444 PROFESSOR CHALLIS, ON ATMOSPHERIC TEMPERATURE 



do 

 in which equation -j- expresses the variation of temperature corres- 

 ponding to a change of height, so far as it varies independently of 

 change of density. If also p be the pressure where the density is 

 p, and g be the force of gravity, we have 



% — gp, (2). 



Lastly, we have the known relation between the pressure, density, 

 and temperature, given by the equation 



p = «V (1 + ad), (3). 



in which the temperature is supposed to be reckoned in degrees of 

 the centigrade thermometer, a^ is the pressure where p — \ and 6 = 0, 

 and a is the numerical coefficient 0,00375. With respect to the equa- 

 tion (2) we may remark that though it is in strictness applicable 

 only to the air at rest, it is very nearly true when the atmosphere 

 is in motion ; for the direction of winds is necessarily nearly parallel 

 to the Earth's surface, and consequently the effective accelerative force 



in the vertical direction is very small. Hence ~-^ is nearly equal to 



the impressed accelerative force, that is, to the force of gravity. 



The equation (3) differentiated gives, 



I =«■£(' -»)-•-©• 



Hence by means of (2) we get, 



d% 0^(1+ ad) 



and by substituting this value of -^ in (1), it will be found that 



d0 gp de 



(de\ d% (r{\ + ad)' dp 



m- 



- ap dd ' ^*^- 



1 +-^ —Fi • T- 



1 + aO dp 



