MACHINES, CALCULATING. Before computers had attained great proficiency in performing arithmetical operations by the pen, machines by which the results of such operations could be obtained by inspection were in almost constant use. The Roman abacus [Asacusj continued to be employed in the south of Europe till the end of the 15th century, and in England to a later period. An account of the prismatic rods invented by Napier for the performance of arithmetical operations is given under NAFIER'S BONES ; and the nature and use of the logarithmic scales, under Sunrise RULE.
The celebrated Pascal constructed, it is said, when only nineteen years of age, a machine fer executing the ordinary operations of arithmetic. It was an assemblage of wheels and cylinders. On the convex surfaces of the latter were the numbers with which the opera tions were to be performed : these operations consisted chiefly in the addition and subtraction of sums of money having the denominations of Byres, sous, and deniers, for which may be substituted pounds, shillings, and pence ; and to those denominations the numbers were adapted. Extending round the convex surface of the first cylinder on the right hand of the machine, and one above the other, were the two series, the first of which served for the subtraction and the other for the addition of pence ; the cylinder being turned in the same direction for both operations. Upon the surface of the next cylinder on the left were the two series, 0, 19, 18, 17, 16 119, 0, I, 2, 3 18; • f serving for the like operations on shillings : and on the left of this last were several cylinders, about each of which were the two series 0, 9, 8, 7, 6, 5, 4, 3, 2, I 9, 0, I, 2, 3, 4, 5, 6, 7, 8; and these were used for operations with pounds, or with any numbers in the decimal scale. Attached to the axles of the first cylinder was a wheel having on its circumference 12 teeth ; on that of the second, one having 20 teeth ' • and on the axle of each of the other cylinders was a wheel having 10 teeth. Before an operation commenced, the serve of the numbers in the first or second series above, on all the wheels, were brought by hand to the front of the machine. As an example of the method of timing the machine, let it be required to add together the following sums of money :— By means of a pointer the wheel connected with the first cylinder on the right is to be turned till the eighth teeth, and under it the number 8 on that cylinder, are brought to the front; in like manner the number 9 on the second cylinder and 8 on the third aro brought to the front : this the series of numbers in the fronts of all the cylinders exhibits the first of the above sums of money. Then, by means of the
pointer, the first wheel and cylinder on the right hand are to ho turned till the pistil tooth (after the eighth) comes to the front, when the cylinder having, from its first position, performed on its axle one revolution ond.:!..of another, the number 2, representing 12+2, or 12 Is. 2d., appears in front. Now, by the construction of the wheel-work, one complete revolution of the first wheel and cylinder on the right hand causes the wheel and cylinder on its left to turn one-twentieth part of a revolution ; by which means, in this example, the number 0 being already in front of the latter cylinder, the number 10 is now there: thus the oue shilling obtained by the addition is, as it were, carried. The second wheel and cylinder being now turned by means of the pointer till the fifteenth tooth, after the tenth, is brought to the front, the number in front of the cylinder below is 5, representing 20+5, the cylinder having made 1 from its first posi tion; there Is thus obtained 1/. 5s. One revolution of tho second wheel and cylinder causes the next, towards tho left, to make one tenth of a revolution ; and thus the 11. Is carried, so that the number in front of the third cylinder is now 9 instead of 8. This third wheel and cylinder are next turned by means of the pointer till the fourth tooth, after the ninth, is brought to the front, when there appears on the cylinder below it the number 3, representing 10+3; and the next cylinder on the left, in front of which was previously zero, has now 1, which may thus be said to have been carried. The subtractions are performed exactly in the same manner as the additions, by means of the nnmbers in the upper series on the cylinders.