CALCULATING MACHINES. These machines are classified according to their use, as arithmetical or geometrical; the former dealing with computations of numbers, the lat ter with calculations of lengths, areas or con tents. In the first class the operations per formed by the machine may be simply addi tion, in which case it is called an adding ma chine. Some of these simple machines also perform subtraction. The multiplying ma chines are far more complicated and perform also division, and they can be manipulated so as to work problems in the rule of three, and extract square roots.
In the simple adding machine the number is always progressively added, a unit at a time. Several different devices have been employed by inventors to accomplish this result. The simplest is a train of wheels bearing the nine digits and zero on the face of the wheel near its outer edge. On the first wheel (at the left) units are counted up to 10. At the tenth count the next wheel to the left is moved one cog by a stud which operates each time the "units wheel makes a complete revolution. The gliundredso wheel, next again to the left, is in like manner turned one cog when the "tens') wheel completes one revolution; and so on. The result is read through a "window" show ing the uppermost figure on each wheel. On this principle the automobile speedometer and the trolley-car fare indicator are operated. Other devices include a rocking sector of a circle, operated by a key. On the curve of the sector are nine teeth engaging a counting wheel with nine teeth. When the key marked 9 is depressed, the entire sector moves in gear with the counting wheel giving it a complete turn. When the key 4 is depressed only four of the teeth engage the wheel which is thus turned only four-ninths of a complete revolu tion. A second sector placed to the left of the first and operated in the same way would count tens, and a third sector still farther to the left would count hundreds; and so on up to as many places as desired. Several variations of
this system have been utilized. The key may not move the sector when it is pressed, it may simply set a stop or check, and the movement may be produced by a lever, or by electric mechanism. This is the device used in the cash register, and in the Burroughs Adding Machine.
Another application of the same fundamen tal idea is the stepped cylinder, in which ridges running lengthwise of the cylinder take the place of cogs on a wheel or sector. These ridges are of different lengths, appearing as steps, each succeeding ridge being longer by one unit than the ridge preceding. By sliding a toothed counting-wheel across the cylinder, a distance regulated by the position of the de sired number on a scale, and turning the cylin der by a crank, the respective number of ridges at that plane will operate the counting-wheel. This device is utilized in the Arithmometer and other machines of the Thomas type. A vari ation of this idea consists of a series of racks in place of the ridges on the cylinder — as in the Mercedes machine.
Another basic device is a cylinder having cogs which may be withdrawn into the body of the cylinder by adjusting a cam-shaped ring. The teeth or cogs which remain projecting be yond the surface of the cylinder are those which operate the counting wheel. The action may be similar to that of the sector, the teeth operating in one plane, or it may follow the plan of the stepped cylinder, and the teeth be •stepped° and operate on a sliding carriage. This device is used on the Brunsviga machine, and the many modifications of it. Adding ma chine attachments have been devised for type writers, whereby figures set in a column by the typewriter are added by the attachment and the total may be printed in at the foot of the column.
The Abacus, described elsewhere in this en cyclopaKlia, in one of its varied forms is widely employed in India, China and Japan for mak ing a variety of mathematical calculations, generally for commercial accounting.