ON THE ENERGY OF STORMS MARGULES 547 



These expressions become more perspicacious by the introduction of 

 the following abbreviating symbols: 



- (V 2 



K = J -—- dk = the kinetic energy of the whole mass of air in 



the closed system. 

 P = I [iWdk = the potential energy of position. 



f C v P 



I = C v I T ft.dk = „ J pdk = the internal energy. 



The changes in the values of these quantities in the time t are indi- 

 cated by dK, #~P , d I and are completely determined by the initial 

 and final conditions. 



The three following quantities depend on the path that each 

 elementary mass pursues; these time integrals extend over the 

 same interval /. 



^ j ( the work of the pressural forces, 



— 3 A = - \ dt \ dk . ~\ or the work of expansion in the 



fidt { time t. 



the work of the frictional forces 



Jr* r tne worK 01 tne inctionai iorces 



dt Re cos (Re) fidk I or loss of energy, R, by friction, 

 J t in the time t. 



Jr> j q r the quantity of heat communi- 



df I — udk \ cated to the closed system, in the 



J dt ' { timet. 



We therefore write the equations for the kinetic energy, thermal 

 equilibrium, and total energy of the whole mass, respectively as 

 follows : 



Kinetic energy d (K + P + A) + (R) = . . (4*) 



Thermal energy (Q) = d I - d A (5*) 



Total energy (Q) = d (K + P + I) + (R) - (6*) 



§(12) In the case of friction there can be no steady motion without 

 a corresponding continual addition of heat. K, P, I remain 

 unchanged in steady motion and the equations reduce to (Q) = 

 (R) = — oA • The additions of heat (necessarily consisting of posi- 



