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Happy in detecting a ray of the beautiful upon the humblest blade of grass gemmed with dew; happy in seizing the poetic elements of an incident the most prosaic in appearance he was incapable of tracing all to a common source, and recomposing the grand ascending scale in which, to quote a beautiful expression of Herder's "every creature is a numerator of the grand denominator, Nature."
Ans. .1 raised to the millionth power; or 1 preceded by 999,999 decimal ciphers; or a common fraction with 1 as a numerator and a million figures as a denominator; or 1 chance out of a number expressed by 1,000,000 figures, which would fill 3 volumes like this book. Such changes were absolutely impossible, but necessary for evolution.
The phenomena of isomerism, or identity of composition and proportions of constituents with difference of qualities, and of isomorphism, or identity of form in crystals which have one element substituted for another, were equally surprises to science; and although the mechanism by which they are brought about can be to a certain extent explained by a reference to the hypothetical atoms of which the elements are constituted, yet this is only turning the difficulty into a fraction with an infinitesimal denominator and an infinite numerator.
We soon find that we are not so much worse off than most of our neighbors as we supposed. The fractional value of the wisest shows a small numerator divided by an infinite denominator of knowledge. I made some explanations to The Teacups, the other evening, which they received very intelligently and graciously, as I have no doubt the readers of these reports of mine will receive them.
If the operation consists of the same element repeated over and over, the time of each may be set down separately; or, if the element is very small, the total time of, say, ten may be entered as a fraction, with the time for all ten observations as the numerator, and the number of observations for the denominator.
Granted that he had not the place to himself; granted that the old house had inexpressibly caught and engaged his spirit; granted that, by virtue of the common denominator of the place, this unknown co-tenant stood in some relation to himself: what next? Clearly, the nature of the other numerator must be ascertained. And how?
The ratio of that number to the number of all the possible cases is the measure of the probability; which is thus a fraction, having for its numerator the number of cases favorable to the event, and for its denominator the number of all the cases which are possible.”
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