As the objects 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 this purpose, has already been mentioned.
In use, this theodolite should be placed on a repeating table or tri pod, such as is to be found figured and described in Itereariso ernes's and the repenting-tripod upon the stand. This was not done hi the present plan for the make of clearness. To adjust the repeating tripod, place the levels as described in the first adjustment, and clamp the theodolite. Bring the foot-screws of the theodolite over the foot screws of the repeating-tripod by the motion of the tripod. and then by touching the foot-screws of the tripod or theodolite set the level bubbles in the middle. Turn the upper plate of the tripod half round, and again bring the bubbles into the middle, half by the tripod foot. screws, half by those of the instrument, and repeat the operation until the revolution of the repeating-table does not alter the position of the level-bubbles. The repeating-stand is now clamped, and the instrument itself is to be adjusted exactly as we have described above.
The course of observation after the instrument Is adjusted is very simple. The problem is to measure the horizontal angle between two objects. Turn the telescope two or three times round in the direction 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 ie 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 hack on the first object, by the motion of the repeating-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 merely restored the telescope to its original direction, without altering the readings of the circle ; and that if the telescope be turned on the 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 bo 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 revolu tions as nearly as possible, when the excentrieity 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 are pretty distant and this caution superfluous, when the venders are nearly at the divisions at which you yet 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. Aa 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 repetitious iu our excellently-divided circles will reduce the error arising from turd-division 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 ehall 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 in 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 egret, as they should do within the limits of casual observation, the mean is probably free from all other 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 uuder what precau tions, repeating was a safe as well as a convenient and economical process, which at present is rather a ve.rata guerttio, unless the decisiou be supposed to be against all repetition, to which we do not bow.