Whoever wishes to acquire a deep acquaintance with Nature must observe that there are analogies which connect whole branches of science in a parallel manner, and enable us to infer of one class of phenomena what we know of another. It has thus happened on several occasions that the discovery of an unsuspected analogy between two branches of knowledge has been the starting point for a rapid course of discovery.

Many persons entertain a prejudice against mathematical language, arising out of a confusion between the ideas of a mathematical science and an exact science. ...in reality, there is no such thing as an exact science.

Value is the most invincible and impalpable of ghosts, and comes and goes unthought of, while the visible and dense matter remains as it was.

The wind, as a direct motive power, is wholly inapplicable to a system of machine labour, for during a calm season the whole business of the country would be thrown out of gear. Before the era of steam-engines, windmills were tried for draining mines; but though they were powerful machines, they were very irregular, so that in a long tract of calm weather the mines were drowned, and all the workmen thrown idle.

Fertility of imagination and abundance of guesses at truth are among the first requisites of discovery; but the erroneous guesses must almost of necessity be many times as numerous as those which prove well founded.

The whole value of science consists in the power which it confers upon us of applying to one object the knowledge acquired from like objects; and it is only so far, therefore, as we can discover and register resemblances that we can turn our observations to account.

Repeated reflection and inquiry have led me to the somewhat novel opinion, that value depends entirely upon utility.