THE THEODOLITE.] 



ASTRONOMY. 



997 



point O. But it frequently happens that the angle com- 

 prised, between the vertical plane Z O A, Z O B, which 



Fig. 103. 



passes botween these two points, is required that is, the 

 angle a O 6, formed by the intersections, OaOfc, of the two 

 planes, vertical with the horizontal plane, H H. Our 

 knowledge of the angle A () B, measured by the repeating 

 circle, added to that of the angles, Z O A, Z O B, which 

 are the zenith distances of the points A and B, enables 

 us, by deducting the angle a O 6, either by geometrical 

 construction, or by trigonometrical calculation, to deter- 

 mine the angle. But it is sometimes more convenient to 

 ascertain its value by direct measurement ; and the theo- 

 dolite we are about to describe enables us to do this with 

 gr> at exactness. 



This instrument is represented in Fig. 194. It is corn- 

 rig, iw. 



Fig. 193. 



Ft 



poed of two graduated circles, of which the one is verti- 

 cal, the other horizontal. The first of these two circles. 



A, is adapted to the horizontal axis B, round which it 

 turns. The axis B is carried by the upper extremity of 

 the vertical axis C, round which the circle A and the axis 

 B can be turned by one common movement. The weight 

 D acts as a counterpoise to balance the circle A, pie- 

 serving it steadily on the vertical axis C. The second 

 circle, E, has its centre upon the same vertical axis C, 

 and turns on its plane round the axis. The foot of the 

 instrument is furnished with three double screws like the 

 repeater, by means of which the instrument can be ren- 

 dered perfectly vertical, which is ascertained by means of 

 the spirit-level, F, on the axis B. This spirit-level is not 

 carried round with the circle, as in the repeater, but a 

 slight motion can be given to it by means of the screw a, 

 thus slightly raising or depressing one of its extremities, 

 and making it turn round a small axis at its other ex- 

 tremity. In this manner it is so managed that the bead 

 of the level will be exactly in the centre of its tube when 

 the axis C is in a vertical position ; and, consequently, 

 the plane of the circle A will be vertical 

 also. As a test of the circle and the 

 axis C being perfectly vertical, and the 

 axis B horizontal, the movable spirit- 

 level (Fig. 195) is used. This instru- 

 ment is made so as to rest on the axis B ; 

 the feet of the spirit-level being adapted 

 to it for that purpose, while it is supported in its place 

 by the fork h (Fig. 1U4). 



The telescope G is adapted to an inner circle, which 

 moves round the interior of the circle A. In like manner 

 the parts of the instrument attached to the horizontal 

 circle, E, are fixed to an inner circle, which moves round 

 its interior, the outer extremity of each circle carrying a 

 graduated scale, to which the inner circle acts as an index 

 guide. A clamp, d, having an adjusting and guiding 

 screw, serves to fix the circle E to the pedestal ; while 

 another clump. ', in a similar manner, serves to fix the 

 Tipper parts to it ; and a third clamp, /, serves to fix the 

 limb A in such a manner as to be in opposition to 

 it when turnod round its centre. A fourth clamp, not 

 seen in the figure, attaches the telescope G to the 

 circle A. 



A second telescope, H, is adapted to tho pedestal of 

 the instrument, having movements which, from its posi- 

 tion, are very limited ; it serves no other purpose, how- 

 ever, than to show that the foot of the instrument is 

 steady while the observation is in progress. With this 

 object, profiting by the limited movements it can take, 

 its optical axis is trained in the direction of a point which 

 can be easily recognised ; and from time to time, while 

 shifting the instrument, it serves to assure the observer 

 that the telescope is directed to the same point as at the 

 commencement of the operation. A guiding-screw, g, in 

 the foot of the pedestal, serves as a slow movement, by 

 which the optical axis of this glass may be trained to the 

 required point. 



To measure the angle comprised between the two ver- 

 tical planes passing between two objects, turn tho whole 

 upper part of the instrument, independently of the 

 graduated limb, E, so that the index traced upon tho 

 inner circle coincides with zero of the graduation, and 

 fix this circle to the limb E in this position by means of 

 the clamp e. By turning the limb E and all it carries, 

 and at the same time moving the telescope G round tlio 

 centre of the circle A, so that the optical axis is directed 

 to the nut of the two objects to be observed, the first 

 operation is completed. Fix the limb E in this position, 

 by means of the clamp d, for the second operation, throw- 

 ing loose at .the same time the clamp e, and turning the 

 upper instrument round its axis so as to lead the tele- 

 scope G direct to the second object. The index of the 

 circle, moving in the interior of the limb E, has described 

 upon this limb an arc representing the value of the angle 

 sought, and of which we cau read the amount on the 

 graduated scale. 



If it be intended to apply the principle of repeating 

 the angle, fix the higher instrument to the limb E in 

 the position it has now attained ; loosen the clamp d, 

 and turn the limb E, with all above it, so that the tele- 



