CALCULATING MACHINES. Before computers had attained great proficiency in performing arithmetical operations by the pen, machines by which the results of such opera tions could be obtained by inspection were in almost constant use. The principal of these were the Roman abacus, which continued to be employed in the south of Etirope till the end of the 15th century, and in England to a later period ; and the Scliwan-pan, which in China has long been the principal means of making computations. [ABACUS.] For the operations of multiplication and division the ivory rods of Napier, commonly called Mipier'e Bones, were for a time used ; and, for solving trigonometrical problems, Gunter's Scale or the Logarithmic Scales were once very gene rally employed by navigators.
The celebrated rascal constructed, it is said, when only 19 years of age a machine fdt executing the ordinary operations of arithinetie. Subsequently to the time of Pascal, Leibniti invented a machine by which arithinetical computations could be made ; but no account of it appears to have been published.
All former contrivances for Perforiniing such operations may be said to have been cast in the shade by the machine invented by Mr: Babbage, which, should it be Comple ted, will constitute one of the , most superb monuments of human ingenuity. Not only are its operations accomplished with certainty, but the results may be transferred to copper plates, from which any number of Copies may be printed without a possibility Of error. A very brief notice however of the manner of using it, and of the principles on which it is constructed, can be here given.
In any series of numbers arranged in 11124 or column, if the difference between the first and second, between the second and third, and so on, be taken, there will be formed a line or column of what are called first differences ; if the difference between the first and second, between the second and third, and so on, of these last numbers be taken, there will be formed a line or column of what are called second Proceeding in like man ner to form third, fourth, &c., orders of differences, there will at length be found a series of differences which are either constant, or to a great extent are nearly so. Than
having any one of the numbers in the first column, and the numbers corresponding to it in the several columns of differences, all the succeeding numbers of the series may be found by mere additions or subtractions, and the latter process may be avoided by using arithmetical complements.
The machine accomplishes these additions by the movements of a number of cylinders having on the convex surface of each the series of numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 0; and the operations are of two kinds : by the first, the additions are made ; and by the second, there is introduced the 1 which should he carried to the ten's place every time that the sum of two numbers is greater than 10.
Let it be imagined that there are side by side several vertical axles, on each of which are several cylinders one above another; and that these axles with their cylinders are capa ble of being turned by whoelwork, so that any one of the ten figures may be made to stand on the face of the machine, and immediately under a fixed index. Let it be further ima gined that the figures composing a given number are under the indices in front of the cylinders on the first vertical axis towards the left band; and the figures composing the several orders of differences in front of the cylinders on the other axis successively towards the right. Then, the general axle of the machine being, by a winch, turned one quarter of a revolution, only the first, third, fifth, &c. axles turn, and every cylinder on each of these axles turns, at the same time, through as many tenths of a revolution as are expressed by the figure in front of the cylinder imme diately on its right band.
There is thus brought to the front of each turning cylinder the unit's figure in the sum of the figure previously in front of that cylinder, and the figure in front of the cylinder on its right. When any of these sums exceed 10, a turn of the general axle through a second quarter revolution causes each of those cylinders, whose number should be increased by the 1 carried to describe one tenth of a revolution, and thus the number in its front becomes greater by 1 than before.