Francis Baily

“ It would not be very complicated to place three such machines by the side of each other, and cause them to transfer their results to a common axis, with which the printing apparatus might be connected. Such a machine would, amongst other tables, compute one from the expression
A sin θ + B sin 2 θ + C sin 3 θ the utility of which, in astronomy, is well known. In fact Mr. Babbage is of opinion that it would not be impossible to form a machine which should tabulate almost any individual equation of differences. ”

“ Independent of their very limited extent, the elements from which they were deduced, have been superseded by others more agreable to actual observation; which, together with their exclusion of the solar nutation, and other minute quantities which cannot safely be neglected in the present state of astronomy, renders these tables of doubtful utility to the practical astronomer.
The number of zodical stars (without including the very minute ones) is considerably above a thousand: each of which may, in the course of a revolution of the nodes, suffer an occultation by the moon. ”

“ From the simplicity of the mechanism employed, the same principles may be applied in forming a much larger machine for computing tables depending on any order of differences, without any probability of failure from the multitude of wheels employed. The liberality of our government (always disposed to encourage works of true science and real merit) has induced and enabled Mr. Babbage to construct a machine of this kind, capable of computing members with four orders of differences ”

“ The logarithms of numbers from 1 to 108000 have been already computed, with a greater or less number of figures; but this has been the work of various authors, and of several successive years: the labour is so immense that no human being has ventured to undertake the whole. The table which now exist are chiefly copies from those original and partial computations. By the help of the machine, however, this immense labour vanishes, and new tables may be readily computed and re-computed as often as may be required by the public. ”

“ Nevertheless laborious, yet useful, operation of computation cannot safely be left to inferior hands. The merit of each is however very unequally estimated by the world. Euler had three hundred pounds granted him by the English government for furnishing the elements, and Mayer three thousand for the actual computation of the tables of the Moon, which were published by the Board of Longitude in the year 1770. ”

“ In the year 1808 M published his tables of Jupiter and Saturn: but in 1821, owing to the progress of discovery and the advancement of physical astronomy, it was found necessary to revise the elements; and an entire new set of tables was then published by this distinguished astronomer. In order to deduce the geocentric places of these planets, it is requisite to compute no less than 116 tables depending on the sine or cosine of certain arcs. ”

“ Another volume, of the same size, which is announced by the same author, will render these by far the most valuable of their kind, provided their accuracy can be relied on. The quantity of mental labour saved, in the construction of such tables, by the help of the machine, is literally infinite: for, in fact, no previous calculation is at all requisite; and it will be necessary merely to put into the machine, at the end of every two pages, the number whose multiples are required. ”

“ With five orders of differences, a table of logarithms may be computed to eight places of figures, which shall be true to the last figures, and it would not require more than half an hour to compute each set of differences; particularly as the higher numbers require very little labour, two or three terms of the series being quite sufficient. ”

“ Tables of the products of numbers. The numerous tables of this species which have been published at various time, and in different countries, sufficiently attest their utility and importance: and there can be no doubt that, if their accuracy were undeniable, their employment would be much more frequent. ”

“ These occultations are ascertained to be visible at sea, even from the unsteady deck of a vessel under sail: and afford the surest means of determining the longitude, provided the position of the star could be well ascertained. ”