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I^U ^y^^^^^ \J(^ f 
 
 G^:Nr^DA. 
 
 » T5 11 
 
 SPECIAL APPENDIX B 
 
 TO 
 
 REPORT OF MINISTER OF PUBLIC WORKS 
 
 FOB 
 
 FISCAL YE3A.K, 1807-68 
 
 MEMOKAND, 
 
 ON THE 
 
 
 SEMime SiMET 
 
 ^' )^* 
 
 AS ADAPTKD TO PRECISION LEVELLING 
 
 IN CONNECTION WITH A NEW ROD 
 
 BY 
 
 R. STECKEL, ]Vr. Oan.Soo. C.E. 
 
 Engineer in charge, Canadian Geodetic Levelling 
 
 OTTAWA 
 GOVERNMENT PRINTING BUR 
 
 1899 
 
mmm 
 
 s 
 
C^N^Di^. 
 
 SPECIAL APPENDIX ''B'' 
 
 TO 
 
 REPORT OF MINISTER OF PUBLIC WORKS 
 
 FOB 
 KISCAL VK^VK 1807-0© 
 
 MEMORANDUM 
 
 0\ TIIK 
 
 SEIF-REDMNG SMGUET TACHEOBM 
 
 AS ADAPTED TO PRECISION LEVELLING 
 
 IN CONNECTION WITH A NEW ROD 
 
 BY 
 
 n. ST ECKEL, M. CaiL.Soc. C.E. 
 
 Enyineer in charge, Canadian Geodetic LeceUiny 
 
 O T T A VV A 
 
 G U V E 11 N M E N T P R T N T I N G B U R E A U 
 
 1899 
 
«Tl'» 
 
 SPECIAL APPENDIX " B 
 
 TO REPORT OF MINISTER OF PUBLIC WORKS 
 
 FOR 1897-98. 
 
 LIST OF ILLUSTRATIONS 
 
 CONTAINED IN ACCOMPANYING POCKET. 
 
 T_"Tach^om6tre Sang -et " (auto-r^duoteur) an adapted to Geodetic Levelling in - 
 connection witli a now geodesic rod. 
 
 II-New geodesic rod with accessories, for use in connection with the Sanguet 
 tauhcomcter. ^ full size. 
 
 Ill— Details of new tacheometer rod and accessories, | full size. 
 46 47 48 49 and 50-Five typical double rages of proposed tiold book for tacheomo- 
 ' ' trio surveying and precision levelling combine^'., showing sights, readings, 
 entries and computations required. 
 
 5 and 6-Two typical double pages of tacheometer field book, showing sights, read- 
 ings, entries and computations required for geodetic levelling, without 
 survey. 
 
I-. I mM9 
 
 \ 
 
 1 
 
 \ 
 
 (,t 
 
 E. P. E. : 
 
 Seci'i 
 
 Sin,- 
 
 ' 8olf-re 
 
 'id ol 
 
 y< 
 
 dt 
 
 «.. .. Je 
 
 eanctionec 
 
 order for 
 
 December 
 
 unavoidabl 
 
 himeelf, M 
 
 ori/!jinal tr 
 
 alterations 
 
 the ensuing 
 
 connection 
 
 too long to 
 
 the reason 
 
 H 
 
" SANGUET TACHEOMKTER 
 
 ?) 
 
 KOH 
 
 I'KHCISION LHVIiLLING. 
 
 Department of Pcblic Works, Canada, 
 
 Chief Engineer's Office, Ottawa, 30th July, 1898. 
 
 E. P. E. Ror, Esq., 
 
 Secr6tary, Public Works Dept.-, Canada. 
 
 ' « «!!f '"/ '"'J'" '""" '" """'™'* ''^""'■^'^- -'^ ^«--- -'<»^ ill-trationH on 
 
 e f..oduc.n, San,uot Tachoo^ete.- as adapted by .e to precision ieve.lin, ^ifa 
 
 Mu of a new Goodesio Kod. f, "'im 
 
 >ou are uw.re, .ho |,„™h«.e of one of th«e poHeclod t„oho„,„cler., oioaiSod 
 
 dance w„h the view. I c<,n,n,„„„„tej to Mr. Lo„„ C„.le, Chief Engineer 
 
 .. .. Jepaitment, undo,- Jate of April Wth, 1896, wa, upon hi, rocommo.Lion 
 
 Z: '7 t,f """""'^ "" "'"'*^' ■" ""' "»" "' '«. »"« accord ;,; an 
 
 o.der o,. the ,n..,.„,.c„. ™, «nt by me to C.h..H„n. of i,,™, ,, „, ,'-„J "^ 
 
 Decem^rof the ..me year. Owing to varione delay, cau.od pr ncipally hy .he 
 navo, ahiy iong corrcpondeoce I had U. carry on with .ho ,„a J and hoLL o 
 
 or ,<-m.l ,„odel of h„ ,nvcn.,o„, and difflcul.ie, oxporioncod in makin>, the .aid 
 ter..,o„,, the .mprovod .acoeometer with it. aece.,orie» reached Ot.„;a on,; „ 
 
 thaen.n,ngSopU,n,borC1897). Again, the now geodcic rod I dovi.od for „e " 
 onnocon w,.h the modifled .elf.reducing tacheomotor, could for variou. reto^" 
 oolo„gt„ennn,er„.o,not be .ati.f.„torily completed hofc-e July,^^ 7Z 
 
 the reajon for not .nhmit.ing this Memo, to you at an earlier date 
 
The San^uot tacheomotor -supplied by Mr. ('aliHHHon which hoars the order 
 number 115, In all thaJ, oouiil bu tloslrotl, both in ;ioint of < oni-tiiiction and rtnish, an 
 far an can b« jud/i;od ncn a cIomo indoor t-xaminution and a few veriticationH made 
 on Piirlinmonl Sqiinre. It ih what may properly bo termed ii iiidvornal mirve^.ng 
 ir..-itrumeiit, lioing admirably contrived for mt'Unuring. ii. all portitioiiM, di^tancu« 
 automatically reduced to their horizontal projo'^tionts, and that more a.Huratcly and 
 expeditiously than those horizontal distancoH could ho measured under the most 
 favourable circumHtancoM, with cither chain, tajie or any other measuring devio, 
 besideH which the tacheomotor is equally serviceable for levelling and taking hori- 
 zontal and vertical direniions an<l compass readings. 1 have no doubt that when 
 test'jd in a practical niatincr in the Held, our new tacheometer will prove satisfactory 
 in every way for carrying on expeditiously aiui economically, not only the precise 
 lovolling and surveying operations, this particular instrument is more especially 
 destined to be used for ; but also al! ordinary ongineei-ing tield oj)eralions. 
 
 The now geoilesic rods, of which th<)re are three, were manufactured at Ottawa, 
 inclusive of all the accessories, viz.:— in ,^c•cordallco with the drawings ' furnished, 
 and under my ilirect supervision; for bein^; of home manufacture, the rods are none 
 the less artistic pieces of workmanship. The woodwork was executed at the govern- 
 ment vorkshop under the superintendence of Mr, F. Breton, clori-: of works, the 
 metal mountings and fittings by Mr. Geo. Bailey, of Wellington Street, and last but 
 not least, the painting, inclusive of seal divisions, under the direction of Mr. Alfred 
 Cot^, who is in charge of tha govornmoDt paintshop; although not machine divided, 
 the scales are remarkably neat and accurate, and the figuring is very distinct and 
 Btriking. 
 
 I must confess that, notwithstanding many elaborate reports made on variouw 
 occasions, by prominent engineers in different countries, to show the advantages to 
 be gained by the regular and extended use of the ordinary stadia wire tachoometor 
 for engineeiing field work generally, J was never l^vourably impressed by the results 
 obtained with such instruments, taking into consideration the troubiosorao and bulky 
 reductions, etc., which have to be ationded to, and failed to see how such tacheome- 
 ters could ever really be of much service to the engineering profession, except for 
 reconnaissance work, running trial lines and other operations o! a similar nature. 
 I now feel satisfied, however, that in a comparatively short time we shall see the 
 improved self-reducing Sanguet lachoomoter or some similar apparatus take the 
 place of nearly all other surveying instruments used at present for engineering pur- 
 poses, aiid that chain or tape measurements of long horizontal distances will soon be 
 a thing of the past. 
 
 With a view of verifying, in this country, all the good points claimed for this 
 tachoometor, and at the same lime affording the engineers of the Department an 
 
 
opportunity of hoc loiug ucqiiutiited with its pmotioal n-orkinjj, I would Hu^^gect 
 
 that it Hliould W ^Hod in tnultinj^, umior my direction, mi accuriito plan wi^h 
 
 level contour I ,on of Parliament Squiiro, AIuJoi'h llill ami Nopoun Point, that in to 
 .say: a plan showinj^ the precise i)Oundftriert and olevuiionB of the j^i'ound of all our 
 pro|)trtieH lyinj^ Houth ot the Ottawa Uiver as far back as Queen Street, and west of 
 SuHHOx Street and the Riduaii Canal up to Bank Street. 
 
 I may way in thin connection ; 
 
 1. That there in no Huch plan in existenco, as tar as I have heen able to make 
 out. 
 
 2. That aside from the f^reat desirability and convenience of the iJopartraent 
 having such a document at itH command for its own particular mon, wo have, on 
 Severn! occasions, been asked, in vain, for information that a contoured plan would 
 readily hav afi'orded. 
 
 3. ''.i.;u iidw a combined railway and highway bridge is boini? br.ilt, abutting 
 on the '-)Vornmont lands of Nepeaii Point and railway companies are endeavouring 
 to obtain access to the new Central Station by passing over the said hinds and 
 electric rompanies may also apply, in the naar future, for the privilege of crossing 
 them. 
 
 It therefore appears to me to be highly advisable that the survey in question 
 bo undertaken without delay, apai't from any consideration such as tliat above put 
 forward in reference to the desirability of testing the new tacheomotei' and accoro- 
 ])anying rods in the tield, on a large scale. 
 
 I would furthermore suggest that the re-levelling with the tacheometer and the 
 new rods, of a 25 mile section or so of the continuous double rodded lino of levels 
 which I ran along the St. Lawrence with our U. S. C. & G. Survey goodeaic level No. 
 1, be authorized, with the object of establishing a comparison between the results 
 afforded by the two instruments and the two corresponding methods respectively ; 
 such levelling to be undertaken as soon as practicable without unduly interfering 
 with more pressing work. 
 
 In conclusion, I may be permitted to point out to tne Depaitment: — 
 
 1". That the information afforded by the precise levelling and gauging opera 
 tions commenced under my dii-ection in 1883-84, and carried on b}'^ me from year 
 to year up to 18U5-1^(J, a^ regularly and expeditiously as more urgent official duties, 
 
and tho funds granted by Parliament for such purposes would permit— has already 
 proved of considerable practical utility and scientific interest, in connection with tho 
 improvement of the St. Lawrence Ship Channel and other extensive works, as also 
 the Dominion Tidal Survey and various other Government and Municipal Services. 
 
 2°. That in viow of the valuable results already securad, just ioferred to and the 
 prospoctive reduction of all elevations, whether on laud or water, throui-hout the 
 Dominion to a standard datum plane coineidiiif.^ with the mean level of the sea, viz., 
 that of the Atlantic Ocean at the mouth of tho St. Lawrence, as practised in all 
 advanced civilized countries, it is very desirable that our (ieodotic Levelling opera- 
 tions bo resumed with as little delay as possible. 
 
 3''. That the advisability of continuing this work of national importance will be 
 still more tully realized by perusing tho exhaustive Report of the United States 
 Deep Waterways Commission, dated Detroit, Michigan, December, 18!)«, which was 
 transmitted by the ['resident to the Senate and House of Eepres.nitatives at 
 Washington, January, 18iJ7. 
 
 I have the honour to be, sir. 
 
 Your obedient servant, 
 
 R. STFX'ivEL, 
 Engineer in charge, Canadian Geodetic Levelling. 
 
 
 ! 
 
 : 
 
THE SANGUET TACHEOMETER .self-reducino 
 
 AS ADAPTKD TO 
 
 PRECISION LEVELLING 
 
 IN COXNKCTION WITH 
 
 A NEW GEODESIC ROD. 
 
 I believe I am quite sute in stating by way of introduction, that there is scarcely 
 a sins^le step of any importance to be taken in life, that does not involve the measure- 
 ment of space in some form or other: linear, euperticial, solid, angular. 
 
 Confining here our attention to linear spaces or distances, it ie evident that 
 when such a space is easily accessible all ai'ound, its magnitude may, in general, be 
 readily ascertained by a|)plying lo it a properly constructed and verified standard 
 of length, such as a chain, a tape, a rod, a foot rule, a scale, etc., provided always we 
 are prepared to devote sulHcient time and attention to the measuring and testing 
 operations to ensure correct results. 
 
 This primitive method of measuring linear space has been followed from time 
 immemorial and, it may be said, continues to be almost universall;- adhered to up 
 to this very day with little or no variation, whether distances have to be determined 
 in or outdoors, notwithstanding many difficulties that are experienced. I believe it 
 will readily be admitted by all those who have any knowledge of the subject, 
 that the laborious measurements required between accessible points, in connection 
 with the extensive field operations whii-h are inseparable from the ordinary practice 
 of a civil engineer and that of a land surveyor, are unquestionably those whore the 
 old method yet followed presents the greatest drawbacks. 
 
 The principal, if not the oidy reason of the backward condition of what might 
 be termed the science of measuring distances between accessible points on a large 
 scale, appears to be duo to the fact that nearly all the measurements which have to 
 be made in the tield either for engineering or purely surveying purposes are 
 horizontal measurements, and that previous to the time (not more than ten years 
 ago) when Mr. Sanguet, President of the Society of Topogruphiea! Etigtnoers of 
 France, first hrought out his perfected selfreducing tacheometer, there was no 
 instrument available to civil engineers and land surveyors, that would enable them 
 
 7 
 
 I 
 
to measure horizontal distances expeditlouBly witii the degree of precision and 
 reliability required for the field work, whatever its nature, which is nowadays 
 genen.lly exacted of them to keep pace with the advancement of science in every 
 other walk of life. 
 
 This statement may, perhaps, appear a little overdrawn to civil engineers and 
 surveyors genoially, as many have, no doubt, availed themselves, to a greater or less 
 extent, of the facilities afforded by properly mounted stadia wire telescopes for 
 making distance measurements with the aid of a suitably divided rod, or used such 
 instruments as Edgeworlh's stadiometer, Eckhold'a omnimeter, or one or the other 
 of the various kinds of ordinary or impr:.ved tacheometcrs of the J'orro type with 
 stadimetrical telescopes having supplementary lenses, such as Richers', Colonel 
 Goulier's and other similar distance measuring theodolites which have been brought 
 out since about 18(i0, or may bo the more recent "Milner distance measurer and 
 level." In this connection J would point out, that notwithstanding the superior 
 mechanical .skill displayed in the construction of most of tlie distance measuring 
 instruments hitherto devised, and the fact that many of them have rendered good 
 service when used for reconnaissance field work, and preliminary surveys for 
 projected linos of railways, canals and other important public works, it cannot be 
 denied that they have all proved to be sufficiently wanting in one particular or 
 another, to prevent them from being extensively taken up by professional men, for 
 use in their general practice for the purpose they were chiefly intended by their 
 inventors and constructors, viz., measuring horizontal distances. 
 
 1 do not intend to describe here in tietail the short-comings oi' each one in ])ar- 
 licular of the class of instruments n^ferred to so far as 1 might be in a position to do, 
 for that would be a big undertaking, and I see no practictil advantage to be gained 
 by following such a course. J will content mysef by pointing out: 
 
 1. That, as a rule, the distances measured with those instrun)ents are not the 
 horizontal projections of right lints drawn between two stations, which alone are 
 necessary for plotting purposes; but distances measured in each casein thedirection 
 of the line of sight, which have to be reduced to the horizon and otherwise corrected 
 by means of computations more or less complicated according to the degree of 
 accuracy aimed at. 
 
 2. That in nearly all such instruments the raoasuiement of a distance is effected 
 by comparing the micrometrical interval which separates two stadimetrical wires 
 stretched on a diaphragm, with the distance or hoi, ''t intercepted on a curofuUy 
 divided rod by the visual v&ys determined by the said wires. 
 
 Now, the height intercepted on a rod by two visual rays determined by stadia 
 wires, is dii'ectly proportional to the distance from the i-od to the anterior focus 
 (in front) of the objective, when an oniinary astronomical stadimetrical telescope is 
 used, and to the distance from the rod to the centre of the instrument, when such 
 centre is rendered anallatical, that is to say, when the summit of the di'astimetrical 
 angle is moved from the anterior focus of the objective to the centre of the instru- 
 ment, viz., by means of an extra lens interposed between the objective and the eye- 
 
piece, as was first done, about 1840, by Poito, a distinguished officer of the Pied- 
 raontOHe engineer corps. But readings taken on a rod held vertically with the aid 
 of any one ot the instruments just mentioned, seldom give us a horizontal distance, 
 which is the only one we care to know when we want to make a plan of a tract of 
 land, a railway, a canal, etc.; bvt almost invariably a length of some inclined line to 
 which a correction or corrections— the so-called reduction to the horizon— must be 
 applied before it can be used lor plotting purposes. 
 
 And should we feel disposed to adopt the neither very simple nor very expedi- 
 tious "method of obtaining linear distances, and also of taking levels on sloping 
 ground, witbi t moving the staff or the instrument," which is rocommencJcd by the 
 inventor of the "Milner Measurer," in a leaflet issued about Juno, 1897, viz., by 
 holding in every case the rod perpendicularly to the line of sight, which operation, 
 if performed as suggested, must of necessity be, in a Hcnsc, mere guess work, the 
 differonco between two readings corresponding to the lines of - ht determined by 
 two stadimetrical wires would again give us but a distance, rod to instrument, 
 along the inclined lino of sight. Not only has this sloping distance to bo reduced to 
 a corresponding horizontal one; but it is furthermore necessary to diminish or 
 increaso, as the case may be, the length so obtained by the small distance interven- 
 ing between the jioint on the ground at the foot of the rod of which the poMtiou is 
 to be established, and the horizontal projection of the point of intersection of the rod 
 as inclined, Vvith the line of collimation or optical axis of the telescope produced. 
 
 True, it may bo said, a correction such as that last described is not needed when 
 a vertical rod is employed, or by holding a stadia horizontally over the point the 
 position of which is to be established. As a matter of fact, the vertical stadia is 
 almost invariably used because it is easier to maintain a rod correctly in this position 
 than in any other; but or. account of the obliquity of the axis of its divided face to 
 the visual rays, when these are inclined, as is usually the case, the height intercepted 
 on the rod by the wires is greater than that which would obtain, in the same conditions, 
 on a rod hold perpendicularly to the line of sight, therefore the distance computed 
 with such a height used as the argument, is greater than that which actually inter- 
 venes between the rod and the instrument along the lino of collimation, and has to 
 be correspondingly corrected. 
 
 In view of the rather complicated and tedious corrections and reductions which 
 are found to be an unavoidable accompaniment of the, at first sight, apparently very 
 simple and attractive ordinary processes of stadimetrical distance mpasurements, 
 when it is important to attain a certain degree of accuracy, it is not surprising that 
 inventors should at different times have seriously applied themselves to devise 
 mechanical moans for securing horizontal distances by direct observation, as far as 
 practicable. 
 
 Between, say 1850 and 1852, several ingenious devices applied to instruments of 
 the Porro type and to others have been proposed at various intervals, chiefly by 
 French and (Torraan authors, for reducing by moans of special processes and mani- 
 pulations, the distances measured to their horizontal projections, all of which met 
 with but a limited measure of success. Among such may be cited : Porro's sthenal- 
 latic telescope, Peaucellier and Wagner's telescope, the Wagner P'ennel reducing 
 
i 
 
 10 
 
 device and 8ome ticheometers of Swiss construction with adjustable stadia wires as 
 regards the intervening space, so as to secure a conHtant generating number for one 
 and the same ..istance, whatever the inclination of the line of sight. 
 
 Fi^nailj, there have been brought out since 1865, a few instruments which effect 
 the reductions to the horizon entirely automatically, that is to say : where the posi- 
 tions to be given to the telescope to attain the desired en<i are determined by purely 
 mechanical means, without one having to make either special readings, adjustments 
 or other operations or computations. 
 
 In 1865, Mr. Sanguet, the inventor of the instrument which forms the subject 
 of this Memo., constructed a distance measuring instrument to which he gave 
 the name of " Long! metre." Finding that this instrument had certain draw- 
 backs, he modifiod it in several particulars and then gave to the public in 1806 his 
 self-reducmg tachoometer as first constructed by him. Again, at the Universal Ex- 
 pos.tion held ,u Paris in 18M), an instrument culled Charnot's tacheomeier was exhi- 
 b.ted which much resembles Mr. Sanguet's original '• Longimgt.e," and although an 
 ingeniously contrived, accurate and fairly serviceable self-reducing instrument in 
 the true sense of the word, presents still some of the defects found to be inherent to 
 the " longimgtre," and to the original model of the Sanguet tacheometer, and does 
 not permit of combining hitherto unattained percision with complete and unfailini.- 
 control of the results in the ordinary run of field operations, with the same extreme 
 facility and feeling of satisfactions as with the more recent perfected self-reducing 
 tacheometer known under the name of " TacheomSire auto-rdducteur Sanguet " For 
 this perfected instrument the inventor was justly rewarded with a gold medal af the 
 same International Exposition of 18d9, thus receiving the highest honour conferred 
 on exhibitors in recognition of the merits of their contributions.* 
 
 After receiving from the Department the necessary authority for the purchase 
 direct from the makers, of one of these unquestionably original, ingenious and on 
 the whole truly remarkable instruments modified as I had suggested 1 lost no 
 time in placing the order for the new " Tacheomgtre Sanguet " with Mr. Cabasson 
 ot Fans, who is the sole agent for the same. 
 
 This gentleman placed me in direct communication with Mi. San-met the 
 inventor himself, with whom I entered into a full discussion of the pros and cons of 
 the proposed modifications and additions to the original model of his instrument as 
 got up for general use in France, with a view of securing a tacheometer- (a) That 
 
 would prove especially serviceable forprecision levelling and for measuring correctW 
 greater distances than those falling within the every day practice of a surveyor or 
 an^gineer at work in thickly settled countries, more particularly such long 
 
 of plane tal.le tlu-odul 1 s^w icl Lt m^^^ th,. ,nstr,un..nt b..l„nKs U, tl,o class 
 
 for special pu.•lKw.^^ '' '•"^^"^'■'' *''"' ""^f'' '^r.- varmns f„n„s „f such in.stn.,ne.„ts inado 
 
 arc .u.arly alike. I an. doubtful, ncverth AesV, ' tt 1^ • on h, t^u^^^^lhlT'''""'^'^'''''"'''''^''''"''''^' 
 
! 
 
 11 
 
 Btretchoe as have to be measured when orossing wide streams, ravines, valleys, etc. 
 (b.) That would permit of angles being measured in degrees and minutes, or accord- 
 ing to the sexagesimal division of the circle, as is still the custom in Canada and 
 English speaking countries in general, in place of the grades and centrigrades of the 
 centesimal division now almost exclusively used in France. 
 
 As a result of our deliberations, Tacheometer No. 115 supplied lo the Depart- 
 ment was constructed so as to meet my views just stated, as far as practicable : tht; 
 fundamental principles of the original invention were, however, in no way 
 departed from. 
 
 The modifications and additions just referred to which I considered necessary, 
 will be described in detail, and the reason of their introduction explained, after we 
 shall have gained m insight into the working and resources of this new raea^^uring 
 instrument from the following summary dchcnption of its parts and their combi- 
 nation, which is on much the same lines as that given by the inventor himself in 
 the pamphlet he sends out with each tacheometer. 
 
 The "Tach^omgtre Sanguot" (see Illustration No. 1) is composed of two prin- 
 cipal parts, one of which is destined for measuring azimutal or horizontal angles, 
 and the other for measuring distances and declivities. The same as in all theodo- 
 lites, the first part consists in a graduated horizontal limb which revolves about a 
 vertical axis mounted on a metal stand having three arms, each of which is pro- 
 vided with a levelling screw C. An improved declination tube D is screwed to the 
 under side of the divided circle. 
 
 The base of the second or upper portion is an alidade circle provided with 
 verniers which turn round inside the divided circle, being concentric thereto. On 
 top of this inner circle is fixed a horizontal bar B which carries to the right: a fork- 
 shaped pillar y with wyes for the journals of the transverse axis around which the 
 telescope revolves to turn in, to the left: a divided vertical straight' edge FII, and 
 in the centre a spirit level N, for levelling the instrument. 
 
 As in all transits and theodolites, iho rotation of the whole instrument about its 
 vertical axis, as well as that of the alidade or vernier circle alone can be stopped at 
 will, viz.: by tightening the clamp screws P' and P", and the positions in azimuth 
 of both the divided and vernier circles can be adjusted respectivoly with the aid of 
 the tangent screws R' and E". 
 
 At each end of the diviiled flat straightedge FH there is a lug G, fixed at right 
 angles to its axis, and cylindrical guide holes are bored through both lugs on one and 
 the same vertical axis. In these holes turn the close fitting ends of a prismatic guide 
 rod T, which is parallel to the straight edge, and rests on the point of a vertical 
 adjusting screw R. 
 
 A clamp carrying a vernier is fitted to the rod T, which can be moved from end 
 to end and fixed at any point of its course by means of a tightening screw P. To 
 this clamp is fixed in the middle of its rear face, a steel knife intended for use as a 
 support for the telescope at its eye end. 
 
 The telescope is actually not in equilibrium when supported only on the 
 journals of its transverse axis ; the latter being secured to the telescope near the 
 
12 
 
 objective, viz., several inches from its centre of gravity. On ihe right and left hand 
 Bides of the telescope small steel straight edges ^ are fixed to the tube near its eye 
 end, having their flat faces in planes perpendicular to the azimuth circle and those 
 edges which rest on and slide over the steel knife, one at a time, parallel to the 
 optical axis or line of collimation. 
 
 The inclination of the telescope can thus be modified at will ; after having 
 loosened the clamp P, we can slide it together with the telescope along the prisma- 
 tic guide rod T, to screw it tight again when the object to be sighted comes within 
 the field of view. The slow motion screw ii! enables us afterwards to rectify the 
 pointing of the telencope in a vertical plane. The vernier carried by the clamp P 
 indicates (usually) on the vertical divided straight edge, or scale of slopes, the incli- 
 nation of the visual ray in decimal parts of the horizontal projection r, of the por- 
 tion of the said ray extending from the axis of rotation of the telescope to the line 
 of the knife edge, taken as unity. 
 
 The telescope of the " Tuch^omgtro Sanguet," is a simple astronomical telescope 
 similar to that of an ordinary inverting level, transit or theodolite, with but two wires 
 at right angles to each other for sighting, and having no supplementary lenses or 
 cross hairs or other lines for sighting purposes of any kind. As there is but one 
 horizontal wire, it is clearly impossible to read on a speaking rod. a height above 
 different from that which the telescope points to, ho long as the inclination of the 
 latter remains unchanged. The measure of distances is based on several successive 
 rod readings which are obtained as follows :— 
 
 The nut of the slow motion screw R is connected by moans of a vertical crank 
 to theendof theshortarmof a lev L having as afulcrum a horizontal axisimbodded 
 at if in the rear face of the divided vertical straightedge orslope scale FH and the 
 long flat arm of which extends past the fork shaped pillar Y where it is terminated by 
 a rounded handle. In the long flat handle L there is screwed near its fiee end a 
 cylm.lrical steel pin or peg, the flat end of which touches the lateral face of the fork 
 shaped pillar while the lever remains in one and the same position ; the upper side 
 of the peg butting against one or other of four similar steel pegs or pins a b C d 
 screwed into the side of the pillar, along an arc of a circle described from the 
 fulcrum axis as a centre ; a being the lowest and d the highest of this series of pins. 
 
 Solicited by its own weight, by that of the telescope, and by the action of a 
 spiral spring S, the prismatic guide rod T always tends to descend. And by draw- 
 ing the long lever arm lightly to one side, so as to make the pin inseited in it clear 
 that in the pillar against which it abuts, the rod T together with the short arm of 
 the lever drops with a snap and the next higher peg in tne pillar is struck hard by 
 the pin in the long arm in its upward motion ; at the same time the telescope turns 
 on its transverse axis. 
 
 As the lever L can lake the four positions corresponding to pins a, b, C and d 
 the inclination of the optical axis or line of collimation of the telescope, can be made 
 to a:!sume four dittorent values by the simple handling of this lever, which <^ive us 
 four readings on the rod affording differences that bear constant ratios to th"^ hori- 
 zontal distance to be measured. There being six such difl-erences (for six is the num- 
 ber of po.ssiblo combinations of four readings taken two bv two), the result is that 
 we have at our command six elementary ratios between rod interval and distance, 
 
13 
 
 of which any single one is Bufficient for determining the distance of the rod from 
 the InBtrument. I may here obeei-ve that the lever L with one arm, say 'on times 
 longer than the other, han evidently been brought, into ie([ui8ition by the inventor, 
 'vith the important object in view of-so amplifying the very small arcs or heights, 
 which the eye end of the telescope has to traverse to determine visual rays that afford 
 rea.ings on the rod differing only by from -,o^„ to j-^IJ^ of its distance from the 
 instrument— as to render the use of an automatic device for the determination of the 
 said small displacement of visual rays, practicable both as regards mechanical execu- 
 tion and facility of operation. 
 
 Now the three intervals ab,¥c, and cd botwceii consecutive pins, which are 
 adopted for the tacheometer of the ordinary construction, bear tu each other the 
 ratios of the numbers 10,8 and 4. That is to say: in the tacheometer of the common 
 type the pins are inserted at such intervals in the side of the fork shaped pillar, that 
 by raising or depressing the lonu' levor arm through the distance ab, the short arm 
 will depress or raise the prismatic guide rod T and with it the telescope, through a 
 vertical space equal to i ,',„ part of the radius r adopted for the unit of the scale of 
 tai.gentB or slopes, or which is the same thing, for the length of the perpendicular 
 let fall from the centre of the transverse axis around which the telescope revolves, 
 on to the vertical path described by the steel knife edge when sliding up or down 
 along the rear of the guide rod, and hence such working of the handle of the long 
 lever arm. will also cause a corresponding change in the rod reading equal to ^^^^ 
 pai t of its distance R, or to (O-Ol)i?, from the same transverse axis. 
 
 Again, by moving the same long arm through bc the corresponding change 
 which obtains in the'' rod reading is equal to: (0-008)/?, and finally by passing 
 over cd. with the lever, the rod reading will be altered by 0-004^. 
 
 In the ordinary " Tach6om§tre Sanguet" the four displacements of visual rays 
 determined by the four pegs afford six corresponding rod intervals which are all 
 different, and when arranged in the order of their importance, the values of these 
 intervals are : 
 
 dc = ukT)R^ cb = -nnnr^) ba = 1-50,7-^. 
 
 bd = Torm-B, ac = Tff.Trv^. and ad = toto^- 
 The most generally useful of these six relations between the intervale inter- 
 cepted on the rod and its distance from the instrument, is evidently the third, viz. : 
 that afforded by a displacement ab of visual rays causing ik pa>'t of the distance ^, 
 or a height of (0-01) i2, to be intercepted on the rod. . 
 
 With a view of controlling the readings and increasing the precision of the 
 results, it is however advisable to combine two or three of the above six elementary 
 ratios of rod interval to distance, whenever time will permit. 
 
 Thus if we combine : 
 
 ■^ ■j5q_ (0008) «, and bd = (0-012)5, the following relations must obtain 
 when all the readings are correctly taken, viz. : ^ __ 
 
 be i bd r- (0-020)i2 and M — bc =- (0004) M = bc = bd = be + bd . 
 
u 
 
 2. Tno combination of ac - (0-018) R with ad = (0-{)22) Ji, gives: 
 
 ac + ad = (0-040) « ami ad — ac = (0-004) « ^ ac + ad. 
 
 10 
 
 3. If wo combine the three ratios: ab'^ (0-0 10) A, ac =^ (0018)/? and 
 ad = (0-022) fl, the relations which afford us a means of checltinir in tho office the 
 operations performed on the ground are: 
 
 ab + ac + ad = (o-05)fl and ab + ac + ad = ab. 
 
 5 
 
 Tlie last combin:itioriaftbrd,s tho greatest degree of precision attainable with a 
 minimum number of pointings, it should alway.s be used when great accuracy is 
 desired. When an obstacle between the rod and tho observer prevents making one 
 or the other of tho throe readings without changing the position of the damn P on 
 tho guido rod, it is usual to omit such reading altogether. 
 
 Whon the visible part of tho rod is too short to permit of reading on it heights 
 equal to: (0018)/2 and (0022)ii!, the interval corresponding to (O-Ol )Ji is fir. t road 
 after which having loft tho lever arm buttod against the pin b, the clamp is moved 
 up or down and the cross wire again made to bisect the zero mark by woiking the 
 slow motion or micrometer screw E, that is to say : anew pointing is made which 
 will enable us to read off the rod intervals corresponding to bc == (0'008)i2and 
 bd= (0-012) ft. 
 
 We have, in such case, the following re.ations to control the rod observations, viz. : 
 ab + be + bd r= (0-030) ii: and ab + bc + bd = ab. 
 
 Xow for determining the horizontal projection E of the radius vector of a point 
 on tho ground of which the position is to be established, that is tosay: tho distance 
 from tho rod to the transverse axis of the instrument reduced to the horizon we 
 have tho relations : ' 
 
 JS=100ab = l^0ac: 
 
 : iOOad 
 •^'2 
 
 ad — 100 be = loo be + i oo bc — loo bd : 
 
 mcd 
 6-4^ 
 
 «-8 4 "T2" 
 
 and by combination, 56 additional means of arriving at the value of this radius 
 such as: ' 
 
 100 (ab + ac + ad) 
 
 5 
 
 100 (ab+ad) 
 
 4 
 
 100 (ac fed ^ 100 (ad + bc). 
 3 3 
 
 As it might be a matter of some interest to engineers to know for what parti- 
 cular reason tho displacements of the visual rays were arranged for. so as to cause 
 consecutive intervals to bo intercepted on the rod, bearing to each other the ratios 
 of the numbers 10, 8 and 4, whon 10 and its submultiples 5 and 2, or some other 
 simple numbers might apparently have proved equally well, if not better suited for 
 the purpose intended, I may state that the ratios ^^^, J , and ,U wore selected 
 because, while they permit of combinations sufficiently simple being made to render 
 the finding out of mistakes in the office and the correction of the same a compara- 
 tively easy task, yet they necessitate, when p.-issing from one roading of tho series 
 
15 
 
 to anothor, an aiithraetical operation which cannot be performed with such groat 
 rapidily, as to loave room for suBpicion that tho operator may have boo-i tempted, 
 in order' to suvo time, to Hubstitiito for tho actual supplementary rod readings askod 
 of him, tictitiouH loadings deducod by computation from tho interval between 
 the two first readings. It is moreove. chvimed: that the variety of the six ele- 
 mentary ratios corresponding to the numbers 4, 8, 10, 12, 18, 22, as given above, 
 permits of properly adjiiHting the range of the instrument in accordance with tho 
 degree of precision to be attained and getting readily over diffloullies which arieo 
 when a part of the rod is hi<lden from the observer by an intervening object. 
 
 From what I have just stated, it will be seen that tho " Tach^omfitio Sanguet" 
 affords to engineorsartd surveyors, advantages and resources for the accurate measure- 
 ment of distances in the field, far ahead of any presented by other instruments pro- 
 posed as substitutes for tho chain or steel measuring band or tape. Indeed it lead:* 
 to results HO much superior to the best secured with all other such instruments 
 equally as regards accuracy, despatch and control of field operations, that 1 feel con- 
 vinced the new tacheometeror measuring instrument, needs only to be placed in the 
 right light before practical professional men and contractors to come into general use 
 before very long to the exclusion of nearly all their other ordinary surveying instru- 
 monts, excepting of course a suitably divided rod. 
 
 In support of this opinion I may state that while it is found, in general, that tho 
 result of a very good chain measurement is afi-ected by an error in excess amounting 
 to between 3 and hundredths of a foot per 100 feet, the calculated mean error 
 which one may make in measuring a distance of 100 feet, with the new tacheometer 
 by combining'three rod intervals, is but f./^ of a foot, and the results of numerous 
 experiments show, that the mean error which actually obtains is even less than at 
 the rate of 0-2S foot per 100 feet, viz. :— little over 0-2 ft. per 100 feet. 
 
 Again, with a view of testing the practical working of the tachoometric method 
 of surveying, a plot of ground 538-7 acres in iiroa and containing 605 parcels of land 
 having the f-lrm of elongated trapeziums was surveyed in France both in the ordinary 
 way, viz. : by running lines between angles and measuring them with the chain, &c.. 
 and also entirely with the aid of the new tacheometer and a properly divided and 
 figured rod. 
 
 The survey of this plot of ground actually kept the party which operated in the 
 ordinary way, 336 hours at work in the field, while the party that worked with the 
 Sanguet tacheometer completed the whole field work in 121 hours The party 
 surveying with the tacheometer had to be more numerous than the other ; but the 
 cost of the tacheometer survey proved smaller than that made in tho ordinary 
 way, in the ratio of 411-4 to 789-6. So that it may be said that by the use of the 
 new'self-reducing tacheometer, the expense was in this case, reduced by one-half and 
 the time spent on tho work by two-thirds. 
 
 I may add that the "Tach^om6lre Sanguet" was critically examined in detail 
 and expeiiraonted with by the Official Commission appointed to examine the instru- 
 ments of precision exhibited at the Paris International Exposition of 1889. and more 
 recently by the " Commission extra parlemontaire du Cadastre " of France. 
 
16 
 
 Both the«o Commi«Hion»ofH,.ienliHo ami pructiail men oflhohiKhest Hiamlin.' have 
 rondoroi the verdiC : that thin is the moHl. porfoot it.Htrumont for survoyin.r pur- 
 poses that human ingenuity can well .iovise. and hohco hostowo.l the hiffhoHt oncom. 
 lum^ on its invonlor for IiIm ^rroat achievomonl. 
 
 Finally, the Commiswion of Inventions, instituted at the National School of 
 "Fonts etChuuss^os" in Frtnco. stron^^ly reported in favour of the oxtendoa 
 UHO of the " rachoomfitre SaoKuet " by the members of this juHtly celol.rated corps 
 of en«u.oorH, and ordere.l ihe pun^haso of some instrumontH to bo kept in their 
 depot at the disposal of engineers who would requirj the samo. 
 
 Lot us return now to our sperini Tacheomet.r. No. 115. Tn this instrument : 
 (a) The magnityint,' power has been increased from about 35 (o my 50 which could 
 bo done without difficulty ; (he only slight drawback to iho change beir.g the little 
 extra weight which bad to be added to the instrument in lengthening the telescope 
 from 10-8.:! to l.ySA inches and au-menting its diameter correspondingly for we 
 had no supplementary lens to reckon with, intercepting a large portion ..f the light 
 that passes through the objective, such as the lens used by Porro to render his tele- 
 scope unnallatic. 
 
 The incro.ise in the power of the telescope was considered ncussary in 
 order to render the instrument more especially serviceable for precision lovellin.'- 
 operations, and (or the accurate measurement of greater distances than tbo^o falling 
 w.th.M the every day practice of a surveyor or an engineer, in old settled countr-es 
 like hrance, as alrea.iy stated. 
 
 Now it would manifestly be of a little use to have at one's command a telescope 
 of sufficient power to enable us to distinguish and bisect correctly a target stripe say 
 3.000 or 4,000 feet otf, if we had not also the moans of measuring vorv accurately 
 the inclination of the optical axis when directed to the centre of this target either 
 in reference to the lino of sight passing through the centre of anothn- target Hxed 
 on a rod at a known distance from the former, or in reference to a truly horizontal 
 lino or one running in any given direction above or below the horizon. Jlence : 
 
 (b) The ordinary slow mot'on or adjusting screw R on the end of which the guide 
 
 rol.tbeclamp with knife edge and tbeoye end oftheteieseope are supported in common 
 and by moans of which they are adjusted in position, has been replaced by a micro- 
 meter screw with a pitch corresponding to 100 revolutions per inch, which is about 
 the limit, as regards fineness of thread, where the number of revolutions indicated on 
 a ngured scale can still be comfortably read off with the naked ce. 
 
 Again, it is evident that the micrometer screw R together with the prismatic 
 guide rod T and the knife edge should be placed as far as practicable from the axis of 
 rotation of the telescope, otherwise some difficulty might be experienced to measure 
 with precision, small spaces which could be easily distinguished looking through 
 our telescope of increased optical power. It is ah,o necessary that sufficient room 
 be available between the transverse axis of the telescope and the longitudinal axis of 
 the micrometer screw for the convenient installation of a spirit level with an air 
 chamber at one end, and of a degree of sensitiveness commensurate with the small 
 change of inclination produced by moving the micrometer head over one of its 
 divisions. 
 
17 
 
 Now, with a micrometor Bcrow of tho pitch nettled upon, the moHt oonvenlont 
 length to adopt for the unit ot tho vorticul Hoiile of titngentH, that iH to m\y: for the 
 radius r 1 ot I ho Hmallost circle that can ho doscibod from a point on tho axiH of 
 revolution of tho teloBcopo near ilH 0|)li(;iii axin as a contro, ho aw to bo tan^'ent to the 
 patii followed by tho knifo edge, would evidently be 10 inchen or ;] of a foot — for, ia 
 Huch case each division of a micrometer lioad divided into 100 partH would indicate 
 a vortical tnoticn of tho Hcrow equal to ,„i,imio'"* (0.000.010) r. Thin dimonRion 
 would be moro than HuflBcient to »<atisfy ail recjuiromenlM in olhor roHpects, unfor- 
 tunately, however, tho incroa-e of r from Hi contimetor(»=6'30 inchoH, itM length in 
 the Hanguot tachoomeloi- ac now usually constructed in France, to 10 inchoM, would 
 roiidor tho instrument altogether too bulky and heiivy to bouHod for tho oidinary run 
 of field opoiiilions. Hence: 
 
 (c) The minimum dihtance i)etvvee:) the axis of rotation of tb'" tolo«copo and the 
 kiiilb e<lgo (or tho lino nf tangent«) had to 'jo reduced to 8 inchoH r= jj ft. and tho 
 iiumhor of divisions on tho micrometer head increased from 100 to 125, each of 
 which still roprosonls , ,,,j!„„o part of r or (0.000.010) r. 
 
 On account of tho ordinary slow motion screw whicn is provided in tacheomoter 
 No. 1 undei tho prismatic guide rod for adjusting the inclination of the telescopo, etc., 
 being re|)laced by a tine micromotor screw E in tachoometcr No. Ho, (See III. I in 
 pocitel) tbozoioof the vertical or slope scale of this instrument — instead of being 
 placed, as usual, near the centre of tho flat vertical straii,'ht e;lgo F H, and so as to 
 correspond as nearly as practicable to a truly horizontal axis when tho instrument 
 is accurately levelled — was lowered to the toot of the said straii^ht edge; the object 
 being to eliminate all negative (luantiiies from tho field book, both as regards the 
 vernier and micrometer readings, also to obviate the necessity of making such road- 
 ini.'-s in contrary diroctions. On iho vortical scale of tachoimetei No. 1 15, a porfetitly 
 level lino of coUimation corresponds therefore very nearly to reading 050 instead 
 ofO. 
 
 A detached cliambered double faced level, O, is used on tho telescope, the 
 bubble tubes of which aie ground to a circle of such radius that a division 
 of tho circumfoionce jV-inch in length will correspond to an angle of 5 seconds. 
 This level has thus been rendered four times as sen>itivo as tho single face 
 level on the alidade bar, and about twice us sensitive as tho double faced level used 
 in tho ordinary instrument. An air chamber is provided^' at one end to permit of 
 regulating the length of the bubble according to tho temperature of the atmo-phere, 
 etc., so as to keep it within convenient limits. 
 
 The diaphragm placed in the telescope for defining the position of tho optical 
 axis carries no cross wires or hairs. Instead, tino lines are engraved at light angles 
 to each other, thiough the centre of the plane face of the ou> r or field lens of the 
 Ramsden eye piece; tho diaphragm servos to delimitate the pencil of rays disposed 
 symmetrically around the line of sight which joins tho intersection of the cioss 
 lines on the lens and tho centre of the field of view att'orded by the objective. Lines 
 engraved on glass aro preferable to w. -, or spider webs, as they are not affected 
 by tho humidity of the atmosphere, nor can they be broken, tiieeye piece has. how- 
 ever, to be adjusted to the proper length, according to the sight of tho observer, 
 to render the lines plainly visible to him. 
 2 
 
18 
 
 Tho luijiiHtmunt lor coilimatioti it* made in procinoly the Hiime maniior aH wlien 
 wirois uro umaI, viz., with Iho anl <•(' tour wtoel cupstun rtciovvH V. 
 
 I hftvo jiiHt rnontioiio'l ilonblo tiKUMl lovel"<. Su( Ii lovols do not i»|)|)(»fir lo he 
 much known oulsido of ContiiuMilal Kiirupc; Ihh wtdl deceive to ho more widely 
 known nnd hottei- appieciatod than thoy aro, j^onorally H|)oakiii^'. 
 
 A (ioul>io t'acoil lovol con.'istM, an all other spirit hfveU, of a lonLjitudinally curved 
 glasM vial or tube tilled entiroly with alcohol or ether, excepting a small volume of 
 air imprisoned to form a bubble at the highoHl point of tho tube. The bubble tube 
 of Huch a levtd iH, however, formed of two halves of Hoini-;'ir(!ulai' eroHs M'ction, hav- 
 ing their inner or concave HiirtacoH ground longitudinally «o aw to aissume u 
 uniform convex curvature, and which aro snbsefiuently united along their sides and 
 hermetically Healed at their endH after being tilled with npirits, as just described. 
 Scales having divisions Huitably pi-oportioned to tho degree of longitudinal curvature 
 aro engravoii on th(> upper and lower outside faces of tho lube, symmetrically on 
 either side of a plane passing through tho centres of tho generating circle^ of tho 
 upper and lower inteiior ground surfaces of the spindle shaped tubular envelope, 
 and the whole glass tube when completed is inclosed in a brass tube mounted on a 
 brass j)late. So that, if the air bubble is brought to the centre of tho divided portion 
 of the<loublo faced tube on one side, upper or lower, it will also lodge precisely 
 in the middle of tho scale engraved on the opposite side when the tube is reversed ; 
 tho bottom being brought lo the top, or vice versa. 
 
 When a double faced level is lixed lo tho side or top of a tcletjcope, mounted as 
 that of tho tachoometer, it is evident that unless tho air bubble, alter boit^g brought 
 to the centre of tho divided scale and summit of the tube on one side, aUo v^.nos to 
 rest in the centre of the scale when tho telescope is inverted, by lifting the transverse 
 axis out of its wyes and causing tho journals to exchange places, — the optical axis 
 of tho telescope cannoG be a truly horizontal lino in either its oioct or its inverted 
 position — and that when the instrument is not in such perfect adjustment the hori- 
 zontal line of sight must invariably lie midways between tho pointings made with 
 the telescope in tho said erect and inverted positions. 
 
 Hence, in oidor to establish the correct elevation of a truly horizontal line of 
 collimation, we need only take the moan of two rod readings, one of which is taken 
 when the telescope is in its erect position, or say with the pinion head on top and 
 tho double faced level on its right hand side, and the other when it is in its inverted 
 position or with the level on its left side and tho pinion head below the tube. For, 
 by inverting tho telescope, we not merely correct the tirst reading for the inclination 
 of the lino of sight to the horizon, but also for any error of collimation by which the 
 said li might bo affected. 
 
 It will ibus be seen thai by working with adouble faced level, we reduce by one. 
 half the number of readings that have to be taken when an ordinaiy pivot or 
 geodesic level, with independent striding level, is used in carrying on precise level- 
 ling operations. For, in such case we have to make one reading with telescope erect 
 .„iid level direct, another with telescope oroctand level reversed, athird with level 
 reversed and telescope inverted, and a fourth with telescope iiiverled and level direct. 
 
19 
 
 This in not Iho only (ulviinttii^o whicli i;an ho oliiimed for iho (i(ml)l»» facod lovol. 
 Hy iHinj? tliiH lovol wo tiooil no longer foel anxioiw lost Homo ronulu might ho vitiiitoti 
 on acroiint of (iusl or dirt having a<lhoro«l to tho foot of tho indopondont or striding 
 lovol or to Iho collurrt on whioh it roHtn; nor are wo lilcely to have to «|.end m much 
 time in adjuMting the levol aftor carrying it for a «hort time over rough ground, and 
 e-t] acially after jumping fencoH or ditchot* and climbing ovor rock-', an when working 
 wilhadoi;icho(l rtiriding level, the Htool Ki)lral wpringrt of which bf . uoourtily dirtte:)d 
 od or oUo rtultcnid. 
 
 The double fttceil levol need never bo detached from the telodcopo during the 
 progroHrt of the Hold oporationn, whelhor they are «'arricd on with the ordinary 
 instrument (No. I) or with tachoomoter ''o. 115. in the latter oaso, when tho 
 instrumental work to ho done from a station is completed, tho recorder must lift 
 tho telescope, inclusive of levol, out of tho wyen to take it in a special leather case 
 hunir Mvor his shoulder, to tho next station, thus relieving the observer of '4 pounds 
 «»l ihc part of tho iiistrumout he usually has to carry and reducing tho weight left 
 in his charge to 20^ pounds, tripod included. The tacheometor of th^ ordinary con- 
 struction weighs but \H^ pounds with tripod, exclusive of double fac-'d level, which 
 has a weight of fi-ora * to f j)0und. The Qniiod States Coast and (Jeodetic Survey 
 procivion level weighs 23 pounds with tripod, not incluiliiig tho striding level which 
 has to 1)0 carried separately. 
 
 Now u telescope with the magnifying power increased to about 50 diameters, 
 5)erraits of hundredth-i of a yard being read and thousandths of a yard being 
 estimated on a rod suitably divided in^' ' undrodths and half hundredths of a yard, 
 at distances up to from 2Y5 to 350 yai .. a'jcording to the strength of tho observer's 
 e\'e sight. That is to say : when tho f^loscope is pointed to zero on tho rod the num- 
 ber of whole yards contained in tho distance Ji, rod to instrument, may be read off 
 directly by displacing the optical axis so as to intereopt a height on tho rod equal 
 to }(j of the said distance R, or equal to O-Ol iK, and tenths of yards can bo estimated 
 by the eye. It appears therefore that in order to be able to read on a rod tho three 
 intervals corresponding to: ,,V,!o. tsoo ""^ \Mo "» »' di«t"'>ce, without moving tho 
 clamp, it would be necessary to have at otio's command a rod 0'022 x 350 = 7-7 
 yards in height, which is nearly double the length of tho rods commonly used for 
 precision levelling operations. 
 
 By making use of a rod 12 to 13 feet long, viz., a rod of as great a length as 
 practical experience has shown can bo easily hold vertical, conveniently handled, 
 carried in tho field ami put up for the transportation and kept tolerably straight and 
 in good order generally, tor any length of time, many of the sights that can be 
 e isily taken with a telescope of tho power mentioned necessitate a second pointing 
 and sonio a third jointing, in order to secure at every sight three consecutive rod 
 
 intervals intorcopte.i by visual rays, lespectively equal to : 
 
 . , and 
 
 1000 1000 1000 
 
 But it may be asked, what „ eat necessity is there for establishing at every 
 8i"ht the values of the whole three intervals in question, in connection with preci- 
 sion levelling, considorinir it is not essential that the distance rod to instrument, be 
 very aciiurately known i')v determining the difference in elevation between two 
 
 points, 
 
 2.^ 
 
20 
 
 Quite true, it is not absolutely necessary to meanure very correctly the dintance 
 rom the instrument to .ho rod for Buch purpoHo; but it i.s very important for uh to 
 be ma position to exercise such a perfect control over all the rod rcadingH, includ- 
 ing those corresponding to the horizontal or fore and back sights, as will enable us 
 readily correct on the ground, or in the office, by means of l^ho entries in the field 
 book any error that may bo discovered after the removal of the instrument from 
 1 station whence an erroneous reading was made. 
 
 Now it i8 only by making the four rod readings required, to establish the 
 
 ength of e«ch one of the three contiguous spaces intercepted by the horizontal wire in 
 the positions ofthe telescope determined by thetuur pins or pegs, a, b, C, d, or failing 
 which by making all the rod readings found to be necessary to establish the len-th 
 of each one ot throe corresponding spaces which are not all contiguous, that wo can 
 manage to .eeure the desirable perfect control in question, hence the advisability of 
 invariably taking such a set of four or more readings whenever possible. 
 
 A little reflection will convince us that all the four readings mentioned are 
 really essential to fully ensure the desired control. 
 
 Suppose fcir a moment, we confine ourselves to three readings, viz. those corres 
 ponding to_lhe_po8iiions a, band c of the lever; those readings will give us the 
 intervals ab, bc, and ac bearing to each other the ratios of the numbers 10 8 and 
 18. ' 
 
 iNow let us say that instead of the true height b corresponding lo position b we 
 read by mistake a greater height B, we will then have a5 ab and iSc<bc', while 
 
 ac retains its true value, and hence we have also: ?L? 
 
 10 „ . ac 18. 
 . and <- -^ 
 
 8 a"^^ «• 
 
 These inequalities are, no doubt, a sure indication that a mistake has been 
 made somewhere; but they do not supply the means of locating the error For 
 this purposeafourth reading, and an additional contiguous interval cd are indisnens 
 able; this interval will show us which one of the three spaces ab, b^C, ac is l-ighi 
 and therefore enable us to detect the wrong reading and correct it. 
 
 In the case just supposed, we readily find out that cd>,t Be and cd< ' a.B ■ 
 but that ac- 4-5 or very nearly so, which is as it should turn out, whence we 
 necessarily conclude that readings a and c are right and that readin-- B is w.-oul. 
 VIZ., too large. _ As will bo shown «''n-ther on, however, when two linos of precise 
 evels are run simultaneously, or which is the .amo thing when a line of such levels 
 .s double rodded, more expeditious means of verifying and controlling rod pointintrs 
 and readings are available than by taking supplementary readings „s above x! 
 plained-and ,n order to save time, can be taken advantage of when aceurucy in the 
 measurement of horizontal distances is only of secondary importance. 
 
 xNow, when a tachoometer is more especially intended for use as a levellinL^ 
 instrument, as is the case with No. 115, tho horizontal fore and ba-k sight rrdi2 
 are always the most important of the whole series, and the intervals u, be inter 
 copted on the rod by moving tho lever L from ore of .},„ ..jn, ,„ ^ j,j . . . ^ 
 
 one. have necessarily to be reckoned on either side troin the intersex Uon' °' Vho.T 
 
21 
 
 zontal line of sight with tho rod, at whatever figure suoh a li^e may strijje the 
 scale; that is to say : almost ir.va-Idbly from a complex number including several 
 deoimalH, instead of from a round or other exact whole number, as is usually 
 done when distance measurements are made for ordinary purposes. There exists 
 therefore, in the case of a tachoometer intended chiefly for precision or geodetic 
 levelling, not tho same danger of an observer being tempted to put in fictitious 
 figures, in place of those that would be afforded by actual readings, in order to gain 
 time, and there is no longer the same ground for hesitating to dispose tho butting 
 pins so as to determine visual rays that will intercept intervals on the rod, beating 
 to each other more simple consecutive ratios than those of the numbers 10, 8 and 4, 
 which have been adopted for tho ordinary tacheometor. Acoonlingly, for No. 115 
 the numbers used for such ratios were limited i.o two, viz., to 10 and its submul- 
 tiple 5; the butting pins a, b, C, d being placed so as to give rod intervals corres- 
 ponding to: 
 
 lOii! 152? „„. 20R . , e WR 18i2 
 
 1000' 1000 '^"^ ioTo' '" ^'''^ ''-■ rooo' iouo 
 
 and 
 
 2222 
 
 1000 
 
 and tho number of different latios thus reduced from six to four, viz. : 
 from 4, 8, 10, 12, 18 and 22— to 5, 10, 15 and 20. 
 
 While with tho oi-dinary tacheometer (No. 1) the sum of tho rod intervals 
 determined by the three pairs of rays, ab, ac and ad, viz., the greatest height 
 that can be intercepted by any three pairs of the four rays a,»b, C and d is equal to 
 OObOR, the greatest corresponding rod space that can bo obtaine i with tacheometer 
 No. 115 is but 0-045 i?. 
 
 When, however, wo take into coMsidoratioii the fact that in tai'hoometer No. 
 115 the magnifying power and the radius r (oi' perpendicular distance of the centre 
 of the conical gun metal axis of rotation of tho telescope, from the plane travelled in 
 by the steel knife edge), have been increased, viz., the former from ;'bout 3o to 50 
 and the latter from 6-30 to 8 inches, it becomes apparent that although the pencil 
 of visual rays determined in the ordinary tachoometer by passing the lever L from 
 pin a to pin d or vice versa, and which intercepts a height (0'022)ii!on the rod, has 
 been slightly contracted, viz., so as to reduce this distance to (0-020)^, it cannot 
 be said that the accuracy of the results as regards distance measurements, has been 
 diminished, indeed the reverse is the case, as we shall see presently. 
 
 At the same time a tacheometer such as No. 115, where the combination of four 
 consecutive readings from a single pointing — which gives the best results as regards 
 distance measurements — determines an aggregate rod interval of but 0"045i2, is 
 evidently not so well adapted oii '^-^ whole for mea'^uring distances, as a tacheometer 
 of the ordinary construction, where the aggregate rod interval determined by the 
 corresponding combination of four readings from one and tho same pointing is 
 exactly equal to 0'05i?. 
 
 While in the latter case we have simply to multiply the sum of the rod 
 intervals, or 0'05 R, successively by two and then by ton, in the former, we have to 
 multiply tho sum of tiie said intervals, or 0*045 /' by two by ten and then by 
 
 IMiilll When, however, more than one pointing lias to be made, inorder 
 
 to secure the four readings corresponding to the positions a, b, C and d of the 
 
22 
 
 levor, the conditions are reversed ; that is to say, tachoometer No. 115 is, as a rule, 
 more advantageous than the ordinary instrument. 
 
 That the accuracy of distances measured with the aid of corresponding combi- 
 nations of rod intervals determined with tacheometers No. 115 and No. 1, is invari- 
 ably greatest in the case of the measurements made with the former may be 
 demonstrated as follows* : — 
 
 The errors we are liable to make under any circumstances are : — 
 
 1. Errors, Ec, of contact of the levoi- with each one of the butting pins, a, b, C 
 and d. 
 
 2. The error, £■;?, of the p inting made on the target line in the first position 
 of the telescope, viz., say that determined by pin a. 
 
 3 The Errors, Er, in the rod readings for the other sights. 
 
 Let us consider the case of a rod observed on at a distance of 100 yaids. 
 
 The error of contact may be estimated according to Porro at: ^^^ part of ^^'j^ 
 of a yard. The effect of this error is reduced in the ratio of the arms of the lever 
 L, viz , as 8 to 1 on the ordinary instrument (No. 1) and as 10 to 1 in tacheoraeter 
 No. 115; and it is amplified in the ratio of the space between the two points of 
 suspension of the telescope, to the distance sought, viz., in the ratio of r to R, or of 
 0-l'750 yard to 100 yards with tacheometer No. 1 and 0-2222 yard to 100 yards with 
 No. 115. Tlie mean error Ec on the rod caused by an error of contact between the 
 lever and a butting pin is therefore in thousandths of a yard : 
 
 (a) With the ordinary tacheometer or No. 1 : 
 
 V. 1 1 1^0 100 ^, .,^„ ^ J , .. 
 
 ■CfC, — V -- V - =:„„=0 357 thousandths ot a yard. 
 
 200 8 0- 1750 ~" 280 
 (b) With tacheometer No. 115 : 
 1 1 100 
 
 Ec 
 
 100 
 
 1 1 .'! 
 
 200^ 10 "^ 0-2222 — 444-4' 
 
 : 0*225 thousandths of a yard. 
 
 The mean error of a pointing E-p, deduced fiom special experiments made by an 
 experienced operator with a rod put up at a distance of 100 yards under oidinary 
 conditions, appears to be ajout \ of a thousandth of a yard. 
 
 Finally, the mean error of a reading Er made under the same conditions, maybe 
 assumed at J thousandth of a yard for tachoometer No. 1, and for No. 115 at say ^\ 
 of a thousandth of a yard, when the interval which separates the cross wire from 
 the centre of the next lower target line is estimated by the eye, and at less than \ 
 thousandth when the said interval is measured with the aid of the micrometer screw, 
 or say on an average at 0-376 of one thousandth of a yard. 
 
 That such a degree of accuracy can be attained without difliculty, appears from 
 the following considerations. 
 
 1895. 
 
 * 8o« ■• Lin iauln-oiMHlris uuKi ri-iiiictt-iirK " par E. Frevot, C(m<lucte\ir dea Fdnts Ht ChauBseeB, 1 
 
 'arm 
 
23 
 
 as a rule, 
 
 ng combi- 
 I is invari- 
 ' mny be 
 
 The magnifving power of the telescope being about 50, a division of one 
 hundredth of a yard on a rod put up at a distance of 100 yards, is viewed in the 
 telescope, in tho same manner as a division ,5'^^ of a yard wide with the naked eye, 
 when about inches distant. It is not hard to satisfy one's self that under such 
 circumstances, the tenth part of a hundredth yard division and even much smaller 
 spaces, can quite easily be estimated with the eye, and therefore that the error we 
 are exposed to make can easily be placed at irom ^V to .^^ of such a division. 
 
 IS, a, b, c 
 It position 
 
 Is. 
 
 !•* of 1 Ait 
 tbo lever 
 sheoraeter 
 points of 
 o R, or of 
 '•ards with 
 tween the 
 
 lade by an 
 ' oidinary 
 
 IS, may bo 
 i at say j\ 
 wire from 
 ess than J 
 iter screw, 
 
 lears from 
 
 iBtiees, i'arin 
 
 Mean error of a distance R of 100 yards measured by means of the 
 
 relations : 
 
 ^__ab + ac + ad__20 (ab + ac + ad) for tacheometer No. 1, and 
 
 U'l/D 
 
 R z= ?:^?'^t^J^ _ 22-22 (ab + ac + ad) for tacheometer No. 115. 
 045 
 
 This operation comprises 1 pointing and .^ readings and hence 4 contacts. 
 Moreover we have to bear in mind that while the error of pointing £?j» does not 
 affect the value of tho whole number selected as a starting point for measuring the 
 rod intoivals, it modifies by the same quantity Ep each one of the succeeding read- 
 ings. In making the sum of the rod intervals, the error of the pointing is therefore 
 trebled, that is to say it is increased to 3 Ep. According to the theory of errors, 
 tho total error E of the sum of rod intervals ab + ac + ad determined at a distance 
 of 100 yards is therefore in this case, in general : 
 
 E = 1 '(^HEp) ' + 3 (iiV2-) 4 ., (^Ec2) 
 
 Now replacing the symbols l)y thoir values in thousandths of a yard, as above 
 established, we have for tho total error of intervals determined with tacheometer 
 No. 1 : 
 
 E, =::: l/^(3"x 0-25) '^ +3 (0-5)2+ 4(0W7)2—, 0-^^^^^ 
 and for the total error of intervals determined with tacheometer No. 115 : 
 
 El 1 5 = I (3 X 0-25) ••= + 3 (0-4)'^ + 4 (~0-225)- 
 = 1 \-24tb= 1115 
 
 ^/ 5(i25 + 0-48 + 0-2025 = 
 
 The corresponding errors Er - Er 
 
 on the distances are: 
 
 Er =r 1-35 X 20 = 27-00 or U-O2T0O yd. ... 
 Er = 1-115 X 22-22 = 24-78 or 002478 yd. 
 
 115 
 
24 
 
 Mean error of a distance i? of 100 yards measured by means of the 
 
 relation : 
 
 Rz= 
 
 ab 
 
 qTqJ =: 100 ab, with both instruments. 
 
 This measurement necessitates 1 pointing, 1 reading and hence 2 contacts, 
 therefore : 
 
 For tacheometer No. 1 the tot .1 error E, , of the rod interval ab determined at a 
 distance of 100 yards is: 
 
 E, = l/r7X0-25)"2n~x|0-5)2+2xX0-357p = 1 (rM26T0-25T0-2549 = 
 = 1 0-5674=..07533. 
 and for tacheometer No. 115: 
 
 B,,,-. = I Ix (0-25)2 +YxlO^)^T2^7o¥25)2 -= i '00625 + 0-16 + 0-1012 = 
 ^ I" 0-3237 — 0-5b'87. 
 Hero the corresponding errors on the distance are: 
 
 Er =^ 753;s X 100 = 75-;J3 or 007533 yd. and 
 
 Er =- 5687 X 100 :. .^fi-87 or 0-05687 yd, 
 
 116 
 
 Mean error of a distance ii; of lOO yards measured by means of the 
 
 relations : 
 
 „ ab + bc + bd i<)0 ^ , -^- , , 
 
 K= ..... =: .^ (ab + bc + bd) for tacheometer No. 1 and 
 
 O.OM 
 
 + bc- 
 
 • 025 
 
 p_ ab + bc + bd 100 --^ :^ — , „ 
 
 -« — - A„- — ~^^ (ab + be + bd) for tacheometer No. 115. 
 
 When carrying on levelling operations, it may be found convenient to use this 
 relation, with the intervals counted from a single pointing made near the centre of 
 the rod with the lever abutted against pin b. 
 
 In this case we have, therefore, as in the first, 1 pointing, 3 readings and 4 con- 
 tacts; but the error of pointing, ^;>, modifies the adjoining intervals ba and bc on 
 each side in opposite directions, so that an error on ba is neutralized by an equal 
 and opposite error on bc, and the only interval affected by Ep is bd. Hence : 
 
 and replacing the symbols by their numerical values, wo find for the total error of 
 intervals measured with tacheometer No. 1 : 
 
 E, = i (025)2 +3 (0.5^^2 +4(0-357)2 = i/0-U62i>+0-075 + U-5098=r^i^^^^^^ 
 and fur the total error of those measured with tacheometer No. 115; 
 
25 
 
 ans of the 
 
 Bi 1 5— (/(0-25)2 + 3 (04)2"+ 4 (0.225)2=j/00625 + 48 + 0-2025=1 0-7450=0-863 
 Again, the corresponding errorb on the distance are: 
 
 1-15x100 
 Er = -3 = 38-33 or 00383 yard. 
 
 E „ = 0863 X 1 00=:34-52, or 00345 yard. 
 
 1 15 
 
 If instead of the intervals being determined with one pointing made w hiie the lever 
 is abutted against pin b or against c, two pointings are made, the error of the pointing 
 which is used for two readings is doubled, and we have for the total error of the 
 intervals : 
 
 E = v'Bp^ + (2 J?p)2 +3 (Er)' +4 (J?c)-^ 
 
 Whence we deduce for the total error E; o\ ■_ int-^rvals measured with tacheo- 
 meter No. 1 : 
 
 E =1 (0-25)« + (0-50)2+3 (0-50)'^+ I (0-357)'^ =,/0-0t)25 + 0-:i5 + 0-75 f 0-5098= 
 1 
 
 I 157^3=1-253 
 and for the total error of those determined with tacheometer No. 115: 
 
 E =,/(0-25)2 + (0-50)2 +3 (0-40)2+4 (0225)=|/0-0u25 + 0-48 + 0-2025= 
 
 115 _ 
 
 /0-9950=:0-997. 
 
 Once more the corresponding errors on the distance are: 
 
 1-253 X 100 
 Er = 3 =41-8 or 0-0418 yaid, and 
 
 0-997 X 100 
 Er = 2.J.- =39-88 or U-0399 yard. 
 
 The inventor of the "Tach^omfiLie auto-r^ducleur" has himself given the loUow- 
 ing formulas, which, ho states, indicate the error we are liable to make on any 
 distance E with the two firt«t combinations above mentioned of rod intervals 
 determined with the ordinary instruraont (No. Ij, viz.: 
 
 1st. By using the relation ^ — 001 : 
 
 Yard ^ 
 
 e« =="'0^+4Foo 
 
 •(A) 
 
 2nd. By using the relation 
 
 Er 
 
 ab + ac + ad 
 
 M 
 
 = 0-05: 
 
 1 1 
 
 Yard fj 
 
 ,— ^'^^ + ioouo 
 
 .(B) 
 
 By snbhtituting 100 yards for B in iualions (A) and (B) wo have: 
 
 E , = 0-0f)2 yard. 
 
 With ratio ^*' = 0-01 
 
 . ab + ac + ad „ ^^ 
 With ratio ^ =0-05; 
 
 = 030 yard. 
 
 1 1 5 
 
2t) 
 
 It miiy not bo Riiperfluous to repeat hoi-o that while the roaiilt of a very j^ood 
 steel tape meusurement will bo in cxcesH from O-O!^ yd. to O-OG yd. per 100 yards, an 
 already stated, the tacheomoter moasiiroment may indicate in very dry weather a defi- 
 ciency of from 02yd. to 0-03 yd. The difference of j (3 + 2) = 5 | to | (6 + 3) = 9 I 
 hundrodlhs may change t*ign in very cold and wet weather. 
 
 With the butting pins placed as above described, it is evident that ho long as the 
 actual ditterenco of level between the horizontal optical axis or lino of coUimationof 
 the telescope and the zoro of the rod remains within the limits of the latter, or say 
 within from 4 to 5 yards, and the distance, rod to tacheomoter, does not exceed 300 
 yards, it is always quite possible, not to say easy, to obtain with tacheomoter No. 
 115 a sufficiont numbe of rod readings to determine three intervals which are either 
 themselves contiguous, the same as the spaces intercepted with one pointing, or that 
 will correspond to those spaces, provided we take care to have the lever butted 
 against the proper pin, previous to finally setting the telescope truly level with the 
 aid of the micrometer or slow motion screw and the sensitive double-faced level, for 
 taking the horizontal fore or back sight. 
 
 As regards the distance, it may be said that it happens very seldom that the 
 atmosphere is sutfici ntly clear and pure and the light as well as the ground suitable, 
 for us to venture taking even 300-yard i-ighis on each side of the instrument, for any 
 length of time, and this distance may properly bo considered to be the extreme limit, 
 which should not be overstepped in carrying on geodetic levelling operations. It is 
 only under exceptionally'^ favourable circumstances that a few sights between 300 
 and 400 yards long can be taken consecutively in running linos of precise levels. 
 
 With view of devising a rational and expeditious method of taking series of 
 combined level and distance readings for geodetic levelling purposes, or sets of 
 geodesic readings with tacheomoter No. 115 — after having levelled the hoiizontal 
 limb or circle of the tacheomoter by moans of the throe ordinary thumb levelling 
 screws Mtid the level tube fixed on top of tlio cross-bar — lot us take a seriesof read- 
 ings on a lour yard rod 200 yards dintant, with the long lever L successively butted 
 against the pins a, b, C and d, and commencing with reading 0, while tho lever is 
 kept in place by pin a, and let us designate by Pn, tho series of intersections of the 
 pencil of visual rays determined by the pins a, b, C, d, with the rod. 
 
 In such case we evidently subdivid3 by means of the said pencil of rays, the full 
 height figured on the rod into three paits: U,2, 2,3, and 3,4, which boar to each other 
 the same ratios as ab to bc to cd, intersecting as we do. the rod with tho four rays 
 in question; at at the foot ; at figures 2 ai d 3 near the middle, and at figure 4 at the 
 top. Now, if any one of tho four rays producing the series of intersections P,; be 
 level, it is clear that the three additional intersections and corresponding readings 
 required for geodetic levelling purposes arc secured without any special pointing 
 being necessary, that is to say, without the clamp P and knii'o edge having to bo 
 moved up or down on the prismatic guide rod T. 
 
 The four positions of tho pencil of riiys determined by the pins a, b, C, d, cor- 
 responding to position P,„ in each of which a different one of the said rays is hori- 
 zontal may be termed the fundamental positions of the standard pencil of rays 
 
 i 
 
2T 
 
 ery good 
 
 yardfi, na 
 
 ler a dofi- 
 
 3)^:9} 
 
 3nf^ as the 
 imationof 
 er, or say 
 xceed 300 
 neler No. 
 are either 
 ng, or that 
 ,'er butted 
 with the 
 level, foi* 
 
 I that the 
 d suitable, 
 it, tor any 
 eine limit, 
 ons. It is 
 ^veen 300 
 levels. 
 
 : series of 
 or sets of 
 tioiizontal 
 levelling 
 68 of read- 
 oly butted 
 10 lover is 
 ions of the 
 
 7H, the full 
 each other 
 I four rays 
 ire 4 at the 
 ions P,i be 
 g rcadiuf^s 
 I pointing 
 71 ng to be 
 
 C, d, cor- 
 P'H in hori- 
 !il of rays 
 
 I'poees 
 
 )rre8poi 
 
 )rocision levelling, and the level rod pointings 0, 2, 3 
 
 positiou'i may be culled the fundamental series of level 
 
 powumg« ».... ......^....„. .., the rigures ((»), (2), (3) and (4), where (0) denotes a 
 
 level pointing to figure with the lever L butlo I against oin a, (2) a level pointing 
 to tigure 2 witl< the lever butted against pin b, (3) a level pointing to Hgure 
 3 with this lever butted against the pm c, and (-4) a level pointing to tigure 4 with 
 the telescope while the lever L is butted against pin d. 
 
 For .listancos, lacheometer to rod, of less than 200 yards, a level pointing may 
 strike more or loss above or below its corresp-)nding fundamental position, according 
 as the distance differs more or less from 200 yards, without a special pointing 
 becoming nocossaiy for the purpose of securing the intersection whether of the 
 upper or of the lower visual ray of the corresponding pencil a, b, C, d, with the 
 rod. But when the said distance exceeds 200 yards, such a special pointing becomes 
 indispensable to attain the said end, and occasionally oven a second one. 
 
 Now, as the intervals 3-4 and 2-3 are only one-half as large as the interval 0-2, 
 it is evidently best for us to secure, as much as piacticable, the special pointings 
 required at the lower end of the rod, which can be managed by abutting the lever 
 against that particular pin which corresponils to the fundamental level reading next 
 above the intersection of the horizontAl lino ot eollimation with the rod, whenever 
 this is possible. That is to say, by butting ihe lever against pin d for all level read, 
 ings between 3 and 4 yards, against pin a for all readings between 2 ai.d 3 and 
 against pin b, for all level leodiLgs between I and 2 yards. 
 
 In all cases, however, where the level reading strikes the rod between the 
 figures and 1, it will be best to start our series of readings with the lever abutted 
 against pin a, for by so doing we raise the fundamental level pointing (0) less than 
 we would have to depress the next higher pointing (2). 
 
 With a rod about 4^ yards long, sucha^ that proposed to be used, the pins a, b, 
 C d may continue to be used lespectively tor J yard above the Hguros 1, 2, 3 and 4; 
 this extra i yard is, however, chiefly intended to cover any small error in the horizon 
 tality of the line of eollimation, that may result from the provisional levelling of 
 the instrument with the aid of the level tube iV^ fixed on the cross bar instead of the 
 more sensitive level attached to the telescope. 
 
 The subjoined table shows that by operating in the manner indicated, it is only 
 when the distance-rod to tacheometei— exceeds 250 yards, that a second special 
 pointing becomes indispensable to secure a complete set of four standard rod read- 
 ings, and then only when the level pointing strikes the rod between figures 2 and 
 3.25 yards, or between 6 and 9-75 feet. 
 
 The sketch in the first column of tho table given on next page shows at a glance 
 the limits between which each one of the pins a. b, C, d, should, as a rule, be used for 
 maintaining the telescope in a level position with tho aid of the long lever, in order 
 that the complete set ot lour rod readings in question may be obtained with a mini- 
 mum number of pointings 
 
28 
 
 SKJtIES OF RRADINGS with fundamontal level pointings (2), (3), (4), lowered one 
 yard (3 ft.) and with the same raised ^ of a yard ($ft.); also with fundamontal 
 pointing (0) raised l^ yards 3J ft). (See sketch in margin,) 
 
 
 
 
 laH&i 
 
 
 
 
 -is 
 
 l)ist»iit't' ^J t; 
 
 Iimtrdiiioiit i-c — 's 
 
 ExtieiMc KeRdiiiKM, <(. 
 
 N((inliHr iif 
 Spfciid i'liintiiiKH 
 '/. r, (/, in Yard«. reiinin-d to hccui-o h com- 
 
 
 
 ti. Hod. 
 
 1,5-3. 
 
 
 plt'tf .set of four 
 
 
 
 
 1 
 
 
 Staiidunl Rending'*. 
 
 
 
 ' ' (0)' 
 
 <i .--- 000, '- : 1-0(M), ,• 
 
 1-500, -/ 2-000 Noil... 
 
 
 
 
 '"'l;« = 1-250, h -= 2 2.50. «■ 
 
 2 7.'">0, d 3 2.50 " 
 
 
 
 
 ,.,, 1 \h ^ l-(00, = r.5(MI, f/ 
 
 2 (MK), tt (» (X)0 „ 
 
 
 
 lottyartls.. 
 
 1 '-'"1 
 
 1 
 
 h = 2-250, c =^ 2 750, »/ 
 
 3 2.50, .( - 1 250 „ 
 
 F«et 
 
 it.rs* 
 
 
 
 m{ 
 
 c ^ 2000, rf== 2 500, /, 
 
 1-500, ,( 500' „ 
 
 _ 
 
 
 
 c ^3-260, d^ 3 7.50, /, 
 
 - 2 750, il - \"*^ „ 
 
 
 
 
 
 l, H.( 
 
 rf = 3-600, c = 3 (MX). /. 
 
 2 500, (( 1 ,500 ., 
 
 
 4- 
 
 YARDS 
 
 
 d = 4-250, (• = 3 750, /, 
 
 - 3 250, « -^ 2-2.50: ,. 
 
 
 
 ( ' (■:« ^ 0-000, 6 = 2-000. <• 
 
 3 000. d |(KM)'Xoiu'. 
 
 
 
 
 
 , m 
 
 a = 1-250, h ^ 3 250, ,■ 
 
 4 250 Out' cxti'a |K)iiitin(jr, 
 
 "P 
 
 
 
 
 y 
 
 '■ 
 
 3-250. -/ ^ 4 2.50 
 
 
 
 
 
 ( h ~ 1000, p - 2-0(Hi. ,/ 
 
 3-000 j 
 
 
 
 Feat 
 
 »9.75 
 
 
 (2)-^ h 2-000 
 
 (( 0-000'One cxti'ji |H>iiitin«, 
 
 
 + 
 
 2(«)y:ir<ls.. 
 
 I '- 2 250. (( 2.50, c 
 
 3-260, -/ 4 2.".0\()iic 
 
 
 
 
 
 
 1 '■ = 2(100, (/ - ;r(MM», /, 
 
 1 (KH) 
 
 •.oot.. 
 
 « 
 
 
 
 
 (3)-^ 1, 
 [ e -- 3-250, h -^ 2 2.50. .< 
 
 ( d = 3-000, ^ 2 ()(Kl. /, 
 
 H)- i '' 
 1 L(/ 4 -250, c - ;{ 2,50, /< 
 
 2(KKl. ,1 O-0(KI()iiecxtni iioiiitiiiif. 
 250, (/ 4 2.50\oi)e. 
 
 1 (MM» 
 
 
 
 ;, 
 
 i 
 
 
 - 2000. il - (K)(M)„(. .Ntra pciintiiiL'. 
 
 
 
 
 
 
 2-250, il 2.5(»Xoii<. 
 
 
 
 r tt ^ 000, h - 2-500, ,. 
 <»'\- 1 250, /,. .3750 '■ 
 
 - 3-750 
 
 «.7Sr 
 
 + 
 
 
 
 
 -3000. (/ 4 250 ()iii. cxtiii pdiiitiiijjr. 
 
 
 4 
 
 
 fi.00 
 
 
 '. 1 7..H. r 
 
 3 OUO, d - 4 250 
 
 
 
 
 
 '■ rOOO, (■ 2 250, (/ 
 
 3 500 
 
 ; 
 
 
 
 
 ,.,, h - 2-.50f» 
 
 " (MK) „ 
 
 ■ 
 
 
 
 
 *-'i h -- 2-250, rt OOo, ,■ 
 
 3 .5(M) 
 
 ^ 
 
 
 
 250yiirds.. 
 
 3 (M)0, (/ 12.50 
 
 
 
 
 
 / '• 2-.5(Ml, d :< 2.50, /, 
 
 ^ '\ <■ : 3-250. '- :: 2 ' 000. ,( 
 
 [r r 3 -000 
 
 7.50 
 
 
 
 Feeft 
 
 
 ^ 2-500, d - 0000 
 
 
 + 
 
 ^.75 
 
 
 O-(MM) 
 
 
 
 
 
 d - r2.5o „ 
 
 Feet 
 3.00' 
 
 ^ 
 
 YARD 
 
 
 1 d '- 3 -0(H), -■ -: 1 750. // 
 
 (4)J i '' 
 ' 'l d --^- 4,250, c :. 3-(HM), /, 
 
 5(M) 
 -^- 2-5110, „ .- (lOOO 
 
 
 
 
 
 1-750 
 
 
 
 
 
 ' /, 
 
 - 2-,5(K), rt = 0000 
 
 
 
 C9 
 
 1 
 
 ;' i( 0(1(1. /, ;■! 000 
 
 ' '] « 1 250. /- =. 4 250 
 
 '. ^ 1-2.50, .■ 
 
 2 7.50, (/ 4 250()iic extra iiiiiiitiii^'. 
 
 
 
 
 
 
 
 
 
 
 2 7.50. -/ -- 4 2.50 
 
 
 O 
 
 
 
 h --' 1-000, (• 2 .5(10. ,( 
 ,.,v '- -- 3-000 
 
 4 (MHI 
 
 ^1 000 
 
 
 
 
 '"' fc = 3-2.50, « = 2.50 
 
 
 
 
 
 ' '/ - 1 250 ,. 
 
 2 7.50. ,/ 4 2.50 
 
 
 
 aoOyal-ils.. 
 
 (• 2-000, -/ ;r5oo, /, 
 
 1 '' 
 
 (3)- <• 3-2.50, /, r- l-7.-,o 
 , '/ ^ 3-000, '( 
 i I. c - 2-750 
 
 (/ 3(100, <• - 1 .500, /, 
 
 ^^H rf = 4-230, e = 2.750, /', - 
 
 .5(Mi 
 
 3 (HM(, ,/ OfHMI 
 
 ""*• jTwo extra pdiiitiiiofs. 
 ./ = 4-250 
 
 (MHI 
 
 3 OOO, (( (HlOOiie evtra pniptini' 
 
 
 
 
 - 1250 ■ ■ '■ 
 
 
 
 
 ^ '' 
 
 : 3-(M)0, ,/ - OOOO' 
 
29 
 
 THE NEW (GEODESIC TACHEOMETEU liOD. 
 
 paiiitiil^'". 
 
 An indinpotiHable adjuncl to every tiichcomcter in -i properly constructed and 
 suitably divided rod. Of coui^e any itind oi levoliing or tolonjeLer rod answers, in 
 a way, for use in connection with the " taclidomSti-e aulo-r^ducteui-," some better 
 than others, yet I know of none, which ullogethe" "UtiMfies, in my estimation, the 
 requirements of an ideal tacheometer rod that be used advantajfeously for 
 
 ordinary engineois' and surveyors' Held work as dl as for precision levelling 
 operations. 
 
 I therefore ventured to add a speaking levelling and measuring rod constructed 
 in accordance with the particular views I entertain in this re.si)oct, to the already 
 long list of r-ucli rods of various patterns wliich are in existence. The proposed 
 geodesic rod, inclusive of all the accessories required for carrying on successfully 
 taclioomelrif; operations of all kinds is shown on illustrations Nos. II and III, which 
 are to be found in the acompanying pocket, with details enlarged ; the figures being 
 accompanied by explanatory references. 
 
 The new rod is similar, as regards general construction, to the geodesic levelling 
 rods E and F designed t)y me, which have been used exclusively for some ten years 
 past, on the geodetic levelling operations carried on under my direction on the 
 St. Lawrence, etc., for the Public Works Depa<tnient, viz.: eversince the rods were 
 returned to the Department from the Indian and Colonial Exhibition held at London 
 in 1886; but instead of having a scale of feet, tenths and half-tenths with a white 
 target line 0.008 foot wide, pain'>d at every half tenth of a foot on a black strip on 
 either side, like the said levelling rods, the now rod has its scale marked out in 
 white as follows, on a black ground or strip 0-05 foot wide, painted on one side of 
 its face, viz. : — 
 
 let. When the foot is adopted us the unit of lineal measure, at tlie quarter, half, 
 thre u Afters atid whole tenths of a foot, by white target lines 0'02 foot wide, 
 connci.,3d in the centre by a white bead 0-005 foot wido; the whole and half-tenth 
 white stripes being left the full width of the scale strip, but the quarter and thiee- 
 quarter tenth lines only one-half this width. The half-tenth target lines are further 
 distinguished from the quarter-tenth lines by black points painted at their inner 
 ends, and the whole tenths from the quarter and half-tenths by heavy black lines 
 run across the whole width of the space left for the figures beside the scale strip. 
 
30 
 
 2nd. When the yurd is adopted iw the unit of length, the wcale in mm kod out by 
 whito target linos 0.004 yunlH svido at lu.ch hmi'lrodlli und caoh halt'ii hnndivth of 
 a yiiid, which arc coiiiiocttHl in the i-oiitro hy u while houd v, .)Ul yd. wide ; tlio 
 wiiolo h.indroaih linoM biuiiij lofi iho full width of the (^culi! htrip, but tho half 
 hundrodlh limw only oruj-half iliis width. Tho diruction in which tho londingH are 
 ini'icanin',' is moroovcr hhown by four heavy him-k linos of irrudually increasing 
 longths, put in opposito Iho tii>l, socond and third iiuarlers >f oach tunth and at tho 
 nppor end of the sanu'. 
 
 The figuros denoting the feet or yards are painted red, while thnso indicating 
 the tenths aro painted blai'k and a liltle Minaller than '.ho foimer ; each figure 
 invariably having it« centre opposite the centre of the corr -Hponding division. On 
 the roil divided into yards, the number of whole yards cut otf by the cioss wire 
 above is also indicalod in the centre of oaeh tenth of a yard, by a coriospoiiding 
 number of dots painted red. 
 
 A rod with •< scah of yards and decimals has tho advantage of being less 
 charged with figures than a solf-roading rod subdivided into foot, tenths and hun- 
 dredths, but a roti divided into feet, such as shown on plates II and III in pocket, 
 is perhaps Iwtter adapted, on the whole, to the requirements of the engineering pro- 
 fession. With a view of facilitating the precise determination of rod intervals at 
 short range, supplementaiy division lines, one-half humlredih of a foot centre to 
 centre, have Ic'en drawn in black along tho whole length of tho foot scale, so as to 
 interfere as little as practicable with the clearness of the main white target linos. 
 
 Tho indiscriminate use of one and tho same target lino or stripe or series of 
 target linos of the same width, for very short as well as for comparatively long 
 sights, does not appear to me to permit of tho observer making uniformly accurate 
 pointings througnout, or of the eye estimating with a uniform degree of precision the 
 space that intorvenes between the apparent line of intersection of the horizontal 
 wire with the rod and the nearest division woilc of the rod scale. 
 
 In operating with tho self-reading telemeter or tacliooinoter rods at present in 
 use, so far as I am aware, it is apparently taken for granted that the subdivision by 
 the eye 01, say one centimeter or any other standard interval, into decimal or other 
 aliijuot parts, leads to tho same relative degree of accuracy in the results whether it is 
 effected at a distance ot say ^ or ti meters, or at 100 or 200 motors, and in all cases 
 where no micrometer measurements are made the smallest subdivisions read otf and 
 recorded are usually either thousandths of a meter or thousandths ofa foot, whether 
 the rod is put up very close to the instrument or very far from it. Yot, it must be 
 admitted we CiMi, in general, !io more determine the elevation ofa level line of sight 
 with the same degi'ee of accuracy, by locating it with the eye within the limits ofa 
 centimeter divi 'on of u rod oidy 5 or b" meters off, as by locating it within the same 
 rod division, at a distance of from 100 to 200 motors — than wo can lay off an angle 
 ofa given number of degrees and minutes with a 3-inch protractor as accurately as 
 w'th a 3-fool circle ; an error made at 5 meters is, in comparison to the distance, 
 evidently much greater than the s:\nie error in the reading made at a 100 or 2'i0 
 meters from the instrument. 
 
 i 
 
31 
 
 inked out by 
 himdivtli of 
 , vviilo ; tlio 
 but Iho half 
 roiidingH are 
 y iiicri'iiKini^ 
 \\ and at the 
 
 <o indicating 
 
 oa(di tignro 
 
 ivision. On 
 
 cross wire 
 jrr'o-tpoiiding 
 
 )f iioillg lortS 
 
 lis and hiiM- 
 II in pocket, 
 inoering pro- 
 
 1 intervals at 
 )ot centre to 
 cale, HO as to 
 .rgot linoB. 
 
 or series of 
 atively long 
 Tily accurate 
 |)recision the 
 te boi'izontal 
 
 it present in 
 ibdivision by 
 ual or other 
 whether it is 
 in all cases 
 > road ott' and 
 foot, whether 
 t, it must be 
 1 lino of siu;ht 
 he limits of a 
 hin the same 
 ; off an angle 
 accurately as 
 the distance, 
 I 100 or 2"0 
 
 Whatever may I'e the kind of rod u«od, the readings should always bo taken 
 along the centre lititt or axis of the row of target stiipes or other divi^ion marks, 
 for, when the lino of sight is inclined to the horizon and the face of the lo I obliijuo 
 to the vertical plane swept out by the axis of the tolescopo, the plane passing through 
 the transverse wire and the optical axis no longer cuts the rod invariably in a direc- 
 tion HL parallel to the longitudinal uxisof the target lines; but in general, obl'tjuely 
 theielo, as shown by the flgure in the margin, and it becomes indispensable to take 
 all the readings on one and the same vertical, vl, if correct roil intervals are to be 
 obtained. The bead which connects all the target etripes serves as a reminder to 
 
 the observer, that the rod intervals are all intended 
 to be measured along the axis or .'entre lino of the 
 row of white target linos painted on the rod. 
 
 Instead of estimating the distance between tiie ap- 
 patent intoisection of the horizontal wire with the 
 scale on the face of the rod, and the conlro of a white 
 target line, this space can be more accurately measured 
 with the aid t.f ttie micrometer screw ; leaving Ihedis- 
 I tance, tacheometor to rod, to be determined in the 
 
 ordinary way ; for, it is always easier to subdivide a 
 small rectangular space correctly into equal parts, 
 tl ,.; to cut off the said space any other aliquot part, 
 whether at one end or the other. 
 
 The new rod i« well adapted for making such pre- 
 ciee measurements at all distancesat which the power 
 of the telescope and the state of the atmosphere permit 
 of making the s-aid measuremonts. When a very long 
 sight has to be taken, as acroge a river, a gully, etc., 
 two, three or four moveable targets can be tixed at 
 known heiglits above on the rod and the corresponding intervals determined on the 
 vortical scale, or scale of tangents of the tacheoineier, very accurately rneasuicd with 
 the aid of the micrometer screw which gives directly the r.,-,,,,! ffoo P'-*'"t of a foot and 
 a still smaller space by estimation, whence the rod reading corresponding to a level 
 optical axis and the horizontal distance, rod to tachoometer, can be easily deduced, 
 without there being any necessity for signalling to the rodman to move his target up 
 or down. 
 
 Four standard target positions are indicated by white lines painted on, or by 
 grooves cut into the sido'^ and rear faces of the rod, which determine three consecu- 
 tive intermediate intervals bearing lo each other the ratios of tho whole numbers 10, 
 8 and 4, which ratios are the same as those of the intervals between the pins of the 
 "Tach^ometreSanguet" of the ordinary construction. Those lines or shallow grooves 
 correspond with figures O-:?, 2-58, TU and 12-8.1 feet above 0, tho intervals determined 
 by them are therefore disposed in tho inverted order of those determined by the pins 
 a,b,C,d, of the said lacheomeler (No. 1); the largest interval (10) being at the top 
 and the smallest (4) at the foot of the rod. The ordinary series of intervals has been 
 inverted on the rod in order to prevent it, as much as possible, from being rendered 
 top heavy and difficult to handle during strong winds when the four targets are put 
 on. 
 
;J2 
 
 Tho Bumo UH jjoodonic lovellin^? rodf* E and F. iho new tacheomotor rod cofiHir^U 
 of llireo httl,ten8>ir Mcantlinf^H dC mahogany /y,, B.,, fi.,, which when [mt to^'ethor 
 form a rontinuouH rod IHO'J Jeot nv VM yiirdn lon^'. Tho bottom hcuntlint,' or lower 
 faco bar //, meaHiiioH ♦i'51 feol or 217 yai'd« in lon^ih, oxcluHive of tho ball support O 
 of phosphor bronze, O'lO foot «;r OO;^ yard hij,'h. added at the foot; it embracen the 
 portion of tho dividud Mcalo oxlondin^; t'rom up to (!•;{() foet or 2'12'J5 yarda and 
 thonco down to— (>-lSi» fool or— (K>50 yard. The lower .{itOO foot or MJOd yanU, or 
 from — 150 toot or— ((-((SO yard to ;! 75 fcoi or 1-25 yard, \h hqiiaro in craws noction ; 
 tnoaHiirin^f 0-15 foot or U05 yard hy 0-15 foot or (1-05 yard— and the nppor 2-(;i0 foet 
 or 0-8725 yard, or from ii'l't ft-ot or 1-25 yard to 6:Ui feet or 2-1225 yardu, in flat 
 and moasiiro.-i 015 foot or 005 yard by 07H toot, or 0-02(; yard. Tho top faco bar 
 R.^ Ih tlat and meaHuros 015 f )ot or 0,') yard in widtii, 0-07H foot or 0-0i6 yard in 
 thicUnoHM and (i-51 foot or 21t)75 yardn in lonutli; it embraces the portion of tho 
 Hcalo botween (i :{({() foet or 2-1225 yards and 12 87 foot or 4'29 yards. Tho inter- 
 moilinte bar Ji.^ soivos to connuol tho U|)p(ir with tho lower halt o*' the scale and 
 moiisiiros 0-15 loot or 0-05 yard in width by 0072 toot nr 0024 yard in tliicknoH.s 
 by ()-51 f.'ot or 2-17 yards in len<i;ih and oxtonds from divisiDii ;{ 75 foot or 1 25 yard 
 to division l0-2t) foot or H' '2 yards. 
 
 Tho original intonlion vva> Isl. 'l\, mak; tin- rear bi<v out of tho same piece of 
 mahogany as ll:o other bars and apply it In the back of the latter in « reversed posi- 
 tion, so that any ten loiu-y to warping or twisting in the face bars might be cheeked 
 by a pioiiable eijual am. >imilar Wot king of tho rear bar in an opposite direction. 
 2iul. in order to prevent tho portion of tho faco bar li.,, which projects 2-(il foot or 
 08725 yartl above tho upper end ot tho intermodiatt or coMiiecting bar B .^ from 
 warping, this bar was to bo formed of two halves (mahogany and pine) each 0-03t) tt. 
 orO-Oi;{yd. thick, screwed or dowelled nndglueil together and paratined. This plan 
 had to bo abandoned as tho wood available would not stand this Ireatmont without 
 giving 6ucb signs of warping and twisting, that it was considered unsafe to relv on 
 tho bars lemaining straight after being exposed to tiie weather. 
 
 Thoroupon, it was decided to build up each ono of the bars which are respec- 
 tively 0-072 foot or 0*024 yard and 0-078 foot or 02(5 yard ihick, of three battens, a 
 piece of clear white pine ^\, of tho total thickness of a bar being interposed between 
 two pieces of mahogany thai form each {\, of the said thickness, and all throe firmly 
 glued together. This plan gave satisfactory results; tho desired increased rigidly, 
 of the upper 2-t)l feet of the face bar Z^.,, which project above the connecting bar, 
 ^2 in the roai,and hence aio unMipported by the same, was secured without any 
 trace of twisting or warping being noticeable in the battens after they were gluod 
 together. 
 
 The intermediate or connecting bar i9.,, is tirndy secured to tho fnce bars by 
 means of stoel fillister bead screws ^' with laigo heads screwed into circular brass 
 socket plates F, xnnk into the faco bars, throe to each bar; each plate boim>- fixed to 
 the bar by two small brass screws s,. A groove is cut on each side of tho rod to 
 serve as u guide for sliding a target V ot tho ordinary const ruction with clamping 
 screw C, fron\ top lo boUom along Iho faco bars. On tliis target, which is matio of 
 aluminum to r-^.-ue a minimum weight, a narrow stripe L, is painted in tho centre 
 
33 
 
 for une when comparatively lonj,' Hi^hlH are taken and wider rectangular markH M 
 on either Hide for very Ion,; Bi^htB. The target T in exactly OSO foot or 0-17 yard 
 long and 0-40 fool or OU yard wide, out to out, an<l can be tixwl in position ho m tc 
 bring itH centre exactly at any doniied hoight above by mean- of two metal ntrips 
 t Holdored on itH i-overHO si.le with thoir outer faces precJHely 0"^0 foot or 0-07 yard 
 on each nido ..f the -^aid centres. It han also a centre lino painted on the back all 
 round by meanfl of which it can bo pliiced cloHely in position at any one of the 
 standard heightH of 0-3, *2-58, 7U ar.d 12-84 foot above indicated on the sides and 
 the rear of the rod, by white lines or grooves. ThcHo heavy white lines or grooves 
 Hre however, intended to serve only as guidcH for Hxing the targetH > rovisionally 
 in position at the said Hlandurd elevations above the of the rod ; the final dose 
 adjustments of targets should in all cases be made with the aid of the metal strips t 
 just described, which are better suited for the purpose. 
 
 The foot of the rod is shod witi « -rass shoe H firmly secured to the w d with 
 three brass screws w extending from front to rear of nhoe; the face of the shoe i« 
 cut out between the fillets ho as to reduce its b ^ight to^O-140 foot or 0-04(; yard, viz to 
 a level 00100 foot or 0-0020 yard below the ... point, in order that the whole of 
 the scale above this point may be entirely pa'nted on wood, so that the zero target 
 line fa very important one for tacheometric measurements) may no. become de aced 
 by the accidental rubbing of branches, weeds, &c., against the brass on the held, or 
 when the shoe is removed from the rod tor packing it in a box, which would be quite 
 likely to hapi)en soon, if the zero line was painted on brass at the extremity of the 
 rod, as is often done. 
 
 The shoe carries on one side a circular level 1 mounted on parallel pl.tes with 
 three capstan adjusting screws a working against spiral springs; this lev, is used 
 by the rodman i^ all positions in which a similar level 1 inserted in the rod abou 
 3 ^ feet or M7 yar.l above the foot and which will be presently described-cannot 
 be seen by him-o« account of being too high up or because he cannot Mand in rear 
 of his rod, or for some other reason. 
 
 One half of the number of rods used should have the circular level on the right 
 hand Bide and the other half on the left hand side of the shoe for it happens some- 
 times that the projecting level as fixed on one side, prevents the rod from being held 
 up verticluy'whiie it would not thus interfere with the proper holding of the rod if 
 it were attached on the opposite side. 
 
 To the lower plate under the lower level 1 can be fixed, when found requisite, a 
 gaugii attachment provided with a straight or hook pointer j, for the accurate 
 determination of water levels. 
 
 The pointer j proper is screwed into the end of a brass tube k vLo lateral 
 openings or slits, which slides along a steel centre pin P and can be hxed a. any 
 dSheight on the pin by means of either of two clamp screws e. The .tec 
 Inu-e pin ts divided lengthwise into hundredths of a foot or yard by marks cut al 
 
 :::r;t, .ndthousandths of a to. . of a ya. c^;;;>-:- (;::^rrr^s\:^ 
 
 3 
 
31 
 
 ings which are cut in tho saiJ lube, to expose the divided pin lo view. A Hmall 
 brass pin i screwed into tho steel cenire jiin at its lower end, prevents tho tube from 
 sliding ott' altogether, should we inadvertently omit to tighten either of llio clamp 
 screws. The point j, — tho tip of which is level with the underside of the ball sup- 
 port when tho slide is clo.'sed up tight against the projecting head of the pin P and 
 tho index on the tube is opposite tiie on tho pin,— can be lowered by O'lO foot or 
 0-05 yard at a time, l)y adding extension rods r provided for the purpose. The 
 Bteol pin is bored out in the centre and contains a hollow spring bolt which is ter- 
 minated at its upper end by a barrel shaped head that causes the three prongs into 
 which the bolt is split to close up when forced up or down through an appropriately 
 tapered opening lurned in a steel bushing inserted in the centre of tlie lower parallel 
 brass plate under the level 1. 
 
 The ball support of phosphor bronze, O'lO foot or 003 yard high, already 
 referred to, has been added to the rod for use in connection wiili a cast iron foot 
 plate F having a cavity turned on top about O'KJS foot diameter and 0-033 f^ot deep, 
 which forme part of a sphere of 0!> ft. radius. This support is kept in place by a 
 tapered brass pin q which pasi>»c8 tln'ough one side of the brass shoe, the wooden rod 
 and the brass shank of tho ball and is screwed at the other end into tho opposite or 
 rear side of the shoe. The pin being made with a taper, presses the shoulder of the 
 ball tight up against the flat end of tho shoe overy time, without fail. 
 
 The ball is not inserted in the rod so as to be ])rcoisely in the centre between 
 the front and roar faces of the shoo; but with its axis O'OtiT loot back of the divided 
 face. The sum of this distance and tho horizontal piojection ot the interval between 
 tho centre of tho tacheometer and the centre of the axis of revolution of the tele- 
 scope, viz., J r=:0'333 foot, gives us for tho constant to be added to tho distance — 
 centre of tacheometer to axis of rod — the round number 0-4 ft. 
 
 Should it be found desirable to use convex headed pins and stakes and nails for 
 supporting the rod, instead of placing it in a sphoi'ical cavity on a cast iron foot 
 plate, the ball su])port can be removed and a shank V with disc fitting exactly the 
 hole in the bottom of the shoe, substituted ; if preferred, truncated pyramids of 
 hardened steel can, of course, also be inserted in tho shoes to be used as supports, as 
 practised on the United States Geological Survey. 
 
 For tacheomotrical operations, in general, the use of a foot plate with a spheri- 
 cal cavity in connection with a corresponding ball support on tho rod, is however, cal- 
 culated to give tho best results. For, a rod with such a support placed on the concave 
 surface of a spherical segment must necessarily, when hold up plumb, always have its 
 longitudinal axis in ono and the same vertical, so long as the plate remains undis- 
 turbed, no matter in what diriM-tion the face of the rod may have to be turned, or 
 how many times we may have to remove it from the plate before tho work is com- 
 pleted from a station. 
 
 The same cannot be said when a rod with a flat base is used in connection with 
 convex heac'jd nails or turtle back foot platos, when the rodman can barely help 
 shifting his rod latterly more or less, at overy turning point. In taking directions 
 or measuring horizontal angles with the tacheometer, the lodman is instructed to 
 
36 
 
 place hit? rod with its fuce as nearly as possible perpendicular to the line of sight, 
 and the vertical wire is brought in lino with the axis of the rod by dividintr the 
 black points opposite the long white target stripes into two parts of equal area. 
 
 As already stated, at a point about 8'17 feet or M7 yard above the foot of the 
 rod, a second circular level 1' mounted on parcllel plates by means of three hexagon 
 hesded adjusting screws Xwith spiral springs, is inserted in the rod, viz., in an 
 opening ,7 of rectangulai' section with sides and top flaired out towards the rear, 
 so as to enablo the rodrcan to clearly distinguish the bubble and plumb his rod with- 
 out hnving to stoop. 
 
 A circular level in every respect similar to level 1' might be inserted in the 
 rod at a point about 1 and § feet above 0, as a substitute for the level 1 on the side 
 of the shoe, in which case any precise water level required would have to be deter- 
 mined by means of a separate pointing apparatus or hook gauge. A circular level 
 encased in the rod is not so liable to be deranged, than one projecting on ono side; 
 but when in the former position it is, on the whole, not so easy for the rodman to 
 see it distinctly and compare it with the upper level. Moreover, if the two spheri- 
 cal levels were both inserted in the rod, wo could not sot it up plumb without 
 removing every time the struts from their sockets in the rear, which is not always 
 indispensable nor yet desirable, as for instance, when wo are taking levels of the 
 ground where it is sufficient for all purposes to read within the nearest half tenth or 
 •so of the true elevation and where a slight variation in position is of little or no con- 
 sequence. 
 
 With a view of assisting the rodman in holding his rod steadily in a truly ver- 
 tical position, he is provided with a double knife-shaped wooden handle B, which 
 he can pass transversely through a slit cut in the centre of the rod at a height of 
 about 4 feet above 0, partly in the rear or connecting bar B„ and partly in the front 
 bar ^,. 
 
 When not in use the double or knife handle is housed lengthwise in a corres- 
 ponding recess cut in the^rear half of bar B^, near the foot of the rod, viz :— with 
 theflat side sunk flush with the face of the bar. The recess is undercut at the 
 lower end so as to prevent the rounded point of the knife ff' ' > leaving it, when the 
 handle end is secured in place, and permit of the latter being lilted up by pressing 
 down the point with the thumb, when wo wish to remove the knife from its recess. 
 The upper or handle end, is prevented from falling out of the rod by means of a 
 short spring bolt b, inserted in the side of bar B, with its head left flush with the 
 wood, and which passes through an eye screwed ii\ the end of the handle, viz.:— 
 when' the spring is released after being pulled out to clear the way for the eye. 
 
 The rodman is moreover, provided for the same purpose, with a steel shod and 
 brass tipped hardwood strut U armed with a pruning knife for cutting away 
 branches that obstruct the view in the line of sight, which he can plant in a vertical 
 plane directed upon the tacheometer, and thus ortectually stop all oscillations of the 
 rod to and from the latter, which are the most important to avoid. 
 
 When, with the object of securing the very highest degree of accuracy that can 
 be attained in the determination of rod intervals and corresponding elevations and 
 distances with the tacheometer, we are prepared to devote to the field operations 
 3i 
 
36 
 
 I 
 
 the additional attention and time needed to meaeure with the aid of the micrometer 
 Bcrew, etc.. as above dcBcribed, the spaces intervening between the point of inter- 
 section of the cross wire with the rod scale and the centre of the next lowest target 
 line, it is advisable when practicable, to use two plain light strut poles some 6-« feet 
 long, made of steel tubing, such as T,. T. on Illustrations II and III, for the pur- 
 pose of keeping the rod, steadily in a vertical position, instead of placin- only 
 one wooden strut with pi-uning knife in the line of the tacheometer; the steef struts 
 being planted one on each side of the said line, as may be found most convenient. 
 
 Indeed it is quite possible, not to say probable, that in this country at least the 
 rodman will generally find it most advantageous to use either one or two light steel 
 tube struts like T, as may be considered most advisable, to the exclusion of the 
 rather heavy wooden strut with pruning knife and to curry a small hatchet when 
 required, for clearing away branches, etc. 
 
 In order to enable the rodman to carry along two such struts with ease provi- 
 sion IS made for securing them to the rod by means of two ring clasps fixed to its 
 rear face, viz.:-one (7^) to the brass shoe and the other (Y.) on top of the inter- 
 mediate bar B,, at a point 6i feetabove 0. When a rodman is ready to proceed from 
 one turning point to the next, ho can pass the rounded top of either strut through 
 one of the rings of the upper clasp, Y,, and then force the pointed end on which an 
 annular cam c is riveted, into the corresponding socket or ring of the lower clasp 
 r^, pushing aside with the aid of the cam, one of the flat springs g fixed to the shoe 
 the rod, and thus effectually preventing the tube from sliding back through the 
 clasp ring. When the tubes have again to be taken off the rod for use as struts the 
 rodman has only to pull them upwards with sufficient force to cause the cams to 
 clear the springs and then remove them from the rings by pulling them downwards, 
 ehghtly out of the line of the two clasps. 
 
 For safe keeping or transportation over long distances, the three bars of which 
 each rod ,s built up can be disconnected by taking out the screws which hold them 
 together, and the shoe can also be thus removed, viz., in order to permit of a set of 
 three complete rods inclusive of nhoes, ball supports, pointer tubes, six aluminum 
 targets, six steel tube steadying struts and other accessories being enugly packed 
 into a wooden box not exceeding TJ feet in length by 0-71 feet in width and 0-65 
 oot in he^ht outside ; total weight of box, with rods and accessories complete 100 
 lbs. See figure Y, 111. II, ^ 
 
 When the rods have to be transported only over comparatively short distances, 
 the bars £,, B B can be screwed together, with the divided faces placed over 
 each other and the lower level and the bronze bull support protected by brass caps 
 as shown on illustrations II and III , for this purpose the screws used in mounting 
 the rod are amply sufficient. I may observe that the rod bars while thus screwed 
 one on top of the other, when not in use are effectually prevented from taking a 
 slight set one way or the other. See figure 1, [11. H. 
 
 In order that this may be easily a.complished, an enlarged oblong brass plate 
 P, carrying two tubes or 80cke= t„ t, threaded with the same tap as all the 
 other screw plates, but in opposi: directions, is inserted into bar B, near the top in 
 
37 
 
 place of an ordinary circular plate or button, another threaded tube or plate is 
 inserted in the same bar near its foot, viz. : between the two battens on each side of 
 the target groove, before they Jiro glued together, and a third supplementary 
 threaded tube on a circular plate is inserted into bar B^ near its upper end. All 
 these tubes are disposed so as to traverse the face bars in the space reserved, on one 
 side of the rod, for the figures and at places where they do not disguise the latter 
 any more than they interfere with the target stripes or line divisions. Three extra 
 screw holes corresponding to the tubes are also bored in the rod, viz., one (h,, ho) at 
 each end of the bar 5.,, and one (h^,), near the top of bar B„. Moreover, in order 
 that the upper clasp F, may be of service for keeping the steel tubes T, , T", in posi- 
 tion on the back of the rod, as well, when it is put up for transportation, as whenitis 
 mounted for operating in the field, — instead of being fixed directly to bur B^, this 
 clasp is screwed on the top of a thin brass band about |-inch wide, passing over the 
 top or rear face and sides of this bar. In the centre of the band a tube is brazed to 
 its underside, which is imbedded in bar -B.^ right down to the brass plate in bar 5, 
 affording a passage to the screw which connects intermediate bar B^ with front bar 
 £j, and the ends of the band rest on bar J5, and are turned in sufficiently, to butt 
 against the bottom of the groove in the side of the rod along which the aluminum 
 target slides up and down, so that when b;u- B., is removed the band with clasp is 
 still properly supported and effect' ally prevented from turning round. 
 
 I will now place before the Department a few typical pages of a |)roposed field 
 book with columns disposed so that the book may be of service, not only for regist- 
 ering geodetic levelling japerations; but also all other kinds of engineers' and sur- 
 veyors' field work carried on exclusively with the tacheometer and accompanying 
 rod. 
 
 lu these five double pages (See illustrations Nos. 46, 47, 48, 49 and 50 in accom- 
 panying pocket) 1 made all the entries that could be required in carrying on a series 
 of supposed fiold operations, in b'^ck ; the otHce work generally in red, and the mental 
 computations in green, with a view of showing in a practical manner the work to 
 be done by using the self-reducing Sanguet tacheometer, generally, for surveying 
 and levelling operations, as a substitute as well for the chain, as for the transit or 
 theodolite and the spirit level. The field operations and computations indicated are 
 typical of those required in running simultaneously two lines of geodesic levels in 
 cases where accuracy in the horizontal distances, is deemed to be as great a desider- 
 atum as precision in the elevations. 
 
 It will be seen that in column 1. we enter : — 
 
 1. The nature of the sight, whether it is a fore, back or intermediate sight taken 
 for levellinir purposes alone 11 for levelling and surveying purposes combined, or 
 simply a sight taken for establishing the position of a survey point. The word sight 
 is printed and we have only to prefix the proper qualifying adjective as required. 
 
38 
 
 2. The number of the station occupied witii the tacheometer, viz.. after the 
 printed words " From St." 
 
 3. The distinfjui.shing letter of the particular rod unod, viz., after the printed 
 words " To Eod." 
 
 4. The point or station at which the rod is put up. 
 
 5. The series of continuous levelliiigs to which the sight belongs, if deemed 
 necessary. 
 
 Columns 2 and 3 aie required for entering: — 
 
 1. Rod readings in feet A, B, 0, D, which are obtained with the long lever 
 successively abutted against pins a, b, c, d. 
 
 2. Vertical scale readings in decimals of radius r=. f foot, of vertical circle 
 described fr-)m a point on the axis of rotation of telescope near the optical axis 
 tangent to the path followed by the knife edge, viz., readings (a), (6), (c), (d) and 
 
 (0). (1)) (2), (3) , (n), which we obtain either by sightingsliding 
 
 targets fixed at the standard elevations of 0-3, 2-58, 7-14 and 12-84 feet above 0, which 
 are indicated by special marks on the rod, or by directing the line of sight to such 
 targets fixed at any other elevations that might be found more suitable in particular 
 situations, such as 1, 2, 3,4 iV^, feet above of rod. 
 
 In column 4 are to be entered : — 
 
 1. Bod uitervals A in feet determined by readings A, B, C, D, such as AB, AC. 
 A£> ; Sa, BO, BB, etc., with the long lever arm abutted against pins a, b, c, d. 
 
 2. Scale intervals S, in decimals of radius r = §foot, which are determined 
 either by scale readings (a), (6), (c), (d), obtained by directing the line of sight 
 successively to sliding targets fixed at the standard elevations of: 0-3, 2-58, 7-14 and 
 12-84 feet above of the rod or to the target lines at the said elevations— or which 
 
 are determined by scale readings (1), (2^ (3), (4) (n), corresponding 
 
 to sights taken to sliding targets fixed at any suitable elevations above such as 1 
 2,3,4 iV.feet. 
 
 3. The sum 2A, of the rod intervals A just described, which are determined in 
 each case, viz. : in feet. 
 
 4. The sum I^, of the ncale intervals i, which are determined as just stated 
 viz.: in decimals of radius r=:§ foot. ' 
 
 Column 5 contains : — 
 
 1. The collimation or height of the optical axis of the tacheometer above 
 datura, which is represented by C. In each one of the series of continuous levellings 
 A, B, of a double roddod line the collimation is equal to the sum of the backsight 
 and the elevation of the zero point of the rod; but for intermediate sights, the 
 height of the optical axis of the instrument is assumed to be equal to the mean 
 value of the two sets of coUimations of the continuous series of levellings such as • 
 i (11-05562+ 1104760) = 11-05061 on field book page 49 in accompanying pocket. 
 
 2. The rise or fall 7„ to the zero of the rod from the transverse axis of the 
 telescope, viz : 1„ = RJ^ (n) - c) } ^N, where (n) denotes the scale reading cor- 
 
39 
 
 responding to the lowest sliding target or target line observed on, viz: — at iVfeet 
 above 0, and c is a constant havitii^ a value in the immediate vicinity of 0'5, such as 
 0*49925, the value assumed for Iho sot of typical field operations submitted, which 
 represents the precise scale reading when the optical axis is in a truly horizontal 
 position. 
 
 3. The elevation of the zero point of the rod, viz.: E^^ =C — R-{ (ji) — c }-, in 
 which relation the symbols have the same meaning as above. 
 
 4. The radius R of the vertical circle passing through the optical axis and 
 having its centre on the axis of revolution of the telescope and its circumference 
 tangent to the rod diiectrix along which the scale divisions are laid off, or to this 
 line produced. 
 
 100 AB = 200 BC'= 200 OD = 100 B~D ^4\b~A + BG+Bd\ x 10 - 
 
 = 2 (AB + AC + AD) X |iO + 1 + 0-1 + 0-01 + | = 
 
 5-7^4-56^2-28 1254 6 84_ 17-10 28-50 
 
 cd 
 
 R 
 
 ba 
 
 he 
 
 ad 
 
 t'd 
 
 ba + bc + bd ab + ac + ad 
 
 In column (i, the readings of the three verniers, A, B C , which give the 
 directions of the survey lines, are entered. 
 
 The actual direction of a line is indicated by vernier C in degrees, minutes and 
 half minutes. Vernier A gives the correct number of degrees, less ISO'' plus f of 
 the total number of minutes indicated by vernier C, and vernier B indicates the same 
 number of degrees as vernier A plus 15^ and the remainii , 'i of the total number of 
 minutes. So that : 1. The sum of the minutes read with A and B must always be 
 equal to the minutes read with C. 2, The degrees road with B must be equal to 
 the degrees indicated by l(jBs 180" and to the degrees rend with B less 15°. If 
 these relations do not obtain, it is a sign that an error "has been made; anyone 
 erroneous reading, taken with either of the verniers, can always be corrected by 
 means of the other two readings. 
 
 Column 7 is ret«erved for notes lelative to state of weather, description of points, 
 water surfaces, &c. 
 
 In column 8 sketches are drawn showing the features of the country traversed, 
 the lines run and levelled, &c. The computations of heights and distances, which 
 have to be raeusuied with the aid of micrometer scale intervals corresponding to 
 known rod intervals, are also made in this column, as well as any other arithmetical 
 operations that may be found necessary. 
 
 As already stated, the standard target positions marked on the rod are at : 0-3, 
 2-58. 7-14 and 12-84 feet above and determine consecutive intervals ot 228, 4-56 
 and 5-7 feet, which bear to each other the same ratios as the intervals ab.bc and cd 
 between the pins a, b, 0,4, of the ordinary tacheometer, pattern No. 1, viz., the 
 ratios of the whole numbers, 4, 8 and 10. These intervals have been selected because 
 they are found to be, on the whole, perhaps better adapted for making accurate 
 distance measurements, independently of levelling than any other. 
 
40 
 
 In view of the fact that as shown above, by using the " Tach^om8ti-e auto-r^ 
 ducteur " : 1. No corrections are required owing to any want of parallelism of the 
 optical axis to the horizon indicated by the sensitive telescope level, whatever may 
 be the distance, rod to tacheoraoter, provided we use the mean of two readings, one 
 of which is taken with the telencope in the erect position and the level in the direct 
 one, and the other with the telescope in the inverted position with the level reversed. 
 2. Horizontal distances can bo measured with extreme facility, within the eri'or 
 limits of 0'06 foot and 0-12 foot per 100 feet, respectively, by taking advantage of the 
 relations: R = ab = 100 ab and E = be = 200 be, it is clear: 
 001 o-065 
 
 (a.) That in any case only corrections for curvature and refraction need be 
 applied, and these only when the ditference between the fore and back si/rhts exceeds 
 Bay 3 or 4 feet. 
 
 (6.) That when the computations of such corrections by means of the automati- 
 cally determined horizontal distances, tacheometer to rod, have to be made only for 
 such small .ii.^tances as the ditferonces in length between fore and backsights 
 approximately equalized by pacing with the aid of a passometer— preferably one 
 with stem attachment for setting the needles to zero at will-they become extremely 
 easy and s:mplo, in fact so simple, that the results sought can readily be deduced 
 from an attentive inspection of the factors involved and entered at once in tb level 
 book without any figuring whatsoever being requisite. For, in such case the cor- 
 rections in question may be calculated mentally with more than sufficient accuracy 
 for all purposes, at the uniform rate of 0000002 foot of rod interval per foot of hori- 
 zontal distance, as shown in green on the sample pages of the proposed tacheometer 
 book. ' 
 
 Now an approximation to equality in the lengths of the fore and back sights 
 quite sufficient for the purpose intended can, as a rule, be readily ^ecured by leaving 
 the disposition of the rod'stations. as just explained, entirely in the rodmen's hands 
 without there being any absolute necessity for the whole staff to lose a portion of 
 their time m endeavouring to more closely equalize the intervals between the rod 
 and the instrument by means of stadia measurements, than can bo done by the 
 rodmen left to themselves : u ceremony which must often prove much m< e tedious 
 o the observer than he anticipates, chiefly on account of his signals to the rodmen 
 to move their rods being wrongly interpreted by them, for want of attention on 
 their part, or tor other reasons. 
 
 The ordinary corrections for curvature, refraction, inclination, &c., which accord- 
 ing to the geodesic methods now followed, have to h .pplied to all readings without 
 exception w,ll thus be required only in special cases, viz. : when the rough ground 
 or other difflcuUies encountered, absolutely preclude the practical equalization of the 
 back and fore sights or the ren ling of the rod scale without the use of the sliding 
 targets, or would cause unwarrante.l loss of time and a corresponding increase in 
 the expense. 
 
 In order that precision levelling operations may be carried on expeditiously 
 and economically ,n the manner proposed, it appears desirable that at least three 
 intelligent and attentive rodmen be employed. 
 
41 
 
 On a double rodded lino the distance between two consecutive fore sight aud 
 two consecutive backsight points may Ijo taken at from 10 to 25 paces. As regards 
 the proper diblunce to be left between an instrument station and an adjoining fore 
 or back sight point, that depends largely on the conflguration of the ground, the 
 state of the atmosphere, the power of the telescope, &c., but as already stated, it 
 should not exceed 300 paces when a tacheometer such as No. 115 is used, and in 
 general should be much less. 
 
 The first Hjght indicated on the typical pages of the [)roposed field book is one 
 taken from station 49 to rod Eat station 48. After levelling the tacheometer and 
 setting vernier C on the direction taken from station 48 to station 49, increased by 180 
 degrees, viz.: on 72° + 25J'+ 180°r=252°-f 25^', the telescope isdirectedto station 48 
 by the observer, who clamps both parallel plates and completes the adjustment of 
 the line of sight in the direction of the rod with the loM-er tangent screw M'. As the 
 distance appears to him to exceed 1,000 feet, he measures it with the long lever 
 abutted against pegb, making a pointing on the of the rod which the recorder 
 enters in column 2; the stations 49 and 48, and the rod, E, having been pre 'ously 
 entered by him in column 1 and a sketch made in column 8 showing the proposed 
 operations from station 49. The observer now draws the lever lightly sideways, so 
 as to make it clear pin bund cause it to strike pin c, when he takes the rod reading 
 o*962 which the recorder enters in column H. P'inally verniers A, B, G, are read 
 and the directions entered in column 6, viz. : 72°+10', 87° 4 15' and 252°-|-25J'. That 
 vernier C was correctly set is shown by the fact that we have : 
 
 87*— (252°— 180 —72-) = 15° and 10 + 16 = 25 minutes. 
 
 As this sight is taken chiefly with a view of fixing the directions to be taken 
 from station 49, in reference to those taken from station 48, it is considered suffi- 
 cient to measure this distance with one rod interval, viz.: — the interval BG 
 determined by two readings B and G made with the lever L abutted against pins b 
 and c. In such case, as we have seen, it suffices to multiply the difference between 
 readings B and G, viz. : 6-962, by 200 in order to obtain the radius E, This ^ives 
 us 1392'4 feet for E which number is entered in column 5, and the sum of the 
 readings, which is here 6'962 — there being only one reading made — is put down in 
 colinnn4. 
 
 The second sight taken is a back sight from station 49 to Rod E put up at 
 point No. 9, which particulars are, as before, entered in column 1 by the recorder. 
 The observer having found by trial that when the axis of the telescope is nearly 
 horizontal, the line of collimation intersects the rod near the foot, the lever is abutted 
 against pin a and the telescope again levelled, viz., with the aid of the micrometer 
 screw, when reading A ■- 0'589 is taken and entered in column 2. The telescope is 
 now inverted and the double faced level reversed, by causing the journals of the 
 transverfle axis of the telescope to change wyes, and the steel straiget edges fixed to 
 the sides of the telescope near its eye end, one of which always rests on the knife 
 edge, to exchange places simultaneously. 
 
 The errors of collimation -iind of i'lclination of level to optical axis being thus 
 balanced, a second rod reading (0'541) is taken with the lever abutted against pin 
 a, which is entered immediately under the first (0'539) by the recorder. Subse- 
 
42 
 
 quontly ,vo tako rofttiiiig R = 7'326' with the lever restinj,' u-ruinst b and entor it in 
 column ;{. Ah (7-:{26 — ((•541) x 2 would evidently sti-iko above thu upper end of 
 the rod, the obwervor mw mukes a now pointing on nay 5-000 with tho levor 
 remaining,' aj^ainst b which is entered in column 2, and he af;orwardri completes tho 
 set of four rondirigs by passing tho lover successively to pins c and d and taking the 
 corresponding readings, viz.: C= 8-3925 and D =z 11-785 which aro entered in 
 column .'J by the recorder. 
 
 The third sight taken is a foresight from station 49 on rod P at point 10. As 
 before, after having found out by trial that the horizontal optical axis will strike 
 the rod a little below Hguro 5, the lover ih butted against pin b, and tho telescope set 
 perfectly level with the aid of tho micrometer screw— when tho two readings 
 B — 4-876 and B — 4-873 aro taken consecutively with the telescope and level res- 
 pectively in the erect and inverted and in tho direct and reversed positions ; also 
 readings ^ = 8-383 and D = 1MI02 with the lever successively held in position by 
 pins c and d. As 1 1-9 less 4-8 is equal to 7-1, it is evident that a new pointing B is 
 necessary for taking reading A. The lever is therefore returned to pin b, tho inter- 
 section of the cross wires directed to figure 9-000 on rod which pointing (5) is en- 
 tered in column 2, and the levor handle lowered so as to strike pin a, when reading 
 A = 1*974 is taken and recorded. 
 
 Next in order comes another foresight, viz. : that fron- station 49 to rod P at 
 point 11, when a similar set of operations is performed ; this time beginning with 
 direct and reversed level readings: D = ll-82() and D = 11-830 and ending with 
 reading A = 1-494 ; an extra pointing « = 8-000 having had to bo made. 
 
 The last of the set of four sights required from station 49 for precision level- 
 ling and distance measuring or general surveying purposes, is a back sight on rod 
 E at point 8. In this case it is found that it is best to take tho direct and reversed 
 level readings with tho lever arrested by pin c, viz. : C = 9-156 and C = 9-160, so 
 that one pointing may suffice for the whole set of four. 
 
 If it is important that the correct positions of the levelling turning points be 
 established, points Nos. 8, 9, 10 and 11 have again to be sighted, for the purpose of 
 registering the directions indicated by the verniers, as shown in column 6. 
 
 Sights aie now taken to rod P at station 50 and to rod G at points 9|- and 9^ 
 and the directions of those points duly noted. A single rod interval is deemed to be 
 sufficient for the determination of each one of the points last named, which are 
 Bpecially described in the column headed " Notes, etc.". The interval read is that 
 AB, which afiords j}^^ part of the distance R. 
 
 From station 50 the first sight is again taken to the station last occupied, 
 VIZ.: 49, for the purpose of setting the tacheometor right in reference to the 
 meridian or axis of ordinates fixed upon at the start, and also for verifying the dis- 
 tance between the said stations as measured from station 49; the upper limb or 
 interior circle having previously been clamped with vernier C set at the fi<rure 
 read from station 49— when the telescope was pointed in the opposite direction— in- 
 creased by 180 degrees, or at 243°-H 11'. 
 
43 
 
 The back and foresightB from Htatiori 60 aro mIho taken and recorded in » 
 «imilar manner m from station 49; but the intormodiato Mights to points Nos. 14, 
 15, 16 and 17 havo to be treated bomowhut ditlorontly from the intermediate Hiirhts 
 taken to station 50 and to points 9^ and 9^ from station 49. 
 
 Point 14 is too hli^h up lo bo U'vellod to in one sight, hence the inclination has 
 to be measured by moans of the scaly of tangents and the micrometer screw, 
 the horizontal distance has however been determined in the most oxpoditioiis manner 
 possible, viz. by usingtlie relation ^=: 100 x AB = 100 x 8-543 = 854-3 feet. 
 
 Here by pointing the optical axis to the at the foot of the rod, the scale read- 
 ing: 0-39752 obtains. Hut when the telescope is truly horizontal the scale reads : 
 0-49925, hence the tangent of the inclination from the instrument to is -39752— 
 •49925 — 0-10173 and the rise to = 854-3 x (0-10713) = 86-9079 feet, which being 
 deducted from the collimation 11-0506 gives 97-9585 feet for the elevation ofO at point 
 14. Again, point 15 is too far off to permit of a rod being used without a sliding 
 target and the same remark applies to point 16. We therefore take in the case of 
 point 15, the scale readings (a), (6), (c), (d) determined by the sliding targets A, 
 B, C, D Hxed at figures 12'84, 7-14, 258 and 0-30 feet on the rod, and^ perform in 
 column 8 the numeiical o-jorations required to deduce the distance from the relation 
 -S = A B+aL' +A D which represents ir. this instance : 28-50 = 1648-35 feet. 
 
 (oX-fflc+a^ 0-01729 
 
 The elevation ofpoint 15 is arrived at by multiplying the tangent of the angle made 
 by the optical axis when directed down to the target fixed at 0-3 above the zero on the 
 rod, with a truly horizontal line, viz.: (0-50362— 049925 = 0-00427) by the dis- 
 tance 1648-35. This gives us 7-03846 which number plus 0-3 viz.: 7- 33845 ft. 
 must be deducted from the coHimation to obtain the elevation: 3*71216 ft. of the 
 zero point of the rod at survey point No. 16. 
 
 When the point of which we desire to establish the position and elevation is 
 one of only secondary importance, such as for instance No. 16, it is sufficient to 
 make two scale readings, viz. : (d) = 0-50146 and (a) = 0-49518, when the relation : 
 R = AD = l2-b4t^ gives us the distance: iB= 1996-81. 
 ad •00«^^ 
 
 In this case the elevation of the zero point is equal to : 
 
 11-05050— [(0-r)0I46— 49925 -0 00221) X (1996-81) =4-41295]— 0-3 = 6.33755 ft., 
 the whole of which is worked out in detail in column 8, where the figures can be 
 easilj' turned to for verification, if found necessary. 
 
 So far, no correction for curvature aiid refraction was applied, it being assumed 
 that the elevations arrived at proved sufficiently accurate for all purposes. 
 
 When, however, we desire to determine correctly the elevation of a water sur- 
 face, such as that of the brook a* int 17, or the height of some other important 
 point, fnim a Ktation on the contini. double line of levels, it V>Cv!0mes nece^isary to 
 take the effects of the earth's curvati and the lef ction of the atmosphere, into 
 consideration, and to iipply corrections accordingly. 
 
a 
 
 The readingH A and B on ml F at point 17 easily give us the distanco between 
 station 50 and point 17, which in equal to 100 (B-A) -| y-4=690'6; aino the uncor- 
 rected elevation of the zero whinh w touna to be equal to : 
 
 ii.rtRn«i («912 + «-906) 
 
 ll-050bl — ' 2 ' = 4 14161 
 
 where as already shown, 6-912 and 6-906 lepreHcnt the rod readings in the erect and 
 inverted poHitions of the toloHCopo and the direct and leversed positions of the level, 
 viz. : when the lino of night is very nearly horizontal in each case. 
 
 As detailed in column 8— the mean length of the back sights whence collima- 
 tion ll-0.50fi was deduced is equal to :i3:)-60 feet— and the corresponding correction 
 required to determine tho effects of curvature and refraction is 0-01856 while the 
 correction needed in the case of the foresight of 590 feet is only 0-00731, the 
 diffirence to be applied to the being thus 0-01124, which when deducted from' the 
 uncorrected elevation 4-14161 gives: 4- 13037 for the correct elevation of the zero of 
 rod F. Finally, in order to arrive at the elevation of tho water- surface, we have 
 further to subtract from 4- 13037 the height of the above the water. This height 
 is equal to 0-25 foot, tho height of the index or of tho pointor scale, (which is at 
 the same level as the zero of the rod) above the underside of tho ball support— plus 
 the reading 0-114 foot afforded by the index of the said scale, when the point touches 
 the water— or in all 0-364 foot. A small table of corrections required for curvature 
 and refraction at every 100 foot, up to say 1200 feet or more, printed in each field 
 book, will prove very convenient in this connection, for use in the office or on the 
 ground. 
 
 Now, if we had decided to follow for tho fore and back sights the still more 
 accurate, although somewhat longer method of determining the elevations above 
 referred to, which consists in measuring with the aid of the micrometer screw and 
 vertical scale tho distance i between the apparent intersection of the horizontal wire, 
 (or line engraved on the field glass of the eye piece) with the i-od scale and the next 
 lowest whole hundredth foot division, instead of estimating the said interval with 
 the eye— we would nave to take four micrometer readings, in addition to the rod 
 readings, as shown in the case of the back sight from station 49 to point 8, and 
 compute the thousandths, and ten and hundred-thousandths to be added to the feet, 
 tenths and hundredths entered in column 2, page 47 o/ tacheomoter book. Tho first 
 micrometer reading (28 0) entered in column "J, page 47, shows the ponition of the 
 micrometer drum, with the telescope in tho erect and the double faced level in the 
 direct position with bubble ir. centre of glass tube. The second reading (31-0) indi- 
 cates tho position of the micrometer head for a pointing made with the telescope 
 and level in the same relative po"-'--s on tho whole hundredth of a foot next below 
 the horizontal sight first taken. third reading (172) shows tho position of the 
 
 microraoter head for a pointing made to the same whole hundredth division with the 
 telescope inverted, and the level reversed and the fourth reading (220) shows the 
 position of the micrometer head with the telescope inverted and the level leversed. 
 
 The micromotor reading corresponding to the mean horizontal pointing is, in 
 ■thecase under consideration, equal to: 28 + 22-0 =: 25 
 
46 
 
 and thomean micromoter reading coiroHponding to the pointing on the next lowest 
 whole hundredth divinion to: 31-0+ 17.2 r= 24*1. 
 
 it 
 Hence, conBidorin<f: IhI. That, an already explained, the pitch of the micro- 
 meter Horew in Huch that by turning its head ii','ht or loft over one divinion the piiw- 
 matic guide rod wich knile Hiipport in moved up or down through a Hpaoo equal to 
 the ,,H,',H.() pai't of the radiuH r= 1, of a circle drawn fi-om a point on the axirt of 
 rotation of the telescope as a ceiitro in a plane perpendicular to the «aid axiH ho an 
 to be tangent to the plane followed by the knife edge. 2nd. That the interval inter- 
 cepted on the vortical scale by any two lines of sight boars to the interval intercepted 
 on the rod between the same linen, the ratio of {r=z I), to i2— the horizontal dintance 
 from the said axis of rotation to the rod— wo have in tho present case for the 
 interval i between the intersection of the truly horizontal lino of sight with the rod 
 and the hundredth division at 9-15 pointed to from station 49: 
 I = (25 — 24 -1 = 0-9) xR 0-9 X 605-24 
 
 100-000 
 
 100-000 
 
 0005447. 
 
 This space t when added to 9- If) gives for the precise reading of the back sight 
 from station 49 to point No. 8: 9-15rj447 feet, in place of 9-158 feet the moan of the 
 two heights estimated by tho eye, and for tho precise collimation from station 49 of 
 series of levels B : 12-264477 feet instead of 12-26763 feet. 
 
 It would bo interesting to know how a line of levels A 25 miles long or more, 
 run entirely according to the method just described, would compare with a lino B 
 run simultaneously with the rod intervals t all estimated by the eye. It is my 
 intention to establish such a comparison at the first opportunity that will present 
 itself. 
 
 In the case of a single i^dded line of precision levels, it is advisable, although 
 not indispensable, not to remove tho tacheomefer from a station until the recorder 
 has entered three distinct rod intervals in column 4, and satisfied himself, by com- 
 paring them rapidly with each other or with their sum or with their mean, that no 
 material error has been committed; tho remaining entries in columns 4 and 5 can 
 be made in the oflSce. When, however, the- line of precise levels is double rodded 
 such as that indicated in the typical pages of field notes given above, this verification 
 of readings on the spot can be made in a more simple manner and the field work 
 correspondingly expeditpd, viz.: by comparing the difference between the two back 
 sight readings taken from tho station occupied with the difference between the two 
 corresponding foresight readings taken from the previous station. For instance 
 before leaving station 50 we would compare the difference between tho back sight 
 readings to points 11 and 10, or 10-612 - 3-657 = 6-955 feet with t'le difference: 
 11-830 — 4-876 = 6-954 feet, between the corresponding foresight readings taken 
 on the same points from station 49, and finding the two to agree within 0-001 foot 
 would conclude that ■ \\ the operations have been correctly performed. 
 
 Furthermore, when such a double rodded line of levels is run exclusively with & 
 view of establishing permanent bench marks and determining the precise filevations 
 of the same in reference to the mean sea level or some other datum piano, together 
 with perhaps some important water or railway levels in a part of the country of 
 
46 
 
 which tho topo^Tuphy Ih well known iind correctly indicated on oxlHtinj^ nmpH, iind 
 whoro tiioref'oro, uccurjito tnoiiKiircmontH of diMtancoH aiwl an^lcM with tlio tache- 
 oniotor for locating tho lino or for any other nimilar pui|»o.-io, would bo Hiiporfliious. 
 the ordinary run of field oporationrt required from any of ilio tachoometer Htations— 
 Hiicli as Xos. 4!t and 50 of the HiippoHfad ojjeralionH recorded ahove on Mainpio paj^en 
 4() 10 41> of tho proposed field book — can ho limited to thoHo cnlerod or. munpie <iouble 
 field book paj^oH 5 and (! to be found in tho pocket which acc<impainuH ihin Memo. 
 On these two do'ihlo paijoM, tlie ohsorrationM, enlrioK md computations which hnvo 
 to be made on (ho ground are, as heretofore, indicated in black, they are moreover 
 numbered in blue in the order in wliici) they should bo taken, the ofHce work recjuired 
 alHO is shown, viz. in r''d, and tho mental calculationrt in green, ua before. 
 
 Kronfj the indication)* given on sample double |)agcH 5 unrl ^' in accompanying 
 pocket just referred to, it will bo seen that the rod i-eadinj.^ ^'rom each station, six- 
 teen in number, are to bo taken in tho following manner; r .< <)ver being invariably 
 8uppo.«od to bo abuttoil against that particular pin of tho soi- - a, b, C, d, which per- 
 mits of the greatest number of standard readings detormintu by those pins being 
 made without changing the position of the clamp on the prismatic guido i-od, ac- 
 cording to tho directions given abovo to that effect, viz. : — 
 
 (a) With the telescope in the erect ■position —milled head of the slide pinion on top— and 
 the attached double faced level in the direct position, or on the right hand side look- 
 ing towards tht objective: — 
 
 (1) A level foresight pointing (1,68()). See III. numbered 5-B, in pocket toge- 
 ther with an adjacent distance reading (11-310) on the rod furthest ahead of tho 
 station occupied (50). 
 
 (2) A level backsight pointing (10-617) and a distance reading (08o0) on the 
 furthest rod in the rear. 
 
 (3) A level foresight pointing (8-534) and a distance leading (12-827) on the 
 nearest rod ahead. 
 
 (4) A level backsight pointing (3-663) together with a distance reading (8-181) 
 on ' QO nearest rod in the rear of the tacheoraeter station. 
 
 (6) With the the telescope in the inverted position — milled head of the rack pinion which 
 works the slide underneath the tube— and the attached chambered level in the reverse 
 position, or on the left hand side : — 
 
 (5) A level foresight pointing (8-531) together wit'; an adjacent distance read- 
 ing (12-827) on the nearest rod ahead. 
 
 (()) A level backsight pointing (3-057) and a distance reading (12687) on the 
 nearost.rod in tho rear. 
 
 (7) A level foresight pointing (1-683) and a distance reading (11-307) on the 
 furthest rod ahead. 
 
 (8) A lovol backsight pointing (10-612) and a dis.anco reading (5-730) on the 
 furthest rod in the roar of the station occupied. 
 
47 
 
 Ileroall ihepoiiitin/^HniochofkodHimply by ropoiitinj? them and (he same may l)o 
 BuidofHomoorihodistuiu'u roudiii^H. UutallMUch lopotilioriH iiro made at sutlicionlly 
 long intorvulH of time, to bocomo virtually h-osh dutonjiinutioiiH of praclicttlly the 
 Hame olcvationH und corroHpondinj^ rod spacoM, for, under ordinary circiimMtancoR 
 noithor tho diapliraf^m nor thu It v' of the ttdencopo in over Hoiisibly disiurbod 
 durinj,' tho HJior' time spout hotwotn two conm'cutivo stationw. HertidoH, by com- 
 paring tlio ditferonce (6'955) in tlie elevation between the two badfuight level road- 
 ingH taken froiii any Mtation (50), with tho diflorom'o (()-!)&4) which obtained be- 
 twooM the two correnponding lovol foresighi readings from tho preceding rotation 
 (4!0 as proposed, wo cannot fail lo doteot at once any lotabie change in the dis- 
 oropn jy in readings caused ijy a defective coUimat ion or an imperfectly adjusted 
 teioficope lovol, and ice can make a proper allowance for lh>> aame, or proceed to 
 rectify tho adjustmen on (ho spot as may be found most desirable, 
 
 Tho method of carrying on geodetic levelling operations with the " Sanguot 
 Tacheometor " and the new rod just doscriijod, will prove much mure expedi- 
 tious i..an that generally followed by the United States Coast and Geodetic Sur- 
 vey with the geodesic pivot level and their rod with chain target and the similar 
 metliod adhered to by me for some tifteon years past, in the ruriing linos of pre- 
 cision levels along tho Jtichelicu, (he St. Lawrence, &c. With tho new method, the 
 number of entries to be made in the field book becomes reduced by about ono-balf 
 and nearly all the ordinary, somewhat bulky, computations are dispenwed with, 
 without the precision and reliability claimed for the present geodesic methods beii'g 
 in any way lessened. 1 believe, on (he contrary, that ...ore precise results are 
 likoly to be secured and at loss expense. 
 
 R. STECKEL, 
 Engineer in charge, Canadian Geodetic Levelling.