In the geometrical class of calculating ma chines the simplest type is a measuring wheel which is graduated on its circumference, and is run over the lines to be measured, a record ing mechanism at the axis showing the total distance traversed. The slide rule is a device of some little antiquity, having been invented in the logarithmic type in 1620 by Gunter. Many other mathematicians followed with vari ations and adaptations. The slide rules are classified as (1) those working with movable indexes, and (2) those with adjacent sliding scales. To the first class belong the circular scales of Oughtred, Scott, Nicholson and Weiss; and the spiral scales of Milbume, Adams, Nicholson and Lilly. To the second class be long the straight rules of Partridge, Everard, Roget and Mannheim; the circular rules of Biter, Sonne and Charpentier; and the cylin drical rule of Thacher. The standard British slide rule is of the Mannheim type, and carries four scales, two on the stock and two on the slide. The slide is set for the problem in hand, and the result is read by a °runner," or the rule may be turned over and read from scales on the back. The Integraph is a me chanical apparatus for solving graphically dif ferential equations. Planimeters are machines which measure lines and the areas of plane surfaces. There are several types, but only one, the polar planimeter, is in use at the pres ent day. There are two separate fixed points on this machine, one of which is the pole. From these points reach out arms to a carriage on which is a tracing wheel and calculating mechanism mounted on a sleeve, which slides along graduations on one of the arms. A modification of this machine has a long straight rail against which a guide is held while the machine is being operated. The Integrator is another form of planimeter by which many intricate problems may be solved mechanically. The name "Harmonic is given to another machine of similar construction. The °Tide Predicters° of Roberts and Lord Kelvin are among the remarkable mechanisms de vised to solve mathematical problems. With these machines set with a duplication of the component forces operating upon the tide at any port, the mechanism delivers in about two hours a tracing showing graphically the move ments of the tide at that port for a year in advance.
The Hollerith electric tabulating mechanism used by the United States Census Bureau is prominent among the remarkable calculating machines that have been developed in America. Three separate machines constitute the outfit. The first one punches holes in cards, in any one or more of 240 places; the second tabulates the cards, while the third sorts them. Machine No. 1 has a keyboard of 240 keys, this being the number of answers called for in the census blanks of the bureau. Th.! operator takes a return blank, representing the report of some individual, and, as he reads it, strikes the appro priate keys, which results in the punching of ,a card, that becomes a mechanical counterpart of the original return. As the average number of questions answered on each return is but 15, the work is not so tedious as might be inferred from the statement as to 240 questions.
When the cards of a State have been punched, they are brought to the tabulating ma chine, which is the real calculator. This ma chine reads the holes of the cards that are fed into it, and makes an electrical record of each hole, according to its position, adding up the totals for each hole, and showing them on dials. When the cards are all fed through, the total of each of the 240 replies is enumerated. The third machine a sorting box, which serves to secure answers to cross-questions. For in stance, if it is desired to know how many white persons are among the total number convicted of crime, the sorting box will locate all cards having the holes corresponding to these two statements, and give the total. In this way a great variety of statistics are made available which it would be too expensive to gather or i compute in any other way. For other nforma tion on this subject, see CASH REGISTER; COM PUTING SCALE. Consult Cajori, F., 'A History of the Logarithmic Slide Rule' (London 1909) Horsburgh, E. M., (Modern Instruments and Methods of Calculation' (London 1914); Pick worth, C. N., The Slide Rule: A Practical Manual) (London 1910).