In this paper, Mr. Henry describes an instrument by the aid of which he has actually obtained the values (to four figures) of many thousand products, being the D values in the various tables he has published. The principle of the instrument, which he claims as entirely his own invention, may be briefly described as follows:—

Let ABC be a right-angled triangle, of which AB is the base and AC the hypothenuse, and from any point D in the hypothenuse let fall DE perpendicular to AB; then from the similar triangles ADE, ABC, we have