MATHEMATICAL AND SURVEYING INSTRUMENTS. 65 
of the lower geodesy, but for trigonometrical surveys, and even for the most 
delicate astronomical measurements. It rests upon a tripod, K, with which 
it is fixed on a special stand, or upon the plate of a plane table. At the end 
of the feet are the setting screws, a, b, and e, by means of which a perfectly 
horizontal position of the instrument can be attained. At the junction of 
the three feet there is erected a shaft, which carries the entire upper portion. 
Over this is slipped a socket, with a foot plate, L, which can be turned about 
the shaft by the action of a male screw, c, upon an endless female screw cut 
in its periphery ; the plate may be fixed by the clamp d. This socket carries 
a correcting telescope, IH, which may be turned about the vertical shaft, 
independently of any motion of the foot or of the upper portion of the 
instrument. Over this socket rests a pierced circular plate, A, which can be 
fixed to the shaft, and upon which turns a circle provided with a limb, and 
capable of being fixed by a clamp screw, G. On the inner edge of this 
circle rests the accurately fitting alidade ruler, B, which, in some instru- 
ments, may form a full circle. This ruler, or alidade circle, carries an index 
provided with a vernier, as also the tube level C, by means of which the 
horizontal position of the instrument, and in particular of the circle A, may 
be insured. The bearer, F’, of the telescope, DE, stands vertically over the 
centre of the alidade, the telescope supplying the place of the sight vanes, 
and being capable of motion in a vertical plane. A graduated arc, with 
index and vernier, is attached, for tne purpose of measuring angles of eleva- 
tion and depression. In using the theodolite, it is placed upon the stand, 
or the plane table, and fixed in a perfectly horizontal position by means of 
the setting screws, a, 0, e, and the level C. ‘The lower telescope is now to 
be directed to some fixed object, or, if none such present itself, to a tempo- 
rarily fixed movable one, as a signal flag, whose centre is intersected by the 
vertical cross hair. This adjustment is made by means of the spindle c 
acting on the female screw in L; when completed, the clamp is to be 
applied, and the telescope fixed. It must now remain in this position 
throughout the operation, to insure the immobility of the whole apparatus. 
The clamp screw G is then loosened, by which means the circle A is set 
free: this, with the alidade, is to be turned until the cross hair in the tele- 
scope DE meets one of the two objects whose angular distance is to be 
measured, consequently lying in a vertical plane with one leg of the angle. 
The limb is now to be fixed by the clamp screw G, and the alidade B turned 
until the cross hair in the telescope DE meets the second of the objects, the 
telescope thus lying in a vertical plane with the second leg of the angle. 
The interval traversed by the index, in shifting from one leg to another, will 
represent the angular separation of the objects, and will give the angle 
required. If the objects lie in different horizontal planes, the telescope must 
be elevated or depressed to meet this case. The vertical limb will give the 
angular value of this elevation or depression. 
When observations are conducted in a certain manner with this instru- 
ment, it becomes a repeating or compensating circle. In reading off the 
angles, slight errors may creep in, even with the greatest care taken to 
avoid them: to compensate for these, the operation must be repeated. For 
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ICONOGRAPHIC ENCYCLOP 4DIA.—VOL. I. o 65 
