[Illustration: FIG. 22.] [Illustration: FIG. 23.] THE BOUCHER CALCULATOR.—This circular calculator resembles a stem-winding watch, being about 2 in. in diameter and ⁹⁄₁₆in. in thickness. The instrument has two dials, the back one being fixed, while the front one, Fig. 22 (showing the form made by Messrs. W. F. Stanley, London), turns upon the large centre arbor shown. This movement is effected by turning the milled head of the stem-winder. The small centre axis, which is turned by rotating the milled head at the side of the case, carries two fine needle pointers, one moving over each dial, and so fixed on the axis that one pointer always lies evenly over the other. A fine index or pointer fixed to the case in line with the axis of the winding stem, extends over the four scales of the movable dial as shown. Of these scales, the second from the outer is the ordinary logarithmic scale, which in this instrument corresponds to a straight scale of about 4¾in. in length. The two inner circles give the square roots of the numbers on the primary logarithmic scale, the smaller circle containing the square roots of values between 1 and 3·162 (= √(10)), while the other section corresponds to values between 3·162 and 10. The outer circle is a scale of logarithms of sines of angles, the corresponding sines of which can be read off on the ordinary scale. On the fixed or back dial there are also four scales, these being arranged as in Fig. 23. The outer of these is a scale of equal parts, while the three inner scales are separate sections of a scale giving the cube roots of the numbers taken on the ordinary logarithmic scale and referred thereto by means of the pointers. In dividing this cube-root scale into sections, the same method is adopted as in the case of the square-root scale. Thus, the smallest circle contains the cube roots of numbers between 1 and 10, and is therefore graduated from 1 to 2·154; the second circle contains the cube roots of numbers between 10 and 100, being graduated from 2·154 to 4·657; while the third section, in which are found the cube roots of numbers between 100 and 1000, carries the graduations from 4·657 to 10.