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The two fundamental conclusions—that the Newtonian law is universally valid, and that the solar system is a stable structure—were reached by immense and sustained labours. Their establishment was due, in the main, to the mathematical genius of Clairaut, D’Alembert, Lagrange, and Laplace. But refined analysis demands refined data; hence the need for increased accuracy of observation grew continually more urgent. Attention was accordingly concentrated upon measuring, with the utmost exactitude, the places at determinate epochs of the heavenly bodies. The one thing needful was to learn the “when” and “where” of each of them—that is, to obtain such information as the transit-instrument is adapted to give. In this way the deviations of the moon and planets from their calculated courses became known; and upon the basis of these “errors” improved theories were built, then again compared with corrected observations.

For these ends, large telescopes would have been useless. They were not, however, those that Herschel had in view. The nature of the orbs around us, not their motions, formed the subject of his inquiries, with which modern descriptive astronomy virtually originated. He was, moreover, the founder of sidereal astronomy. The stars had, until his career began, received little primary attention. They were regarded and observed simply as reference-points by which to track the movements of planets, comets, and the moon. Indispensable for fiducial purposes, they almost escaped consideration for themselves. They were, indeed, thought to lie beyond the reach of effective investigation. Only the outbursts of temporary stars, and the fluctuations of two or three periodical ones, had roused special interest, and seemed deserving of particular inquiry.