CALCULATING MACHINES (from Lat. ea/en/arc. to reckon, compute; see Mechanical contrivances designed to facilitate computations, to relieve the calculator 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 their 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 machine.
The earliest known 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 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 a- the Chinese svan pan, the Russian Stehoty, or the Japanese Soro Bun. The ordinary swan-pan consists of a frame divided into two sections, holding several paral lel rods, each containing several movable heads.
In the Chinese swan-pall, each head 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.
The first improvement over the ancient abacus consisted in the use of counters, on a plan at tributed, probably erroneously, to Boethius. Later these counters bore numbers, and were at tached to rods. disks, or cylinders. which could be moved so as to indicate the desired results.
.1 notable example of this type is the set of rods invented by Napier and known as virgula.: or, popularly. as Napier's roils or bones. These con sist of flat pieces of hone 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. spaces are numbered from 1 to 9.
To illustrate the process of multiplication, consider the product of 5978 by 937. Arrange
the proper rods, as in the figure, so that the numbers at the top indicate the multiplicand. and on the left place the rod headed I. 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 figure on the right is 11: this is written in the units place in the first par tial product. Next add the 5 and 9 in the ad joining oblique row, which gives 4 in the tens place, with 1 to carry. This makes S 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.
.11s4C, 17034 53:412 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 (1S47) accomplished this by running parallel rods in grooves: Lagrous (1828) by concentric rings: Djakoff and Webb by bands on rollers.
Another form of the calculating machine is the slide 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, more eomplicated problems may solved. llerolring slide rules are employed to increase the virtual length of the scales and the munher of decimal places to which results may be read. In the Thacher calculating instru ment, a cylinder 4 inches in diameter and inches long revolves within a framework of tri angular hars, each of Bch irh a scale on two sides. The scales, contain 33.000 divisions. and 17.000 engraved figures, executed on a di viding machine made expressly for the purpose. Fuller's spiral slide rule consists of a wooden cylinder containing a spiral scale 12 feet long.