Verification. Direct the telescope so that the intersection of the wires bisects some well defined point at a distance. Rotate the telescope so as to bring the level to the top. If the intersection still coincides with the object, the adjustment is perfect. If it has changed its position, bring it half-way back, by the screws a, a, and verify again.

188. Fourth Adjustment. The line of collimation must be perpendicular to the horizontal axis. Verification for the Transit.

Set the transit on a piece

C

Fig. 66.

of level ground, as at A, (Fig. 66,) and level it carefully. At some distance-say four or five chains-set a stake B in the ground, with a nail driven in the head, and direct the telescope so that the crosswires may bisect exactly on the nail. Clamp the plates, turn D the telescope over, and place a E second stake C precisely in the

B

line of sight. If the adjustment is perfect, the three points B, A, and C will be in a straight line. To determine whether they are so, turn the plate round until the telescope points to B; turn it over, and, if the line of sight passes again through C, the adjustment is perfect. If it does not, set up a stake at E, in the line of sight: then the prolongation of the line BA bisects EAC.

CAD is therefore equal to

twice the error. Now, if the plate is turned until the line of sight is directed to B, the axis will be in the position F'G'. Turn the telescope over, and the angle EAF'= F'AB; CAE is therefore equal to four times the error.

Hence, to rectify the error, the instrument being in the second position, place a stake at H, one fourth of the distance from E to C, (Fig. 67,) and, by means of the screws a, a, (Fig. 51,) move the diaphragm horizontally till the vertical line passes through H. Verify the adjustment; and, if not precisely correct, repeat the operation.

189. The above method is inapplicable to the theodolite, as its telescope does not turn over. For the means of detecting and correcting the error, see Art. 190.

190. Fifth Adjustment. The horizontal and the vertical axes should be perpendicular.

Verification for the Transit. Suspend a long plumb-line from some elevated point, allowing the plummet to swing in a bucket of water; then level carefully, and bisect the line accurately by the vertical wire. If, on elevating and depressing the telescope, the line is still bisected, the adjustment is good. If not, the error may be corrected by filing one of the frames. Instead of a plumb-line, any elevated object and its image, as seen reflected from the surface of mercury or of molasses boiled to free it from bubbles, may be employed.

Verification for the Theodolite. If the instrument, treated as above, shows a defect, the error may be either in the axis, or in the position of the Y's. To determine which, turn the plates half round, and reverse the telescope. If the deviation is now on the same side as before, the Y's are in fault. Their position in most instruments may be corrected by screws which move one of them laterally. If the line deviates to the opposite side from before, the position of the axis may be corrected by filing, as directed for the transit.

This adjustment may also be examined by directing the telescope to some well defined elevated object, and then to

another on or near the ground. If none such can be found, let one be placed by an assistant; then reverse the telescope in its Y's if the instrument is a theodolite, or turn it over if the instrument is a transit, and direct it to the upper object. If the cross-wires still intersect upon the lower point when the tube is depressed, the adjustment is perfect.

191. Adjustments of the Vertical Limb. Having verified the various adjustments for horizontal motion, as described in the preceding articles, and rectified them if defective, the instrument is ready for use for horizontal work. To take angles of elevation, or to use the instrument for levelling, the following adjustments must also be examined::

1. The level beneath the telescope must be parallel to the line of collimation.

2. The zero of the vernier must coincide with the zero of the vertical limb when the plates are level and the telescope horizontal.

192. First Adjustment. The level must be parallel to the line of collimation.

Verification. Select a piece of level ground, and drive two stakes, A and B, (Fig. 68,) four or five chains apart. At C, equidistant from them, set the instrument. Level the plates, and bring the bubble in the telescope level, to the middle of its run; then let an assistant hold a graduated staff on A. Note exactly the point in which the line of sight meets the staff: then let the assistant remove the staff to B, and drive the stake B until the telescope points

to the same spot on the staff. The tops of A and B are then level, whether the instrument is in adjustment or not.

Now remove the instrument to G, and level as before. Direct the telescope to the staff on B, and note the point I of intersection. Let the assistant carry the staff to A. Again note the intersection K. If the instrument is properly adjusted, these two points will coincide. If they do not, the line of collimation points too high or too low. Take the difference between BI and AK. This difference will be LK, the difference of level as given by the instrument at G. Then say, As the distance between the stakes (BA) is to the distance from the instrument to the far stake (GA), so is the difference of apparent level of the stakes (LK) to the correction on the far staff (MK).

This correction—either taken from the height AK if too great, or added to it if too small—will give AM, the height of a point on the same level as the instrument. Direct the telescope to this point, and rectify the level, by raising or lowering one end by means of the capstan screw until the bubble is in the middle of its run. If the operation has been carefully done, the adjustment is perfect. Verify again; and, if needful, repeat the operation.

193. Second Adjustment. The zeros of the vernier and of the vertical limb should coincide when the telescope is level.

When the first adjustment is perfected, and the telescope is still level, examine the reading on the vertical limb carefully: if the zeros coincide, the vernier is properly adjusted; if they do not, note the error, and have it marked somewhere on the instrument under the plates, that it may not be forgotten. It must be applied to all angles of elevation taken by the instrument.

If the index-arm is movable, as is frequently the case with transits, it should be adjusted before taking vertical angles.

194. When all the preceding adjustments have been examined, and rectified if necessary, the instrument is ready for work. It would be well, however, to examine carefully the reading of the verniers, to see that they are properly divided. However placed, no two lines of the vernier

except the first and last should coincide with divisions on the arc. If two are found to do so in any position, there is an imperfection in the graduation. If the division is very fine, a number of lines in the immediate neighborhood of the coincident lines will differ very slightly from coincidence; but, when carefully examined with a good magnifier, they should recede gradually.

Place the instrument where a good view of a fine point, some eight or ten chains distant, can be obtained. Level carefully, direct the line of sight to the point, and note the reading on the horizontal limb. Reverse the telescope in its Y's, or, if the instrument is a transit, turn it over; turn the vernier-plate till the line of sight passes again through the point, and note the reading. It should differ by 180° from that before obtained. If it does not, the divisions are not perfect, or the telescope is not over the centre of the plates. Either defect should condemn the instrument, as it can be remedied only by the maker. This verification should be tried in various positions of the divided plate. If these tests, and those formerly mentioned, are found to detect no imperfection, the instrument may be pronounced a good one.

195. Taking Angles. Set the instrument precisely over the angular point, and level it, being careful to have the levelling screws pressed tightly against the plates, that the instrument may be steady. Set the index to zero, and clamp the plates, and, if there be more than one vernier, note the minutes and seconds of the others. Loosen the lower clamp, and bring the telescope so that the wires may intersect on the left-hand object; clamp, and perfect the adjustment by the tangent screw. If there is a watch-telescope, set it upon some well-defined object,—such as a lightning-rod or the corner of a chimney, and clamp it tightly. Loosen the vernier-plate, and turn the telescope to the other object, perfecting the adjustment by the tangent screw. Examine the watch telescope, and, if the instrument has shifted, bring it back by the tangent screw, and readjust the telescope by moving the vernier-plate.