The apparatus consists of a piece of inch-board, about 10 inches long by 7 inches 
broad, pierced with a circular hole of 1 inch diameter for a vertical axis: the edges 
of the board serve as guides for the frame L, which carries the guide-ring, and resting 
on the board we have the frame M, itself guided by the frame L: the two frames 
move independently of each other, but they can be clamped together; the axis has 
upon it a square nut, the sides of which work in the slot of an eccentric, the throw 
of this being adjustable by means of a screw passing through the nut and axis, and 
there is above the eccentric a square nut shown in the figure. This is capable of 
rotation round the axis, so that two of its sides may be placed either parallel with 
or inclined to the sides of the slot; but I fix it with two sides parallel to those of 
the slot by means of a screw run into the axis. The upper surfaces of the last- 
mentioned nut and of the guide-ring are flush with each other; and we then have 
a table or bed having, on its under-surface, guides which work on the outer edges 
of the guide-ring and on two edges of the nut. It will be observed that the bed 
may be placed in two different positions, viz. the guides may work on either pair of 
edges of the nut, those which are parallel to the sides of the slot, or those which 
are at right angles to it. 
Supposing the bed placed as above upon the guide-ring and nut, then if the 
frames L and M are disconnected, and the former of them is fixed, the frame M will, 
on rotation of the axis, be carried backwards and forwards by the eccentric, but this 
will in no wise affect the motion of the bed; the arrangement is then equivalent to 
the oval chuck, and a pencil fixed above the bed in any given position will trace out 
upon it an ellipse. If, however, the frame L, instead of being fixed, is clamped to 
the frame M, then the two frames, and therefore the guide-ring, are carried backwards 
and forwards by the eccentric, and the curve traced out by the pencil is no longer 
an ellipse; it is, as I proceed to show, a special form of trinodal quartic; viz. there 
is a tacnode (=two nodes) at infinity, and a third node, which may be a crunode, 
cusp, or acnode. In the last-mentioned case, the acnode or conjugate point is, as 
usual, not exhibited by the mechanical description, and the curve has no visible 
singularity.