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Updated: June 27, 2025
The stone falls on Sirius by the same law of gravitation as on the earth; the distances of the planets, the combinations of chemical elements are based on arithmetical ratios, and everywhere the same causes produce the same effects. Nowhere in nature is there anything arbitrary, but everywhere law.
Another thing, in which Mr. Malthus attempted to clench Wallace's argument, was in giving to the disproportionate power of increase in the principle of population and the supply of food a mathematical form, or reducing it to the arithmetical and geometrical ratios, in which we believe Mr. Malthus is now generally admitted, even by his friends and admirers, to have been wrong.
Even if the theory of atoms were abandoned, the generalisation would remain, as an accurate and exact statement of facts which hold good in every chemical change, that a number can be attached to each element, and the weights of the elements which combine are in the ratios of these numbers, or whole multiples of these numbers.
Thus far attention has been called only to combinations of circular wheels. In these the velocity ratios are constant, if we except the cases in which two independent trains converge, the two sun-wheels, or one of them and the train-arm, being driven separately and even in those, a variable motion of the ultimate follower is obtained only by varying the speed of one or both drivers.
One wonders, relishing the impossible, manifesting himself in characteristic, spontaneous ways; the other delights in rule and rhythm, in ordered sequences, in authority and precedent, following the law. One carves the gargoyle and ogrillion, working in paths untrod, the other limits himself to harmonic ratios, balanced compositions, and to predestined fenestration.
It will be more convenient to divide these ratios by one million, to avoid the large numbers otherwise involved. If one millionth of a millimeter is taken as the unit of wave length, the length of this unit on the map in millimeters will give the same measure of the dispersion as that just described. When the map is not normal, the dispersion of course varies in different parts.
By the eleventh census, the ratios of which will probably not be changed materially by the census now under way, the total population of the United States was about 65,000,000, of which about seven million were black and colored, and something over 200,000 were of Indian blood.
The stationary oyster is of higher organization than the free-swimming medusa; and the cold-blooded and less heterogeneous fish is quicker in its movements than the warm-blooded and more heterogeneous sloth. But the admission that the several aspects under which this increasing contrast shows itself bear variable ratios to one another, does not negative the general truth enunciated.
The areas of the two surfaces are thus as four to one; the volumes of the waters in the two cases will be in the proportion of two similar solids, the ratios of their dimensions being as two to one. Of course this means that the water in the one case would be eight times as much as in the other.
It is needless to lengthen the description by analyzing the data for each setting, since the reader by carefully scanning the columns of data in table 5 may observe for himself the various tendencies and their mutual relations. Similar irregularities appear in the daily ratios of right to wrong first choices presented in the last column of table 5.
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