B. Galitzine on Radiant Energy. 125 



for the pressure of light we arrived at equation (10a). In 

 that case the operation considered was an adiabatic one, and 

 consisted in giving to a new portion of space, or let us say a 

 new volume of aether dh, a quantity of energy 



dq = edh. 



This transfer of energy to a new mass of 93ther is accom- 

 panied, as we have seen, by a certain expenditure of work 

 Vdh. We have, then, two correlative phenomena, and in ihe 

 limit, for infinitely small displacement, only ^ of the energy 

 transferred can be converted into external work. We have, 

 indeed, from (14), 



da ~ 3 * 



The previous investigations enable us to calculate the same 

 ratio, for adiabatic displacements of finite magnitude ; and 

 this ratio is only a function of the initial and final temperatures. 



From the same equation (10a) it follows that, if we wish 

 to concentrate a certain quantity of energy into a smaller 

 mass of gether, this can only be done by the expenditure of 

 external work, the first law being obeyed throughout the 

 process. In this lies the closer explanation of the second law. 



From equations (10) and (9) we find, for finite displace- 

 ments, 



e 1 h 1 — e 2 h 2 = T = U 1 — U 2 (24) 



U x and U 2 denote the quantities of energy in the cylinder at 

 the beginning and end of the operation. 



From equations (14), (16), and (17) it follows that 



eh^SCC^T (25) 



Insert this in equation (24) and note that 3CC! 3 may be 

 determined from the initial conditions ; we have 



T=f CTx-T^. 



The available work is directly proportional to the fall in 

 temperature (Second Law) . It is only in the case of T 2 = 0, i. e, 

 when the given quantity of energy XJ X is distributed over an 

 infinitely great mass of aether (since according to (17) T=0 

 only when A = co ), that the whole energy can be transformed 

 into externa] work. 



In conclusion, let us compare the quantities of energy 



