

THKODOLET. 



THKUDOLET. 



artists at ham and abroad ; but the reader who desires to tee what had 

 beta dune up t 1851 is referred to the Jury Report, Clan X., where 

 the surveying and levelling instrument* ami theodolite* of the Great 

 Exhibition .>:. prvtty fully noticed, as to their new poinU and from 

 the personal observations of Mr. UUisher. The general properties of 

 a theodolite, that it should be firm, well balanced, Ac., will be easily 

 r~yii^>,l by a person who know* how to make good use of the 

 instrument, and we shall advert in the course of this article to some 

 of the qualities which are, and to others which are not, essential. 



We have given on the preceding page a sketch of the theodolite in iU 

 .jmpWt form, such as would be proper for the secondary triangulation 

 of a national survey, or for the most accurate private survey. The 

 tripod which carries the instrument rests with three foot-screwa in brass 

 notches let into the top of a wooden stand. The legs of the stand are 

 not fully represented, but the two parts of which each is composed end 

 below in a strong and sharply-pointed metal socket. The circle is fixed, 

 and the upper works, telescope, verniers, levels, Ac., turn on a centre, 

 which may be seen just under the cross of the telescope. The adjust- 

 ments are very simple. The wooden stand is first sot down with a good 

 opening of the legs, and the top nearly horizontal. The foot-screws ore 

 placed in their notches, the plumb-line hung from its book, below the 

 centre of the circle, and the telescope turned round till one level is 

 parallel to the line joining two foot-screws, while the other level is in a 

 line from the third foot-screw to the centre. Bring the bubble of the 

 first-mentioned level into the middle by raising one of the two foot- 

 screws and depressing the other, and then adjust the cross-level by raising 

 or depressing the third foot-screw alone. Now turn the telescope round 

 ISO*, and if the bubbles ore not in the middle, bring them half way 

 there by touching the foot-screws, and the other half by screws which 

 adjust the levels themselves. When this has been nicely done, the 

 bubbles will remain in the middle in every position of the telescope. 

 If the objects to be observed lay all in the horizon, or in a plane 

 parallel to it, the above adjustment would be sufficient ; but when the 

 objects are out of the horizontal plane they must be referred to it by a 

 perpendicular, that is, the plane described by the telescope must be a 

 great circle, and must also pass through the zenith. There ore 

 generally two wires at least in the focus of the telescope, one horizontal 

 and the other vertical. Place the eye-piece to give sharp vision of the 

 wires, and turn the milled screw, seen towards the object-glass, until 

 the objects you are going to observe are distinct. Place the vertical 

 wire on any well-defined object, making the bisection near the crossing 

 of the wire ; raise or depress the telescope until the object is nearly at 

 the bottom or top of the field ; if it is still bisected, the wire is rightly 

 placed, but if not, twist the tube carrying the eye-piece so as to effect 

 a bisection. To make the telescope describe a great circle, select some 

 well-defined object near the horizon, and bisect it : now take the 

 telescope very carefully out of its Y'S, reverse it, and look again at the 

 object. If it is still bisected, there is no error; but if not, the bisec- 

 tion is to be effected half by the tangent-screw of the instrument and 

 half by the screws which carry the wire-plate, screwing up one and 

 releasing the other. Restoring the telescope to its first position, it 

 will be seen whether the adjustment is correct, and if not, the process 

 must be repeated until the bisection is the same in both positions of 

 the telescope, the clamp and tangent-screw remaining fixed. For the 

 adjustment of the axis of the telescope a level would be convenient, but 

 in this instrument the axis is supposed to have been correctly placed by 

 the maker, and the only mode of correcting any error is by tiling the 

 T'S. It may be ascertained whether the axis is tolerably correct as 

 follows : Bisect an object as far above or below the horizon as the 

 motion of the telescope will allow. Reverse the telescope, and if the 

 object is still bisected, the pivots of the telescope ore the same size : 

 if not, the observer must deduce the difference of the pivots from the 

 altitude and the error observed, which is not difficult. When this has 

 been satisfactorily executed, bisect, as in the lost instance, on object as 

 far as possible from the horizon, and read off the verniers. Turn the 

 instrument round 180*, return the telescope end for end, bisect the 

 object again, and read off the verniers. If the mean readings differ 

 exactly 180, the axis is horizontal ; but if they do not, the observer 

 will have sufficient data from this, and the altitude or depression, for 

 determining the quantity and direction of the error, which he may 

 correct by the file or by calculation, according to his pleasure. There 

 is a much easier method of examining the position of the axis by 

 observing an object directly and as seen by reflexion from a fluid, as 

 mercury, oil, or water. The axis is truly horizontal when the vertical 

 wire bisects the object and its reflected image without moving the 

 tangent-screw. It must be recollected that the adjustments of the 

 horizontal circle already described must be previously and very 

 scrupulously performed before attempting the examination or adjust- 

 ment of the cross-axis. 



As the object* in a survey are at very different distances, an adjust- 

 ment is required for forming the image exactly on the wires.' The use 

 of the milled screw, seen towards the object-end of the telescope for 

 irpose, lias already been mentioned. 



In mo, this theodolite should I* placed on a repeating table r tri- 

 pod,mich as is to be found figured and described in KEPKATIM. i 

 and the repenting-tri pod upon the Htand. This was not done in the 

 present plan for the sake of clearness. To adjust the repeating tripod, 

 place the levels u described in the first adjustment, and clamp the 



theodolite. Bring the foot-screws of the tln<l<>liU> over the foot- 

 screws of the rcpeating-tripod by the motion f the tripod, an 

 by touching the f. Kit-screws of the tri|..l or theodolite sot Uu- 

 bubbles iu the middle. Tun) the upper plate of the tripoJ 

 and again bring the bubbles into the middle, half by the 

 screws, half by those of the instrument, and repeat the opernii.ni until 

 the revolution of the repeatiug-table does not alter the posit 

 the level-bubbles. The rcpeating-stand is now clamped, and the 

 instrument itself u tq be adjusted exactly as we have described 

 above. 



The course of observation after the instrument is adjusted U very 

 simple. The problem is to measure the horizontal angle between i \\ 

 objects. Turn the telescope two or three times round in t : 

 in which you intend to observe, then bisect one of the objects, read 

 off the verniers, and take a mean ; bisect the second object, read the 

 verniers, and take a mean. The difference between the two means 

 is the angle required. This is all that can be done by the instrument 

 as usually mounted ; but with a repeating-table the operation is con- 

 tinued, thus : Bring the telescope back on the first object, by the 

 motion of the rcpeating-table, using its clamp and tangent- screw, and 

 by the motion of the instrument bring the telescope on the second 

 object. It is clear the motion of the repeating-table has mer. -ly 

 restored the telescope to its original direction, without altering the 

 readings of the circle; and that if the telescope be turned on ihr 

 second object by its motion alone, without disturbing the circle, the 

 difference between the mean of these new readings and the preceding 

 mean will also be the angle required. By continuing the process, the 

 angle may be measured as often as the observer pleases. It is evident 

 that all readings-off, except the first and last, are superfluous, save as 

 checks, or as giving the means of estimating the accuracy of the final 

 result. The series should terminate after a whole number of i 

 tions as nearly as possible, when the exceutricity of the repeating-table 

 will be eliminated, a matter of possible importance if the objects are 

 near and the repeating-table carelessly made, or, if the objects ore 

 pretty distant and this caution superfluous, when the verniers are 

 nearly at the divisions at which you set out, which gets rid of or at 

 least diminishes any errors of division. The latter condition is how- 

 ever rather a speculative than a practical one. As the error of divi- 

 sion is divided by the number of observations, and the casual error of 

 observation only by the square-root of the same number, it is evident 

 that a moderate number of repetitions in our xoaQently-divided circles 

 will reduce the error arising from mal-diviaion to a much smaller 

 quantity than that which belongs to the class of casual error of 

 observation. 



The essential condition of repetition is, that the motion of the theo- 

 dolite shall not disturb the repeating-table. The motion of the latter 

 therefore should be as heavy as will admit of nicety in the tangent- 

 screw, while the motion of the parts which move with the telescope 

 should be as light and free as is consistent with firmness. There is, 

 we believe, no difficulty whatever iu effecting both these points ; but 

 lest any error should arise from repetition, we should recommend a 

 careful observer to determine his angles by two series, one by always 

 moving the telescope and its tangent-screw forward, and the repeating- 

 stand and its screw backwards ; and another, by reversing the process. 

 If the two results agree, as they should do within the limits of casual 

 observation, the mean is probably free from all otjier error ; and if 

 they do not, the observation should be repeated and varied until the 

 quantity and probable law of the error is ascertained. We should 

 then bo able to say decidedly where, when, and under what precau- 

 tions, repeating was a safe as well as a convenient aud econ< 

 process, which at present is rather a rexata guaalio, unless the 

 decision be supposed to be against all repetition, to which we do 

 not bow. 



The foregoing description has been confined to a form of theodo- 

 lite which is not iu ordinary u.-e, though from its simplicity and 

 power it is well adapted to the purpose of explanation. The e. minion 

 theodolite is generally carried by a pair of parallel plates, fixed on 

 a three-legged staff. The lower of these circular plates is screwed upon 

 the staff, and has an aperture above the screw. The upper plate has a 

 strong descending shank which passes loosely through this aperture. 

 A button of a spherical form is fixed on the end of the shank, the cur- 

 vature uppermost, and rubs against the under surface of the lower 

 1 1 a.-, which is dome-shaped to fit it Four strong screws pass through 

 the. upper plate and abut with their lower ends against the |.r...r 

 plate. When the screws ore turned the plates ore separated until the 

 button and the spherical surfaee on which it rubs ore brought into 

 squeezing contact. To level the theodolite, set the levels each parallel 

 . ,-oiial pair of screws of the ]aiall.-l plat. v. Then .-eiew one 

 pair until yon coma to a bearing, and by releasing one screw ami 

 screwing up the other, but not very tight, set the corresponding level 

 horizontal; leavin;; thi> pair an 1 taking h"M of the other jrnir set the 

 second level also right, an, I if tl>< lirst level is deranged, as it pi 

 will be a little, restore its position by screwing up the proper 

 Turn the telescope half round and corrcet the error, lialf by the 

 parallel plate-screws, and the other half by the level adjustment* them 

 elves. It is desirable t the final adjustment is made, the 



screws shouM hard, otherwise there is a great chance that 



the upper plate will turn a little during the observation. This olijec- 



