The whole of the _numerical_ constants throughout the works of Laplace, Plana, Le Verrier, Hansen, and other eminent men whose indefatigable labours have brought astronomy to its present advanced state, might easily be recomputed. They are but the numerical coefficients of the various terms of functions developed according to certain series. In all cases in which these numerical constants can be calculated by more than one method, it might be desirable to compute them by several processes until frequent practice shall have confirmed our belief in the infallibility of mechanism.
The great importance of having accurate Tables is admitted by all who understand their uses; but the multitude of errors really occurring is comparatively little known. Dr. Lardner, in the “Edinburgh Review,” has made some very instructive remarks on this subject.
I shall mention two within my own experience: these are selected because they occurred in works where neither care nor expense were spared on the part of the Government to insure perfect accuracy. It is, however, but just to the eminent men who presided over the preparation of these works for the press to observe, that the real fault lay not in them but in _the nature of things_.
In 1828 I lent the Government an original MS. of the table of Logarithmic Sines, Cosines, &c., computed to every second of the quadrant, in order that they might have it compared with Taylor’s Logarithms, 4to., 1792, of which they possessed a considerable number of copies. Nineteen { 139} errors were thus detected, and a list of these errata was published in the Nautical Almanac for 1832: these may be called
Nineteen errata of the first order . . 1832.
An error being detected in one of these errata, in the following Nautical Almanac we find an
Erratum of the errata in N. Alm. 1832 . . 1833.
But in this very erratum of the second order a new mistake was introduced larger than any of the original mistakes. In the year next following there ought to have been found
Erratum in the erratum of the errata in N. Alm. 1832 . . 1834.
In the “Tables de la Lune,” by M. P. A. Hansen, 4to, 1857, published at the expense of the English Government, under the direction of the Astronomer Royal, is to be found a list of errata amounting to 155. In the 21st of these original errata there have been found _three_ mistakes. These are duly noted in a newly-printed list of errata discovered during computations made with them in the “Nautical Almanac;” so that we now have the errata of an erratum of the original work.