﻿the Height of the Atmosphere. 355 



To consider the effect of temperature and moisture upon this 

 result, suppose that the force of gravity is constant; then, since 

 a, = 0003665 when t is expressed in the Centigrade scale, we 

 may safely neglect any terms whose coefficients are the second 

 or higher powers of « ; and therefore from (1) and (2) we get, 

 by eliminating p, 



therefore 



J-2— a-* 



alog e /> = C— z + cx. \ tdz, 



where C is some constant introduced by integration. 



Now there is no fixed relation between t and z, so that we 



cannot integrate any further ; but 1 tdz = zt m , if t m be the mean 



Jo 

 temperature of the column of air whose height is z, and hence 

 we get 



and thus the temperature may be supposed to combine with the 

 moisture in making a variable ; for Professor Airy (On Sound 

 and Atmospheric Vibrations) has shown that if the tension of the 

 vapour be equal to mp, then the height of the homogeneous 



atmosphere will be a ( r — ) . 



Thus our result will be corrected for temperature and moisture 

 if in equation (7) for a we write 



«(1+-W(i±£) (8) 



8 



Now since t m can never be accurately determined for any time 

 and place, it follows that h cannot be accurately determined, and 

 a more rigorous investigation would be practically useless ; we 

 proceed to obtain a probable value of t m for these latitudes, or 

 for the whole earth. 



Sir J. Herschel has shown (Meteorology) that an equation, 



t = T + r ] p + Tc i p 2 f 



exists between the temperature and pressure at any point in the 

 atmosphere out of reach of local disturbing causes, in which t , 

 t l , and t 2 are constants for only a short space of time, and which 

 must therefore be determined by balloon -ascents when required. 

 Their mean values for these latitudes, the temperature being 

 measured in the Centigrade scale, and the pressure in inches of 



