Two points deserve special attention.  In the first place, the fixed frame is abolished, and the horizontal motion of P (Fig. 3), the guide point, is produced by putting the whole frame on friction rollers; in the second place, as a necessary result of the first change, the guide point carries about with it its own polar system, which renders the changes in length of “rays” much more manageable. f f, f’ f’ is a frame moving on four roughed wheels, e e e e, so that it can only move in the direction, f’, which we may term horizontal. f f and f’ f’ are rails guiding the chariots, A and B, from f to f and from f’ to f’.  Of these chariots, A contains the guide point, P, to trace out the primitive with, and B the pencil, P’, to draw the sum curve, i.e., the tracer.  The chariot, B, like Boys’ tracer, is heavily loaded. g g is a horizontal bar rigidly attached to the crossbars, q q and q’ q’, of the frame.  On g g is a movable pivot, to which h, which determines the pole, k0 h being the polar distance. k0 is the position of a second point, k, on the chariot, A, when the guide point, P, is on the initial line, g g. l l is a bar with a long slot in it, in which work the pivots, h and k; this bar represents the “ray.”  A projecting arm k k’ has been introduced to enable me to shorten the polar distance down to 2 in. and under by removing the pivot, k to k’. m m is a bar attached to the block, n, which runs on l l, so that m m is always perpendicular to l l.  On the chariot, B, is another bar, m’ m’, capable of turning round the pivot, d, and always maintained parallel to m m by the rods, m m’, m m’.  Attached to m’ m’ is a wheel, w, whose axis is parallel to m’ m’.  This wheel, therefore, always moves perpendicular to m’ m’, and therefore to m m; hence it moves parallel to the ray, h k.  A pencil, P’, attached traces out the sum curve.  If we wish to use the machine as an integrator, we have merely to measure the vertical distance traversed by P’, or the distance B has run along f’ f’.  This is done by means of a scale on f f’.  If k be brought down to k0, w runs parallel to g g, or P’ traces out a horizontal straight line, which is thus the base line.  If k be fixed as near as possible to k0, which is done by means of a screw in f f at k0, the chariot, B, can be run down f’ f’ as nearly opposite to k0 as can be guessed at; a horizontal line may then be drawn as base line, and the guide point, P, brought into this line by a clamping screw with which it is provided.  The instrument is then ready for action.  There is a brake on one of the roughed wheels to check or stop the motion of the integraph when required.