All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers.

It is of great advantage to the student of any subject to read the original memoirs on that subject, for science is always most completely assimilated when it is in the nascent state.

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

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.

But when we face the great questions about gravitation Does it require time? Is it polar to the 'outside of the universe' or to anything? Has it any reference to electricity? or does it stand on the very foundation of matter-mass or inertia? then we feel the need of tests, whether they be comets or nebulae or laboratory experiments or bold questions as to the truth of received opinions.

It is a universal condition of the enjoyable that the mind must believe in the existence of a law, and yet have a mystery to move about in.

The vast interplanetary and vast interstellar regions will no longer be regarded as waste places in the universe. We shall find them to be already full of this wonderful medium; so full that no human power can remove it from the smallest portion of space or produce the slightest flaw in its infinite continuity.