MECHANICAL EQUIVALENT OF PRESSURE MARGULES 517 



case of constant temperatures the whole work done by the pres- 

 sural forces cannot be expressly or exactly stated, for it depends 

 on the path along which the transfer takes place. Generally the 

 question is as to the changes of A with time and these can be com- 

 puted provided that the serial succession of conditions is known. 

 But the total potential energy can only be given under certain 

 assumptions; an estimate of its value can however be obtained by 

 means of the formulae here deduced. 



APPENDIX TO PART I 



(6.) THE EQUATION OF ENERGY OF A FRICTIONLESS MOVING MASS 



OF AIR 



Retaining the notation of the last section we have for a unit mass 

 of air the following equation for the living force or kinetic energy: 



1 d (G 2 ) _ dG _ _ 6V _ G dp 



2 dt dt ds /x ds 



where V or the potential of the exterior force is so chosen that 

 the negative derivative with reference to any coordinate expresses 

 the force acting on the unit mass, in the dissection of that coordinate. 

 We will also introduce the Eulerian Symbol 



dt dt ds 



= — . -\- U + V + w 



dt dx dy dz 



which expresses the variation with time of the variables associated 

 with the elementary mass. If V is only a function of the location 

 then the equation of energy becomes 



ld(P = _ d Z-h(it^^) (III) 



2 dt dt fx\dt dt ) 



This holds good also for movements relative to the earth. 



