62 MATHEMATICS. 
meets the signal at a. After making all necessary adjustments, as examin- 
ing the compass, observing whether the point 6 of the paper is vertically 
over b of the base, &c., the objects, or signals, C, D, E, S, sighted from 
a, are again sighted from b, and sight lines drawn until they intersect the 
corresponding lines from a. The points of intersection are indicated by the 
letters or numbers of the sight lines, and well marked, by the pricking of a 
fine needle, so as to allow the erasure of the lines. The different points 
thus obtained are finally connected, by straight or curved lines, as the case 
may require. In accurate measurements, where there is much curvature 
and few objects, staves, numbered in order, are first of all set up at all the 
points to be ascertained. In sighting, the signal-carrier, with his flag, goes 
to each of these stations in succession, and remains until sighted. If the 
operation is to extend beyond the reach of a single base line, points must 
be selected from which it may be continued afresh. The position of these 
new points must be determined from the first base. Further measurements 
with the chain are not necessary ; if, however, certain important points can 
be sighted from one spot, and not from another, they may be first sighted 
and measured, and then transferred to the paper, according to the proper 
scale of reduction. For amore detailed account of the use of the plane 
table, we must refer our readers to special treatises on the subject. 
The transition from instruments for measuring lines, to those for deter- 
mining angles, is furnished by the instrument represented in fig. 30, pl. 5, 
and invented in 1742. This, ina less perfect form, is mentioned in Speckle’s 
Festungsbau, 1608. Zollman has improved it so much, however, that it 
now bears his name. It is represented in our figure as improved by Ger- 
stenberg, of Jena. It consists of a tripod stand, upon which is fastened the 
board A, as in the plane table. The erecting compass C serves to set up 
the instrument properly. There is a pivot at the centre B, upon which the 
diopter ruler, the alidade D, with the two sight vanes, EK and F, can turn. 
The board is covered with the drawing paper, and upon it is placed the 
frame seen on the exterior of the board. This frame is graduated to degrees 
of the circle, and marked accordingly. The instrument is now set up at a 
station, at which a certain number of angles is to be ascertained, and the 
legs of these angles determined by sighting through the diopters, afterwards 
to be measured by a protractor, or by the graduation in the frame. The 
advantage of this instrument consists in its giving the angles themselves, 
and not, as in other angular instruments, their numerical values. 
Of the purely angular measuring instruments, the first to be mentioned is 
the astrolabe. It is exhibited in fig. 31 on its tripod stand. — By this is not 
to be understood the astrolabe of Hipparchus, used in determining the alti- 
tudes of the stars, but the common astrolabe, used by surveyors for hundreds 
of years, and which even now maintains its place, when well constructed, 
as an excellent means of measuring angles. It consists, in the semi-astro- 
labes, of a large semicircle, D, divided to 180°, and in the full astrolabes. of 
a large circle divided to 360°, and generally graduated also to quarter 
degrees. A strip, A, is attached in the direction of the diameter, which 
passes through 0° and 180°; this strip has a tongue at H to enable it to be 
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