Speculations apparently the most unprofitable have almost invariably been those from which the greatest practical applications have emanated.

Occurrences which according to received theories ought not to happen, are the facts which serve as clues to new discoveries

Almost all the greatest discoveries in astronomy have resulted from what we have elsewhere termed Residual Phenomena, of a qualitative or numerical kind, of such portions of the numerical or quantitative results of observation as remain outstanding and unaccounted for, after subducting and allowing for all that would result from the strict application of known principles.

The end of the eighteenth and the commencement of the nineteenth century are remarkable for the small amount of scientific movement going on in this country, especially in its more exact departments. Mathematics were at the last gasp, and astronomy nearly so; I mean in those members of its frame which depend upon precise measurement and systematic calculation. The chilling torpor of routine had begun to spread itself over all those branches of Science which wanted the excitement of experimental research.

Music and dancing (the more the pity) have become so closely associated with ideas of riot and debauchery among the less cultivated classes, that a taste for them, for their own sakes, can hardly be said to exist, and before they can be recommended as innocent or safe amusements, a very great change of ideas must take place.

It can hardly be pressed forcibly enough on the attention of the student of nature, that there is scarcely any natural phenomenon which can be fully and completely explained, in all its circumstances, without a union of several, perhaps of all, the sciences.

There is a gentle, but perfectly irresistible coercion in a habit of reading well directed, over the whole tenor of a man's character and conduct, which is not the less effectual because it works insensibly, and because it is really the last thing he dreams of.