Supposing the velocity of the moving parts of the Engine to be not greater than forty feet per minute, I have no doubt that
One multiplication of two numbers, each of fifty figures, in one minute.
One division of a number having 100 places of figures by another of 50 in one minute.In the various sets of drawings of the modifications of the mechanical structure of the Analytical Engines, already numbering upwards of thirty, two great principles were embodied to an unlimited extent.
1st The entire control over arithmetical operations, however large, and whatever might be the number of their digits.
2nd. The entire control over the combinations of algebraic symbols, however lengthened those processes may be required. The possibility of fulfilling these two conditions might reasonably be doubted by the most accomplished mathematician as well as by the most ingenious mechanician.
The difficulties which naturally occur to those capable of examining the question, as far as they relate to arithmetic, are these,—
(a). The number of digits in each constant inserted in the Engine must be without limit.
(b). The number of constants to be inserted in the Engine must also be without limit.
(c). The number of operations necessary for arithmetic is only four, but these four may be repeated an unlimited number of times.
(d). These operations may occur in any order, or follow an unlimited number of laws.
