The Mannheim slide rule consists of a body, called the rule, a movable part of the same material with tongues on each side to fit in grooves in the rule, called the slide, and a rectangular frame carrying a piece of glass or other transparent material on which is engraved a hairline, called the runneror cursor. The term Mannheim when applied to a slide rule, always implies a certain combination of four logarithmic scales, marked A, B, C, D, and always requires the use of a runner; this combination was devised about 1850, by a French army officer whose name was Mannheim. There are usually other scales, but any slide rule having scales A, B, C, and D on its face and carrying a runner may be called a Mannheim rule. As at present manufactured, the standard 10-inch Mannheim rule, made of wood, and with white celluloid faces. has seven calculating scales—two on the face of the rule, two on the upper side, or face, of the slide, and three on the under' side of the slide. The four scales on the face of the rule and slide frequently have the letters A, B, C, D printed at the left-hand end of the scales they designate; if not so printed, they are understood to be there in the explanations that follow. The four scales A, B, C, and D are used for multiplication, division, involution, and for extracting square and cube root, and for combinations of these operations. The reader is supposed to have a slide rule with these scales, and is earnestly advised to refer to it constantly as he reads the following descriptions and explanations, and he should make all settings mentioned in the text. By so doing, he ought to be quite proficient in the use of the rule when he has finished reading this work. Scales C and D will first be described and their use explained. — The Slide Rule and Logarithmic Tables