the Luminiferous ^Ether. 411 



provided it can be shown to be true — a condition which, at 

 present, is not accepted. 



Substituting r from (31) in (30), and integrating between 

 the limits of z and z = 0, gives 



e =e e- aJ t^-»; .... (33) 



which ultimately will equal the weight of the molecules in 

 the top layer. Hence, substituting numbers, we have 



8 X 1 70§ X 1 16 296000x08 g| 

 2116= 6 211(5 <« -1); 



17xll) 27 



which gives 



3 = 86 miles (34) 



It is evident that the very low temperature of the higher 

 portions of the column will shorten very much the hypo- 

 thetical column of uniform temperature ; but there are other 

 conditions which will modify the preceding analysis. The 

 assumptions in regard to layers and columns would not be 

 realized even under statical conditions, and much less for the 

 conditions in nature. Statically, the molecules would arrange 

 themselves more like shot in a pile, each being over the space 

 between the molecules in the layer below, instead of over a 

 molecule. This arrangement would give a less number in the 

 horizontal layers than assumed above. But the hypothesis of 

 constancy in the number of molecules in the layers is open to 

 greater objections. For the distance between the molecules 

 will increase with the elevation on account of the diminution 

 of the pressure of that part of the column above the point 

 considered, and the elastic force will be correspondingly di- 

 minished ; while, horizontally, in the plane of a layer of the 

 molecules, the elastic force would remain constant. In other 

 words, in the medium arranged as assumed the tension would 

 not be the same in all directions, and hence would be in 

 unstable equilibrium. As a refinement, we notice that in 

 every heavy fluid the downward pressure at every point 

 exceeds the upward by the weight of a molecule. 



Considering, now, that the molecules in the hypothetical 

 layers are distributed uniformly throughout the spaces imme- 

 diately beneath them, the number in the new top layer will be 

 less than in the former case, and the column will rise to a 

 greater height, and hence will exceed 86 miles ; and, in turn, 

 the new column would need another correction, and so on. 

 Assuming that the number in the top layer is 10 10 , and that 

 the vertical component of the elastic forces follows the law of 



