The scale on the present instrument is very inconvenient, as it is often almost out of sight; the curve it draws, on the other hand, I consider very satisfactory, when the pencil is loaded, say, with a planimeter weight. On the whole, I think you will agree with me that this integraph goes a good way, if not the whole way, toward fulfilling the conditions of a practical instrument. I next turn to its construction and the claim it has to be considered in any way new. Let me briefly remind our members of the process by which an element Q R of the sum curve (Fig. 1) corresponding to the point P on the primitive is drawn; P M being the mid-ordinate of L N, a horizontal element, P B is drawn perpendicular to any vertical line A B; and O A being a constant distance termed the base or "polar distance," Q R is drawn between the ordinates of L and W, parallel to O B. If P' be the point where P M meets Q R, we note the following relationship of P' to P. 1. If P moves along a horizontal line, O B remains unchanged, and, therefore, Q R or P' must move in the straight line Q R parallel to O B. 2. If P moves along a vertical line, P' does not change, but Q R turns round it, remaining parallel to O B. [Illustration: FIG. 1, 2, 3] Without taking the trouble, as I ought to have done, to inquire what previous investigations had achieved in this matter, I thought, three years ago, I could get an apparatus to save me the trouble of drawing sum curves, made somewhat after the following fashion. P (Fig. 2) is the guide or point to be taken round the primitive. It is attached to a block, D, which works along the bar, B C, which in its turn moves on the four wheels, e e f f, upon the frame R S U T fixed upon the drawing board. O A is fixed perpendicular to R U, and is such that O may be fixed at various points to determine the polar distance. O B D is a light bar passing freely through B and forming one side of a parallel ruler of two or more points, g g, h h, i i. Along i i is a slot and in this works a loaded block containing a wheel P', whose plane is always parallel to i i. This block also passes through a slot in D E, an arm at right angles to B C. A little consideration will show that P', if worked at all, would trace out the sum curve of P. It was only when I showed the rough idea of this to Professor Kennedy, with the view of ascertaining what would be the amount of back-lash and friction, that I learned that Mr. Boys had already invented a very similar integrator. In his model the double parallel ruler is replaced by two endless strings and pulleys, and the bar, B C, by a T square. Although this integrator was afterward made in a less crude form, I do not think it has ever been a practical instrument for the draughtsman. Shortly afterward I came across a work by Abdank-Abakanowicz, entitled "Les Integraphes," being a study of a "new kind of mechanical integrator."