70 MATHEMATICS. 
Q, and R, upon which the plate L’ rests. This is so connected with the 
plate I, as that the setting screws, e, e, e, can render the latter horizontal, 
and with it the whole apparatus. The screw, N, serves in addition to turn 
the instrument horizontally about its axis, and the screw, M, is a clamp to 
hold it in any position desired. The compass, I, lies in the middle of the 
arm FG, and at one end is the support E. for the telescope; the other sup- 
port, D, stands upon a screw, by means of which it can be placed somewhat 
higher or lower in the arm FG, for the sake of ascertaining certain neces- 
sary corrections in the parallelism of the whole instrument. The supports 
are called Y’s, from their shape, which affords a steadier position to the 
telescope than if they were semi-cylindrical. The collar bands, f, are 
attached to the Y’s by hinges. The level cd is suspended from the tele- 
scope AB, by special collars, and is firmly fixed to A; by this the parallelism 
is more perfectly secured. This telescope has a cross hair which can be 
brought out of the axis by the screws, b,b; a is the handle for managing 
the telescope when it becomes necessary to reverse its position. 
The levelling compass (pl. 5, fig. 47) has for its object, in addition to the 
purposes of the preceding instruments, that of measuring altitudes. It is 
fixed on a tripod stand by the socket A and screw a, and has an arrange- 
ment, by means of the screws, b, c, for producing a horizontal position and 
a rotation. It consists of a compass, I, to whose border the level D is 
attached. By means of the clamps d and 8, the circular limb E is attached 
near the level, and perpendicular to the plane of the compass. About its 
axis the telescope C, fixed to the alidade GH, rotates vertically up and 
down. The alidade has a vernier at G, which can be fixed at the zero of 
the scale on the limb E, by the clamps at F and H. This will be the case 
when the axes of the telescope and level are parallel. T’o measure altitudes, 
the clamp screw, H, must be loosened, and the tube directed towards the 
object while the instrument still remains horizontal. 
The levelling circle (fig. 48), which is actually only a modification of the 
- repeating circle, may be used as a universal measuring instrument. It has 
a foot, A, with the screws, a, a, a, for horizontal adjustment. The correct- 
ing telescope, CD, is attached to the socket B, and is capable of being fixed 
by the screw contrivance, c, b. The telescope carrier, H, with the vernier 
alidade, G, moves on the limb EF, being managed by the screw c. The 
telescope IK rests upon the support H, and can be fixed by means of a 
special arrangement, at any position in a vertical plane The level, L, 
rests upon a plate, M, with two small processes, which pass between the 
beds e and f of the telescope. 
In addition to the levelling apparatus already mentioned, there still remain 
the levelling staves (figs. 51, 52), and the sight vanes, or targets (figs. 58, 54). 
The staves are divided into feet, inches, &c., and the height is read off from 
the ground to the point where the sight line of the diopters or telescope 
intersects the staff. P/. 5, fig. 51, exhibits one of these staves divided on 
the right hand side into feet and inches, and on the left into decimetres. A 
vane or target moves up and down the staff, until the central horizontal 
line of the vane falls in the horizontal plane of the level, the corresponding 
70 
