56 MATHEMATICS. 
so that the centre of each moves parallel to its frame, the paths described 
being perpendicular to each other, thus constituting the axis of the ellipse. 
The ellipse itself is described by one point of a small pair of compasses, M, 
during the working of the two circles, the other point being placed in the 
foot H. f and f are buttons by means of which the circles are moved 
along, while the frame lies upon the paper. The frame is held down with 
the left hand by means of the buttons N and O. Any required eccentricity 
can be given to the foot H, as it slides with its frame, g, in a groove, and is 
united to the rack-work, h, which is moved by the pinion L. Fig. 18 
presents a clearer view of the whole arrangement ; it is a section perpendi- 
cular to the two beams, a, a, of the circles Aand B. Fig. 12 is a side view 
of the instrument. 
If both the circles are placed concentric with each other, and the point M 
placed in the centre, the latter will describe a point when both circles are 
moved in the frame. If L be turned, M becomes more and more eccentric, 
and will describe a circle in the movement of the circles, or an ellipse with 
equal axes. By turning K, both circles become eccentric. If M stand in 
the centre, it describes a straight line in the movement of the circles; in 
other terms, an ellipse with one of its axes =O. The different ellipses are 
obtained by the eccentricity of M. The two buttons, N and O, pass through 
the ruler, P, which has slits, as well as the prolongations of F and Q, so that 
the whole instrument can be moved without displacing N and O, which is 
necessary to the adjustment. 
Another instrument for describing various curves, principally epicycloidal, 
is the eccentric compasses, represented in pl. 5, fig. 14. This was invented 
by Suardi, who described 1273 different curves which could be drawn with 
it. The three legs, A, B, C (the head only of C is visible), form a stand, at 
whose point of union, C, is placed the principal axis, a. Upon this the tube, 
b, provided with a milled head at 7, may be turned. The strip d is fastened 
to the tube so as to turn with it. The wheels, e and f, are attached at d in 
such a manner that the axis of e may be moved in a slit made in d, and that 
of f may be moved on d by means of a slide; g is a toothed wheel, fixed 
upon the main axis, a. All three wheels may be interchanged or replaced 
by others, according to the character of the curve. They must all, however, 
be kept in close contact during their use. The pierced head, 7, is attached 
beneath the prolonged axis, f, in which may be moved the small strips, h, 
earrying the drawing point, hk. 
The Pantograph, in its original form, is an instrument invented by Father 
Scheiner, intended to reduce or enlarge drawings to any required scale: in 
other words, to draw similar figures. As the similarity of figures can 
be attained in various ways, it follows that there must be various forms of 
pantographs. The two principal systems have been represented in figs. 15, 
16. Passing by the earlier and more imperfect forms of the pantograph, 
we represent, in fig. 15, the first of these systems. Two rulers, AB and BC, 
are connected by a joint at B; two others, DF and FE, hinged together at 
F, are combined with the first two at D and E, so as to forma parallelogram. 
However much the angular positions of these four rulers may change, they 
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