SPERRY’S POCKET CALCULATOR, made by the Keuffel and Esser Company, New York (Fig. 26), has two rotating dials, each with its own pointer and fixed index. The S dial has an outer scale of equal parts, an ordinary logarithmic scale, and a square-root scale. The L dial has a single logarithmic scale arranged spirally, in three sections, giving a scale length of 12½in. The pointers are turned by the small milled head, which is concentric with the milled thumb-nut by which the two dials are rotated. The gearing is such that both the L dial and its pointer rotate three times as fast as the S dial and pointer. All the usual calculations can be made with the spiral scale, as with the Boucher calculator, and the result read off on one or other of the three scale-sections. Frequently the point at which to read the result is obvious, but otherwise a reference to the single scale on the S dial will show on which of the three spirals the result is to be found. [Illustration: FIG. 26.] _The K and E Calculator_, also made by the Keuffel and Esser Company, is shown in Figs. 27 and 28. It has two dials, of which only one revolves. This, as shown in Fig. 27, has an ordinary logarithmic scale and a scale of squares. There is an index line engraved on the glass of the instrument. The fixed dial has a scale of tangents, a scale of equal parts and a scale of sines, the latter being on a two-turn spiral. The pointers, which move together, are turned by a milled nut and the movable dial by a thumb-nut, as in Sperry’s Calculator, Fig. 26. [Illustration: FIG. 27.] [Illustration: FIG. 28.] SLIDE RULES FOR SPECIAL CALCULATIONS. ENGINE POWER COMPUTER.—A typical example of special slide rules is shown in Fig. 29, which represents, on a scale of about half full size, the author’s Power Computer for Steam, Gas, and Oil Engines. This, as will be seen, consists of a stock, on the lower portion of which is a scale of cylinder diameters, while the upper portion carries a scale of horse-powers. In the groove between these scales are two slides, also carrying scales, and capable of sliding in edge contact with the stock and with each other. This instrument gives directly the brake horse-power of any steam, gas, or oil engine; the indicated horse-power, the dimensions of an engine to develop a given power, and the mechanical efficiency of an engine. The calculation of piston speed, velocity ratios of pulleys and gear wheels, the circumferential speed of pulleys, and the velocity of belts and ropes driven thereby, are among the other principal purposes for which the computer may be employed. [Illustration: FIG. 29.]