQ-26o A/ = + 6745A/# = + 1":335 This is not, however, the probable error of an observed latitude,-for this reason, that some of the points in the English arc have already received a correction for local attraction. The corrections to the observed latitudes of these points will be— High Port Cliff' . Week Down Boniface Down -- #405 + o-373 + O. 592. Dunnose . . Clifton Burleigh Moor . &/ — 1.827 • – 3•o'79 • - 4. I31 ICellie Law . Monach . Ben Hutig f/ + I-222 | % ;t 3. FIGURE OF THE EARTH. 771 The sum of the squares of these corrections is 45.90I ; that of the corresponding quan- tities in the preceding table is 18.780, so that the sum of the squares of the corrections to the observed latitudes is 219. 360 + 45.901 – 18.780 = 246.481, and the probable error of an observed latitude becomes— + 6745 # = + 1".415 This quantity is somewhat larger than that obtained in the non-elliptic figure, but the difference is immaterial. - * * * If we would obtain the probable error of the observed latitude of any point taken at random, it must be remembered that in the preceding calculation two Stations have been omitted on account of the large amount of deflection at those points; namely, Cowhythe and Evaux. The expressions for the corrections of the latitudes of these two points are— Cowhythe – 6.91.5 + 2.8048 u — o'834o v + æ, Evaux – 7:045 – 1.3378 u + o-1360 v + c, Substituting in these expressions the values of u v and r, , they become— Cowlythe – 16 rio i. 4. Evaux • — 7.613 of which the sum of the squares is 160. 170. We may therefore take as the probable error of an observed latitude—. . . . . •48 3. + 6745 V. *:::: sº #78 = + 1".786 This quantity is affected to a small extent with errors in the different geodetical operations: the influence of these, however, is certainly very small; but their effect is obviously to render this quantity too large as the representative of local attraction. We shall not probably be far from the truth in taking + 1".75 as the probable effect of local attraction upon an observed latitude. -- Determination of the Aves, &c. By means of the values of w and v, and the relation 6 A C – 5 B’ = o, we get for the radius of curvature of the meridian the following expression— º - º g = 20896805 — loé673 cos 2 x + 227 cos 4X And for the length of a meridian arc whose amplitude is p and mean latitude = x, * s = 208908o3 * – io9673 cos 2 x sin q + 113.5 cos 4x sin 24 For the axes a and b we find— - a = 20.926.348 b = 20855233 a b = 294.26 : 293.26 772 PRINCIPAL TRIANGULATION. To find the probable errors of these determinations, we remark that— a involves – 2093:1 u + 696.3 v b involves – 2086.1 w – 696.3 v a + b involves – 6 v + 3 vſ. l * a - b 25 The probable error of au + 8v we have seen to be— * I'335 (ooºol &” + “oo4412 & 3 + or 9038 g) which, by making the proper substitutions, gives— a = 20.9263.48 + 186 b = 20.855233 + 239 #: # } = 293-76 + 1.06 The mean degree of the meridian is 20890805 into the arc of one degree: it involves 36.46 w; hence, Mean degree = 3646-3-33 + 3-oo feet. from which it would follow that the length of the imaginary mêtre = 39.378240 + ooo.324 inches. * § VI. Evamination of the preceding Results. We have now obtained results for the Figure of the Earth on two different hypotheses: in the first, the curve has been left altogether indeterminate as to the constants A, B, C ; in the second, a relation has been assumed between the three constants such that the curve must be an ellipse. In the first hypothesis, the mean value of a correction to an observed latitude is + 2". oG4; in the second, the mean value is + 2"...og8. On examination of the corrections in the two tables, it appears that the English arc and the Indian arc are equally well represented on either hypothesis; the Russian arc is rather better represented by the elliptic corrections; but the French arc, especially towards its southern extremity, is not so well satisfied by the elliptic as by the non-elliptic curve. On the first hypothesis, the sum of the squares of the corrections to the six latitudes in the French arc is 3o. 513; on the second, it is 44. 1207. This difference is, due almost entirely to the station Montjouy, at which there is apparently a northerly deflection exceeding in amount the mean quantity. Upon the whole, the number of Stations in the southern part of this arc is too small to bear much weight against the elliptic hypothesis, g d * :: i: : : i ſ FIGURE OF THE EARTH. 773 The following table shows the differences of the two systems of values, and from it will be seen how small is the difference of the two figures, as far as represented by observed latitudes:— Stations. c—c' Stations. c—c' Formentera + 1 "308 || Staro-Nekrassowka . + & 176 Montjouy . + o' 953 || Wodolui . . . — o' or 3 Barcelona . . + o' 95o | Ssuprunkowzi . — o' 183 Carcassonne + o' 713 || ICremenetz – o '298 Pantheon . + or oS4. Belin . — o'428 Dunkirk — o'o69 || Nemesch . – or 525 Jacobstadt – o' 532 St. Agnes . – o 'oos | Dorpat . — o' 482 Goonhilly . . — o' or 7 || Hogland , — o' 383 Hensbarrow . — o'o.43 || Kilpi Maki — o' I35 High Port Cliff *— o 'os 8 || Tornea + o' 356 Week Down . — o' os3 Stuor-Oivi + o' 965 Boniface Down – o 'oj9 Fuglenoes . + I 484. Dunnose .. – o 'o6o º Blackdown – o 'o65 | Punnoc . . . . — o' 821 Southampton . - or oSo | Putchapolliam . . — o' 402 Greenwich – o' I 17 | Dodagoontah . – o' I49 Precelly — o' I46 || Namthabad . + o-o/1 Cambridge – o' I60 || Daumergida . . . + o' 296 Arbury i. — o' 160 l Takal Khera . . . + o'417 Delamere . . . — o' 206 || Kalianpur. & © + o' 422 Clifton. • — o' 215 Kaliana + o' 167 South Berule . — o' 236 # Burleigh Moor – o' 246. Trivandeporum — o'og6 Durham — o' 25o Paudree . + o- og6 Ben Lomond . . — o' 258 Rellie Law . -— o' 257 | Trunz . . + o' oro Ben Heynish . º — or 256 Königsberg O * OOO Great Stirling * — o' 238 || Memel. - O “O LO Monach . I — o' 206 Ben Hutig . — o' 198 || Tarqui — o'293 North Rona — o' 169 || Cotchesqui + o' 293 Iłalta . – o 'o';4 Gerth of Scaw . — o' o48 Göttingen. + o' o48 Saxavord . . . – o 'oa/ | Altona. — o'o.18 Lauenburg + o' ozo Lysabbel . - O "O2O In the non-elliptic curve the axes, mean degree, and compression are larger than the corre- sponding quantities in the elliptic, as may be seen by the following table:— Quantities. | Elliptic. Non-Elliptic. Diff. (! 209263.48 + 186 20927.197 ± 385 849 b 20855233 + 239 20855493 + 257 26o b Degree 364613°33 + 3' oo 364624-57 E 5'36 II:24 : 774 PRINCIPAL TRIANGULATION. The quantities in the elliptic curve are all much more accurately determined, for it is more easy to determine a curve of two parameters than one of three. By combining these axes as if they were independent results, we should obtain— a = 209.26509 ~ * b = 208553.54 , a + b . . . . . . . . ; =7 = 293.60 All these linear results are in terms of O, , and depending upon the assumed value of the toise, and also assuming the toise to be identical in the different Continental measures. These assumptions must be to a certain extent erroneous; and therefore let us suppose that to reduce them all to the Ordnance Standard, the distances in the different arcs require the multipliers, - - * - 6 French º ſº º tº º ſº * º • . " I I - + IOOOOO wº. Russian tº * : ſº * ſº º º {} * ſº I' + r v 2. • , - . IOOOOO Indian, South i • * * * * I •+ . 3 * “, S. in Portion "TC3:36 * * - • - .6) - Indian, First Arc . . . . . . . 1 +...+== * - IOOOOO º t ſº º & tº º º º {º} º I’ * - Iº e Prussian º + º Peruvian . . . . . . . . . I + 66 IOOOOO * - - - 6 - Hanoverian O tº tº º º • * e - s I + 7 * * * r - IOOOOO Danish . . . . . . . . . . I + 8 - IOOOOO The consequent increments to the different absolute terms of the expressions for the corrections to the latitudes will be as follows, omitting the multiplier p. page 737, which differs from unity by a very small quantity:— French. Tºussian. Indian, II. Indian, I. Drussian. Reruvian. Hanoverian. Danish. – 404 6, + 061 0, – 355 6, + oš7 6, + ox86, + 112 0 | + -o/30, + oš56, — .307 6. + 1236, – 233 6, + -oj4 6, - – 306 6, + 172 6, – 181 6. w . . . " * * * — .240 6, + .242 6, — . Io9 6, – 'o686, + .336 6, º + .o.4I 6, + .402 6, ` + 470 6, + .532 6, + 624 6, - + •739 6, - - | + 842 6, | + 914 6, - - - * *** * * * * * * * * * * * : *** *- : *w- - ºr . . … . . . * * * * * * * *** * * * ** * : ** + 4 = * * * * * * * * ::-s | . FIGURE OF THE EARTH. 775 The consequent increment of au + 8w is easily determined by means of the expression for that quantity previously given; it is found to be— + (-oiègi, a -ooºo, 3) 0, 4. (– 630806 a + 'o624165) 6. + (- oiaiso a - ogºg, 3) 0, 4 (– ooooº, a -ooogió 6) 0, + (-ooooº; a + 'ooooº; 6) 0, 4 (– coosz, a -oo:3346) 0. + (– es. occeſ 6) * + (— occeſ, + occo;6 3) 0, If in this expression we make z = – 2093, 3 = + 696, we shall obtain the increment to a ; and similarly, putting & = – 2086, 3 = — 696, the increment to b will result: their values are— - - da = + 37.856, + Io?.92 0, - I-40 6, - o-o2 6, + o-I4 6, - o-I4 6, + o-23 6, + o-I4 6s db = + 41.20 6, + 20,826, + 52.30 6, +, o.42 6, + o-o5 6, + 1.71 % + o-I3 6, + o-oé 6s We may get rid of O, as the unit of reference altogether, in the following manner: Let the distances we have adopted in the different arcs require the following multipliers to reduce them to one standard unit:— tº - - 6 A IEn lish º º º º t º tº º º º I O g -- IOOOOO French tº º tº † º * * wº tº tº I + - - IOOOOO + * * 6.7 Russian . . . . . . . . . . I + i IOOOOO &c. &c. &c. -- º - - 6,” * * Danish . . . . . . . . . . I + 8 . . IOOOOO Comparing these multipliers with the former system— W (1 + #:) (; + H+) = 1 + H+. IOOOO Iooooo/ T 1 OOOOO 6, = 6,' – 6.’ The value of a and 5 will receive the increments 209. 26 0.’ and 208,556."; wherefore— a = 209263.48 + 64.54 6.’ + 37.856,' + 107.92 6,’ — 1.40 6, -o-o:26,' - + o-140, - or 1464 + o-23 6, + o-146;ſ b = 20855233 + 91-86 6.’ + 41.20 6,’ + 20.826,' + 52.30 6,' + o-42 6,' - -- O-O 5 6,' + I-71 6.’ + O'I3 6,’ + o-off 6s' - # a + b a — b = 293-76 + 1139 & 4 or 446. – 3589 8, 4. 2222 6' 4 oors 6, – “ooo.4 6,' -H •oo76 63' — •oooA 9,' – ‘ooo? 6,' 776 PRINCIPAL TRLANGULATION. From these expressions we see at a glance the relative influence of the different units of measure, and also how small is the influence of the smaller arcs in the final results. Colonel Lambton’s arc from Punnoc to Daumergida, about which there is some doubt as to the unit of measure, has unfortunately considerable influence in the determination of the ellipticity, and also of the minor axis. - If we combine Colonel Everest's arc from Daumergida to Kaliana with the English arc from St. Agnes to Saxavord, we get for w and v this equation— o = + 51.0759 + 56.2645 u – 9-8335 v o = – 20-1055 – 9-8335 u + 9-7506 v w = — o'6645 : v = + 1.39.18 Weight of au + 3v = (ozić c.” + “O435 & 3 + . I245 g)" Trom which we obtain the value of the mean degree = 364623.5o + 7. I5 and a b = 292.39 : 291 - 39; probable error + 2.67. * By combining the same Indian arc with the Russian arc, the relations for determining w and v aré— -- o = + 92.8511 + 116.3957 u – 38-9285 v o = — 42.6IIo – 38-9285 u + 24.4891 v w = — o'4607 : v = + 1-oo76 Weight of au + 3v = (oiás a. + oş83 aft + -o872 g)" From which we obtain the value of the mean degree = 364616- oz + 6.59 and a b = 294-58 : 293-58; probable error + 2.27. The three arcs combined give the following equation :- o = + 145.9871 + 163-3818 u – 54,9690 v o = – 61.0593 - 54.9690 u + 30-odg2 v w = — o'5464 : v = + 1.0317 Weight of &?! ..+ 8v = (or;9 cz” +-off.8I &6 + ob64. g)" I From which we obtain the value of the mean degree = 364619. 19 + 6. I4 and a b = 294,44; 293.44; probable error # 2.26. Until the exact latitudes of the thirteen Stations in the Russian arc are known, we cannot state the precise elements best representing all geodetical operations. They cannot, however, be far from the following:—” Mean degree of meridian . . . . . . 36.4616 feet of Ord. Standard. Tatio of semiaxes . . . . . . . . ' ' ' 293 : 294. With respect to the Indian arc, an examination of the corrections to the observed latitudes, either those at page 764 or those at page 770, will show that there is no indication whatever of any disturbance from the Himalayan masses. If there had been a larger number of astro- i #*k*. .* *# FIGURE OF THE EARTH. 777 nomical points in this arc—an observed latitude at each degree, for instance—they would have added very greatly to the weight of the determination of the earth's figure, and would, besides, have thrown much light upon the question of Himalayan influence. As it is, the points are so few and far between that the hypothesis of Archdeacon Pratt (at page Ioo Phil. Trans. 1855) as to the non-appearance of any disturbing effect of the Himalayan masses has little weight. It may, however, be improved in the following manner: Making use of the points Daumergida, Kalianpur, and Kaliana only, we may determine for any assigned system of latitudes an ellipse which will make the latitudes accord exactly with the measured distances. Let x, x, x, be the latitudes of these points as corrected to the mean ellipse, so that the observed latitudes are— - - -- " * ºn - - - - g — I’’.81 At - o”.o.5 , X, + 3”. I6 , X, Now by means of the two equations in u and v connecting the corrections to these three latitudes (page 767), it is easy to show by transformation that ^* + š, ; \a -- e, , As + š, will give these values— w = - 0.3856 + 1.8500 e, – 4:4446 s, + 2.5946 e, v = + I'o620 – 3. Io98 s, + 6-6056 s, – 3:4958 sy From this it appears that (making s, = — o”.o5; s, - + 3", 16; s, = – 1".81) ex- tremely erroneous values will result from the use of the observed latitudes ; more erroneous, indeed, than if (making s, = + 6”. 9; s, = 1.2”. o ; s, - 27".8) we adopt the corrections for attraction assigned by Archdeacon Pratt. Let us therefore ascertain that ellipse whose deviation from the known figure of the earth (w = — o. 3856, v = + 1 . offzo) shall be a minimum, while it exhibits errors in the observed latitudes the sum of the squares of the differences of which from the computed deflections shall be also a minimum ; that is, determine s, such as to render the quantity - (, iº 6.9) + (, tººk 126) -- (, mº 27.8) -- c. ( 1.8500 s, - 4.4446 , + 2.5946 ..) ſ: . E I 2 2. + ºx (— 3. Io98 s, + 6,6056 s, – 3:4958 º) a minimum. The quantity o is arbitrary; by increasing it our ellipse will approach the mean ellipse, but the quantities s, s, s, will increase their differences from the computed deflections, and vice versä. * By making a = I we get— 3 5, - 5.8o ; ea = 16. II ; , = 24.79 w = — o:3856 + 3,448 = 3.062 v = + 1-off 20 + 1.718 = 2.78o ; F 778 PRINCIPAL TRIANGULATION. If we make a = 5 we get, s, = 8.04 ; s, - 16 or ; s, = 22.65; and, w = — o'3856 + 2.483 = 2.097 v = + 1-off 20 - 1.573 = 2.635 Neither of these values of u and v differ very egregiously from the mean values. The corresponding corrections to the observed latitudes are as follows:— & E I Cº - 5 a = 2.0920328 a = 20922.247 a : b = 284.7 : 283.7 a : b = 285.5 : 284.5 Aff f/ Daumergida .......... + 5.85 || Daumergida . . . . . . . . . . + 8-og I(alianpur . . . . . . . . . . . . + 12.95 || Kalianpur ......... • ... + 12.85 I(aliana . . . . . . tº dº ſº º tº º + 26.60 || Kaliana . . . . . . . .• . . . . . . . + 24. 46 The first of these sets of corrections is remarkably near to the computed results of attrac- tion, while the curve differs very little from the mean figure of the earth; in fact, the value of a differs only 574 feet from the value adopted by Colonel Everest for the basis of the Indian Atlas. It would make the arc more convex, raising the middle parts by fifty feet. There are, however, no grounds for the supposition of an irregularity of the earth extending over such a surface; and if we take into consideration the station Takal Khera, it becomes the more improbable, as the latitude of that point will differ altogether from what it should become on the supposition of Himalayan influence. - The hypothesis of an irregularity in the form of the Indian arc is merely the supposition of the existence of another disturbing force whose action is opposed to that of the mountains. Having in itself no à priori probability, and being unsupported by evidence, we must have recourse to the hypothesis of the Astronomer Royal for the most probable explanation of this phenomenon. It must be admitted, however, that the value of this measure is considerably diminished since the investigations of Archdeacon Pratt, contained in the Philosophical Trans- actions for 1855. - * The account of the Arc at the Cape of Good Hope is not yet sufficiently advanced to make it available in the determination of the Figure of the Earth. If the approximate data given at page 42 of the Professional Papers of the Corps of Royal Engineers (Vol. I.) be at all near the truth, the disturbances in this arc are extremely large : so much so that the measure would appear to be of little use, unless the number of observed latitudes has been considerably increased. l .. : i - k:x * i GEOGRAPHICAL POSITIONS OF WARIOUS L I. G. H. T H O U S I. S ON TIIE COAST OF GREAT BRITAIN AND IRELAND. 4 * * * * * * * * * # * * * * 780 PRINCIPAL TRLANGULATION. Lighthouse. Latitude. Longitude W. Lighthouse. . Latitude. Ilongitude W. • P C) J ** C f Jº O f #1 O J WJ Aberdeen . . . . . 57 8 32 ° 9 2 4 5 - 6 | Flatholm . . . . . 51 22 30.6 3 7 2-8 Aberystwith . . . . 52 24 48° 9 4 5 24'2 | Fleetwood, New . . . 53 55 34'7 3 O 22 °3 Agnes (Saint) . . . 49 53 3o'8 6 20 40' 6 || Fleetwood, Old . . . 53 55 42. I 3 O 27 ° 9 Air (mouth of Dee) . . 53 2 I 24' I 3 19 I5' 3 || Formby . . . . . 53 32, 19° 3 3 3 55' 6 Annan River . . . 54 57 58' 5 3 I5 53° 5 || Happisburgh, Lower . 52 49 5’2 E. I 32 56°o Arran (Galway Bay) . 53 7 38°3 9 42 6’ 3 || IIappisburgh, Upper . 52 49 12 2 E. I 32 19:6 Avon . . . . . . . 5 I 3o 2 '4 2 42 I5' I | Hartlepool • . . . 54 4 I 47 'O 1 Io 26.7 Ayr (Firth of Clyde) . 55 28 8.7 4 38 II “o | Harwich . . . . . 51 56 38-3 E. I. 17 25' I Ayre Point (Isle of Man) 54 24 56' 3 4 22 I I | Holyhead . . . . 53 18 50' 3 4 37 7' 6 Dailey, S. E. Point of 2 I Aio '8 6 . . . Hook Tower . . . . 52 7 24°3 6 55 42 '9 IIowth Peninsula } 53 40 3 5'3 | Howth . . . . . 53 23 35' 2 6 3 56-8 Bardsey . . . . . 52 44 58-7 4 47 55°o Hoylake . . . . . 53 23 3o' 3 Io 52 '8 IBarnaby Moor . . . 54 33 24' 3 1 7 14-6 || Hunstanton . . . . 52 56 57°2 E. o 29 43°2 Barra Head . . . . 56 47 8-2 7 39 9°5 || Hurst, East . . . . 5o 42 26-4 I 32 56°7 Beachy Head. . . . 5o 44; 15 o E. o 12 57.8 || Hurst, West . . . . 5o 42 20:6 I 33 3 ° 9 Beeves . . . . . 52 38 59° 7 9 I 18°4 || Ila Rhins . . . . 55 4o 23° 3 6 3o 44°o Bell Rock . . . . 56 26 4-2 || 2 23 6-9 |Inchkeith . . . . 56 2 o'8 3 4°9 I3erwick . . . . . 55 45 53° 3 I 58 57°4 || Inisgort . . . . . . 53 49 35'4 9 4o I2 °5 I}idstone . . . . . 53 24 2-4 3 4. 22.8 || Inistraliul . . . . 55 25 56' 6 7 I3 37 ° 4 Black Itock (Liverpool) 53 26 38-7 3 2 27°6 | Isle of May . . . . 56 II 8' 5 2 33 2 I 5 Black Rock (Sligo Bay) || 54 18 26.8 8 37 I o | Isle of Glass . . . . . 57 51 25' 9 6 38 27 ° 4 I}ran Sands . . . . . 54 37 41' 3 I 8 17' 5 Rilcradan . . . . . . . 52 34 46'8 9 42 34” I Braunton Sands, Lower 51 4 16.9 4 12 19: I | IGillingholm, High . . 53 38 48' 8 o 13 I '7 I}raunton Sandsor]Bide- I 8 ..., | Rillingholm, Low . . . 53 38 46' 5 o I2 52 2 ford tº ...} 5 I. 4 I 3 4. I2 5' 3 Ringstown (East Pier). || 53 18 7" I 6 7 30.8 Buchanness . . . . . . 57 28 14' 5 1 46 22 °o || ICinsale, Old Head . . . || 51 36 44-9 8 3 I 59' 6 Budden Ness, Higher . 56 28 7. 9 2 44 53°6 || Kirkcudbright . . . 54 45 56°4. 4. 5 I 2 Budden Ness, Lower . 56 28 I 5 2 44 37°o | Leasowe . . . . . 53 24 46-4 3 7 28. I Burnliam or 13ridgewater | 5 I I4 54'3 2 59 52 I | Lee Scar . . . . . 54 51 46 o 3 24. 4.3 °2 Caldy . . . . . 51 37 52 ' I 4 4o 59° 5 || Lismore . . . . . . 56 27 20° 7 5 36 22 °6 Calf of Man, Upper . . 54 3 13. 9 4 49 37°o | Lizard, Fast . . . . . 49 57 34' 5 5 I2 4°o Cantyre . . . . . 55 18 37.6 5 48 8' o | Tizard, West . . . . 49 57 34' I 5 I2 7° 3 Cape Clear . . . . 51 26 2-3 9 29 2 7 || Llanddwyn Point . . 53 8 5' 7 4 24 5I '8 Cape Wrath . . . . 58 37 33 - 1 4 59 52' 3 || Longstone . . . . 55 38 37' 5 I 36 33’ I Cardiff, East . . . 51 27 46 o 3 9 45°4 || Loophead . . . 52 33 38°2 9 55 54° 7 Cardiff, West . . . 51 27 46 o 3 9 47°4 || Lowestoft . . . . 52 29 II 6 E. I 45 27°6 Carlingford . . . . 54 I I I 2 6 4 4o 7 Lundy . . . . . 51 Io o' I 4 4o 20°2 Clare Island . . . . 53 49 38' I 9 58 58' 3 || Maiden Rock, N. . . 54 55 47 7 5 44. I?’ 4. Copeland. • . . 54 4 I 45 °o 5 31 20° 7 || Maiden IRock, S. . . 54 55 41 '8 5 43 5o" 2 Coquet . . . . . 55 2 o I '8 I 32 17-4 || Maryport . . . . 54 43 o' 3 3 3o 2 I ‘2 Corsewall . . . . 55 o 25'4 5 9 29°8 || Metal Man . . . . 54 18 13° 3 8 34 30°3 Cromer . . . . . 52 55 27:4 | E. I 19 5’ 6 || Mull of Galloway . . 54 38 5' 5 4, 5 I 2 I ‘9 Crosby . . . . . 53 30.49° 9 3 3 45° 2 || Mumbles . . . . . 51 33 58° 9 3 58 II '7 Cumbrac, New . . . 55 43 16.2 4 57 56°8 || Mutton Island . . . 53 I5 I4'o 9 3 Io'7 Cumbrae, Old . . . 55 43 I5'4 4 57 24' 3 || Nash Point, East . . 51 24 I 3 3 33 3 °3 Dungeness . . . . 5o 54 46' 6 E. o 58 18' 2 | Nash Point, West . . 51 24 2'4. 3 33 IQ “o Dunnet Head . . 58 4o 18.6 3 22 29° 5 || Needles . . . . . 5o 39 40' I I 34 31 °6 Eagle Island” ſº 54. 16 59' 9 || Io 5 32' 3 || North Foreland . . . . 51 22 27°6 E. I. 26 48’4 IEddystone . . . . 5o Io 49°4. 4 15 53'4 || North Wall (Dublin) . 53 20 47° 3 6 I3 33'5 Fannet . . . . . . 55 16 34° 3 7 37 52°4 || Orfordness, N. . . . 52 5 35' 6 E. I 35 12" 4 Farn Island, N. W. . . 55 36 59' 5 I 39 zoº 7 || Orfordness, S. . . . 52 5 o' 2 | E. 1 34 33°7 Farn Island, S. W. . 55 36 55-2 I 39 15°o | Paull . . . . . . 53 43 7-2 o I3 57° 7 Flamborough, New . . 54 6 58. I o 4 51 “4 | Peel . . . . . . . . . 54 12 45° 5 4 42 32 ° 9 | Flamborough, Old, º I6'2 Pentland Skerries, Lower 58 41 25: 1 2 55 23 ‘I Telegraph Tower 54. 7 4°o O 5 Pentland Skerries, Upper | 58 41 26°o 2 55 23°4. : In the “List of Lighthouses” published by the Admiralty, the latitude of this point is erroneously printed 54 7' o”, . * {. *:wiº :;f---*.:º: . iſº POSITIONS OF LIGHTHOUSES. 78r - Lighthouse. Iatitude. Longitude W. Lighthouse. Latitude. Longitude W. C f f/ O f f f O J MM C) f J/ Pladda . . . . . . . . 55 25 36' 5 5 7 I 7 || St. Catherine, Old . 5o 35 29° 7 I 18 5'9 Plymouth Breakwater . 5o 20 2.2 4 9 27-3 || St. John's Point. 54. I3 34" 2 5 39 30°2 Poolbeg. ... . . ...... 53 20 30° 7 || 6 9 1 4 || Stack (South) 53 18 23°4 || 4 41 54°5 Portland, North Bill 5o 31 17: 9 2 27 17: 9 || Staples, East. 55 38 2:8 I 37 26°o Rhins of Ila . . . • 55 4o 23° 3 6 3o 44°o | Staples, West 55 37 I 3 I 39 I4 ° 9 Roche's Point (Qº) I * 8 • 6 Start Point (Devon) 5o 13 18:4 3 38 28-2 town) . . . . . . ] 5' 47 33°4 I5 I4. Start Point (Orkney) 59 16 41 ° 6 2 22 30°o Ronaldshay, North . . 59 23 5-2 2 22 Io. 2 | Stornoway º 58 II 29° 9 6 22 9°7 Seaham . . . . 54 5o 19°8 I 19 33 - 5 Sumburgh ſº 59 51 16-8 I 16 22:7 Seaton . . 54 4o 7 ° 9 I 12 14- 1 || Sunderland, No. 1 54. 55 5 °4. I 21 36'7 Shields, North 55 o 3 I ‘o 1 26 10-3 || Sunderland, No. 2 . 54 55 7" 5 I 21 3o I Skelligs, Great . 51 46 5'8 Io 32 28' 8 || Sunderland, No. 3 . . 54 55 2 5 I 2 I 31 ° 2 Skerries . i. 53 25 IS ‘4. 4 36 25'8 || Swansea . . . . . . 51 36 54°9 3 55 44' 6 Skerryvore . 56 19 23° 9 7 6 45° 2 | Tarbert . . . 52 35 30 I 9 2 I 47° I Skinburness . . . 54 52 46' 6 3 22 46. I | Tarbetness . . . 57 5 I 55 ° 2 3 46 30°7 Slyne Head, N. . . . 53 23 59' 4 || Io 14 1-4 || Toward . . • . . 55 5 I 43° 7 4 58 42 '8 Slyne IIead, S. . 53 23 55° 5 || Io 13 58-9 | Trevose Head . . . 5o 32 55’2 5 2 2. ' Smalls . . . 5 I 43 I4°o 5 4o 8*6 | Troon . . . . . 55 34 37' 5 4 41 38°6 South Foreland . 5I 8 23° 3 | E. I. 22 22 I | Tuscar . . . . . 52 I2 9°3 6 I2 21:9 South Rock . 54 23 56' 5 5 25 4.' I | Tynemouth . . . 55 I 5 °o I 24 52 °3 Southampton Pier 5o 53 41 ° 7 1 24 22 7 || Usk . † : 5 I 32 24' 5 2 59 33 °3 Southerness . . . 54 52. 2 I 9 3 35 37°4 || Valentia . . . 5I 56 o' I | Io 19 15' I Southsea Castle . 5o 46 38-9 1 5 I4° 5 || Walney Island • 54 2 54° 5 3 Io 33° 3 Spurn Head, High . . 53 34 41'4 . o 7 10-8 | Whitehaven, Pier Head 54 33 9.7 3 35 5o" 2 Spurn Head, Low 53 34 39°8 . o 7 16" 7 || Wicklow, Lower . . . 52 57 54' 5 5 59 58°6 St. Agnes . . 49 53 3o'8 6 20 40" 6 || Wicklow, Upper . . 52 57 54°o 6 o 5 °4. St. Ann's, Lower 51 4o 50°8 5 Io 21 5 || Winterton . tº 52 42 45° 2 |E. I 41 49'9 St. Ann's, Upper 5 I 4o 55° I 5 10 28.2 Wyre River . i. 53 57 I2 °5 3 I 46°3 St. Becs . . . . 54 30 48' 3 3 38 8 1 || Ynys Gadarn . 53 23 I 3 '4 4. I 5 II ‘6 St. Catherine, New . 5o 34 30' 3 I 17 47' I - The positions of these points were calculated with the following approximate data— a = 20923713 , a b = 299-33 : 298.33 Latitude of Greenwich tº º ſº tº ſº tº 51°28'38".30 In order to correct these results, if necessary: Let x o be the latitude and longitude calcu- lated as above, and x' a' the values that would have resulted from the following data (see page 712)— a = 20927005 , a b = 280.4 : 279.4 Latitude of Greenwich . . . . . . 51°28' 40". I6 The corrections x' – A, and a '— w, are given in the following tables:— * 782 PRINCIPAL TRIANGULATION," * VALUEs of x'-x, Longitude. Lat. # Lat. 3 | | | | | | | | | | | 3 | f | 3 || 5 | is 45|+4.3, 4's 448. 448, 4486 |49el 449; tº 44% tº is +3* |45 56 +2'45 +2'46 +2'47 +2'49 || +2'52 | +2'56 +2' 60 +2-66 +2.72 +2.79 +2-87 50 51 | +2'o6 || +2 of +2 o8 +2' Io +2 - 13 +2' 17 | +2'22 +2 27 2 °34 || 4-2 °4I | +2 °49 || 5 I 52 |+1 '63 | + 1 '64 +1-65 + 1.67 + 1.70 | +1 '74 || + 1 '79 + 1 '84 + 1 '91 +1-98 +2-66 52 53 | + I 16 +1:17 +1 18 + 1 20 | +1-23 +1-27 | + 1 32 + 1 37 + I '44 | + I 5 I + I 59 53 54 +o'65 +9:65 +o'67 +o:69 +o 72 | +o. 76 +o '81 +o '86 +o '93 || -- I ‘oo + I o8 54 55 | + o' To +o Io +o II +o. 13 +o 17 | +o 21 +o 25 | +o 31 +o 38 +o '45 --O '54 55 56 |-o' 5o —o'49 —o-48 || –o 46 —o: 43 —o' 39 —o'34 —o-28 || –o 2 I | –o 14 | –o'os 56 57 |—I 13 | – I 12 — I II | –I og | – I'o6 —I '92 || –o '97 —o'91 —o'84 || –o'77 || –o 68 57 58 || – I '8o —I '8o —I '78 || –1 .76 —I '73 –1-69 | –1 '64 — I 58 —I '51 — I'43"| – I 35 | 58 59 |–2'51 —2'50 -2°49 || -2°47 —2:44 —2' 39 —2'34 —2'29 || –2-22 || –2 14 —2°os 59 60 |–3°26 –3'25 –3'24 || -3°21 | –3. 18 —3: 14 | –3:99 || –3’93 || –2-96 || –2.88 –2.89 5o 61 |—4:08 || –4’og —4'oz -4°oo —3.97 –3'92 | –3'87 —3-81 | –3.74 || -3-66 | –3'58 61 VALUES OF o' — w. Longitude. Lat. Lat. O O © s Q. & O C O O O O O O I 2. 3 4. 5 6 7 8 9 IO O ſº J/ J/ ** WM Al Af JJ f/ tº JJ - f/ O 49 o°oo —o’97 — I '95 —z '92 || – 3 '89 —4'87 -5'83 —6'8o – 7'77 | – 8-73 – 9: 70 49 5o o' oo -o '99 || – I '98 || – I '98 || –3'97 —4: 96 – 5'95 || —6: 93 — 7'92 || – 8 91 – 9'89 50 5I o' oo | – I or –2 oz —3 oA. —4'os —5'o6 —6 of —7'o'8 — 8: o3 — 9’ og | – Io' Io 51 52 o'oo | – I o4 —2 of —3. Io —4: 14 —5' 17 —6' 2.0 —7' 23 – 8' 26 || – 9 29 — Io' 31 || 52 53 o°oo — I'o6 –2 12 || –3' 17 —4: 23 —5°28 —6'34 || –7'39 – 8°45 – 9°50 | – Io' 55 || 53 54 o°oo — I o8 —2' 17 | –3'25 —4’33 —5'4I –6°49 —8°57 | – 8*65 || – 9 '72 — Io'79 54 55 o'oo — I II —2'22 || – 3:33 —4:44 —5' 54 —6'65 —7.75 — 8-86 – 9°96 — II of 55 56 o' oo — I 14 | –2 - 28 —3°41 —4' 55 —5' 68 || –6'82 —7'95 || – 9: o3 — Io. 21 — II 34 56 57 o' oo — I 17 | —2° 34 —3 - 50 —4' 67 || –5'84 || –7°oo || –8° 16 || – 9° 33 — Io'49 – 11 64 57 58 o' oo —I 20 —2-40 | –3' 60 —4'8o —6°oo —7' 20 —8' 39 || – 9°59 –Io'78 — II '97 58 59 o°oo — I 24 —2'47 —3'71 —4°94 | –6' 17 —7°41 —8-64 – 9'87 | – II - og – 12 '32 59 6o o' oo –1 27 | –2 55 —3'82 —5’ og —6'36 —7-63 —8'99 || – Io' 17 | – II '43 | – 12°69 || 60 | 61 o°oo — I 31 —2'63 —3'94 | —5' 25 -6'56 –7-87 –9° 18 — Io'49 — II '79 || – 13 Io 61 FINIS. *} { *:tº .:º * ERRATA AND CORRECTIONS. *-- Page 42, line 7 from bottom, for “Plato I.” read “ the Frontispiece. . 60 9 top, , “Ben Hulig" , “Den Hutig.” 9° , º, *, *, bottom, insert reading of R. O. ..... 183° 23'30"oo II 7, Ref. Obj. at Happisburg, for I45 28 59' 61 read I45 27 59' 61 165 at Stede Hill, 33 Io.; I2 I '93 23 284 I2 I '93 I98, line 3 from bottom, 33 1836 35 1846 199 × 4 × 33 33 — 2”. 31 93 — 2"-24 229 × 6 , top, 33 As 33 A* 3 247 × 2 × 3? 33 (#) 33 (#) 2 2 bottom 3. sin # (2 + 3 − 2) sin # (2' + & — «) 47 33 33 9 3. SIIl # (2' + % + a) 33 sin # (2' + & + a) 248 } sin # (2' - 2) sin # (2' — a) 4 33 4. 33 3 33 COS # (c.' + a) 33 sin ; (2' + a) cos º (k - 6) cos (k - 6) 249 2 5 2, 2? - 33 COS # (k tºmº 0) 33 - COS # (k + 6) 25I 2, 12 2, 35 3) & 33 { 264 × 2 ×, » . 33 (33) 33 (35). 266 , 12 , 33 33 ºr 2 ºr ; + 33 24 x 4); f 268 33 I2 33 35 33 # tº 33 # 27o 32 4. 33 39 33 289 32 259 396 » II , top, 35 GCB’ 33 GC/B/ 432, in A 16.... 33 “Inockaskagh" 23. “Knocknaskagh.” 435, in A 18. . . . 33 + 1 '85 35 —I '85 440, in A 4o. . . . 33 422782 '84. 33 42278-28 445, in A 9. . . . 33 158109.76 33 158109-67 488, in A I. . . . 35 5' oooo.226o 33 5' ooof,2460 558, Height of Boniface Down, , 483 - 9 33 783 - 9 559 . . . Inock, 3? II.49° 2 33 1416'9 619, line 9 from bottom, , { I — e” sin #(\!' + A1)} , {1 – c' sin” # (A,' + x.) p 624 » 4 » top, , - k 6 cos & sin (a' tºmº a) 33 — h 9 cos & sin (2' - 2) 693 ), 2 ... bottom, 33 — o' 1486 v 33 + o'og69 v 7-? 2: 715 x 12 × top, 33 –7 33 --- # 2 2 3, 2, 14 2. 3? 33 – #, a + ..., J} - #, a + .... 2, 3, 17 × 3, 33 + 3 'o 35 H: I'5 Page 198. The latitudes given at page 198 as resulting from observations made with Ramsden's Zenith Sector are affected with small errors: the correct results will be found at page 672. Page 270. The last figures, i.e., tenth decimals, in the small table page 270, are not exact. Page 507. In the calculation of the distances of parallels between Clifton and Easington at the bottom of page 507, the errors of the observed azimuths, which were used, have produced an error of about — 2 feet; and in the next calculation, page 508, of the distance of the parallels of Easington and Burleigh Moor, a similar error, amounting to about + I foot, is produced; hence the distance of parallels of Dunnose and Burleigh Moor, as given at page 508, is about a foot too small in consequence of the errors with which the azimuths employed are affected. See page 685. Page 558. The (recently) levelled height of Cowhythe is 254'4 feet, L ON ID ON : Printed by GEongE I2. EYRE and WILLIAM Spottiswoope, I?rinters to the Queen's most Excellent Majesty. Tor Her Majesty's Stationery Office. THE UNIVERSITY OF MICHIGAN GRADUATE LIBRARY DATE DUE #: º * - f º hº s > .# * * *çº +4 ;" …tº errº; “ſºft* º 3. § d - w |.º. 4 Głº * * § - * • - **-**** y 3. * * : , , , t :*:::::ſº: # r | w º: } #4. ſº - - - -*. • *, * * ***** ..? ... * , * * * - *-* ~ * ~ *- * | f | i { ; ( ....HNIVERSITYQEMCH || III. | \ 39015079998 / G fºx. * -- ~ *- y: