412 Prof. De Volson Wood on 



equation (33) , we find 



£ = 95 miles ; 



and if the number in the top layer be 10 4 , we find £ = 104 

 miles, and for one molecule, £ = 110 miles. In a similar 

 manner it would be legitimate to assume that the column was 

 capped by a fraction of a molecule, for that would be equi- 

 valent to one molecule at the top of a column having a base 

 of several square feet. We are unable to determine where 

 this process would end in nature; and hence this analysis fails 

 to fix definitely the extreme height of the atmosphere, even 

 for statical conditions. 



Assuming that the distance between the contiguous mole- 

 cules would be inversely as the third root of the densities of 

 the medium, as they would be with sufficient accuracy where 

 the number of molecules in a cubic foot is immense, w r e have, 

 after substituting e, equation (33), and t, equation (31), in 



( 29 0, 



s r*-«4 ( £-i)i d 3 



So d 3 ' 



where d is the distance between contiguous molecules at sea- 

 level and d the corresponding distance at the height z. Hence 



M> ( jLi)_? 1 



d = d [e e ° a f (35) 



for £=86 miles, d=± of an inch, 

 „ £= 95 „ d— 4-5 inches, 



„ * = 104 „ rf=ll-4 „ 



These values of d are greatly in excess of the distances be- 

 tween contiguous molecules in the horizontal layers, according 

 to assumed conditions. Thus, at the height of 104 miles it 

 was assumed that there were 10 2 molecules on the side of a 

 square foot, in which case the distance between contiguous 

 molecules would be about £ f an inch instead of 11 inches 

 as above. These results ought not to agree exactly, for one 

 analysis assumes that the atmosphere terminates with each 

 assumed number of molecules, while the other assumes that 

 the law is continuous to any height. It is apparent that 

 the laws represented by equations (33) and (35) both become 

 practically discontinuous at a height at or less than 95 miles. 

 For the sake of giving definiteness to the following remarks, 

 we will assume that the mean height for statical conditions is 



