indicate some general conclusions which seem to be established on a tolerably secure basis.
274. The progress of exact observation has of course been based very largely on instrumental advances. Not only have great improvements been made in the extremely delicate work of making large lenses, but the graduated circles and other parts of the mounting of a telescope upon which accuracy of measurement depends can also be constructed with far greater exactitude and certainty than at the beginning of the century. New methods of mounting telescopes and of making and recording observations have also been introduced, all contributing to greater accuracy. For certain special problems photography is found to present great advantages as compared with eye-observations, though its most important applications have so far been to descriptive astronomy.
275. The necessity for making allowance for various known sources of errors in observation, and for diminishing as far as possible the effect of errors due to unknown causes, had been recognised even by Tycho Brahe (chapter v., § 110), and had played an important part in the work of Flamsteed and Bradley (chapter x., §§ 198, 218). Some further important steps in this direction were taken in the earlier part of this century. The method of least squares, established independently by two great mathematicians, Adrien Marie Legendre (1752–1833) of Paris and Carl Friedrich Gauss (1777–1855) of Göttingen,[1] was a systematic method of combining observations, which gave slightly different results, in such a way as to be as near the truth as possible. Any ordinary physical measurement, e.g. of a length, however carefully executed, is necessarily imperfect; if the same measurement is made several times, even under almost identical conditions, the results will in general differ slightly; and the question arises of combining these so as to get the most satisfactory result. The common practice in this simple case has long been to take the arithmetical mean or average of the different results. But astronomers have constantly
- ↑ The method was published by Legendre in 1806 and by Gauss in 1809, but it was invented and used by the latter more than 20 years earlier.
