Page:Popular Science Monthly Volume 52.djvu/699

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IN A WORLD HALF AS LARGE.

properties, whatever their extent. I propose to demonstrate the fallacy of these consequences.

For this purpose I reduce this proposition to its simplest dimension, and speak, in our planetary system, only of the sun and our globe. If this system and all it contains were reduced to one half the present linear dimensions, if the velocity of the earth in its orbit were one half less, the densities of the sun and the earth remaining the same in homologous points, there would be, according to the theorem of Laplace, no other change than of dimensions, and an observer belonging to the system would not perceive any; only an observer placed outside of the system and having a standard of comparison being competent to notice it.

Or the problem may be presented in another way. We might keep the two systems, the original and the reduced one, inclosing them, in thought, one within the other, with the centers of their two suns coinciding. If the two planets were in corresponding parts of their orbits at the same time, an observer at the common center would see only the smaller one, because it would always conceal the larger.

To make the matter plainer, let us call the fictitious planet Mars. In fact, what we are going to say will nearly apply to the real Mars, whose radius is 0.517 that of the earth, and its density 0.95 that of the earth. We remark, also, that Mars receives only half as much heat as the earth. Our imaginary Mars shall be an exact image of the earth; with the same seas and continents, the same flora and fauna, the same peoples, the same cities, and the same monuments; and a person who might be transported in his sleep would be carried from one to the other, provided his own size was correspondingly diminished, without perceiving that he had changed his abode, so long as he confined his attention to the phenomena of space. If we suppose the year to consist of three hundred and sixty-five days of the same length as our days, which we may legitimately do, there would be no change in the relations of time. Generally, there will be no change in the senses of touch and sight, so far as they relate to surfaces.

Supposing our imaginary Martians to have invented a system of weights and measures resting on a like basis with the French metric system, their measures of length will be of half the value of ours; of surface, one fourth; of capacity, one eighth; and their weights, into the valuation of which other elements will enter, one sixteenth.

Hence, if we suppose the mean weight of an earthly man to be eighty kilogrammes, that of the Martian would be only five kilogrammes.

The difference in the relations of the measure of capacity and the weight deduced from it, according to the rules of the metric sys-