MATHEMATICAL AND SURVEYING INSTRUMENTS. de 
spindle f is inserted by means of the spring, c. The end of this spindle is 
round at one end, where it receives the eye of the third leg, c, which may 
be fastened by means of the plate, g, and the head screw, h. In this manne1 
the leg c may be made to assume any given position with respect to b and 
d, and thus any given triangle be taken up with the compasses. 
A convenient variety of the triangular compasses is the plate compasses, 
jig. 55, which consists of a three-limbed plate, AA, provided with a button, 
B. At the extremities of the limbs A, A, A are attached the secondary 
limbs, C, lying in the same plane. Their attached points, a, a, a, may be 
placed at any required position in the plane of the paper. 
It has been seen under the head of perspective and projection, that when 
a circle is viewed from any direction other than one perpendicular to its 
centre, it will appear as an ellipse. As such foreshortened circles very 
frequently occur, and ellipses are troublesome to describe, considerable 
attention has been directed to the invention of instruments by means of 
which these curves may be readily drawn. These are called elliptographs, 
of which various forms have been devised. ‘Two of these are represented 
in figs. 9-13. Fig. 9 is an upper and fig. 10 a perspective view of the old- 
est and most imperfect of these instruments. This consists of a cross, abcd, 
which has two grooves on its upper surface, crossing each other at right 
angles. Under these grooves are four points, which when in use are placed 
in the two axes of the ellipse, so that the middle of the cross stands exactly 
above the centre of the circle or ellipse to be described. The movable 
slides g and h work in the grooves in such a manner that always moves 
in the groove ad, and g in the groove be. The slides have boxes above, 
through which the ruler ef is passed, to which the boxes may be fastened 
by head screws. One end of the ruler f carries the drawing point 7. To 
use the instrument, place the point 7 upon the extremity of the long axis, 
and fix h at the middle of the cross. Then bring 7 to the extremity of the 
short axis, and fix g at the middie of the cross. If now the ruler be moved, 
the box h will slide in ad, and g in bc, by means of which the drawing point 
will describe the ellipse represented in the figure. 
The defect in this instrument consists in the impossibility of describing 
ellipses whose axes are shorter than or much different in proportion from 
those of the cross. 
Farey’s elliptograph, pl. 5, figs. 11—13, is perhaps the best yet invented. 
As far as its size will admit, the entire series of ellipses from a straight line 
to a circle may be drawn with great accuracy. It consists of two circles, 
A and B, lying one above the other in such a manner that, by means of the 
pinion K and the rack-work d, any required eccentricity may be given to 
them. They are fixed at ary position by the screws cc. The two bridges, aa, 
and the curved arms, bb, serve to give the necessary strength to the circles, 
and to make them sufficiently open to see underneath them. The two circles 
may be shoved backwards and forwards between the four beams, D, E, F, 
and Q, which together form a frame-work. These beams lie in two planes, 
as shown by fig. 12, so that F and Q determine the path of the upper, D 
and E that of the lower circle. In this way the two circles may be moved 
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