The true Logic for this world is the Calculus of Probabilities, which takes account of the magnitude of the probability.

Thoroughly conscious ignorance is the prelude to every real advance in science.

Thus number may be said to rule the whole world of quantity, and the four rules of arithmetic may be regarded as the complete equipment of the mathematician.

We define thermodynamics ... as the investigation of the dynamical and thermal properties of bodies, deduced entirely from the first and second law of thermodynamics, without speculation as to the molecular constitution.

In your letter you apply the word imponderable to a molecule. Don't do that again. It may also be worth knowing that the aether cannot be molecular. If it were, it would be a gas, and a pint of it would have the same properties as regards heat, etc., as a pint of air, except that it would not be so heavy.

Every existence above a certain rank has its singular points; the higher the rank the more of them. At these points, influences whose physical magnitude is too small to be taken account of by a finite being may produce results of the greatest importance.

Mathematicians may flatter themselves that they possess new ideas which mere human language is as yet unable to express. Let them make the effort to express these ideas in appropriate words without the aid of symbols, and if they succeed they will not only lay us laymen under a lasting obligation, but, we venture to say, they will find themselves very much enlightened during the process, and will even be doubtful whether the ideas as expressed in symbols had ever quite found their way out of the equations into their minds.