406 Prof. De Volson Wood on 



The mass of a cubic foot of the aether, equation (9), divided 

 by the mass of a molecule, gives the number of molecules in a 

 cubic foot, which will be 



2 22xl0 40 44 1A16 ,' 



n =W^W* X -~T— = 35*10- . . (24) 



which call 10 16 . This number, though large, is greatly ex- 

 ceeded by the estimated number of molecules in a cubic foot 

 of air under standard conditions, which, according to Thom- 

 son, does not exceed 17 x 10 25 , a number nearly 17,000,000,000 

 times as large as that in equation (24) ; and yet, at moderate 

 heights, the number of molecules in a given volume of air 

 will be less than that of the asther. 



Assuming that air is compressed according to Boyle's law, 

 and is subjected to the attraction of the earth, equation (15) 

 will give the law of decrease of the density. Taking the 

 density of air at sea-level at ^ of a pound per cubic foot, 

 O =14 # 7 lb. per square inch, r = 20,687,000 feet, equation (15) 

 becomes 



S=4xl0- 345 4-*. ..... (25) 



If e = oo , S=^ x 10~ 345 , which would be the limit of the 

 density, and it is a novel coincidence that this limit is nearly 

 identical with the value found for the density at the height 

 of one radius of the earth according to the ordinary expo- 

 nential law wherein gravity is considered uniform*. 



If the number of molecules in a cubic foot follows the same 

 law, then at the height z there will be 



17 x 10~ 34 W- 25 (26) 



molecules per cubic foot. Similarly, the value of the length 

 of the mean free path would be f 



2 x 10 345 ^" 6 inches. . . . (27) 



By means of these values, the following table may be 

 formed : — 



* The ordinary exponential law results from dropping — compared with 

 unity in equation (15), giving 



# _ 2 ft. z miles 



$ = S o6 26221 = S ol0 60387 = _ Jo _ X 10—n^ ? 



in the last of which, if z = 3956, the exponent becomes 345. 

 t Phil. Mag. 1873 [4] xlvi. p. 468. 



