CALCULATING MACHINES. struinents havinj^ for their objei-t the rompiit- ing of matlieiiuitical and astronomical tabU^s and the tabulation of funotions. Tliese are. in fact, the only means of producing tlioroughly accurate tables. The idea practically originated with Miiller (17HG), but Babbage (1823) was the first to obtain valuable results with a machine of this kind. The machines of Wiberg (1863) and Grant (1871) are improved forms of this type. Habbage (1834) also invented an 'analytic engine," designed to perform various analytic and arithmetical operations, but it was never com- pleted. The following machines of recent mention are e.xtensively used; the first three are of German make and the last three American, the latter being the more practical: Beher's addition macliine |18'.>2), of keyboard type, limited to sums under .500: lllgen's calculator (1888), lim- ited to sums under 1000: Runge's addition ma- chine, Berlin (1896), adding numbers of several figures: Felt's comptometer, Chicago (1887). keyboard type, performing all four operations; Burrough"s registering accountant. Saint Louis (1888), an addition macliine of 81 keys, with a capacity of 2000 entries per hour, and automat- ically printing both the addenda and the total smn ; Carney's cash register, Dayton (1890), an adding and printing machine of great perfec- tion. C.sii-Registers are a form of calculating ma- chine in general use in retail stores, whose chief functions are to make a record of money received from sales of merchandise in a retail store, as the money is placed in the cash-drawer, and to add automatically this sum to the total pre- viously placed in the drawer; it also indicates to the customers the record which has been made. The more coniplex cash-registers liave been fur- ther developed so that it is possible to include an automatic I'ecoi-d of other transactions which take place in a retail store, including credit sales and the separate sales of individual clerks or of particular lines of goods, so that they may be referred to at the close of the day's business. The first practical cash-regi.ster was invented by James Ritty, of Dayton, Ohio, who secured his patent in 1879. In this first register the rec- ord was made on adding wheels and displayed by hands on a dial, but in later inventions the rec- ord is sometimes made by puncturing printed rolls of pajx'r and is .shown by indicators which rise and fall as the mechanism is operated, a number equal to the amount of the purchase ris- ing as the cash paid is deposited in the drawer, the same operation causing the number which records the previous purchase to fall. In the 'detail adders,' manufactured by the National Cash Register Company, the mechanism is o|)er- ated by pressing the projier registering key. A single prcs^ure of the finger unlocks and throws open the cash-drawer, rings a bell, drojis the in- dicator showing the last transaction, raises an indicator showing the amount of the new trans- action, and at the same time records it on the adding wheels inside the register. Each regis- tering key is connected with a corresponding adding wheel inside the register, which .shows the total amount of registrations made on that key. For example, if the '.5-eent' key ho [iressed five times its corresponding adding wheel shows a total of 25 cents. Thus the total amount of the day's sales can be ascertained at any time by 15 CALCULUS. iuUling together the total amoiuits shown by the
- ulding wheels. These registers can be arranged
to keei> separate record of "charge,' 'received on account,' and 'paid out' tran.sactions, or to show separately the receipts from ditl'crent classes of goods. A drawer cannot be opened without mak- ing both an indication to the customer and an inside record under liuk and key. Electhic T-mLATi.G Machines, such as the one devi.sed by Hollerith for recording and sum- marizing the United States census returns, may be classed under calculating machines. This apparatus is in three parts. The first operation is to punch holes in a card, corresponding to the facts to be recorded for each individual, the punches being operated from a keyboard of 240 characters. After the cards are punched thej' are fed into a machine, which, by means of the holes and certain electric devices, adds one to the total record for the fact indicated by each hole, such as se.x, color, or age. Next the cards are placed in sorting bo.xes, in order to secure a combination of facts, such as the number of black persons who are married, and by means of electric con- nections which are acted upon only by cards hav- ing holes corresponding to the facts to be tabu- lated, the record is made. For descriptions of calculating machines, con- sult: Jlehmke. "Numerisches Rechnen," in En- cyklopadif der mathcmatischen Wissenschaften, Vol. 1. (Leipzig, 1901), containing numerous figures; Linger, "Einige .idditionsmaschincii." Abhaiidhiiigen ziir (leschichte dcr Matheniiitik, Vol. IX. (Leipzig. 1890) ; Shaw, ""Theory of Continuous Calculating Machines," in Phil. Transiictions of Royal Society, Vol. CLXXVI. (London, 1885). CALCULATORS (Lat. calculator, computer; see Calcllu.s), Remarkable. Arithmetical prodigies, often spoken of as "lightning calcula- tors,' having an unusual capacity for combining niuribers. The wonderful feats of these prodigies have been pronounced genuine by competent judges, although their psychological peculiarities have not been fully explained. Two peculiarities, however, seem characteristic of most of the known cases: an extraordinary memory for numerical combinations, and luuisual methods of grouping numbers. That their ability is not entirely the result of special training is attested by the early age at which the power is manifest- ed. Thus, at the age of 6, T. H. Safi'ord com- puted mentally the number (617,760) of barley- corns in 1040 rods, and could extract the cube roots of numbers of 9 and 10 figures. Buxton solved the problem, to find the product of dou- bling a farthing 139 times, the result, expressed in pounds, being a nmnber of 39 figures. Zerah Colburn, at 9 years of age, gave at sight the fac- tors of 294,967,297, and in 20 seconds found mentally the number of hours in 1811 years. Raising 991 to the fifth power in 13 operations, and giving the product of any pair of two-figui-e numbers in 1 1'j seconds, are feats accomplished by Arthur Griflith, who also memorized the squares of all mimbers uj) to 130 and the cubes uj) to 100. Other noted prodigies are Annich, Bidder, Vinckler, Pughiesi, Mondeux, Magimelle, and Inaudi. CALCULUS (Lat., a small stone, or pebble, which ;ts iscd in reckoning, or calcuhitions, by the Romans). A term applied in mathenuitics
