the Luminiferous ^Ether. 409 



the top layer ; and this multiplied by the weight of one mole- 

 cule will give e, the weight in the top layer ; and equation 

 (14) wall give (the temperature of the column being considered 

 uniform) 



u» ,,. -,,,-345— 170*xl0 16 x8 

 14-7x144x10 y+g = 17 X 1027 I 



" 23-35" 



But the temperature is far from being uniform. In regard 

 to a definite mass of a gas, we have the well-known relation 



F -=-^- = a constant = — , . . . (290 

 6t 8 q t q t> 



where p = e = the pressure on the base of a prism, and u=the 

 volume. 



The value of & from this equation substituted in (13) gives 



d i=-v 8 t -T d2 ( 30 > 



But with t an unknown variable this cannot be integrated. 

 If t= t we at once have equation (14) . The relation between 

 t ana z is unknown, if indeed there be any algebraic relation 

 betw r een them. It is, however, known that, as a general fact, 

 the temperature decreases with the elevation ; although local 

 causes and air-currents often cause this law to be reversed 

 for moderate heights. The best that can be done, in this 

 case, is to find an expression that will represent, approxi- 

 mately, the mean values of the temperature. It is usually 

 assumed that the average temperature at the earth is about 

 59° F. or 60° F., and that for latitudes of, say, 40° N. to 

 40° S. the perpetual frost-line is from 14,000 to 16,000 feet 

 above sea-level ; and observations indicate that the rate of 

 decrease of temperature decreases with the height. The last 

 fact is suggestive of an exponential law ; hence assuming 



T = T €-a, (31) 



and making t=493° F., absolute, at the height £ = 15,840 feet 

 and t =520° F., absolute, we find a= 296,000 (or 56 if z be 

 in miles), and our equation becomes 



z miles 



r=520e-^ (32) 



