[F]or every type of experiment there is a numerical quantity, depending partly on the chance of the single event succeeding, and partly on the total number of the trials of it, which we may term the . ... it gives us a measure of the frequency with which deviations of various sizes will occur.

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If my view be correct, Erasmus Darwin planted the seed of suggestion in questioning whether adaptation meant no more to man than illustration of creative ingenuity; the one grandson, Charles Darwin, collected the facts which had to be dealt with and linked them together by wide-reaching hypotheses; the other grandson, Francis Galton, provided the methods by which they could be tested...

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[W]e find out of 16,019 trials, 8053 red numbers instead of 8009 or 8010. We have a deviation of 43 to 44. The standard deviation is about 63; a deviation as great as or greater than 44 would occur in about half the number of times in which 16,019 returns were examined. It presents therefore nothing of the remarkable or improbable.

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Although science claims the whole universe as its field... it confesses that its ignorance is more widely extended than its knowledge. In this very confession... it finds a safeguard for future progress. Science cannot... allow theologian or metaphysician... to the foreshore of our present ignorance, and so hinder the development in due time...

[S]uppose that the Emperor Karl V. had said to the learned of his day: "I want a method by which I can send a message in a few seconds to that new world, which my mariners take weeks in reaching. ..." ...It required centuries spent in the discovery and classification of new facts before the Atlantic cable became a possibility. It may require the like or even a longer time to unriddle... psychical and biological enigmas... but he who declares that they can never be solved by the scientific method is... as rash as the man of the early sixteenth century would have been had he declared it utterly impossible that the problem of talking across the Atlantic Ocean should ever be solved.

Wherever there is the slightest possibility for the human mind to know, there is a legitimate problem of science. Outside the field of actual knowledge can only lie a region of the vaguest opinion and imagination, to which... men too often... pay higher respect than to knowledge.

[T]he records of the tables are published in... Le Monaco and issued weekly in Paris... eight weeks roulette gave a grand total of 33,000 events. ...M. Blanc deserved a niche in the temple of science and Le Monaco a shelf in every mathematician's library.

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There is an old German proverb: "Death has no calendar," which taken in conjunction with our... "Death is no respecter of persons," strongly marks the folk conception... as of one who obeys no rule of time, or of place, or of age, or of sex, or of household...

The whole early history... is... so intimately connected with the names Galilei, Hooke, Mariotte and Leibniz that I have introduced some account of their work. The labours of Lagrange and Riccati also required some recognition. ...These early writers form the basis... not without interest, whether judged from the special standpoint of the elastician or from the wider footing of... the growth of human ideas. With a similar aim I have introduced throughout the volume... memoirs having purely historical value which had escaped Dr Hunter's notice.
Another class of memoirs which I have inserted are... of mathematical value, omitted apparently by pure accident. For example all the memoirs of F. E. Neumann, the second memoir of Duhamel, those of [P. H.] Blanchet etc. I cannot hope that the work is complete in this respect even now, but I trust that nothing of equal importance has escaped...