Page:The New International Encyclopædia 1st ed. v. 04.djvu/27

* CALCULATING MACHINES. 13 CALCULATING MACHINES (from Lat. ealctildii. to ii'ckoii. compute: see CALCrLlS). Meilianieal coutrivaiiees designed to facilitate computations, to relieve the ealciilator from the mental strain of his work, and to insure greater accuracy in results. Calculating machines exist in various forms, and are now made in such perfection that large business houses and banks regard them as a necessity, while many scien- tific computations would have been abandoned but for tlieir help. An instrument which is used for the purpose of illustration or instruction in number work is called a reckoning apparatus, but one which automatically produces the re- sults of number combinations involving the union of different orders is called a calculating mach ine. The earliest kno^ii instrument of calculation of any importance is the abacus. The Chinese lay claim to its invention. Its use by the Egyp- tians as early as B.C. 460 is definitely asserted by CALCULATING MACHINES. 1 5 9 7 8 2 1 / /O ^ / /a / 6 3 1 / / 5 2 / 2 / / z7 /A 4 2 / / 3 / / 6 2 / / 8 3 / / 2 5 2 / / 5 a/ / 5 3 /^ / 5 a/ 6 3/ 5 / /A / 2 a/ / 8 7 3/ b/ a/ / 9 5 / / 6 8 a/ /o 1 / 5/ 6 / /A 9 4 / 6 / / 3 1/ /2 ARRAXGEMENT OF .NAPIER S BODS. Herodotus. It was probably used by the Baby- lonians, and certainly by the Greeks and Ro- mans, from whom it spread to all Europe. It has existed in various forms — the knotted strings, the sand-board, the pebble-tray, the counters, and the frame of beads. The last form is still in use. known as the Chinese sican- ■j)an, the Russian Stchottj, or the .Japanese .S'oro- Ban. The ordinary swan-pan consists of a frame divided into two sections, holding several paral- lel rods, each containing several movable beads. In the Chinese swan-pan, e^cli bead on the bottom row in the right division represents one unit, and each on the bottom row in the left division represents five units. In the next higher row the value of each bead is ten times as great, and so on. Tlie first improvement over the ancient abacus consisted in the use of coimters, on a plan at- tributed, probably erroneously, to Boethius. I/ater these counters bore niuiibers, and were at- tached to rods, disks, or cylinders, which could be moved so us to indicate the desired results. A notable exani])le of this type is the set of rods invented by Xapier and known as virgulae; or, popularly, as Napier's rods or bones. These con- sist of flat pieces of bone or ivory, divided into squares, which (on ten of the rods) are sub- divided by diagonals into triangles, except the squares at the upper ends of the rods, which spaces are numbered from 1 to 9. To illustrate the process of multiplication, consider the product of .5078 by !I37. Arrange the proper rods, as in the figiire, so that the numbers at the top indicate the multiplicand, and on the left place the rod headed 1. In this rod find the right-hand figure of the multiplier, which in this case is 7. Passing across this horizontal row, add obliquely the two rows of corresponding digits, writing the results in each case as the digits of the first partial product. For example, the first figtire on the right is 6; this is written in the units place in the first par- tial product. Xext add the o and 9 in the ad- joining oblique row, which gives 4 in the tens place, with 1 to carry. This makes 8 in the hun- dreds column. Proceed in the same way with the other figures of the multiplier, and add the partial products as in ordinary multiplication. 41U6 17934 5601386 The chief point of improvement over the primitive abacus consists in supplying the in- strument with moving scales, which enable the calculator to form number combinations with- out actually counting together the different ad- dends. Kummer (1847) accomplished this by running parallel rods in grooves; Lagrous (1828) by concentric rings; Djakoff and Vebb by bands on rollers. Another form of the calculating machine is the sliilc rule, which is more generally employed than any other class of calculating instruments, particularly by engineers and statisticians. In its simplest form it consists of two rules, ar- ranged to slide on each other, and so divided into scales that by sliding the rules backward or forward until a selected number on one scale is made to coincide with a selected number on the other, the desired result is read off direct- ly on a third scale. By means of a duplex slide rule, where the rule may be set for four factors instead of two, moi-e complicated problems may be solved. Rcvohiiiff xlidc rules are employed to increase the virtual length of the scales and the nmuher of decimal places to which results may be read. In the Thaeher calculating instru- ment, a cylinder 4 inches in diameter and 18 inches long revolves within a framework of tri- angular bars, each of which contains a scale on two sides. The scales contain .33.000 divisions and 17.000 engraved figures, exceute<l on a di- viding machine made expressly for the purpose. Fuller's spiral slide rule consists of a wooden cylinder containing a spiral scale 42 feet long. Cireular slide rules, resembling watches, are also made. The slide-rule principle is also em- ployed in instruments used to work out specific problems, such as the flow of water in pipes, or the strength of beams. Such computers may be either like the ordinary slide rule, with scales in terms of the factors Involved, or, as in the various Co.x computers, there may be a founda-