MATHEMATICAL AND SURVEYING INSTRUMENTS. 57 
must always form a parallelogram. Small rollers are placed beneath the 
four points, D, E, F’, and B, to allow the instruments to move freely over the 
paper. A, G,and C, are three points on the rulers where pipes are attached, 
and which must always lie in a straight line. C is the fixed point; the 
tracing point to be moved over the drawing, R, to be copied, is at A, and 
the drawing point with which the copy, 8, is made, is at G. It is evident 
that in all movements of the instrument, the line CGA will remain straight ; 
the figures described must, therefore, be similar, and the amount of reduc- 
tion will be greater as G is nearer to A. 
The pantograph represented in fig. 16, or eidograph, as it was called by 
its inventor, Professor Wallace of Edinburgh, has a very different construc- 
tion. The bar D moves in the socket A, in which it may be fixed at any 
point by a screw. To the socket is attached a heavy foot, about which it 
can rotate. The arms, EH and FG, may also be moved, with reference to 
the axis of the bar D, the amount of motion being determined by the amount 
of reduction required in the copy. For this purpose, scales are attached to the 
bar and arms; a tightly stretched endless string, aa, passes round the two pul- 
leys B and C, attached to which are the sockets, in which the two arms, EH 
and FG, slide, so that these must always make corresponding motions. If 
the tracing point be at H, and the drawing point at G, and if the three 
points, H, G, and A, lie in astraight line, then 8 will be the reduction of R. 
It is evident that if the tracing and drawing points change places, the copy 
will be larger than the original, in all pantographs, instead of being 
smaller. 
By a slight change, the pantograph can be so arranged as to copy objects 
on the same scale as the original; and if the drawing pencil acts at its upper 
end, and the tracing point at its lower, then the copy will beinverted. This 
is of great importance to engravers, who are obliged to invert the designs 
on their plates, so as to have the engravings direct. For this purpose, the 
plate is placed above the drawing-point, which here consists of a fine etch- 
ing needle. The pantograph has also been employed for engraving writing. 
Two other drawing instruments of great utility are the spring compasses 
(pl. 5, fig. 17), and the parallel ruler (figs. 18,19). The spring compasses, 
instead of a head, have a strong, curved, steel spring, b, to which the feet, f 
and g, aresoldered. A curved screw, d, is fastened in the foot f, and passes 
through g. Ateis the nut of the screw, against which g is constantly 
pressed, by the elasticity of the spring. By the action of this nut the points 
are separated or approximated. For convenience of handling, a button is 
attached at a. The spring compasses supply the place of the hair com- 
passes, and have the advantage of being firmer, and less liable to derangement 
when once fixed, for which reason they are employed in describing circles 
on wood and metal. 
The parallel ruler is used to draw parallel lines. Its earliest construction 
consisted of two parallel rulers, connected by a cross-piece at each end: 
the more modern instrument, represented from above in jig. 18, and laterally 
in fig. 19, consists of a broad ruler, A, upon which the axle B turns, in two 
small boxes, aa. At each end of this axle are attached small and perfectly 
57 
