Article in Annual Register

Annual Register for 1822 Published London 1823
(Preface dated July 7th 1823)
Page 691 Anonymous

Application of Machinery to the Calculating and Printing of Mathematical Tables. -Charles Babbage, Esq. F.R.S. London and Edinburgh, &c. in a letter addressed to Sir Humphry Davy, president of the Royal Society of London, has announced to the world, that he has invented various machines, by which some of the more complicated processes of arithmetical calculation may be performed with certainty and dispatch. Mathematicians are well aware that tables of every kind may now be constructed by the aid of one of the finest inventions of modern analysis, the theory of finite differences. It is in this way that Mr. Babbage proposes to apply his machines to the purpose of calculation. He states that his first engine is capable of computing any table by the aid of differences, whether they are positive or negative, or of both kinds; and that with perfect confidence he would venture to construct an engine that should compute numbers depending on ten or twelve successive orders of differences. It is a remarkable property of the machine, that the greater the number of differences, the more it will outstrip the most rapid calculator. This machine, by the application of certain parts, may be employed in extracting the roots of equations, and the degree of approximation will depend on its magnitude. Mr. Babbage has sketches of two other machines, one by which the product of any number by any other number may be found; and another by which all prime numbers from 0 to 10 million may be determined. He has also a fourth machine, whose plans are in a more advanced state, by which tables having no orders of differences constant may be constructed. This last is immediately applicable to the construction of Logarithmic and Astronomical tables of every kind; and in order to avoid the errors which might be produced in copying and printing the numbers in the common way, the ingenious inventor states, that he has contrived means by which the machines shall take, from several boxes containing type, the numbers which they calculate, and place them side by side; thus becoming at once a substitute for the computer and the compositor. In order to demonstrate the practicability of executing these views, Mr. Babbage has actually constructed a machine which will produce any tables where second differences are constant, and has exhibited it to some friends, who have witnessed its performance. In the computation of a series of numbers from the formula 12+ae+41 [sic, typographical error for x2+x+41], they were at first produced rather slower than they could be taken down by a person that undertook to write the numbers as they appeared, but as soon as four figures were required, the machine was at least equal in speed to the writer.

References

Annual Register. 1823. pp. 691–.

The Monthly Magazine: Or, British Register .... 1822. pp. 265–.

The Quarterly Journal. John Murray. 1823. pp. 222–.

Thomas Campbell and others(1822). The New Monthly Magazine. E. W. Allen. pp. 408–.