508 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



For the elementary surface dS in equation (I la) we have to sub- 

 stitute 2nrdr and making use of the relation 



f('-;)" 



p) (n + 1) (» + 2) 



we obtain for this special case 



np 2 g 4! \ 5! 6! 



as the average value of the potential energy of the system for the 

 unit of horizontal surface. 



If the barometric pressure in the center at the base is 745 mm [in 

 the disturbed region,] and 760™™ throughout the undisturbed 

 region we then have 



C - -A and P = 10333X 9.806 kg +1 m~ x sec" 2 ; 

 760 



for the temperature o° C. = 273 absolute we have 

 RT 



8000 meters nearly 

 g 



whence 



A 



= 26210 kg sec 2 = 6.3 Kilogram-calories m~ 2 

 rep" 



Assuming the radius of the cyclone to be 5 degrees of a great circle 

 or p = 555,500 meters, then the whole work needed to produce this, 

 diminution of atmospheric density is equal to 6.1 X io 12 calories. 

 This work will not appear so large when expressed in other terms; 

 the equivalent amount of heat would raise the temperature of the 

 whole volume of the cyclone (under constant pressure) by only 

 about 0.0026 C. or approximately by the 4^ part of adegree Centi- 

 grade. 



With the above assumed linear formula for e and the values of 

 c and p we have at sea level a constant gradient of pressure of 3 ma5 

 mercury per degree of a great circle. The average value of Ajizp 2 

 is independent of p and nearly proportional to the square of the 

 difference between the normal pressure and that in the center of 

 the cyclone. A barometric reading of 73o mm instead of 745™°° at 

 the center would increase the above computed value of A/np 2 four- 

 fold. 



