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. The instrument works best when the chariots, A and B, are about opposite to each other; when they are at opposite extremities of f f and f' f' respectively, the pull at P tends to produce a skewing couple. If the chariot, B, could be put upon f f and work, if needful, by a double parallelogram from m m, we should have, excepting the skew pull, some great practical advantages. We might throw the whole of the weight of the machine on the one pair of friction wheels, and replace the other pair by a single wheel, the portion q' f' f' q' of the machine virtually disappearing. Three wheels, of course, would be a real improvement. Further, we should have the sum curve and primitive drawn to the same base line, and the simplification in the number of parts ought largely to reduce the cost of the instrument. To be able to perform "inverse summation" (which in the language of differential calculus is to find y as a function of x, when we are given y=f(dy/dx), and not dy/dx=f(x) as usual), we only want a means of making the plane of the wheel, w, parallel instead of perpendicular to m' m', and it is easy to design a modification in the construction which will allow of this change. I hope the above description of the integraph may have made its construction and method of working sufficiently clear. Those of you who have a taste for mechanical work, and the necessary tools, might, I think, with some patience, construct a workable integraph. I expect the pivots would be the hardest part of the work. I hope, some day, myself to have another instrument made with a more readily changeable polar distance, with trace and guide points working in the same vertical, and a wheel permitting of inverse summation. If this project is ever carried out, I hope I may be permitted to communicate further particulars to our society. * * * * *