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Tliis proof is sent to you for discussion only, and on the express understanding tliut it in not to bo u.sed for any otiier purpose wliat- ever, — (^'ee ^'ec. 47 0/ the Comtitution) , Hoiiodlaij ^cci«ii| of ^ioil ^ngincens, INCORPUItATED 1887. TBAJ4SACTIONB. N.B — Tills Society, us a body, liots i.ot hold iipelf responsible for the facts and opinionH stated in any of its publications. A MICROMETER ATTAmiMENT FOR THF TRANSIT IN8TRUM3NT, WITH EXAMPLES UF ITS USE IN SUR- VEYING, LEVELLING, ETC. By W. T, Thompson, A.M.Can.Soc. C.E. 'I'hu accompanying photojirapli represents a 6 inch reiteration tran.sit, with micrometer attachment, tlie latter was constructed to my order by Mr. Jaines Foster of Toronto, and in connection with the transit telescope affords the mouns of measuring with great accuracy small vertical angles between the limits of 0.8 and 3. It consists of a metal box firmly iittached to the vernier plate of transit in a plane at right angles to the horizontal axis of telescope, and containing a micrometer screw, with divided head and vernier, and two movable nuts N and I, the former hns 40 threads to the inch, and bears against the vertical clamping bar B being kept in close contact by the spring' S. The head of screw is divided into 100 parts, and is read by the vernier Vto the , (y\, o»'' P'"'^' ^^ •* revolution, and .1 • eh complete revo- lution movoRth.1 nut N through ,'„th of an inch, the ^,j>,^^thpart will move it through the , |,|\(^^ th of an inch, and as the length of the clamping bar H from centre of axis to point of contact with nut N is 6^ inches, this will move the telescope through an angle of 0. 8," which is the smnllest that eau be measured with this micrometer. The index nut I is for recording tlie number of revolutions made by the screw : it has 20 threads to the inch, and the edge of box is divided into 20 parts to an inch, so that each turn of the screw carries the index nut through one division ; therefore, in making any observation, the number of complete revolutiouM is rend ollfiom the scale, and any frac- tional part from the divided lieiid and vernier. The clamping bur li consists of two parts so arranged that the teles- cope may bo moved in altitude either by the micrometer or by the ordinary tangent screw T, so that when desired the micrometer may be set at zero or any readit)g, and the telescope accurately .set on any objeet by the tangent T. Ill measuring distances witli this niiorometer, the writer has used lor a bare a light round rod HO links in length, about 2 inches in diameter :it the bottom, tapering to 1 incli lit the top, and provided with a universal sjiirit level to ensure vertiealily, with 3 targets, one 5 links IVoni the bottom, one 10 links above this, and one at top of rod, giving :i clear distancte of 25 links between the outside targets. The targets were lormed of biiiiht tin ami hhiek rubber t;R'k<'d on the rod, as shewn in the miiruin. The tin reflecting lightaiid the black ruhb.r absorbing it, the division between them was very distinct, The lower tai'getH Id links apart were only used in measuring short distances, the (inter targets 25 links apart beiii'j; used in all other cases. If a distance of say 4(1 chains be measured on a pieeeol' level ground or upon the ice, and the number of turns of the micrometer .«crew re(jui:i(l to move the lioriznntai wironfihi! li:iej,cope from one target to another be dennteij tiy 11, then as the base is very short as compared with distances In lie nieaMiivd, it may be considered to represent the I arc which s ibtcnJs the angle at the instrumoat, and this atif^le will vary inversely •.^ith tiio radius orilistar.oo, ThiTuforc at one chain the number of turns of the screw would be represented by 40 u=N. If now the rod be held at any unknown distance denoted by X chuins, and the nuui- N ber of turns of the screw is observed = n' then X: where the base subtending ri' is very small iis citinpared with its distance from the instrument, and the effect of differential reir;iction is assumed to be consiant. As, however, at different distanees from the instrument the differ- ence of refraction of the tarijetH will vary Klii^htly, it is necessary, in order to prepare an accurate table for rcducin;; the observed readings to distances, to note the actual rcudirifis at eiich chiiin of distance from 5 chains up to 50 chains, and interpoliito the readings for differences of 10 links. The distances corresponding to any observed readings can then be at once obtained by inspection. The condition of the atmo- sphere at the time should be iiot;'d, and on ditl'erent days, if one or two distances are cliained, and the observed readinjjs compared with those given by the table, we shall be able to apply oorrceticns to the tabular distances due to ditforent atmospheric conditidiis. The horizontal wire of the tolescop ! should be very fine and the ob- ject glass and eye-piece must be —'ry carefully Hieused. It is also impor- tant that the axis should be securcid witii moderate [iressure in the Ys and to obviate as far as possible the tendency to rise, the spring S must be slightly bent si) as to gri]) the stud against which it bears. The telescope used has an objective of l.T) inches clear aperture and 10.5 inches locus, and the eye-piece a magnifying power of ;i2 diame- ters. With this ii'Struni'->it and the 25 link target rod described, dis- tances up to 40 ehuir lay be measured, with an error seldom exceed- ing I link per oliain, and with a more powi^rful telescope it is probable even closer results could be obtained, We shall now give some examples of the u-^e of this attachment in surveying and engineering operations, I. A method of traversing with the transit and inicrometni- attachment In regard to traverse surveys, the Maruial of Survey for Dominion Lands provides as follows : — " The use of the micrometcT lor siich work will be allowed, provided that the closing error does not exceed one (duiin in one hundred chains. The micrometer must be of an approved pattern, and must be submitted to the Surveyor General before being used on tlu^ survey." The micrometer,attaohmentdeserib(!dcomplics with the reiiuirements, and in connection with the transit affords the means of making traverse surveys with great facility. The method used by the writer is as follows ; the instrument being set up on the shore of a river or lake, and either on one of the survey lines or at a point fixed in position with reference to the same. It is set up iit, till! starlin;: point of the survey, ami carefully levelled, the direction of the line is tised by readings of the horizontal circle, the bubble of telescope level brought to zero and reading of micrometer noted, then the lower target being adjusted to the height of the teles- cope, the rod-man proceeds along the line and liolds the rod at all points where any marked changes of inclination occur, the distance to each point being determined from readings oii thetiirgets, also the difference between the micrometer reading for level zero and the reading on the lower target gives the difference of level by consulting our table. VVe may also obtain the direction, distmce, and difference of level of points on either side of the line referred to the Instrumental Stations, and without planting any stakes cxfiept at these stations, collect the necessary data for preparing a plan, profile and cross sections of the line, from which a location can be decided on, which would then be «haincd, staked and levelled in the usual way, arc which subtends the angle at the instrutnent, and this angle will vary inversely with the nuiius or distance. Thorct'ore at one chain tlie number of turns of the screw would be represented by 40 n=N. If now the rod be held at any unknown distance denoted by X chains, and the num. N ber of turns of the screw is observed = n' thenX:^|^, where the base subtending n' is very small ns compared with its distance from the instrument, and the effect of diiferential refraction is assumed to be constant. As, however, at different distances from the iustrumciit the differ- ence of refraction of the targets will vary slightly, it is necessary, in order to prepare nn accurate table for reducing the observed readings to distances, to note tiie actual reiidings at each chain of distance from 5 chains up to 50 chains, and interpolate the readings for lifferenccs of 10 links. The distances corresponding to any observed readings can then be at once obtained by inspection. The condition of tin; atmo- sphere at the time should bo noted, and on dittereut days, if one or two distances are chained, and the observed readings compared with tho.se "iven by the table, we shall be able to apply corrections to the tabular distances due to different atmospheric conditions. The horizontal wire of tiie telescopj should be very fine and the ob- ject glass and eye-piece must be very carefully focused. If is also impor- tant that the axis should lie secure..! \«ith moderate pressure in the Ys^ and to obviate as far as possible the tendency to rise, the spring S must be slightly bent so as to gri]i the stud against which it luvirs. Tiie telescojie used has an objective of 1.5 inches clear apei tuie and 10.5 inches locus, and the eye-piece a magnifying power of ;>2 diame- ters. With this instrument and the 25 link target rod described, dis- tances up to 40 chains may be measured, with an error seldom exceed- ing I link per chain, and with a more powerful telescope it is probable even clo.«er results could be obtained. We shall now give some examples of the use of this attachment in surveying and engineering operations. A method of traversing with the transit and micrometer attachment In regard to traverse surveys, the Manual of Survey for Dominion Lands provides as follows : — " The use of the micrometer for such work will be allowed, provided that the closing error does not exceed one chain in one hundred chains. The micrometer must be of an approved pattern, and must be submitted to the Surveyor General before being used on tiie survey." The micrometer,attachment describe dcomplies with the requirements, and in connection with the transit affords tlie means of making traverse surveys with great facility. The method used by the writer is as follows : the instrument being set up on the shore of a river or lake, and either on one of the survey lines or at a point fixed in position with reference to the same. It i» carefully Icvollod, at the Imrizimial oirole ieH,din^ for tin: iKirth point noted. Thon the rod-uian proeeLMliiif^ along the shore Imlds the rod at all points whi re marked deviatimis (li-eiir, tlie pnsilioii of each point being fixed in direeiion and di^tme' fidni tin' iii.-iniinental Htation, by readings of the horizontal cirole and niiorouiiter. At suitable points new .stations :nc taken and the survey continued in the same manner. The note" are enieied in the field book under the followinf^ headings, and written from the r'-'toni upwards, the topography being shewn in margin- If a repetition instrument is used, the two columns headed II.C.R and H.C.IJ. on N are not required. on N II l|— s - I. II 1 S - L It is convenie'it to have rod-man travel uniformly from left to right, vi/... in tiie direction given by the hands of a watch, and any topography will then be shewn in left hand margin. If the initial station be called 0, then the points fixed from it may be conveniently designated O,, O.^, O,, etc., to 1 : 1 ,, 1 .^ , 1 , etc. The reduced notes are pitieed in three columns, under the headings: Station, Azimuth, Distance, and from this data the points are plotted on a seale of 20 chains to an inch, and the shore linedetinedby joining these points. No matter how irregular tiu! siioro line may be, a perfect representa- tion of it can be obtained by this method, and in much less time than would be required by the system of survey lines and offsets. Regarding the areas of the broken quarter sections, it may be stated that as a water boundary is a viiriable one. depending on variations of the water level, extreme accuracy in determining these areas is not necessary, and the planinieteror some graphical method will usually give sufficiently clo.se results. II. To determine differences of level and establish gradeson prcliminarv railway and other surveys. The telescope must be provided with a good spirit level, and the hori- zontal wire adjusted to define a horizontal line when the bubble is at zero. Then if we note the point on i\ rod at the distance of say 500 feet where this line strikes, and turn the micrometer screw tlirougii one revo- lution, the distance hetwi>en the twop' ints on the rod beinu' measured, l-,5th of it is the rise or fall in 10(1 feet liir one turn of the sorew, ancl we can now prepare a table giving the number of turns recjuireil for various grades, also of the rise or lall in feet at differeiit distances, these tab' s sliouid include the effect ol'eurvature nnd refraction. We also reiiuire a target rod consisting oltwo pieces sliding upon each other, as shewn in margin, in order that the piece carrying ttie targets may be pusiied up or down, so that the lower target can be set at the hei^dit of the telescope above t!ie ground, and clamped in position. The distance between the targets may be 5 or feet, imd a table for retluciiig observed micrometer rcaditigs to distiinces can bi' prepared in the manner already described. "We are now prepared for surveying and obtaining tiie levels and dis- tances along any preliminary line without the use ot the chain or any other instrument. The mo.le of proceeding will be as follows : The instrument being set up at the starting point of the survey, and carefully levelled, the direction of the line is fixed by readings of the horizontal circle, the bubble of telescope level brought to zero and reading of micrometiT noted, then the lower target being adjusted to the height of the teles- cope, the rod-man proceeds along the line and liolds the rod at all points where any marked changes of inclination occur, the distance to each point being determined from readings oil tiie targets, also theditt'erence between the micrometer reading for level zero and the reading on the lower target gives the difference of level by consulting our table. We may also obtain the direction, di.stmoe, and difference of level of points on either side of the line referred to tlie Instrumental Stations, and without planting any stakes except at these stations, collect the necessary data for preparing a plan, profile and cross sections of the line, from whicli a location can be decided on, which would then be ehainud. staked and levelled in the usual way. 3 A I III. A very important use to which this attachment can be £^plied is the determination of the latitude by measuring small diffcrenceb of zenith iliHtance of North and South stars by a method somewhat MJriiilar to that by the lenith telescope. For this purpose a very sensitive spirit level must be attached to the vertical clamping bar B in a plane at right an^ilesto the horizontal axis of telescope, and the bubble should be adjusted to read zero when the index nut I is at the ceiitie of the scale ; this level should read to say 3, " for one mm space, so ns to readily show a displacement of i ". The time, uzimuth, and approximate latitude may be readily obtniued from observations on Polaris and another star in the same vei tical pliue. Then with the approximate latitude or declination of tlic zenith point, we select from a Star Catalogue, such as the Berliner Jahrbuch, a pair of stars between the 2nd and 5tli magnitmles, which culminate as nearly as possible at equal distances to the north and south of the zoiiith, and within say 30 dejirocs of it, differing not more than 2 de- grees in zenitli distance, nor more than suy 30 minutes in right as- cension. The observer should be supplied with a chronometer or watch ad- justed to sidereal time. Shortly before the time of transit of the first star the telescope will be brousiht into the meridian plane by readings of the "lorizontai cir- cle, and the vertital finding ciicle set for the mean zeni.a distance of the two stars. The latitude level will then be brought to zero by turning the micrometer screw and reading of same noted ; the screw will then be turned to the riuht or loft, according as it is necessary to depress or elevate the telescope, to set it at the zenith distance of the star, and when it appears in the field, the horizontal wire will be set upon it, and a precise bisection made when it reaches the middle wire, the micrometer reading will then be noted, the screw reversed and level again brought to zero, the micrometer reading again noted and mean of the two readings taken as the true reading for level zero at the instant of the star's transit. The instrument is then turned ISC, in Azimuth, and similar observations taken on the other star. With tiiis micrometer, a right hand motion of the screw will increase the readings and zenith distances. If, therefore, we denote the read- ing on the star neurost the zenith by m and the reading for level zer for same star bj m„ , then the arc measured by the micronieier is represented by m„ — ui ; and if we denote similar readings foi the other star by ni] and in,, , then the arc measured will be represented by uii — mo ; and the sum will represent the total change of inciinutiou of the telescope, or difference of apparent zenith distances = mi — m + uig — m„ 1 which must be reduced to seconds of arc by multiplying by R the number of seconds in one revolution of the screw ; this will be deter- mined from observations on Polaris near its elongation, or bynjcasuring the difference of declination of close stars at their transit over the Meridian ; the value will vary slightly with the number of turns, and .should be tabulated for different intervals. Then using the value corresponding to the observed interval, we shall have for the apjjaient difference of zenith distance ( mj — m J m„i — mo)R" = (z - z' ), in seconds of arc, where z denotes the zenith distance of southern and z' ot northern star. In the diagram let P denote the North Pole, Z the Zenith, EQ the Equator, S the Southern, and S' the Northern Star; S E and S' E = S and S' their declinations, Z S, and Z .S', their true zenith dis- tances = Z and Z', and r and r' their refractions. Then denoting ilie latitude ZE by (f). We have cf) - (S -i- Z) = (S'-Z'). Therefore 2 (/> = S -f S' + Z — Z^, and since Z =Z -(- r and -f Z Z' = Z ( s + inserting these values, our Z - 'A' + r— /•' \_/S -f n=e-^ formula S' + r becomes r -) inserting the value of Z — Z, as measured by the micro- meter, the final formula is := nil m + ni„ ..) R" lU have which the sign of the second term is the same as that of (Z — viz., if the southern star has the greater zenith distance it will the -!- sign, awdvicc rrrsa. By eon.-ulting a Star Catalogue it will bo seen that in most latitudes several pairs oi' stars between the 2nd and Stli iiiagnitudes, and differ- ing not more than 30 minutes in R, A, nor luirio than 2 degrees in declination, would be available for observation with a good transit telescope . This method would be found useful in determining latitudes in in connection with micioiueter work, and sliould 'cpl :iry veys ve the latitude within 2" or 3'' W.\[. T. THO.MPSON. \