^cf\/e c ./r ; cf cs» DETROIT OBSERVATORY, ANN ARBOR, MICHIGAN, I)ETERMINK1> BV / THE ZENITH TELESCOPE AND DISCUSSED BY THE METHOD OF LEAST SQUARES. \ 4 ( LATITUDE l‘.Y LUDO VIC ESTES, Ph. D., UNIVERSITY OF MICHIGAN. ANN AlinOK. MICH.; THE KEGl.STEK I'RINTINO AND UUBLISHINO CO. 1888 . ERRATA. Page 8. For AL read AA. Page 42. In third normal equation, for —15.580 read +15.580. TABLE OF CONTENTS. Description of Instrument. . . . . ^ Value of One Revolution of Micrometer-Screw, Value of One Division of Zenith-Level, Star-Places, ....... Observations for Latitude, and Reductions, Discussion of Results, ..... Probable Values of R, D, (j>, . ('orrection of Computed Values of Latitude, Probable Error of Single Observation, Latitude according to Temperature and Zenith-Distance, PAGK 1 8 11 12 19 40 48 49 58 54 rs— r DESCRIPTION OF THE INSTRUMENT. These observations were made with a transit instrument con¬ structed by Fauth & Co., Washington. Settings were made by a graduated circle on the axis, reading to 10". A zenith-level is attached to this circle. It can be clamped to any point on the limb. The available length of this level is about 3.5 in., or 44 of its own divisions. These are numbered each way from the middle. The tube has an air-chamber in one end. The slow- motion screw, for moving the telescope on its axis, bears against a spiral spring. In cold weather this spring often failed to respond promptly to a motion of the screw. The object-glass has an available diameter of 3 in., and its focal length is 3 ft. 10 in. Its cell is screwed into the tube of the telescope, and it has no adjusting-pins. Two eye-pieces were used : a diagonal, erecting eye-piece, magnifying to 79 diameters; and a straight, inverting eye-piece, magnifying to 67 diameters. The latter was used almost invariably in observ¬ ing low stars, and in a few other cases. The instrument is reversed by two arms which, by means of a lever, lift it out of its wyes. The frame on which it rests stands on a brick pier rising about 3.5 ft. above the ground, and extending two or three feet below it. The whole is inclosed in a small wooden building. The micrometer-box can be revolved about the axis of the telescope through an angle of 90°. It bears on one side—when it is in its proper position—against an adjustable pin. The micrometer-wire is parallel to the transit-wires. A positive motion of the screw-head brings the wire apparently nearer the screw-head for both eye-pieces, The rule was always to make the last motion of the screw positive. The whole number of 2 DESCRIPTION OF THE INSTRUMENT. revolutions of the screw was read from a notched scale in the focus, its middle point being numbered 25. The breadth of the field-of-view is about 30'. The eye-piece nan be moved by a rack and pinion across the field. The rela¬ tive positions of the clamp and the screw-head of the microme¬ ter are thus: Direction of Star from Zenith. Position of Clamp. Position of Scriw s. w. Up. N. w. Down. S. E. N. E. Up. The axis of the instrument required adjustment for horizon- tality only once or twice during the series of observations. This was secured by a striding-level. Errors of collimation and azimuth were kept within inappre¬ ciable limits by observations on a distant terrestrial object. However, during October 11-21 the latter adjustment was in error from the fact that in making observation 12, after revers¬ ing, the axis was let down by mistake outside the wyes, so that it was afterwards found to have pushed one of tlie supporting- posts out of place. Yet, as observations for azimuth were made during this period on stars, the observations for latitude were retained and corrected for this error of azimuth, which 'was found to be about 25s. High winds often interfered with the accuracy of the obser¬ vations, by blowing out the lights. For this reason, notes of the fact have been made. The centre of the dome of the Detroit Observatory is 75.3 ft. further north than the center of the pier on which the instru¬ ment employed in these observations rests. VALUE OF ONE REVOLUTION OF THE MICROMETER- SCREW. The value which was used in the separate computations of the latitude was determined by two methods: First, by measuiung the difference of declination of two known stars, this difference not being greater than the field of view. The micrometer-wire was set on each in succession without moving the instrument. Second, by observing transits of stars. All the stars used in the first method were taken from the Berliner Jahrbuch. The symbols in the table of reductions denote as follows: J<5 = difference of declination obtained by means of computed apparent places. J-l/ = difference of zenith-distance, as measured by microm- eter. JL = correction to JF due to change in the level during the observation. J/? = correction to J-k due to differential refraction. Jr = correction to JT due to hour-angle of star. This cor- rection is insensible to the third decimal place in every instance but one. = am -h AL + \p + A", R = Id / a:. Let m, m' be the micrometer readings for the two stars, “ V “ inclinations of the level “ “ “ “ 7 -' — r “ difference of refraction “ “ “ “ X, X “ reductions to meridian “ “ “ all quantities being expressed in terms of R. Then, (3) 4 REVOLUTION OF THE MICROMETER-SCREW. micrometer readings increasing upwards, ^ = (m'—m) ± (Z'—Z) + (r'—r)± — ir)for | ^' | stars; micrometer readings increasing downwards, -(r—C) = (m'— m)±{l' —Z)—(/— r)±{x' —^c)for | | stars. In the annexed table d u placed after a micrometer-reading 1 1 , , 1 T- • ( downwards ) denotes that the readings increase | ^p^r^^ds To each value of R thus obtained was assigned the weight, sV ^ V X no. of times observed. In the second method the determination rests principally on transits of Polaris. The distance of the star from the meridian at each observation was computed by the formula i where I = observed interval in seconds of time, d = star’s declination, / sin 15" k = —-, sin / i = required equatorial interval: / cos d k The values were then combined, two and two, for intervals of a given number of revolutions, and the mean of all divided by the number of revolutions in the given interval. The different observations of Polaris were combined by giving to each value of JR, thus obtained, the weight sV rn, where r = no. of revolutions in the interval taken, n = no. of such intervals. The values of R found from transits of other stars were com¬ puted by the formula i = I cos <5. These values were combined by giving each star the weight i^ssrn, where s depends on the declination of the star and r and n denote as above. The mean value of R in each case was then compared with the particular value from which it was derived; and by giving REVOLUTION OF THE MICROMETER-SCREW. 5 . the squares of the residuals the same weights that were used in finding the mean, the probable error, r% of each of the three mean values of R was determined. These values were then com- bined by giving to each a weight proportional to -; where Vr„ n denotes the number of observations of weight unity used in determining one of the values. Value of One Reoolution of the MiGTometer-^erew, Determined hy Meamred Dijferences of Zenith-Distance. o 00 00 !>3 tr- o 8 w5 to LO 8 00 T—{ tH o O o lO LQ lO LO lO Tfl o -I-:) O 0) lO CD 00 CD 03 ■V_r 03 CO o CD 00 D5 Cl Cl < • • lO l>- lO t- to lO CO Ol CO 03 03 CO CO Q Q Q o o <3 • o o o + 1 + oi 00 03 00 03 03 o 8 o <1 . o o» o O o o o o o’ 'O d d o + !>• 00 CD to lO 03 00 o o rH 03 o 8 o g o <1 • • • • • o o o o o o d + 1 1 ■ + 1 + + -1— CD CD 00 !>• CO lO CD 'Tt' oi o to Cl CO AM t- lO 03 Cl lO t-H t- 00 LO Cl lo’ CO 03 CO 03 03 CO CO + o CO Cl Cl CO c- lO CD CO 'CH CD 03 00 CD ' oi y-H O CD co I>- I>- o CD CD CD 00 OO 'T^ d id t-H d co I>- to l-H d d d 03 'cH 03 CD cS CI( ' CO o t'- C^ CO O c- CO ir^ D- CO o CO o lO 03 to 03 03 lO 03 to 03 a> C ° CD C- co 03 CD lO lO co 03 CD !>• CD r- CD CD 03 03 CD CD 03 03 03 03 CD CD CD CD -d a; Cl o o CD CD o CO '00 03 00 co’ ci 03 CO 03 CO CO CO D S y: 1 - 1 a; o o i_1 t-H t-H CO i-H CD t-H lO r- tH CD !>• 03 CD • CO LO r- CD 00 CD* CD c- 00 lO id CC 00 ' J tH rH b. D 'O 03 Cl o CD 03 03 Cl o tH tH CD LO id 03 d d lO LO id LO 00 oo’ I>- •H I^- CO 03 Q 00 to 'TtH 00 CO O I" 03 !>• LO lO Cl o CD CO O : 03 o CD o o ■rH CD Id- lO CO CD 1^- o 'X) 00 c— CO lO d 03 00 -d 00* § rH tH CO CO rH -rtl m d O > CD cn o ^ cc 05 1) ^-1 —. d d -I CC *0 ^ CO O -d fci) bic' O) OJ t- ?> 02 CD CC CO c3 . O ^ ^ rr\ ^ hh . • be be a; CD 2_| ^ rH bi hi) a; a- PhPh i- CD ai CD X JO d . O !h oi CD 02 CO d . O s- 00 00 Cl Cl Cl o a;i -t-3 00 00 o OJ I'- f ^ Ci Ci If t- (C: t- -rf* 03 03 O \o Oi lO CO r-^ o O c a o o o >iO lO lO lO lO If 'f 'If •If ■If -t- ■rf o o t— 00 Ci 00 c CO Ci lO> o rH CO 00 lO lO (M lO 03 03 00 CO (>3 rH CO 03 CO 03 1 0.010 0.012 CC s ' d o o d 0.012 0.006 O o d iat' d t- CO Q Ci CO -f CO 03 03 o 1-H o o o o O d d d o d o 1 + 1 + 1 00 -If CO Ci 03 o xO o 03 00 CO lO CO cc 00 LO o 00 lO> rH 1.0) 03 lO 03 03 CO CO 03 CO 03 CO 03 t- 00 lO lO Ci lO 00 00 rH lO CO Ci CO CO • ^ CO lO 'f c- 03 CO CO '■f lO) CO rH CC cc r- CO o o t'- CO lO -If lO 03 rH 03 CO 03 '•r' r— C5 CC t- t" 03 03 CO CO 'If 00 cc •'f 00 03 CO o CO t— lO o rr L'- 'f f»^ lO If 03 t— 03 »o CO CO CO lO CO CO o o CO t— o t— lO 03 r— 03 rH 03 CO c— Ci Ci C-- CC ■ ^ Ci CO CO 03 03 lO CM 00 S<1 fC CO 03 1—1 o o 03 03 rH to CO If CO cc 'If 'rJH lO rH CO c- 00 00* d rH d rH t'- d rH 03 CO CO d d Cl 00 00 03 03 00 00 CO rH o rH 03 oo rH rH O 'f CO f'- CO lO to lO 'If 'If t— 'If rH rH d rH 00 '00* to to ZO cc ^ , lO ^ 44.224 8.296 'w o to 03 l.O CO 13.166 03 'f •# rH 31.908 CO 03 lO CO* '>f t 7.667 03 C- tO CO 13.564 7.694 § 42.224 03 CO CO to CO 13.447 < < lO 1—< CO '1^' • in OJ 03 03 03 m “tc 03 03 03 03 a; CO U Sr ^ cz . 0) 03 03 03 O ^ ^ l-H Ci t ‘C to lO to I— 00 00 . o CO iO CO CO • O ^ rr t- • CO 03 00 03 to o r^' • 03 03 on CO L— 03 to pH o O wi c c o 05 lO »o »Q d to to to d CO O 1.0 05 t- 03 03 <1 ^03 05 to C5 to • CO lO CO to CO CO CO CO CO CO rH Q 03 b <1 d 8 d d + 1 03 o 03 o 03 Q tH <1 o o o o o o d O o’ d d d o + 1.0 03 CO 03 03 05 to 03 T— ^ LO CO <1 o O O' O o o o <] • • • • • • • o o o o o o o o + 1 4- + + + + »o 03 o l^- !>- 03 o d b- GO o w* to to GO CO <1 lO to »o' CO 70 CO CO CO CO 1-H + CO CO 00 05 CO GO C- fd oc GO to GO 03 ' 00 00 t-H 05 CO t'- CO CO C5 LO CO o - 4-3 l>- 03 C'* CO d t- CO d CO 1^- CO d 00 Oi T—( CO •rH CO CO CO CO 70 CO tH CO 02 " CO lO CO o CO t'* CO o CO [>- CO o CO !>• o to & CO 03 lO 03 -CtH to 03 to 03 T-H 'Ct4 CO 03 Cu ° C'- C'* CO C'* !>• CO t'- CO CO 1 '- CO C'* t-- <•1^ CO 03 03 o 03 03 o CO 03 03 + a 00 CO !>- 00 o 03 00 o 02 H °d 03 iH t- t— CO CO CO CO CO CO 6 OJ ‘ 5-1 o lO CO o C5 to !>- 05 t-H CO 03 00 05 CO d 7. d 00 00 CO CO CO CO d to 03 b- d to 02 T—H tH 02 id ^‘4 LO 00 o ■rd C'* o 00 00 tH LO CO tH 00 d CO to d 03 CO 03 00 00 !>- 00 t-H T-d c C5 CO 5S C5 I>* 00 00 05 05 05 03 05 CO 03 'Ct^ CO 00 o 00 oo o LO LO 05 03 00 t'- 00 00 C'i CO ^ • 00 03 03 C'- 03 05 05 rH CO 00 CO 05 -H co’ 03 rv"! oo' 03 03 I>- oo’ 03 t'“ h! 5 CO -HH -^4 f-H CO CO a o c3 > (V CO O ^ CO CO OJ -iJ C3 Oi 0) CO 72 Si Si 02 02 PhP4 t . CO 72 50 .CO zn zo . • Xfl xn 72 ;o a'. ^ (-H <4 <1 M CO ^ • d d ^pp to O Si .pp LO 4-4 Q CO '5^ CO ■4*1 4«*i ZD 'to JC pp Si Si •<1 cos 4 f XT 1 a? = i [6.4357] -- for a •‘’tar sin 2 ( ) *Cliauv. Astron. ii., p. 347. Observations for LatiUide. Reductio7is. OBSERVATIONS FOR LATITUDE.—REDUCTIONS. 21 02 . £ y5 o X CO •2 CO lO — CO to ' »cc CO L'- CO 00 1 C2 I- 00 t-- 00 I>- T Tf c • lO CO d 03 d CM d 'TtH + + 1 1 1 1 1 + CO oo oo lO y-H lO . ^ o CO cc CO Cl 03 L'- r- 03 «c t- 03 oo c 1-^ CO CO Cl LO 03 CD CD c • lO + + 1 1 1 1 7 + CO X X L-* O L— Cil Ol lO 1'- ,—>) 03 - X CD o 03 CO X X X Cl LO o L'- LO CO d 0<^ 03 03 03 X 03 LO Ci d CD lO lO 1—1 ■ CO 03 03 ^ LO LO lO "t! ' ^ 03 '-H r- X CO X Cl r+l 03 t-- t-- t- 1-^ CO CO LO) CO LO) lO CO c. ^ 0 !J5 ^LO 0.4 1 LO 03 lO 9.5 03 CO O lO CO —1 4.2 CD CD X i— 03 Cl 03 X CO CO o o 03 CD Cl c- O Gw 03 CD 'Tf 1-1 • CD. 03 X X Cl 00 O c a; ;> a; h-; CO d L'- tH d + o d - C1 CD 00 O 03 • • ^ Ol CO 03 lO O I-H CO • • o Cl t- 03 o _ «0 CO ID O • 03 • Cl • 00 —^ CO Cl t-- l>* 03 Z> c c, CO CO 23 o tH CO iD CO Cl • 03 X t'- 7—1 03 T-^ O 03 CO tH 01 tH ID o CO iD o 03 iD iD X 03 iD CO 3 ID 3 t'- cc iD iD - CO t— ID CO CO Ci CO t'- 03 CO iD Cl O iD cc 03 t'- o t" ^iD L-- iD rH CO CO iD W*’ X X iD o -rt' CO CO CO 03 w** CO ID iD 1 '- t>- CO CO T-^ CO 03 03 03 03 CO 3 -H .* cc c/1 (V cS o; c ht be be be ?*3 OQ •5:^hh do kO * *. t- «• k o n . O c ^03 CO CO X X X Cl tH oi 4-> X t5 1 X +!> /-N o h-1 O 6 X Cl o tH 03 CO rH rH OBSERVATIONS FOR LATITUDE.—REDUCTIONS. 23 ; 49.41 C2 03 03 CO t- ' 00 lo’ 03 lO 47.86 00 47.02 47.72 CO o d + lO T—i d i d + r-H d + »o d 1 r- O d + -0.17 9 to 03 o T-^ CO o rH d d d d d d d 1 1 + 1 1 1 + 1 1 -d o w» Oi CO 03 t-- o th CO -if CO d d CO d d d + + 1 1 1' 1 1 o 00 O •rt< 00 CO O to o t— QO Cw 03 to CO 03 03 'Ttn T~H 03 o t'- to 00 o CD o 1 + 1 1 1 + 1 rH 4- t— oo 00 00 Cl Cl CO !>• to Q "HH CO CO 03 03 C t— Cl to to CO o o t— t>- to 00 00 t— zo o d d 00 Cl CO cd d to CO to 1 -H CO 03 to •rH to —1 c- CO Cl o t- 00 CO CO CO CO 03 GO CO 03 rH CO CO rH 03 to to 03 Gi to ro c— rH CO o to CO Cl o CO to 03 to 03 1-H !>• CO •rH t— CO rd 1 rH 1 + to o to o CO to o o Q to ✓ o 03 • • c- • CO 00 • CO CC Cl c-* Cl CO CO 03 03 03 > E. • > E. E. E. > __j ,_ ^ 00 03 o o CO rH lO 03 O o to I" Cl 03 CO to CO 03 CO t- 03 to GC '■t' c— 03 to to co' 00 CO (•rs d cd cd to CM 03 03 CO o o CO o o GO 5, 5, t— to CO to to CO* 03 d co' cd td d 03 O to L— CO •rH I>- CO CO rH rH r- t-- 03 WH ?C CO ■rH Cl to Cl Q CO 03 oo i— O lO Cl' CO 03 00 03 03 CO 03 Cl 03 CO 00 Cl 03 CO 1—1 00 00 Cl to CO c- 03 CO cd r- cd d CO 03 03 03 03 CO rH •rH CO 03 03 CO tH rH o 02 c3 be 02 • —< Q S O cr 7i +H- V bx) a Oi PhO 1—I tH CO CO 102) fH i-H*' M .-I ^ e O 8 d 3 I- G G be be •I—(■'—' G G be be QO ’jj' (M oi 03 03 CC lO> CC o , (M Cl **Fnuue shifted in reverging. See p. 2. t First observation poor. Hazy. i Setting by zenith-circle, 30° 40’ 20" §Air unsteady. * Probably wrong star observed. Observations for Latitude. liediiotions. 24 OBSERVATIONS FOR LATITUDE.—REDUCTIONS. 05 1-^ O o '/! . CD -f CD Cl 05 05 -M • • . • • • r- 13 I>. CD CD o CD CD C 1—^ '-h 'Cfl CO CD 1—H o O O O 0) • • • • o O O o + 1 + 1 , lO tH CO o 05 5-H o 7-H rH o rH 05 . . • 01 o o o o (d o d cr. s rH 1 + + 1 O _^ CD 05 'CD rH o 01 - CD t-H CO CO rH ^H o o D > O o' lO CO CD CO e- lO CD CD lo" 05 Cl CO d C 1 CO lO -cH lO rH lO CO ICO rH CO 1-^ !>. 05 O rfl CO rH r 1.0 05 Od G CO lO lO rH CO 05 CO CO lO c^ce O Cl lO Cl 1^ o CO Cl lO 05 rH CD CD lO 05 CO lO OJ -cH lO 05 7-^ CO + Baroiii. At. Therm. •'S> 29.390 65 °0 29.375 60.5 29.350 50.0 1 Cl. 'a E. <15 cJ cd' 1-1 iO) CD CD k > W2 u.^ rH CO rH GO 05 CO 05 1-^ CD 'Ch CO > CO •«d d lO CD d co' CD CO CD CD tJh 1>. a o CO CO CO lO Cl o CO CO CO CD Tti lO lO CD lO d CD d CD d i>- r* o !>. CD CO Cl CD lO CO CD CD CD Cl o CD Cl lO 05 lO Cl coi 04 rH lO UO lO CO CO rH ^ CD CD CD Cl o D 05 H 1:^ lO d CO 05 H CO CD CO 05 ’ CO 05 rH CO CO rH 'Cf^ rH CO 05 CO rH li * rH ^ ^ I? O ^ a a bSj bo QQ c O 3 hH-t> tM CD CO S G &1) bJ3 oo iDi ^ O £» 0? be Oi O) a; PhQ O ~fi D1 D1 c ^ be ^ >) QO b Os CO o O Cs Cl CS cs Cl 6 D1 CD LO CD OD D1 D1 (M (M D1 D1 ic Cl ic OBSERVATIONS FOR LATITUDE. —REDUCTIONS. (Cl lC C] t' 30 •rt" REDUCTIONS. . 12 r— 30 30 25 Ol o o d 1 1 + 4- Cl CC L-- lO Oi Cl r—1 CO 1—1 o o d o o d o d 1 1 ! 1 1 + I + 1 1—^ »(0 »o Ol X X o o X o O' CO X o r—I d d o i + 1 4- + 1 1 1 + X lO Cl Oi M CO Xi CO ^O Oi CO d CO CO • • • • X • . X CO Cl • •— 'Tt* • CC o • lO T—H 1.0 Id ?c o CO (••-s o oi 1 1—1 1 1 L'* 1-H 1 lO 1 1 1 1 1 1 1 4- 1 + 1 -r 1^ ic lO CO d Ci L— 'rr L'- L- CC oi CO L'- X X CO W CO O CO' lO CC CO d ^ 1-* ■JM 1-^ X T— lO IC -f- co’ CO CO X t'- lO CO X >-0 d cr: CO t'* CO CO -f d lO >o »o T“1 lO CO lO d 1— CO X CO -f CO Ci d O 1- X — -cf 1' X CO cc ^ '-f CO lO »o JO 'Tl- d CO CO CO X o -r t Ci ^ t— O CO w* 1 C d — r-( CO d CO CO '-f lO d -rt' lO CM — !>• 1—1 f >o o CO O lO o »o o CC o • CM • • • •rC • t'- X Ci lO »C3 Cl d W E. ,—, - - -I lO ,1 ■ ) IC • CC lO ■ ■ ■« Cl c— 1—) -r X CO o ^ Ol Ci T-! O CO o CO CO CO d lO lO >-0 lO C" t- CC X t- 00 X t'- X X t- t- CM t>- CO d »0 00 ” 1-; Ci ^ CM ^ ^ CO t'" T—^ lO lO CO lO :o ^ L- X X X t- t- X X (M ^0 t"* d X lo CO X Ci Cl CO X CO CO ' do ^ CO lOi CO CC ^ X lO Cl Cl CO o X CO o X CC Ci X Ci 1- d o CO CC O Ci iO CC -t* Ol t' Ol lO Ct 1^ ~r X oi O ci CO 1— CO CC T-H d d CO d CO d Cl cc CO Cl CO lO CO CO Hazy. Moonlight. t Very faint. J Con. cles Temps § Faint, and seemed early. **2 s. from edge of field. t+Atmos, conditions good iRrobably wrong star observed. aMicrom. changed rev. sMicrom. changed 10 rev. Observations for Latitude. Reductions. 26 OBSERVATIONS FOR LATITUDE AND REDUCTIONS. 03 . ^ -4.3 OM 03-g CZ2 ® ?o cc t" I— ?o l- !>• L— C^ IQ CO »0) 03 — 1—1 o o d d d d o 1 1 1 d 1 + 1 L— CC 1—1 o t- CO " CO 03 rH o CO irH fC o' o d d d d + 1 + ! + + O 1— oo CO 05 ' QO Ol CO 00 'If 03 QO Ol lO CO -+l d d CO IQ 00 CO o 03 lO 1 ! 1 + 1 + I rH 03 CO 03 03 t'- lO CO rH •o Oi CO CO •O CO 05 C5 C3 t-H t'- CO 00 I'- lO co’ Oi lO rH rH ijr 00' 03 lO iO y-H lO CO iO 03 1—1 CO CO CO 03 o oo 1— -t4 t — 00 CO 1-H lO lO rH CO 03 CO CO CO lO oi t— o CO »o 03 rH rH CO CO CO LO 03 '-ri »o 03 rH 8 LO o Ol lO o CO lO 03 C3 . 03 • CO • • 00 •CC 'O wW LO Ci lO a lo 03 03 03 CL rH CO rH t-- 03 ^00 L— rH rH 03 to rH > O' oo" co' !>• co’ co' »o t'- H i- t'- 00 o CO 03 rr C'- LO lO rH CL H t— 03 t'- CO t-~ co’ t- LO 1 '* i>- ^H a CO rH -ft 00 CO CL CO rH CO 00 00 oo -TtH 03 to 03 00 CL rH 00 CL Sr 00 rH CL 00 O 00 CL c— CL t'- CO 00 CL O C3 co' lO co’ 00 t:^ oo' d 00 00 co’ 3 03 CO rH rH CO CO CO rr 03 03 rH CO 03 CO ^ 03 03 03 .1-3 Ct Sr cri rH H .rH LG a. o e o >- C2 CO CO P ^ fee fee >jx w |c CClh O ^ X 03 :« jT fee CL, 03 o o (M (M ‘x X tS ^ fee a, 03 03 CLO CO CO • 03 CO CO CO o o o CO 03 03 03 03 CO CO CO 00 a P 00 o o 6 00 o 03 CO -t4 CO CO -t4 'itt '•*4 -t+ OBSERVATIONS FOR LATITUDE AND REDUCTIONS. 27 00 00 t" IQ iO CO 00 -f 03 00 w d oo t'- 00 -r o d + 03 03 t— 03 -t* o 03 1 -H ,—1 d o o d d d d 1 1 + + + 1 1 + + »o oi t— 00 CO lO CO CO so d d o d d d + 1 1 1 + + i OJ o L-* o -1- Ci lO lO t'- L-* 00 00 03 CO 00 00 CO 00 03 CO 00 l£0 to CS o LO 1 + + + 1 ’ + + 5^1 CO 03 o o 1 - c; 03 •JO o CO 1—1 iTC I-- C_> 5<1 o 03 03 00 L- t'- Ci 'TT ■00 sO TC d t-- 03 03 :c WW uo cr. CO 03 03 'M ♦ -+1 CO lO 03 CO .—1 03 to lO 03 ?C cc 00 to f'- 03 L— OD CO O —1 00 I'- Ol to lO 03 CO CO lO OJ CO o lO oc- \o ao 1 — 03 CO t- t'- CO 03 oo Ol to L— t- 1 '- t'* -Tri t'- 1 *7^ »o lO o o lO o —' o o o 1—4 O o lO lO CO • CO • Oi • Ci • wv o • • CO • lO • 03 •o • lO • 03 C5 '>tl Oi 00 »o 00 lO 00 cc CO 03 03 03 03 03 03 lO • s lO -f lO X 03 X o 03 lO CO* to t— t— CO CO CO LO !>• 03 lO !>• t- d 1'* o oi a; o wV X o LO Ol 03 ■X oo d CO »o •o LO LO t'* 03 X CO d CO CO CO C'* lO >o t- !>• o -•rs X 03 r- 03 1'- CO CO Cl CO CO X X 03 cc 03 zc: 03 CO CO 00 o 'rr -f Cl o CO CO o CO Cl 00 lo" •X ’t 03 Cl CO d d Cl T—r CO ^—1 CO CO 03 CO 1—1 CO -'■CH CO' rH * o i t- 2- m — JL < rn e O j2 — X 'a^ T. X •o! -M- Jz ^ J. — X, dd. bro, d 3- xz ^ a..2 • fiH c be be cC 3. ^ O dPH >> >-. < o w O ^ oo cj a; 1- ^ 03 03 CO CO o CO 70 CO CO CO 'Ji a, d jiz tXcQ. a, 0; C-O O o 'Z * Am. Naut. Al. Both stars well observed. t High wind $ Newcomb’s St. Stars. Observations for Latitude. Reductions. 28 OBSERVATIONS FOR LATITUDE AND REDUCTIONS. m . C ^ S'*-! o fO w* oo Ol 00 ' JO o o lO C>3 ro 1 d l- o- t' i •i- 'Tt- I i=l o o O) ;-4 o Q O) CD o a> JO d + '00 03 Ol ro iO c CM d oo d + (M d Oi l'- CM cc c— 00 L— rc ' t'* L- — *» • • • • • c 03 rH c to o T—1 # cc 1—1 to _o 00 Pi -CO t-- o (M in ) 1 1 1 r-H 1 1 1 1 1 4- 1 7Q to CO L- o w« L— X Ci — - 00 (M Pi (M lO 00 o lO w* o CO L— CP •4^ d CO CM CO Cft CO 00,. to 't.C' pi ZP O) (M iM to lO to CO a,c« o 38 CO cc CO "o 51 54 52 o 1-H r— cc 44 28 CO 1'- 1— i CO O to t— t- 'pi C— L— CO 05 to + L— CO 1 -h L— CO to CM to OJ lO to o CO o t'- to to o o • o • * • CC 3 -CO to CO 05 CO 05 CO 03 03 CO cc O ;-( OJ o a; ■J2 X CO CO 03 CO 50 70 CO (^1 o 03 'a > 02 lO t'" CO CO t- CO to lO to c- 'Cfi to CD CO X o 03 05 o 1- X ^ • t'- CO t-- CO to CO to I'- to CO a CO -f cc o CO X c-* to 'Ct' 03 03 o 03 X 1—' t'- o CO iO X to C< ' . o X 03 CO CO X 05 o CO X to 05 CD d d X X lO X 03 05* QO CO 03 CO CO 1—1 CO CO 03 03 ^ zn m o) ^ a X D ijcd, — o d a, !» •rH . O t'- X' 0^1- tn <(.—I Pm ■/) c: C b£ be ^4 rC V Q, d cu > P c be be 1 -H CO CO l-M s- “w '-i O 'mJ mD 03 CO CO O . X X X X q:> 4-J 00 • c3 X > q o d CO to t" X 05 to to to to to to to OBSEllVATIONS FOR LATITUDE AND REDUCTIONS. 00 00 03 o 03 00 o CO CO CO t'- t— i-- 00* oo’ L-- 05 rJH CO o o’ o H- o 03 05 03 CO 03 L— o OI o rH 03 d d d d d d 1 1 1 + + 1 1 1 00 05 lO »0) CO o CO o 00 03 o 05 O d d d d d d d ! 1 + 1 + + + CO 00 00 00 coo L'- 1'- O 00 00 • • • • • • • D-- o lO 03 o lO lO • LO lO 00 05 lO lO CO 05 1 1 1 + + 1 1 1 05 1 29 OO CO 1— o CO CO 0 CO 00 »o 05 •rH CO C'- to rH 00 o 00 00 t'- 05 lO 00 tH L'- 0 CO co’ d 03 t- 05 ’ 'CfH 00 co’ LO t'- 00 d 05 ’ 03 rH 03 to 03 03 lO 03 10 LO 00 CO CO CO o 00 lO c— !>• 05 0 05 CO lO 03 lO CO -CfH CO to 10 to rH CO o lO i'* L'- 00 to 03 CO rH t'- 00 CO 1" CO t—H L'- 03 lO rH I>- 03 CO C— 03 1 1—w 1 + + (M CO o o JO L'- lO O ■rH • • CO O*' CO CQ 00 CO '00 05 to wW CO 03 0 0 0 LO CO JO 0 03 0 r-H 05 03 CO t— 03 lO L— lO 00 1—I 03 00 ’ CO 06 00 03 !>• 03 lO 00 CO 03 CO CO CO CO CO CO CO 03 CO ^ fcc3^ O) o PhO CO CO CO • Ph f-M ^ 1-^ • oi I'- 02 O uS 5^ o 0 , 0 ^ C/3 ^ c/2 be a. ^ :fj CO cn 0 ^ * CO 05 o ici - lO *+— lO 03 00 CD 4-3 " (M 00 • • r »o C- 1- d CD op CD* 03 -rfH 'Ttl o „ iX( '*-1 cn o t- •rH tH 03 03 ID o (03 (03 O 03 • • • ' d o o o + ++ 1 L— !>• 05 CO ID CO f-i ' (M lO o o o ID V- • • . ■ • 03 o o o d d d CO C P + + + i 1 1 o _^ o o o 00 03 ID CO *-+^ ' o o o CO (53 o 03 > 03 d d * o dd d CO tH tH P 1 + 1 1 O 03 lO 03 ^ CO (03 t-H Q * " 05 c- 03 O t- (03 05 s C— co’ 05* d d ID CO* O CO C<3 1—1 -ciH ID rH (-1 o 05 05 rH • 03 ID T-l (03 + + 1 + 1 1 ' T-l 03 CO oo 03 CO O 00 C- ID 'CO CD CD CD tH CO 00 03 ID 05 CD 4- 9 CO 00 '^ctH ▼H LO 00 >d' CD d (d ID d T-l kO CO 03 ID ID 1—1 CO ID O 05 00 GO C- 05 00 T—1 » D 05 (03 0( 9 Cd CO CO (03 ''tl lD CO ID ID a, 0 O lO CO t'- CO irH 00 (30 ID 05 ID 00 CO T-l (>3 CO ■rH 03 i»p (03 03 ID ID (03 (03 T-l 1—( 1 1 1 + ' + ■ + S .S lO O (03 O o (03 O <-= tH o • ID • *-i 03 03 t- 00 T-H 05 tH T^l ■T^l ID 03 CO ttJT ttJT P d 6. 6. LO CD d C- 00 ID 00 (03 CO* c CD 00 03 o OO 03 —I CO (03 C— T—1 CO 00 tH lO lO CO 0^4 CO 'cfH CD 00 (35 o o 05 03 lO O ID CO 1- 05 ID 05 o tH !>• p 05 d »D P ID d d 03 d ID P CO 03 03 03 CO CO 03 CO 03 CO c/2 0^ a a P o • • • P c- CXI • CO ^ --- S-> < K-. ca * • r^ C/2 73 &C 73 o; PO I- '>+1 lO CO fcn'p o ^ JO QO QO lO > o »o to kO 05 00 CD 05 CD t" (M t- • Q t'- (M 05 (M t'- CO o o CO OO CO 00 I>- OO <35 d to o d + lO • !>• d CO lO (M co’ to lo” o t— d lO CO 05* lO lO - CO lO CO CO CO CO »o CO lO (M 00 lO CO rH CO CO I^- CO on lO CO o O TfH CO t- 1^- CO rH oa CD CO CD - r^* OO -rr^P-l • 05 TO . gee no 05 * 00050 I—• t-- r- t- t- i^- c— oo 00 * Faint. + Probably wrong star observed. See No. 84. $ Near edge of field. § Microm. changed 9 rev. Observations for Latitude. Reductions. 32 OBSERVATIONS FOR LATITUDE AND REDUCTIONS. C/5 . S3 OM O O) m ;-i O) GO 00 CO CO o (M 1-H o CO I>- r-H CO CM o L- CO* 35 ■rtH 'cH xn u tf-i 05 P f t +0.23 +0.51 L- o 1 +0.05 ! o d + —0.12 GvI o’ + O 1 _ • CO o 'cH lO CO 05 lO o CO o o >• CO o’ o’ o’ o’ T—^ d ;-l d 1 + «• 1 + + 1 C 00 35 CO (M O • - 35 (M CO o !>• (M o <3 O (H o (M + G- a 3 P, CO CO LO LO d CO d lO CO LO LO lO LO CM 00 a' I^- CO O r-H o t-H CO CO 35 (M o ^ t-H d 03 CM + i>- CO d CO lO LO lO CO CO oo’ (M 3 CM •rH CM 00 r- LO LO 35 o C03 CO CO ■rH »o oo CO CO to •^H <50 CO 35 t- CM o o CO o . CO 35 CO tH CO o’ LO CO 00 o’ LO 00 CO lO CO CM 03 CM t-H CO CM CO CM CM CO CO _ m ■ 1 r< r a (M ^.<1^ ^ . PPM _ • CO • O t» CC J C3 O w 00 CO xn 05 05 (D do o ^ C c« p CO 00 oo i'- t'- 00 o (M 00 CO 00 00 »(0 00 CO 00 L'” 00 00 00 OBSEKYATIONS FOK LATITUDE AND KEDUCTIONS. 88 'M Cl X O- 20 1*^ 'T ir: ic CT- <»«■ -r CC -r oc 1- t- 1'- X CC !'• IC -r I.C -r ct C2 W — * d T lO — Ct Cl -V'*' IC Cl w o O o 3 ^ ^ . ^ . d d 1 + 1 I + 1 + 1— X Cl iC O' X X — — d o 'O d 1 1 1 1 1 -F 1 1 1 •J/z -M X X - JL I.C ~r ic Cl ■M - - CC I.C Cl -r Cl -r -Cl oi Cl — IC Cl -J + + 1 t 1 1 d 1 d — CTi CC '.c 1C Cl X Cl CC 1 - X JC “ ::r lC l' CC IC — "S CO X w. CC Cl 1'- - Cl Cl CC -r cr. r-. CC -r Cl L— t— lO -r CC j c ^ Cl T-^ Tt* ic i- ro t'- — - o — • lO L- I'- L— X CC 1— o CO 10! i.C Cl H- iC Cl CC -tH CC CC ic ^ ro 00 lO C'- Cl X IC O -f Cl —I 1—1 CC X ic i'* CO CC Cl Cl ic I.C CC r-^ L'* CC 1 > d c eo 00 -r ic ic 5— X l- ’-C Cl CC Cl — Cl CO 00 lO I-- iC I-- X ic X I.C X 20 -f O'! CV CC rc O X 1-H IC o O O' Ci 1' O'! io 'tT to >0) CC t- X :c IC CC i- ^ CC —i ^ t'- t- -r CC t-- 'rt' i- -Jt CC ic 00 o ol i- CC CC Cl — CC I-H CC c; 1—^ IC -r io> T-H lO CC o IC ^ o r-H 'cr cc d X Cl 1' CC ■rr ic X CC d ^ X (M S'! 03 U (M uO 03 o 00 + i 1 1 1 1 ' 1 CM Zfl lO 'M '.•Vj CM ^ .o lO ' cc Cl lO 00 00 o 03 1- 00 cc 00 4-3 03 03 t" CO CC 00 Cl <03 w* ^ t.«~- 0, CO lO 03 tH TP 03 c: d iO o <55 'Tt- 55 -rt- 50 48 L'- 27 38 cz cc 7C 03 00 iO lO w* o CO o -+< — CO o 00 1 03 i-H _!_ <03 lO o lO CO ^ CO -4- _• lO • X 00 »0 L'- to o ^ t. o • • • S- < 1C lO CO X CO CO Cl Tp tP C3 H 03 Cl. d 1 _ <1J ci o 1 O) CO <03 lO r-F r-i CM r—• T-4 Cl L- 00 a;^ C/2 03 d d »jO L-- lO CO 1'- lO 1C d d > t-- CO oo to -P 03 T-H c* GO OO <03 Cl lO 00 03 (OO 1C tP 00 t-- 1C 03 c 00 (03 tP 00 tP 00 1—( 'GO 1C lO — : Cl CO »o fH <03 (03 03 <03 CO 03 03
    03 »0 00 00 rc 03 I'- JO re 30 00 rr -f -r -f- -r JO lO CO JO 1' 03 03 0 0 ; 03 0 30 CO CO ! + ++ i 1 1 lO o lO 03 + 03 + 03 + l'- o + -4- t- 1-- ir:> lO L-- o ++ 03 lO lO lO + 30 »o 03 o I- 30 30 ;o »o I- i-- 03 + 03 03 03 + -jf -f JO 03 x> 1 -* 30 L— t'- 30 0 03 00 :C '-r CO 03 a? L- 03 C' oo 0 'Tt- 1 '- C'- t' 30 lO t-- lO w» 1 - .3 JO CO lO 30 3 0 -I- 01 03 30 CO 1 -* 0 'V' 30 30 03 30 'Tf 1 —< 1 - CO CO t' 0 CO 30 03 03 03 CO 30 30 03 00 10 , Cl wJ CO 30 0 s 30 00 30 03 TT lO CO CO 03 30 CO CO CO CO 03 •j j -r^ 1 1 ' ‘ + + 1 + 00 CO 00 lO 00 03 lO -• ! c i— ^ d 2 < c 03 03 -^,- o ^ "4 X • • '/^ < < t- 'X -X ^ CO . 72 <0 00 > > d > id , 3^^ 57 CO L'- l- 30 30 CO l— 03 03 03 1-H L— CO , • • • « • • • • • • • • » • c* JO t' C- 03 '30 1'- 1' JO 30 00 0 CO — 03 Cl 30 d wy 30 30 W^' 1'- CO 03 JO 30 •w'F t- JO 30 JO t— -»K t-- Cl 30 t- 03 0 30 30 03 T—( ,3 CO 00 <>1 30 Cl Cl JO 03 Q JO 03 Cl Cl 00 'jfi 00 0 F—1 03 03 Cl c: 30 30 Cl 30 w* CO t'- CO 30 a . « • « • » • • • » • • x> 03 JO C 00 30 ~r 30 03 cc Cl JCj CO 03 03 — — CO CC f-h 03 03 CO 03 03 03 03 03 ^ r. c: Hazy in nortli. t Full moon. Hazy sky. i Roth stars f^arinf^. § Est. Maf>'. .'j.O, i Est. Maj;. r, 3. Poorly bisected. 2 Flaring 3 High wind. ^Microin. changed 5 rev. Observations for Latitude. Red/aotions. I 3(5 OBSERVATIONS FOR LATITUDE AND REDUCTIONS. 'M cc CO A X 1 . - cc CO CO iC • . *. . zz ^ rc 00' ■00 L-- 00 X X 'T ^^4 —+* —r" -y X o CO w. cc • ^ o o 0 d 1 d o 1 4 - + d + - 1 - 1 , OJ ! s-> c; — CC 1 X aj d d ■d 3 CO — 1 1 1 + + 1 1 o • 00 lO 03 (3 to CC * ' ^ a.' ' CO '00 to to lO •— o > d ■r^ CO d d i ^ y 1 1 + 1 1 4 - 1 1 c 03 OJ -?r CO L — ^ 'TfH CC oo — CO ■w*' * •• — • • •- 1 03 cc 03 ■00 X c to 03 to lO to 5 lO T—f to ! 1 1 1 1 “T + r j + lO) L— O CO iC5 z^ O' tr: lO to 3, ■ - ZC L— dd l' 03 -f ZC L'- lO CO cc r- lO o d -f i— ^ ZiZ ac — 1-4 lO i-H- 0* to lO lO to ___ '■H tc 1-^ lO on 00 cc to ^ to 03 iC c- O -t+ 03 lO lO 03 03 'i+ lO' 03 ■ c<^ »o CCS ■O 00 to t— 03 CO X to C^ CO 1 1 t to CO 03 lO lO CO 03 to CO 03 1 I 1 i + + ( _ lO O O O 00 CO O •• • 00 t- • ars 03 CO , 1 •' r-i 1 ^ o’ o' id id -f 1 i 1 -H ^ 2L '—'■ '—' — 03 1 1 . 03 d tC t-H 00 1—1' — CO tC X ■X 1 00 CR CC dd 03 O i'* 0 X CO 0 ” d ’-H 00 'Tf^ lO to X 1" CO ' 03 00 t'-- CO 00 -f CO I'-^ 03 -ft 00 CO 03 aa: 03 CO 1— f 0 d wC' X 1 CO r- O 00 lO 0 03 0 X ai 00 ^ CO '-M c; to d cc 1— 03 t'- i CO 03 03 03 03 03 01 03 03 03 03 CO 1 1 . - Xl X! 1/ cs -r - CO M ■/, c 5 — bio X <— bed 9 ^ T. * - 03 ' to 00 /4 i-M X c Q 2 ! ^ s /— s ^ t /3 w ■/: 03 .C. 03 ^ 4 . <4 X c/j ^ < o C 3 P i-t M •>>> d c <-* 'r-l 00 CO drH e Q 03 d • lO “ 1—1 OO 03 lO t-- •o O O lO CO CO Ol o 1- ~ OJ O'] CO +++ o’ + o’ + n-+ >o + CO 1 1 ~r ~v CO O 1— o & CO CO CO c— rc O JO CO »o WW t'* t- rc JO co’ JO o' o O »—1 3 * Cvl 1 lO lO •o Ol o o o Ol o "M ++ Ol 1 + 1 1 1 i rn^ 1 , 1 L- JO O O O' O' o o 1—4 03 o 50 03 c 1- CO o lO lO CO O' CO o X lO O lO o o' i-H CZ O O CO o o CO 05 >0 d d O] 1—1 (>J CO -rf »o ^ 03 CO lO f-H 03 ^ T- ^ t'- I'* JO lO 03 O CO lO r- lO »0) 03 O ■^H lO O X 1- I'* 'M Ol 'it' o IQ •O •rj' 03 CO CO CO o T—1 CO 00 lO CO CO o X ».o O CO C OJ 03 03 O lO CO 03 »0 03 03 O 03 lO -t ^ »0 CO + o •JO 1'- 03 L X . CO • JO • X . • JO • CO o X 03 03 03 > E. - - ■ ,_1 J_1 1__ ,_, 1_, ^ o X 1—H O . _ ■ 03 ^ 03 03 03 F^ I- (M '(Jfl ^ L- 1- CO '30 o o t - X 03 X CO X l» CO o’ lO lO o L' O o’ CO 1'* t- L.O »o ^ 5C lO 1 — t- —' — o c o cc T-H 'O T- O O X CO lO -f * Oi O O 30 t'- t'- o’ L'- O * ■rf CO co’ t- X CX) 03 03 CO —' Q 03 O 03 X 03 ^ L'- 05 t'- — 1- 00 O -H Ci O 03 03 X w* ■fH CO 05 50 ^ Ol ^ lO L— iO iO CO 1—1 30 r-< 03 1—t O CO 50 CO o lO; CO CO t- —- 00 CO C^l O ^ 03 O X »0 iO Ol OJ 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 . be V _• 03 d be O/ G ^.G (U c X ci C--, i = o o w X! 'Z = ^ - rtO o 'Jn m X rH •* t- “ I-- • 'S c - 1 G a C- )—( S-'TL ^ ^03 r; 1 Cl- ^03 O Cu >o lO L- 1 - o 03 -r lO L'* *(’on. (les Temps. 15 sec. from edge of field. i Zeiiith-level working badly. § High wind. iTrouble with level. sMicroin. reading checked. sMicroin. changed S rev. ■iyiicroni. changed 1 rev. Observations for Latitude. Reductions. € 38 OBSERVATIONS FOR LATITUDE AND REDUCTIONS. ^ . r%0 Ci oo 1.0 -r on CC' ! ; O CO cc cc on i— on . i- 1 '* '00 i>- t'- Oi oo ~f -f •rf -t! -+1 -tt Mer, cc ^ o on d CO ^ ^ ^ 02. !-i ' o o 00 o o o 00 • • • • • • » , 02 o tH o o o -rH C 1 1 + +++ ' P + o • CO on on on 00 t— "co ** t-H i-H ft CO a > OP o d d d d ■rH tH u tft ft + 1 ! 1 1 1 1 o on t- on . _ — o ft • ' oo CO u O CO 01:0^ CD on £ o lO d _ • d d o S-i lO on CO o ^ -t' iO> CO on o * -fH tH i 1 '1 rH + O O '^1 +++ •ft + (C I ft: ft t-H !'• lO 1 — oo on O on CO Oi ICO CD ' CO O Ci '<*1 CD on T—I 00 CO I'- id CO lO Ci d i-H CO o on on d lO 1 -H T—) 1 -H on T-H on ^ lO on 1 -H (M ft lO c- CD lO 1(0 on CD o t-^ CD G lO on co on Ttt tH liO CO on 3 0 c.^ 00 lO CO Di CO 00 CO - ~ j O ICO CO Oi on lO lO) CO T-0 on on on on CD on CO on 1 + rH 1 T—^ + 1 o*^ S-I 22 H O O I'- lO • 1—I GO • 00 • -20 a 00 CO on oi CO OO 00 oo' CO on lO on ;-l (V o 02 Oi 1 ft ■rH co' o 02 (_J tH on t-- con t- r- L-- 1—I 00 00 wV o m i'- CD* id oo* ICO CD CD CD t— CT- C" ■etc d > rH 02 tH lO CD 00 con f '- CO on 00 00 ft coo’ lO CD* ft 00* TJH -JH id 00* CO a on o 00 00 CO T^ CD O 'etc CD Di CO CO t-H T^ con o 'Tfl ^ rH O iO ICO CO Ci o 00 Oi Oi O ICO CO 00 CD 00 00 r-H tH CO CD C2 ICO d CO* lO 00 00* CD lO con 00 d 00 rH ^H h (M on on on CO con con con con CO T“H 1 -H ■etc cc cn O) O) tJD ^ ^ 1— ' ^ CO o c o w o o o o d d d d d d d d -r+T- 1 H-+4- + --J- o o r5 •X) -HH Ol ^ Ol Ol ^ 05 -M -M tC ^ CO CO O; C 05 d d CO 1—I d d + 4-+ “T 1 + 1 X — O lO »0 CO X! o l-- 05 05 LO) t'- I- c: 50 lO CO CO 00* t— -t< J-O 1-H lO r-l Ol O C 'Tl lO o c; oi o lO -T- + - 1 -r-r+ - T— + t- O. 00 CO 05 C CO 03 -t- lO lO 1—1 CO CO 00 t- iO th CO lO 00 o —1 CO o oi t— 00 1—1 CO d 03 (03 CO* 05 T-l 03 •rH 03 1— 1 03 'Tti lO lO 03 X 05 1(0 l.O 03 X 1-0 0!^ -fl Ttl --t "TH 'Tt< lO ^ ^ -TtH CO CO CO o 00 lO CO CO CO o CO o Si3 03 03 X 1-H X 03 03 03 X 03 X + ro 00 lO 05 05 (>] o o >o o 1 LO ^ t- O 03 05 CO 00 CO • 00 • o • 03 • • 05 05 • lO • lO 03 ! 05 00 CO OO CO 05 CO CO 03 03 03 03 E. E. t- t- 1—1 t- 05 03 00 lO CO »o 03 03 i 1- t'- LO X X* t— ^ ^ ^ CO* 00 >0) d i O O 03 lO 1- 03 05 C" o CO 00 X 05 05 1— t- 05 00 t- t'- 03 d 03 —1 LO 00 lO ■00 i 1- CO t'- X 000. O 03 T- (M 03 lO 05 -f GO 00 03 00 CO C— X CO 05 CO 03 lO 00 t— LO 00 Lf5 lO CO 05 X X 03 OO t-H t— »0 lO 05 CO CO 1-M 00 03 03 03 03 03 CO 03 03 03 (M 03 03 tH CO 1 o V s-’.^ c ii as 11 O o -fr CO y) c« CO .o O •d i-H c5 o o > 75 c3 CO .2 ‘C CO c cd ro rc t— rc 00 DISCUSSION OF THE RESULTS OF THE OBSERVA¬ TIONS FOR LATITUDE. The following observations were rejected, either for failure to fall within an assumed limit or for reasons noted during the making of them: namely, 1, 17, 29, 31, 53, 66, 69, 70, 76, 84, 92, 96, second part of 107, 113, 127. Weights were assigned to the observations on the following considerations: First, the atmospheric and other physical conditions. Second, the probability of the adopted star-places. Where both stars are standard stars the weight 140 was given, as also where B. A. C. 7657 was used. The weights of observations in which B. A. C. stars were used were, in this respect, made approximately proportional to the weights of the star-places given in the Table of Star-Places, pp. 12-18. Third, the zenith-distance. Fourth, the exactness with which the observation was made. Fifth, the star’s hour-angle at bisection. The adopted weights were then taken approximately propor¬ tional to the product of the foregoing separate weights, for each star. In observations like 121, where one star is combined with each of two or more, the weight of each result is found by dividing the weight of the whole observation by the number of separate results. The equations of condition were thus formed: Let (5, (V = the declinations of the stars, “ R = the true value of one revolution of the micrometer-screw, “ D = the true value of one division of the zenith-level, “ (j) — the true value of the latitude, “ i?o, Dq, (po = assumed values of the same quantities, “ i? = i^o + a;, D = Do-\-y, ^ = (p^ + 2, (40) ► RESULTS OF THE OBSERVATIONS FOR LATITUDE. 41 Let !> = the difference of refraction, “ It = the meridian correction, “ Jf = I (m' ni), where m\ ni are the micrometer-readings, “ L = ,1 [{n' + n) — (.s'^ -f ^vhere n', n, etc., are the level-read¬ ings, Then .] + rU) + MR + LD + /; + // — (/. = 0. I Also by obs. 1, •j + ^^^0 + ADq -{- i > -\- /j — = 0, whence Mx Ly — ^ + (0i — 9o) — 0. cTg was found by taking the mean of the results from pairs of standard stars of zenith-distance less than 30°, and difference « of zenith-distance less than 11^; the level-correction being less than = 42° 16' 47.87^^ The observations were divided into five sets, according to tem- Xierature, and as many sets of normal equations were formed. In order to reduce :!/, '^x was substituted for x in the equation of condition, where v = 10. 4 42 DISCUSSION OF RESULTS. Temperature 6()°-7o°. No. M L n l/ wt. Equations Weighted. 5 —8.84 —1.27 +0.26 1.0 — 0.88 vx — 1.27 2 / — ^ + 0.26 = 0 6 —14.27 —0.17 —1.42 .9 — 1.28 r-oj —0.15 2/ —0.90.? — 1.28 = 0 7 +7.52 +2.35 +0.02 .9 + 0.68 vx + 2.11 y — 0.90 ? + 0.02 = 0 8 —8.89 —0.30 +0.31 1.0 — 0.89 vx — 0.30 ?/ — ? + 0.31 = 0 9 —10.01 -1.17 +0.61 1.0 — 1.00 vx — 1.17 y — .?+0.61=0 10 +13.63 —0.32 +0.06 .7 + O.dovx —0.22 y —0.70? + 0.04 = 0 11 —1.08 —0.15 —1.27 .6 — 0.06 vx — 0.09 y — 0.60 ? — 0.76 = 0 12 —1.03 —0.02 + 1.01 .6 — 0.06 vx — 0.01 y — 0.60 ? + 0.61 = 0 13 —10.12 —0.05 —1.54 1.0 — 1.01 vx — 0.05 ?/ — z — 1.54 = 0 14 —3.81 0.00 + 1.54 1.0 — 0.38 vx + 0.00 y — ? + 1.54 = 0 15 +0.39 +0.05 —1.58 .4 + 0.02 vx + 0.02 y — 0.40 ? — 0.63 = 0 16 —10.18 + 1.60 -0.55 .6 — 0.61 v2' -f- 0.96 — 0.60? — 0.33 = 0 18 —10.68 -0.52 -0.01 .4 — 0.43 vx — 0.21 y — 0.40 ? — 0.00 = 0 19 +0.54 —2.32 + 0.54 .8 + 0.04 I’a? — 1.86 2/ — 0.80 ? +0.43 = 0 20 —8.92 -0.20 —0.85 .9 — 0.80i'a? —0.18?/ —0.90? — 0.76-.= 0 21 +13.60 —0.17 —0.15 .9 ^ 1.22 vx —0.15 y —0.90? — 0.13 = 0 22 —3.84 —0.30 —0.03 .9 — 0.35 vx — 0.27 y — 0.90 ? — 0.03 = 0 23 —8.95 —0.07 —1.40 1.0 — 0.89 vx — 0.07 2/ — ? — 1;40 = 0 24 —10.09 —0.17 -0.05 1.0 — 1.01 ra? — 0.17 2/ — ?—0.05 = 0 25 + 13.62 —0.15 + 1.10 1.0 + 1.36 w —0.15 ?/ — ?+1.10 = 0 26 —3.89 —0.07 — 1.16 1.0 — 0.39 vx — 0.07 2 / — ? — 1.16 = 0 NORMAL EQUATIONS. + 13.363 + 3.571 2/ + 5.472 ^ +5.462 = + ‘S.7>Hvx +12.218 2/ + 3.228 2 —1.717 = + 5.472 rx' 3.228 2/ —15.580 z +2.460 = SOLUTION. rx + [0.42688] y + [9.61224] ^ + [9.61168] = 2/ + [9.19529] 2 + [9.45045] = ^ + [8.kl32] = The niiinbers in brackets are logarithms. 0 , 0 , 0 .. 0 . 0 , 0 . Value. Weight. Probable Error. / / X = — 0.0464 1093 / t 0.0157 2/ = + 0.2908 11 0.1551 ? = — 0.0551 13 0.1426 m = 21, n = 3, {}in ■ 3] = 10.502, /[nn -3] ' = 0.6745 u' >M — ii = 0.5152. I DISCUSSION OF RESULTS. 43 Temperature 45°-ao^. Xo. U L n 1 wt. Equations AVeighted. Q W +7.60 +1.52 +1.78 0.9 + 0.68 VX + 1.37 ?/ — 0.90 + 1.60 = 0 • > o 5.48 —0.22 —0.54 .9 — 0.49 vx — 0.20?/ — 0.90.? —• 0.49 = 0 4 —2.98 —1.27 +0.88 .7 — 0.21 vx —0.89?/ —0.70? +0.62 = 0 4 —9.06 —0.20 —0,56 . 7 - 0.63 vx — 0.14 y 0.70 ? - 0.39 = 0 27 +7.60 —0.05,+0-.33 .6 + 0.46 va; — 0.03 ^ 0.60? +0.20 = 0 28 —16.54 0.00 —1.67 1.0 1.64 J'o; + 0.00 ?/ ? — 1.67 := 0 30 18.48 +0.47+1.34 .9 1.66 vx + 0.40 y 0.90? + 1.21 = 0 32 —8.96 +0.42 -0.67 1.0 — 0.90 + 0.42 ?/ ? 0.67 = 0 o*> OO —10.10 +0.02 +0.16 1.0 — 1.01 va? + 0.02 ?/ - ? + 0.16 = 0 34 +13.58 —0.50 —1.26 1.0 + 1.36 vx - - 0.50 y ~ ? — 1.26 = 0 35 —3.87 -0.15 —0.26 1.0 — 0.39 i'a; 0.15?/ — ? —0.26 = 0 36 +7.61 —0.22 +0.78 .9 + 0.68 vx - 0.20 y — 0.90 ? + 0.70 = 0 37 - 5.63 +2.30 +0.25 .9 — 0.51 vx + 2.07 y 0.90? + 0.22 = 0 38 *10.85 +1.87 —1.24 .4 - 0.43 vx + 0.75 y 0.40 ? - 0.50 = 0 39 —8.93 -0.17 —0.44 1.0 0.89 I'X — 0.17?/ — ? — 0.44 = 0 40 —10.11 +0.12 —0.16 1.0 -1.01 ? + 0.12 ?/ — ? — 0.16 = 0 41 +13.62 -0.05,+1.49 1.0 + 1.36 v.t;—0.05?/ - - ? + 1.49 = 0 42 —3.88 0.00 —0.12 1.0 0.39 + 0.00 ?/ ? - 0.12 = 0 43 +7.56 +0.17 -0.10 .9 + 0.68 + 0.15 ?/ 0.90? -0.09 = 0 44 —5.56 +0.07 0.11 .9 - 0.50 vx + 0.06 ?/ - 0.90 ? 0.10 = 0 45 —10.84 +1.67 -0.38 .4 -0.43 vx + 0.67 y - 0.40? -0.15 - 0 46 +6.96 —0.15 +0.92 1.0 + 0.70 — 0.15 ?/ ■ ?+ 0.92 = 0 47 +8.76 —0.17 —1.29 .9 + 0.79 w —1.53?/ —0.90? —1.16 = 0 48 +7.57 —0.37 —0.51 .9 + 0.68 )’a? —0.33?/ 0.90? -0.46 -=0 49 — 5.52 +0.05 +1.61 .9 — ^0.50 vx +0.04?/ 0.90 ? + 1.45 = 0 50 —12.08 +0.22 +0.93 .6 0.72 vx + 0.13 y 0.60 ? + 0.56 = 0 NORMAL EQUATIONS. + 18.596 i-jc - 3.813?/+ 4.033 z + 2.610 = 0, 3.813 + 11.238 ?/ 1.094 z + 4.382 = 0, + 4.033 i’.r 1.094 ?/+ 20.120 z^ 0.939 = 0. SOLUTION. + [0.31885 n] ?/ + [9.33621] z + [9.15218] = 0, y + [8.40714 nj z + [9.67286] = 0, . z + [8.85759 w] = 0. Value. AV eight. Probable Error. // // a; = 0.0254 1663 0.0134 y= 0.4689 10 0.1689 r = + 0.0720 19 0.1245 m = 26, /? = 3, \nn • 3] = 15.069, // r = 0.5459. 4 51 52 54 55 56 57 5S 59 ()0 61 62 66 ()4 65 67 (iS 71 71 72 88 89 90 91 i)7 98 ‘)9 DISCUSSION OP EESULTS. Temperature 30°-45°. M L n wt. 60 —0.55 —0.40 1.00 66 —1.95 +0.38 .90 80 -0.10 —1.84 .40 13 +0.22 —0.88 .90 92 —0.10 --0.. 19 1.00 13 +0.37 —0.35 1.00 56 0.00 —0.66 .70 90+0.15 —0.49 1.00 56 —0.22 —0.39 .90 77 —0.32 —0.63 .40 12 +0.02 —0.39 .60 04 —0.40 +0.94 .70 55 +0.10 +0.15 .90 22 +0.50 —0.57 1.00 34 0.00 —0.50 .20 17 _ 0.00 —2.30 .08 88 —0.22 —0.34 .20 37 +0.15 —0.58 .20 89 —0.45 —1.57 1.00 59 —0.05 +1.14 .90 53 1—0.47 +0.59 .90 69 1—0.55 —0.35 .50 ' I 15 +0.22 —0.35 .08 .67 i 0.05 1 —0.43 .50 1 .01+2.72 +0.08 .08.! .35 :-0.47 +0.94 .90 .88+0.10 .30 i Equations Weighted. + 1.36 vx — 0.55 y -f- 0.69 — 1.75 y — 0.43 vx — 0.04 y — 1.09 vx + 0.20 .V — 0.89 vx —O.Wy — 1.01 vx +0.37 y + 0.95 vx + 0.00 y — 0.39 vx + 0.15 y —• 0.50 vx — 0.20 y — 0.43' vx — 0.13 y — 0.73 vx + 0.01 y + 0.49 vx — 0.28 y + 0.68 i’.r + 0.09 ?/ — 0.92 vx + 0.50 y 0.25 vx + 0.00 y + 0.02 vx +0.00?/ + 0.14 vx 0.04?/ .- 0.05 vx +0.03?/ 0.39 vx - 0.45?/ + 0.68 vx 0.04 y 0.50 vx , 0.42^' + 0.18 vx 0.27 y + 0.03 ?'.?: 0.02 y + 0.18 vx — 0.02 y + 0.02 vx + 0.22 y - 0.21 vx 0.42 y 0.24 vx + 0.03 ?/ 2 — 0.40 = 0 — 0.90 ^ + 0.34 = 0 — 0.40 2 — 0.74 0 — 0.90 ' — 0.79 = 0 _ 2 _ 0.19 = 0 — 2—0.35 = 0 — 0.70 2 — 0.46 = 0 — 2 — 0.49 = 0 — 0.90 z 0.35 = 0 — 0.40 2 — 0.25 = 0 % — 0.60 2 —0.23 = 0 0.70 2 + 0.66 = 0 0.90 2 + 0.13 = 0 2 — 0.57 = 0 0.20 2 - 0.10 = 0 0.08 2 — 0.18 -= 0 — 0.20 2 0.07 = 0 0.20 2 — 0.12 = 0 2 1.57 = 0 0.90 2 + 1.03 = 0 — 0.90 2 + 0.53 = 0 0.50 2 — 0.17 = 0 — 0.08 2 - 0.03 = 0 0.50 2 — 0.21 = 0 0.08 2 + 0.01 = 0 0.90 2 + 0.85 = 0 0.30 2 0.63 = 0 1 DISCUSSION OF RESULTS. 45 'Ttmperattire 3()°-45°. Concluded. Xo. 51 L n C wt. Equations Weighted. 101 --3.81 +2.00 + 1.11 .20 — 0.08/’o; + 0.40 2 / 0.202+0.22 = 0 102 -^0.58 +0.40 —1.05 .90 ; j — 0.05 vx + 0.36 y - 0.90 z 0.94 = 0 103 —5.56 -0.17 +0.12 .60 1 — 0.33rx 0.10?/ —0.60 2 + 0.07 = 0 104 —10.80 -0.05 +0.53 .30 i - 0.32 j-.r 0.017/ 0.30 2 + 0.16 = 0 105 +3.63 +1.40 +0.73 .50 i + 0.18 rx + 0.70 y - 0.50 ^ + 0.36 = 0 106 +2.54 +0.35 —1.00 .20 ’ + 0.05 I'a: + 0.07 ?/ 0.20 2 0.20 = 0 107 +8.78 -3.37 —0.61 .05 ! + 0.04 vx - 0.17 ?/ 0.05 2 — 0.03 = 0 108 —7.81 —1.22 —0.42 .30 - 0.2^ vx 0.37?/ 0.30 2 0.13 = 0 109 —0.57 +0.67 —0.02 .90 ^ — 0.05 vx -[■ 0.60 ?/ 0.90 2 0.02 = 0 V2\) -0.56 +0.07 —0.18 1.00 i 1 —^0.06 vx + 0.07 ?/ — 2 ' 0.18 = 0 130 +15.08 -0.05 +0.43 .40 1 + 0.60 vx — 0.02 y ^ 0.40 2 + 0.17 = 0 131 +1.03 -0.20 -0.19 .30 + 0.03 vx - 0.06 y — 0.30 2 - 0.06 = 0 131 +1.12 —0.20 —0.22 .20 1 + 0.02r.r 0.04?/ 0.20 2 0.04 = 0 131 +3.03 —0.20 -0.63 .20 + 0.06 vx 0.04 y 0.20 2 - 0.13 = 0 135 —7.01 +0.12 —0.32 1.00 — 0.70 vx + 0.12 ?7 2 — 0.32 = 0 136 +1.04 —0.30 +0.49 .40 + 0.04va; - O.V2y 0.40 2 + 0.20 = 0 136 +1.19 -1.42 +0.50 .30 + 0.04 - 0.43?/ 0.30 2 + 0.15 = 0 136 +3.0/ —0.77 +0.39 .30 + 0.09 vx - 0.23 y — 0.30 2 + 0.12 = 0 137 +1.10'+0.15 +0.16 1.00 + 0.11 + 0.15 V 2+0.16 = 0 138 +7.28 —0.15 —1.05 .90 + 0.66 vx 0.13 y - 0.90 2 — 0.94 = 0 NORMAL EQUATIONS. + 11.829 vx — 2.556 y + 2.260 2 + 3.290 = 0, — 2.556 vx + 6.290 2 ; + 1.685 s — 0.920 = 0. + 2.260 vx + 1.685 2 / + 21.032 0 + 4.490 = 0. SOLUTION. r:r + [9.33462^2] 2 / + [9.28117] ^ -]- [9.44426] = 0, y + [9.57830] 5 : + [8.56139n] = 0, 2 + [9.29934] = 0. Value. Weight. Probable Error. / t x = — 0.0216 1037 ! 1 0.0093 ?/ = + 0.1119 6 0.1281 z = _ 0.1992 20 0.0676 7n = 47, y = 3, [nn • 3] = 8.749, y =: 0..3008. c 46 DISCUSSION OF RESULTS. Temperature Xo. U L n wt. • Equations Weighted. 75 +7.57 —0.10 +0.34 0 90 1 + 0.68 vx — 0.09 ^ 0. 90 2 + 0 77 +2.52 +0.75 +0.90 20 ! +0.05 vx + 0.15 y 0 20 ^ + 0 78 -9.17 —0.75 -0.23 1 00 i —0.92 vx — 0.75 V - - z 0 79 +3.66 + 0.45 +0.13 50 i +0.18 vx + 0.22 V - 0. 50 ^ + 0 80 +2.26+0.65 +1.20 30 1 + 0.07 vx + 0.19 y - - 0 30 2 + 0 81 --0.52+0.47 +1.55 1 00 - 0.05 vx + 0.47 V - - + 1 82 + 2 . a) -1.62 +0.01 20 + 0.05 vx — 0.32 y - - 0 20 2 + 0 83 +2.49 j +0.25 - 1.53 .20 + 0.05 vx + 0.05 y - - 0 20 2 — 0 85 +3.69 —0.30 - 0.17 .50 + 0.18 vx -- 0.15 y - - 0 50 2 -- 0 86 +2.26 +0.02 - 0.24 .30 + 0.07 vx + 0.01 y - - 0 30 2 -- 0 87 -7.91 +0.50 —1.60 .40 — 0.32 vx + 0.20;v - - 0 40 2 - 0 93 —7.86 -0.05 - -0.58 .40 0.31 vx — 0.02 i/ 0 40 2 - 0 94 0.54 +0.05 -0.39 1 .00 - 0.54 vx + 0.05 y - - X - 0 95 +7.59 -0.15 +0.62 .80 + 0.61 vx - 0.12 y - -0 80 2 + 0 116 +2.50 -1.65 - 0.14 .70 + 0.17 vx --1.15?/ - 0 70 2 0 117 +2.62 - -0.45+0.52 .30 ‘ + 0.08 vx — 0.13 y - - 0 .30 2 + 0 118 2.40+0.72 +0.71 .70 1 -0.17 vx + 0 . 50 1 / - 0 .70 2 + 0 119 +7.10 -0.071+0.83 .06 j +0.04 vx -- 0.00 y - 0 .06 2 + 0 oi oi 0 0 0 0 0 0 0 NORMAL EOI^ATIONS. + 2.321 vx + 0.177 y + 0.384 2 + 1.000 = 0, 0.177 L-c + 2.673 y + 0.758 2 + 1.119 = 0, + 0.384 vx + 0.758 2 / + 6.644 2 — 1.643 = 0. SOLUTION. vx + [8.88229] y + [9 . 21865] 2 + [9.65963] = 0, 2 / + [9.43785] 2 + [9.59132] 0, 2 + [9.51774/i] = 0. Yalue. Weight Probable Error. // // X = - 0.0475 191 0.0195 y = — 0.4805 0 0 0.1679 2 - 0.3294 () 0.1067 // m = 18, y = 3, [nn ■ 3] = 2.396, r = 0.2696. / » DISCUSSION OF RESULTS. 47 Temperature o°-15°. Xo. L 11 y wt. ! 1 / 0 12.30 1.52 —1.24 0.30 +3,80 2.50 —0.93 .50 no 10.80 —0.80 —1.01 .30 111 +3.72 —0.65+0.52 .50| 112 +3.16 —0.50+0.38 .08 114 -0.50 —0.87'+0.52 .90 115 2.53 +3.07+0.20 1.00 120 —0.52 -0.02 +2.08 1.00 121 +1.00 +1.25 —0.06 .30 121 +1.08 +1.25 +0.15 .20 121 +2.96 4-1.65 —0.88 .20 122 +2.63 +0.05 +1.76 .20 123 — 2.9,7 +0.05 +0.89 .60 124 +1.12 +0.65 4-0.50 .30 124 +3.03 +0.62^+0.06 .30 125 —2.46 +2.471+1.60 .40 126 --3.88 +1.45 —2.20 .10 128 - -2.46 +1.95 -0.37 .90 132 +6.01 —0.65 +1.85 .04 133 +15.10 -0.55 +0.39 .40 134 +1.04+0.42 +1.99 .40 134 + 1.12'4-0.42 +1.26 .30 134 +2.97 +1.55 +0.51 .30 i I Equations Weighted, 0.37 rx -f- 0.10 vx — 0.32 vx + 0.19 vx 0.03 vx - 0.04 vx — 0.25 vx — 0.05 vx + 0.03 vx 4- 0.02 vx -j- 0.06 vx. 4-0.05 vx — 0.14 v.r + 0.03 vx + 0.09 vx - 0.10 vx —-0.04 vx — 0.22 vx 0 .02 vx + 0.60 vx + 0.04 vx + 0.03 vx 4-0.09 vx - 0.46 y -- 1.2b y — 0.24 y — 0.32 y - 0.04 y — 0.78 V + 3.07 y — 0.02 y + 0.37 y 4- 0.25 2/ + 0.33 y + 0.01 y + 0.03y + 0.19 y 4 - 0.19 y + 0.99 y + 0.14 y + 1-75 y — 0.03 i/ -- 0.22 y + 0.17y + 0.13 V + 0.46 y ^ 0.30 z -0.50 2 — 0.30 2 — 0.50 2 - 0.08 2 --0.90 2 2 - 2 — 0.30 2 — - 0.20 2 — 0.20 2 - 0.20 2 - 0.60 2 — 0.30 2 — 0.30 2 -0.40 2 — 0.10 2 -0.90 2 - 0.04 2 — 0.40 2 - 0.40 2 -0.30 2 0.30 2 - 0.37 = - - 0.46 = 0..30 = + 0.26 = + 0.03 = + 0.47 = + 0.26 = + 2.08 = — 0.02 = + 0.03 = — 0.18 + 0.35 = + 0.53 - + 0.15 = + 0.02 = + 0.64 = — 0.22 = -- 0.33 = + 0.07 = + 0.16 = + 0.80 = + 0.38 = -f 0.15 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 NORMAL K(^UATIONS. +^0.846 vx — 1.303 y + 0.313 2 + 0.118 = 0, —4.303 vx + 16.720 y — 3.852 2 + 1.358 0, 0.313 vx - 3.852 y + 5.728 2 — 3.350 = 0. SOLUTION. vx + [0.18757n] t/ + [9.56817] 2 + [9.14451] = 0, 2 / + [9.35993n] 2 + [9.01982] = 0, 2 + [9.79817n] = 0. Value. Weight. Probable Error. / / X =3 —0.0311 74 t / 0.0387 7 / = + 0.0392 13 0.0937 2 = + 0.6283 5 0.1517 m = 23, y = 3, [nn • 3] ^4.898, r = 0.3338, 48 DISCUSSION OF RESULTS. As the results of the foregoing five sets of equations indicate no temperature-corrections to the values of E and D, the fol¬ lowing set of equations was formed from all the observations. NORMAL EQUATIONS FORMED FROM ALL THE OBSERVATIONS. -h 46.955 vx — 3.924 y + 12.462 ^ + 12.573 = 0, — 3.924 + 49.139 y + 0.725 4.225 = 0, + 12.462 1W+ 0.725 ?/ + 69.104 ^ + 1.018 = 0. SOLUTION. rx + [8.92205a] y + [9.42391] z + [9.42776] = 0, y + [8.55847] 2 .+ [9.03378] = 0, 2 -f [8.58189a] = 0. Value. Weight. Probable Error. / / - 0.0287 4437 / f 0.0062 y = 0.1095 49 0.0588 ^ = -f- 0.0382 (56 0.050(5 m = 135, y = S, [rm ■ 3] = 48.922, r = 0.4106. Probable Values of R, Z>, o. (Quantity. Assumed Value. Correction. Probable Value. R / f 45.040(5 0.0287 1 1 45.0119 D 2.1192 — 0.1095 2.0097 0 47.87 + 0.04 47.91 Taking 1 " of latitude = 101 ft./the difference of latitude of the two observatories is 75.3 ft. = 0/^75. Adding this to the value above, the result is Latitude of the Detroit Observatory, 42^ 16^ 48.^416 ± 0.'4)51. V ► CORHECTED VALUES OF LATITUDE. - 49 Values of Latitude Corrected hy Comimted Probable Values of P and D. No. Computed Value. 1 1 Microra. Cor. 1 Level. Cor. 1 1 ^ a; a ^ C. ^ S- > C Xo. • Computed i Value. ; 1 £ g O 1 S 1 1 Level Cor. ! i Corrected V alue. 1 t 1 44.53 t • -0.36 ! / —0.34 ! f 43.83 23 t f 46.47 / f +0.26 f t +0.01 t t 46.74 o 49.65 _ 22 — .17 49.26 24 47.82 + .29 .02 1 48.13 i> O 47.33 + .16 -f .02 47.51 25 48.97 — .39 + .02 48.60 4 48.75 + .08 + .14 48.97 26 46.71 + .11 + .01 46.83 4 47.31 + .26 + .02 47.59* 27 48.20 _ 22 + .01 47.99 5 48.13 -f“ . 25 V .14 48.52 28 46.20 + .17 .00 46.67 () 46.45 f .41 + .02 46.88 29 52.95 + .23 .00 53.18 7 47.89 -- .22 — .26 47.41 30 49.21 + .53 —• .05 49.69 8 48.18 + .26 + .03 48.47 31 46.54 + .26 + .04 46.84 9 48.48 + .29 + .13 48.90 32 47.20 + .26 — .05 47.41 10 47.93 — .39 + .04 47.58 33 48.03 + .29 .00 48.32 11 46.60 -f- .03 + .02 46.65 34 •46.61 — .39 + .05 46.27 12 48.88 + .03 .00 48.91 35 47.61 + .11 + .02 47.74 13 46.33 -f .29 + .01 46.63 36 48.65 - .22 + .02 48.45 14 49.41 + .11 .00 49.52 37 48.12 + .16 — .25 48.03 15 46.29 -f .01 — .01 46.27 38 46.63 + .31 — .20 46.74 16 47.32 + .29 — .18 47.43 39 47.43 + .26 + .02 47.71 17 25.86 + .21 4- .04 26.11 40 47.71 + .29 — .01 47.99 18 47.86 + .31 + .06 48.23 41 49.36 — .39 + .01 48.98 19 48.41 — .02 + .25 48.64 42 47.75 1+ .11 .00 47.86 20 47.02 + .26 + .02 47.30 43 47.77 — .22 1 — .02 47.53 1 21 47.72 — .39 + .02 47.35 44 47.76 j+ .16 — .01 ! 47.91 1 22 47.84 i :+ .11 + .03 47.98 45 47.49 !+ .31 1 — .18 47.62 * Mean 48.28, c 50 CORRECTED VALUES OF LATITUDE. Vcdues of Latitude Corrected by Computed Probable Values of 11 and 7). Xo. ^ .:3 o ^ Q Microm. Cor. Level Cor. 1 Corrected Value. 1 1 1 No. Computed Value. i . 0 s—/ r" P 0 0 0 'a! I Corrected Value. 1 46 / f 48.79 r t -0.20 / • + 0.02 / / 48.61 69 / t 6.21 t f -0.08 / / 0.00 f ( 6.13 47 46.58 — .25 +• .02 46.35 70 12.48 + .36 .00 12.84 48 47.36 - .22 H- .04 47.18 71 47.53 — .20 + .02 47.35 49 49.48 + .16 .01 49.63 71 47.29 + .07 — .02 47.34* 50 48.80 + .35 - .02 49.13 72 46.30 + .11 + .05 46.4() 51 47.47 - .39 + .06 47.14 46.63 + .35 -j. .17 47.15 52 48.25 - .22 .20 48.23 1 74 j 46.94 — .11 -h .25 47.08 53 44.80 H .16 + .05 44.01 75 48.21 — .22 + .01 48.00 54 46.03 + .31 .01 46.35 76 43.41 + .16 + .03 43.60 55 46.99 + .35 .02 47.32 i 77 i 48.77 .07 — .08 48.62 56 47.68 + .26 + .01 47.95 i 78 47.64 + .26 + .08 47.98 57 47.52 + .29 — .04 47.77 79 48.00 ' - .10 — .05 47.85 58 47.21 - .39 .00 46.82 80 49.07 — .06 .07 48.94 59 47.38 + .11 \ .02 47.47 1 81. 49.42 + .01 .05 49.38 60 47.48 + .16 + .02 47.66 82 47.88 — .07 + .18 47.99 61 47.24 + .31 + .04 47.59 1 83 46.34 —■ .07 — .03 46.24 62 47.48 + .35 .00 47.83 i 84 1 12.04 + .36 .00 12.40 63 48.81 — .20 + .04 48.65 85 1 47.70 — .10 + .03 47. ()3 64 48.02 — .22 — .01 47.79 86 47.63 — .06 .00 47.57 65 47.30 + .26 — .05 47.51 87 46.27 .23 — .05 46.45 ()6 49.31 + .35 — .05 49.61 88 49.01 — .22 + .01 48.80 ()7 47.37 -f . 35 ' .00 47.72 89 48.46 .16 + .05 48.67 ()8 45.57 .06 .00 45.51 90 47.52 —- .11 + .06 ! 47.47 1 * Mean 47.34. I I COIUIECTED VALUES OF LATITUDE. 51 Vahies-qf Latitude Corrected hy Computed Probable Values of R and D. Xo. Computed Ynlue. 1 Microm. Cor. i_ _ Level Cor. ! Corrected V^alue. Xo. Computed Value. Microm. Cor. Level Cor. Corrected Value. 91 / / 47.52 / r -0.09 f / f0.02 / t 0 47.45 113 r / 43.32 / f +0.23 f t +0.07 / ' 43.62 92 50.90 h .07 f- .05 51.02 114 48.39 + .01 + .10 48.50 93 47.29 + .23 + .01 47.53 115 48.13 + .07 — .34 47.86 94 47.48 + .02 — .01 47.49 116 47.73 — .07 + .18 47.84 95 48.49 — .22 -f .02 48.29 117 48.39 — .07 + .05 48.37 9() 53.36 + .15 -|- . 04 53.55 • 118 48.58 + .07 — .08 48.57 97 47.44 — .10 f- .01 47.35 119 48.70 — .20 + .01 48.51 98 47.95 — .09 — .29 47.57 120 49.95 + .01 .00 49.96 99 48.81 + .07 -|- . 05 48.93 121 47.81 — .03 — .14' 47.64 100 45.76 + .23 — .01 45.98 121 48.02 — .03 — .14 47.85 101 48.98 + .11 — .22 48.87 121 46.99 — .08 — .18 46.73* 102 46.82 + .02 - .04 46.80 122 49.63 — .07 — .01 49.55 103 47.99 + .16 + .02 48.17 123 48.76 + .07 — .01 48.82 104 48.40 + .31 -f- .01 48.72 124 48.37 — .03 — .07 48.27 105 48.60 — .10 - .15 48.35 124 47.93 — .09 — .07 47.77t 100 46.87 — .07 — .04 46.76 125 49.47 + .07 — .27 49.27 107 47.26 — .25 + .37 47.38 126 45.67 + .11 — .16 45.62 107 46.56 .21 + .36 46.71 127 45.27 + .02 — .09 45.20 108 47.45 + .22 + .13 47.80 128 47.50 + .07 — .21 47.36 109 47.85 + .02 — .07 47.80 129 47.69 + .02 — .01 47. TO 110 46.86 .31 -h .09 47.26 130 48.30 — .43 + .01 47.88 111 48.39 — .11 + .07 48.35 131 47.68 — .03 + .02 47.67 112 48.25 — .09 + .05 48.21 131 47.65 — .03 + .02 47.64 *Mean 47.41 t Mean 48.02. c 52 CORKECTED VALUES OF LATITUDE. Values of Latitude Corrected hy Co m'puted Prohahle Values of R and D. No. Computed Value. 1 Microm. Cor. Level Cor. Corrected Value. No. Computed Value. Microm, Cor. 1 Level Cor. I i ! Corrected Value. ' 131 ! t 47.24 / / —0.09 / t +0.02 r ! 47.17* .3,3 47.55 t • +0.20 f f —0.01 t r 47.74 132 49.72 — .17 + .07 49.62 136 48.36 — .03 + .03 48.36 133 48.26 — .43 + .06 47.89 136 48.37 — .03 + - 16 48.50* 134 49.86 — .03 — .05 49.78 136 48.26 — .09 + .08 48.25t 134 49.13 — .03 — .05 49.05 137 48.03 - .03 — .02 47.98 134 48.38 — .09 — .17 48.]2t 138 • 46 ..82 — .21 + .02 46.63 * Mean 47.49. t Mean 48.98, i .Mean 48.37. PK0IL4BLE ERllOll OF OBSERVATION. 53 The following pairs, with the corrected latitudes furnished by them, were used to determine the probable error of an observa¬ tion. The result is 0."539. Names. No. of Obs. / Cygiii I r, a Cygni . ♦)TI. Cepliei I 32VuJpeeulaf |. ‘ r (\ygni [ - ^ ('ygni I. Gr. 3415 ^ ^ A Pegasi . ‘ 20 Pegasi ) i ^ 24(’ephei ^ . 31 Pegasi 31 Cephei ^. ‘ ■ . (. 3 4 ( assiopeijc \ B. A. 0.8195 ^ / Anclromedfe ^. Names. No. of obs. N } Cephei [ c^Piscium C. a Andromeda* [ « Cassiopeia* ^. B, A, C.79 [ -Andromeda ^.. eAndromeda | r- a Cassiopeia ^. ‘ B. A. C. 341 ^ 38 Cassiopeia ^. (p Persei [ r- ,3 Trianguli . 17 Tauri, etc. 9 H. Camelopardalis ^. (5 (Mean values) « VALUES OF LATITUDE DEPENDING ON ZENITH- DISTANCE OF STARS OBSERVED. In forming this table each observation received the same weight as the corresponding equation of condition; and the values here given are each the mean by weight of the separate values employed. Temp. 0" 20° AVt. 0 1 o o 00° -81° AVt. 45 75" t / 47.88 24 t r 48.01 10 / / 47.07 1 30 45 47.03 13 48.55 8 47.03 . 1 0 -- 30 48.37 0 1 48.05 2 47.71 1 The smaller values obtained from the low stars seem to indi¬ cate that northern stars are refracted less than southern, for the same zenith-distance; and that, therefore, the layers of the atmosphere, instead of being parallel to the surface of the earth, are depressed more rapidly toward the north. THE END. (54)