FOR HIGH LEVELS IN THE EARTh's ATMOSPHERE. 79 



The increase of circulation per unit of time, in a closed atmospheric curve made up of 

 air-particles is equal to the total number of unit solenoids embraced within that curve. 



Now the number and position of the solenoids in the atmosphere may be ob- 

 tained in a very simple way from the Ej;; maps. Thus we choose any two points a 

 and h on any two of the lines of such a map as the Ej^;^ map shown in Fig. 12, page 

 71. Imagine verticals falling from these points in the atmosphere to corresponding 

 points on the isobaric surfticesp = 27.5 atid 25.0 which vertical lines we will desig- 

 nate also by the letters a and b. The lower ends of these verticals are connected by 

 the line a-b, which lies wholly in the isobaric surface 25.0 and the upper ends are 

 connected by the line a-b which lies wholly in the isobaric surface p = 27.5. Thus is 

 obtained a closed curve in the atmosphere consisting of two vertical portions aa and 

 bb, and two isobaric portions, ab and ha. The number of solenoids within this closed 

 curve may be determined by carrying out the integration Jvdp around the whole 

 curve. Now along the two isobaric portions ab and ha of the curve, both vdp and 

 /'V/jj, are equal to zero so it only becomes necessary to perform the integration along 



the two verticals aa and bh. The integral along aa may be represented by ( I v-dp] 



and the integral along &6 by ( I v-dp\ , then by virtue of equation (25) we have 



W25.0 / * 



A=( r\^ dp\ -( r\dp\ (26) 



which integral may be simplified by making use of the barometric formula * 



dV = — V dp. 

 By integrating both sides of this latter formula along the vertical aa we find, that 



\ Ja.o / a 



If by (E]5;?)„ we designate the number of level surfaces of gravity lying between the 

 27.5- and 25.0-isobaric surfaces along the vertical a, then we may write 



(Tv dp) =(E-)„. 

 Whence from (7) we have 



Analogously we find that 



( Cv-dp) =(E-»),. 



*See eqaationa (1) and (10). 



