408 Prof. De Volson Wood on 



10,000,000 miles*; but according to the above law it becomes 

 about 792,000 miles. 



If a cubic inch of air at sea-level were carried to the height 

 of \ the radius of the earth, and then allowed to expand freely, 

 so as to become of the computed density of the atmosphere at 

 that point, it would fill a space of 4 x 10 28 ' 12 cubic miles, or a 

 sphere whose radius is 2,398,000,000 miles, which is nearly 

 equal to the distance of the planet Neptune from the sun ; 

 and there would be less than one molecule to the mile. Such 

 are some of the results of extending a law to extreme cases 

 regardless of physical limitations, or of the imperfection of 

 the data on which it is founded. For instance, a uniform 

 temperature is assumed, and, impliedly, an unlimited divisi- 

 bility of the molecules. The latter is necessary in order to 

 maintain a law of continuity. But modern investigations 

 show that not only air, but all the gases, are composed of 

 molecules of definite magnitudes whose dimensions can be 

 approximately determined ; and hence, if there be only a few 

 molecules in a cubic foot, and much less if there be but 

 one molecule in a cubic mile, it cannot be claimed that the 

 gas will be governed by the same laws as at the surface of 

 the earth. 



To find the Height of the Atmosphere* — The atmosphere will 

 terminate at that height w T here the vertical repulsive force 

 equals the weight of the particles in the topmost layer. As a 

 first approximation, conceive that the molecules are arranged 

 in horizontal layers and vertical columns, in a prism whose 

 base is one square foot, and whose height extends to the 

 height of the atmosphere ; the base of each column of mole- 

 cules being one of the molecules in the base of the prism. 

 Considering the number of molecules in a cubic foot of air 

 at standard conditions as 17xl0 25 , and the weight of the 

 same as '08 of a pound, we have for 



Q 



the weight of one molecule of air = ^ — Tn^t- • (28) 



i The number of molecules along one edge of the bottom 



< layer will be V17X10 25 nearly; and the number in the 



bottom layer the square of this number, or 170^ X 10 16 , 



which, according to the hypothesis, will be the number in 



* Phil. Trans. Koy. Soc. London, 1881, Part II. p. 389. 



f This may be used as a unit for measuring the mass of a cubic foot 

 of the aether. Thus, dividing the value in equation (10) by that in (28) 

 gives 4250 ; or the mass of aether in a cubic foot is 4250 times the mass 

 of one molecule of air. 



