Full text: The collected mathematical papers of Arthur Cayley, Sc.D., F.R.S., late sadlerian professor of pure mathematics in the University of Cambridge (Vol. 8)

180 
ON A CURVE-TRACING APPARATUS. 
[509 
the moveable cross-pieces E, E carrying the axes A, A with the attached mitre 
wheels, and circular disks X, X. Each of these wheels separately may be placed (as 
in the figure) out of gear with the two vertical wheels, or it can (by moving the 
Fig. 1. 
cross-piece E) be brought into gear with either of these wheels. Each axis A passes 
through a circular disk H, capable of rotating about it, so that it may be fixed in 
any position, and serving as the bearing for the plane X. 
The disks X, X may be regarded as being themselves the planes II, II (say these 
planes are rigidly attached to X, X respectively); or we may, in any other manner, 
move the plane II by means of the disk X; for instance, X may carry a spur-wheel 
gearing into a spur-wheel on the under surface of II, and thereby communicating a 
Fig. 2. 
rotation of different velocity to the plane II; or the connection may be as in the 
ordinary oval chuck. In any such case, the disk H (which, for this reason, was made 
to project beyond X) serves as a support for the plane II, and the apparatus con 
nected therewith; and observe that the angular position of such apparatus, and 
therefore of the path of any point of II, may be varied at pleasure by moving the 
disk H through any angle. 
Detached altogether from the rest of the instrument, or what is better, supported 
on longitudinal pieces carried by the cross-pieces C, G we have a bridge (see fig. 1) 
capable of adjustment as regards height, and serving as a support for the pentagraph- 
apparatus, or other connection of the one plane II with the pencil which works upon 
the other plane II. 
It is hardly necessary to remark that in the simple form of the instrument where 
the disks X, X are themselves the planes II, II, then putting the mitre wheel of one 
plane X in gear with either of the corresponding vertical wheels, and making the plane 
rotate, the other plane X will rotate with the same angular velocity, in the same or 
the opposite direction, or it will remain at rest, according as its mitre wheel is in 
gear with one or the other of the corresponding vertical wheels, or is out of gear 
with each of them.
	        
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