MATHEMATICAL AND SURVEYING INSTRUMENTS. 63 
placed perfectly centrally upon the stand. This strip carries two fixed 
diopters, or sight vanes, B and C, as well as the centre. Another strip, E, 
turns about the centre, one end of which in the half-astrolabe (both ends in 
the full astrolabe) traverses the graduated limb and carries the sight vanes 
Gand F. The middle line of this alidade coincides with the axis of the 
sight vanes and the centre, and is marked upon the bevelled edge of the 
alidade as an index. The diopters are both ocular and objective, for fore 
and back sighting. The limb of semi-astrolabes is doubly marked, first 
from 0° to 180°, and then from 180° to 360°, the 180° of the second corres- 
ponding to the 0° of the first. A small compass is often attached at the 
centre, and the tongue H fitted up with nut and screw as in fig. 21, so as 
to permit the circle to be brought from the horizontal to the vertical posi- 
tion, thus allowing a measurement of altitudes. T’o measure an angle with 
the astrolabe, it is placed with its centre over the vertex of the angle, and 
turned until the fixed diopters sight in the direction of one leg. The 
movable strip with its diopters is then to be sighted in the direction of the 
other leg, and the angle contained between the two strips, read off. To 
measure several angles from the same station, the first diopter may be left 
fixed, and the alidade moved successively to the different angles. Thus 
if the first angle measured between the fixed strip and the alidade amount 
to 354°, and the second to 973°, the angle contained between the two posi- 
tions of the alidade will be 972°—35}° = 623°. The astrolabe may, with a 
little practice, be made to perform much of the work of the plane table. 
Telescopes are sometimes attached, instead of the alidades. The instru- 
ment in this case falls rather in the class of the theodolite and graphometer, 
to which we shall shortly refer. 
The compass, represented from above (fig. 33, pl. 5), and from the side, 
in fig. 34, is another instrument for measuring angles. It depends upon 
that property of the magnetic needle by which its direction is always paral- 
lel to that of the magnetic meridian, called north and south line. Even if 
the magnetic meridian of several places be not parallel, strictly speaking, 
yet the difference within a degree of longitude is so slight, as to be zero for 
all ordinary purposes. The compass consists of a round or square box, 
AB, in whose centre is a pivot, C, upon which a magnetic needle, DE, plays 
freely. The relative position of the latter may be read off on the limb, 
graduated to half and quarter degrees. ‘To prevent the needle from playing 
when not in use, whereby both it and the pivot would be injured, a stop, or 
arrester, I’, is attached: by this the needle can be lifted from the pivot, and 
pressed firmly against the glass covering of the box. The plate of the 
compass is dressed truly square, with two edges parallel to the north and 
south line, and three of the edges bevelled. In this way the compass itself 
may be used for laying off angles, by which means numerous errors may be 
avoided. In using the compass, it is attached to a tripod stand, by the 
socket I. This socket has a contrivance at G, with nut and screw for fix- 
ing, and a rim, abcd, is screwed upon the plate AB, which serves to carry 
the telescope IH. This is made fast by the screws ef, but may be turned, in 
a vertical plane, about the pointG. The connexion with the socket, I, takes 
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