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Updated: June 27, 2025
Each of the two comparisons is a fully concrete one, because we compare entities of like nature, and only then test the ratios of the two that is, two pure numbers against each other to find that they are identical. To compare a spatial and a temporal magnitude, as is done by the formula in its second form, requires already a certain degree of abstraction.
The antecedent probability of A is to that of B as 2 to 1; the probabilities of their producing M are as 2 to 3; the product of these ratios is the ratio of 4 to 3; and this will be the ratio of the probabilities that A or B was the producing cause in the given instance. For, since A is twice as frequent as B, out of twelve cases in which one or other exists, A exists in 8 and B in 4.
Those who saw him felt drawn to him by that attraction of the moral nature which men of science are happily unable to analyze; they would detect in it some phenomenon of galvanism, or the current of I know not what fluid, and express our sentiments in a formula of ratios of oxygen and electricity.
The meaning of this quotation is that soft steel can be cut 100 times as fast as the hard steel or chilled iron. The ratios which are given, then, after each of these elements, indicate the wide range of judgment which practically every machinist has been called upon to exercise in the past in determining the best speed at which to run the machine and the best feed to use.
She had long since erased Hester's name from her good books, for Miss Laird knew only angles and equations, fixed values and ratios, and had no conception of nor admiration for a mind which was not as her own. Miss Watson laughed at this remark. She was more liberal-minded than Miss Laird and was not disappointed to find that her girls were not all of the same type.
And I am reminded of the Scotch sergeant's reply to his German captive, who asked his opinion about the duration of the war. "I'll tell you what it's the furrst five years that'll be the worst!" We seem in the bases to have slipped through them already, measuring by any of the ordinary ratios of work to time.
Assuming that the length of the deflector is kept constant and in practice this is found to be convenient the ratios can be altered by altering the weights of one or both pendulums and by adjustment of the upper weight. For the upper harmonies, 1:4 down to 3:8, the two pendulums may be almost equally weighted, the top one somewhat more heavily than the other.
Thus arises the following progression: Moon 1, Sun 2, Venus 3, Mercury 4, Mars 8, Jupiter 9, Saturn 27. This series of numbers is the compound of the two Pythagorean ratios, having the same intervals, though not in the same order, as the mixture which was originally divided in forming the soul of the world.
The following table gives a rough approximation of these ratios: These figures are based on incubator data. Eggs set under hens usually give a hatchability of 50 per cent. to 65 per cent., and livability of 70 per cent. to 80 per cent. The reason for the greater livability is that the real hatchability of the eggs is 70 per cent. to 75 per cent., and is reduced by mechanical breakage.
And yet we know of an author viz., one S. T. Coleridge who repeated that same doctrine without finding any evil in it. Malthus again, in his population-book, contends for a mathematic difference between animal and vegetable life, in respect to the law of increase, as though the first increased by geometrical ratios, the last by arithmetical!
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