IN A WORLD HALF AS LARGE. 679 



properties, whatever their extent. I propose to demonstrate the 

 fallacy of these consequences. 



For this purpose I reduce this proposition to its simplest dimen- 

 sion, 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 com- 

 parison 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 kilo- 

 grammes. 



The difference in the relations of the measure of capacity and 

 the weight deduced from it, according to the rules of the metric sys- 



