MECHANICAL EQUIVALENT OF PRESSURE MARGULES 507 



surface dS then we have 



p = Pi 



1L 

 RT 



A 



j o e~ ° RT dz j[P log ^ + P - PjdS. 



= e 



The integral with respect to z between zero and infinity is the 

 so-called height of a homogeneous atmosphere having the tempera- 

 ture T. If T is a function of the altitude still nothing is changed 

 in this expression for the volume of A except that in RT/g in the 

 value of the integral with respect to z, the T now indicates the 

 mean temperature of any horizontal layer. If we write 



P - P (1 + e) 



we obtain the following formula which is more convenient for 

 numerical computation: 



Sifi-h+fi- ■■■) dS - ■ w 



RT ,. I e 2 e 3 g 



Hence the potential energy of the assumed distribution of pres- 

 sure in the atmosphere is equal to that in a layer of air on which no 

 outside forces are acting, whose altitude is RT/g and in which the 

 distribution of pressure in all upper strata is the same as that at 

 the base of the atmosphere. 



If M is the mass above the surface S in the undisturbed condi- 

 tion ; [e 2 ] the average value of e 2 in 5, if moreover the first term of 

 the above series is very large relative to the others, then we have 

 the following approximate formula: 



[s 2 ] 

 A = MRT y 



Example. The following example will serve for a preliminary 

 estimate of the potential energy of the distribution of pressure in a 

 cyclone: 



Let the area of disturbed pressure be a circle of radius p; the 

 pressure in the center at the base be P (i — c) increasing linearly 

 from that point to the circumference, so that 



1 - - 

 P 



