Subsequently to the time of Pascal, Leibnitz invented a machine by which arithmetical computations could be made : but no account of it appears to have been published.
The most extraordinary calculating machine ever contrived is that of Mr. Babbage, which has had an eventful history. In 1822 Mr. Babbago read two papers before the Astronomical Society, descriptive of a machine which he had devised, for working mathematical questions of some complexity, and even printing its own results by means of types. An application was made to the government for pecuniary aid, in applying the machine to the construction of mathematical tables ; and in 1823 the government sought the opinion of the Royal Society on the merits of the machine. A committee almost unexampled in scientific strength met to examine the question ; it comprised the names of Davy, Herschel, Young. Wollaston, Pond, linter, Braude, Bally. Brunel, Colby. and Davies Gilbert; and the highly favourable report sent in by this committee led the government to promise pecuniary aid, in a matter Intended wholly for public benefit, and not for the inventor's emolument. Unfortunately, the arrangement was badly organised, and has given satisfaction to no one. The plan of the machine underwent changes, the drawings prepared were very elabo rate, and artisans had to be specially educated to the work. By the year 1823, a sum of 30001. had been advanced by the government; parliament complained, and the government complained, because no machine was yet forthcoming. A second committee of the Royal Society made a report, countenancing a further application of public looney to this purpose. A sum of 30001. more was advanced, and then 600/.„ in 1829 ; besides a large expenditure out of the private purse of Mr. Babbago himself. In 1930 a third committee investigated the subject at the request of the government ; and the report of this committee led to a further advance of funds, not only for making the machine itself, but also for building a house to contain it. When 17,0004 had been spent, an irreconcileable dispute took place between the government and Mr. Babbage ; no further money was given ; and the operations were suspended. Mr. Babbage developed a new plan by which his machine would perform higher mathematical problems; his first be called a difference rapine; the second would, if ever coin• pitted, be an ansiyticai engine ; but no funds being forthcoming, the operations were never resumed. In 1843 the government placed the
difference engine, so far as it had been constructed, in the museum of King's College, London ; and there it remains to the present time (1560), an unfinished memento of a splendid conception. The machine is barely a yard in height, by half a yard in width and a foot in depth and it certainly appears surprising that no greater result than this has been presented for so enormous a sum of money.
So far as It is possible, we shall now describe the principle nni action of Babtagea difference engine in a brief form: treating it as the machine were finished and at work according to the inventor's plan.
In any series of numbers arranged in lino 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 tho second and third, and so on, of these last numbers be taken, there will be formed a lino or column of what are celled second differences. Proceeding in like manner 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 very nearly so. Thus, taking the series of numbers in the column N below, the several orders of differences will be as in the succeeding columns; the numbers in the sixth column being constant : Now it is evident that, having any one of the numbers in tho 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. It may happen however that while the numbers in the original series increase, the numbers in some of the columns of difference may decrease; and then, in forming the terms of the series, subtractions might take place : in such a case, the arithmetical com plements of the numbers to be subtracted being taken, the operations may still be performed by additions only.