CALCULATING MACHINE. The most remarkable application hitherto made of machinery, is perhaps that through which it has been used to relieve the scientific inquirer to a very great extent of the fatigue of manipulating figures, which consumes so much of his time and energies. Various machines hive been constructed for this purpose, differing in time extent of their faculties—to use words more suitable to think ing beings than to engines—and somewhat in the principles of their construction. By the aritlimometer, for instance, a machine invented by M. Thomas of Colmar, all ordi nary arithmetical operations are executed without fatigue to the operator; and by a machine contrived by M. 31. Scheutz, which rests on the principle of differences (q.v.), on the turning of a wheel, the successive terms of any series whose law may be confided to it, are produced—the machine at the same time printing a large proportion of its results, and this providing for the accuracy of its tables. It is a fact of which the nation should be proud, that our countryman, Mr. Babbage, is universally acknowledged as the instigating and guiding genius in the progress of these remarkable inventions. Among his inventions was a drfferenrc engine, of very comprehensive powers, indeed capable of managing series so complex that the differences of its terms do not reach zero until we ascend to the seventh order (ride art. DIFFERENCES, CALCULUS OF). An immense range of nautical and astronomical tables lie within the limits just defined; and the machine further tabulates approximately any series whatever that can be treated by the method of differences While engaged in constructing the di fference machine, Mr.
Babbage, probably through his increased experience of the capabilities of machinery, was led to form a new conception—that, namely, of the analytical machine. He actually succeeded so far as to devise the means of making his machine perform all the elementary operations of addition, subtraction, multiplication, and division; and it is clear that all changes that can be produced on quantity are merely combinations of these. If, then, he could but have made his machine perform these operations at command, and accord ing to any special order, it could have clearly developed any function whatever law is ascertained and fixed. A solution of this difficulty was suggested by the Jac quard loom (q.v.), iu which the cards oblige a machine capable of working any pattern to work out one particular pattern; and Mr. Babbage having succeeded so far as to form a machine capable of executing any development, expected, by paeans of cards of operations, to compel his C. M. to work according to one fixed law, and no other. Gov ernment, however, did not see its way to make the further grants required for this machine, and at Mr. Babbage's death in 1871, nothing further had been done towards its completion. The difference machine is now lying, an unfinished curiosity, in the museum of King's college, London. Both machines will be found described in the third volume of Taylor's Scientific Memoirs. The difference engine, constructed by Grant for the university of Pennsylvania, is said to he less expensive than Babbage's, and less complicated than Scheutz's, though provided like it with an apparatus for printing the results.