ON THE ENERGY OF STORMS MARGULES 545 



The increase of the total kinetic and potential energy of the particle 

 is equal to the work done by the pressural forces and the frictional 

 forces. The deflecting force of* the rotation of the earth being 

 normal to the path does no work; this is also true of the other por- 

 tions of the term A. Equation (i) differs from the equation of 

 energy for absolute motion only in respect to the meaning of W 

 which contains a term depending on the rotation of the earth in 

 addition to the potential of the attraction. 



We combine the dynamical relation (i) with the thermal relation 



dQ dT 1 dp 

 dt = p ~dt~pdi (2) 



which applies when the quantity of heat dQ is imparted to the par- 

 ticle of air while describing its path ds during the element of time dt. 

 It is here assumed that just as in air at rest, so here the imparted 

 heat dQ serves only to increase the internal energy by the quantity 



C v dT and to perform the work of expansion pdl - ). Conse- 



y ■ 

 dQ dT d (c 2 \ 1 p - - 



quently • 



We must include in dQ not only the heat communicated from with- 

 out but also that portion of the heat due to friction that belongs 

 to this small elementary unit mass of air. 



§(n) The equations (i) and (3) with the factor [xdk when inte- 

 grated over the space k, assumed to be filled with air, give the rela- 

 tions for the total energy of the whole mass within that space. 



In this integration we make use of the equation of continuity 



da d (a u) d (av) 8 aw 



-£ + -^r~ + -r- + f = ° 



dt dx dy dz 



If F indicates a quantity that is considered as attached to a definite 

 elementary mass and can be expressed by a continuous function of 

 the place and time, then by using a well-known transformation we 

 have 



CdF 

 J d7 



CdF CI dF dF dF\ 



-ftdk-J -JifiM + J K^Jx+^jy+nw — jdk 



d f f 



= — - ] fiFdk— J pFc cos (n, c) dO 



