Accurate and minute measurement seems to the non-scientific imagination, a less lofty and dignified work than looking for something new. But nearly all the grandest discoveries of science have been but the rewards of accurate measurement and patient long-continued labour in the minute sifting of numerical results.

In physical science a first essential step in the direction of learning any subject is to find principles of numerical reckoning and practicable methods for measuring some quality connected with it. I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the stage of science, whatever the matter may be.

Science is bound, by the everlasting vow of honour, to face fearlessly every problem which can be fairly presented to it.

When you are face to face with a difficulty, you are up against a discovery.

Symmetrical equations are good in their place, but ' vector ' is a useless survival, or offshoot from quaternions, and has never been of the slightest use to any creature.

We all confidently believe that there are at present, and have been from time immemorial, many worlds of life besides our own. . . . [This] may seem wild, and visionary; all I maintain is that it is not unscientific.

There is nothing in science which teaches the origin of anything at all.