Page:The New International Encyclopædia 1st ed. v. 04.djvu/28

CALCTTLATING MACHINES. 14 lion plate, revolving disk, revolving segment, and index or pointer, with jiroper soales. The vari- ous slide rules proper all depend on the nieehan- ieal use of logarithms, and the scales are gradu- ated on a logarithmic basis. By referring to the article Loc.vrithms. the operation of a simple slide rule will readily be understood, as the vari- ous graduations correspond to the logarithmic functions, iuid the appropriate length of each is determined from a table of logarithms. The figures inscribed on the scales, however, are those of the numbers corresponding to the log- arithms. For example, to multiply 2 by 2, the number 2 on the scale is brought opposite the number 2 on the second scale, and, as a result, the zero of the latter is distjuit from the zero of the first by an amount equivalent to the sum of the two logarithmic graduations. The number corresponding to the j)oint at which the zero or indicator stands is, of course, the product, which in this ease is 4. The complexity of the problems which may be solved with the aid of the slide rule varies with the difl'erent rules; but, in general, it may be said that all problems involving multiplication and division may be solved by any of them, including powers, roots. and proportions, simply by setting the rule and reading off the indicated result. By providing scales with trigonometrical instead of arithmet- ical functions, the uses of the slide rule uuiy be increased greatly, and often the two classes are engraved on reverse sides of the smaller slide rules. The rule is particularly valuable where the same operation is to be repeated many times, as in computing percentages, or where many long and wearisome calculations are to be made. The improved calculating instruments of Slo- nimsky (1844) and T.ucas ( 188.5) effect multi- plication without the supplementary addition required by Xapier's rods. Quotients and re- mainders, in the case of division, are likewise fully determined by Oenaille's instrument. In- struments in which mechanisms are combined for both addition and nuiltijilication are some- times called arithiiiofiniphs. Rous (1869) con- structed an apparatus of this kind, cotnbining a set of Xapier's rods with the abacus. More per- fect forms arc those of Th. von Escrskv (1872), Tron<-ct (1801 ) . and Bollce ( ISIt.j) . , These form the border line between the elementary reckoning apparatus and the more elaborate calculating machine. As numbers are essential to reckon- ing, so number mechanism is the basis of cal- culating machinery. This mechanism is ar- ranged for the decimal system, and combines elements for the various powers of 10. The elements are usually cylindrical disks, on whose plane or curved surfaces arc placed the figures 0, 1, 2. . . . 9. once or several times. What- ever the arrangement of these number disks, their axes of rotation may be parallel and lie in a plane, or may form the elements of a cylin- drical surface, or nuiy coincide so that the num- bers are beside one another on a common cylin- der. This last arrangement, w'hich seems to have appeared for the first time in the machine of Periere (17.iO), is preferred, because it reipiires the least space and brings the figures into close proximity. In every calculating machine the mechanism autonuitically carries over from any order to the next higher. Whenever a luimber disk is rotated so that it points to the figure 9, anv further movement also moves the disk of CALCULATING MACHINES. the next order; that is, for every ten-place rota- tion of any desired nund)er disk, the next disk rotates one place. For addition, it is only neces- sary that each clement of the lunubcr mechan- ism admit of l)cing nuned forard indi'pcndcntly one or more figures. For subtraction, the older nuichines generally contain rows of red figures arranged in reverse order, so that the motion of the disk may still take place in the same sense. It is immaterial whether this motion l)e produced <lirectly by the hand or indirectly by a lever: but it makes a difference in the rapid- ity of the work whether difl'erent figures of the same rank are added by the movement of one and the same element, or by the motion of dif- ferent elements. To the first group belongs the oldest of all calculating macliincs, the machine urit)imcti<iue of Pascal (1(142), designed for adding and subtracting. The modern machines of Roth (1843) and Webb (1868), and Orlin's initamatische Schraubpiirccheiimn/ichine ( 189.3), arc modifications of the iiiiichinc arithm^ique. The necessary speed and accuracy of movement have been gained by the introduction of keys, as in the machines of Stettner (1882) and JIayer (1887). A key being provided for the numbers from I to 9, in the various orders, one has to fi.x the eye upon the numbers of one figure only. The latest improvement is a con- trivance for automatically printing both the addends and their sum, thus leaving little to lie desired in the form of an addition instrument. This is a feature of Burrotigh's registering ac- countant (18S8) and Carney's cash register. Goldman's 'arithmachine' (1898) is one of the latest of the simple and practical machines. In order mechanically to eft'ect repeated addi- tion — that is, multiplication — a rack or special carrying apparatus is necessary. This device makes it possible by a single motion of the hand, as the rotation of a crank, to carry simul- taneously the set of number disks over a desired number of places. Four methods have been de- vised for this, but the most common is the slepped reckoner of Leibnitz, a cylinder with nine teeth of dift'crent lengths, corresponding to units, tens, etc. Another nutans also known to Leibnitz, and lately coming into favor, is the use of toothed wheels, wliose teeth may be shoved in at will, thus rendering the wheels in- operative. Among the instruments of this type, with slight modifications, are the arithmometer of Thomas (1820), the machine of Maurcl and Jayet (1849), and the aritlunometers of Odh- ner (1878) and Kiittner (1894). The machine A calculer of Bollce (1888), designed especially for multiplication, operates on a new principle. The ]iroducts of numbers from 1 to 9 are rc]iic- sented by pairs of pegs, whose lengths correspond to the units and tens of the products. The pegs limit the freedom of the rack, which can be so moved that the product of the multiplicand by each figure of the multiplier is carried over to the addition machinery. In the calculating ma- chine of Steiger (1892) partial products are expressed by pairs of disks, and in Selling's clek- tri.tche {{echrnmuschinc (1894) by electromag- nets. These machines arc defective in that the multiplication must be performed step by step, using a multiplier of one figure only. They are made to perform division by moving a lever, which reverses the motion of the numlier disks. Much care lias also been given to perfecting in-