116 B. Galitzine on Radiant Energy. 



or, from (2), 



«=-y ; ( 3 ) 



e is likewise a function of T only (Kirchhoff). E denotes the 

 amount of energy which crosses any section of the cylinder 

 in a given direction during unit of time. In order, therefore, 

 to obtain the amount of energy contained in nnit of volume, 

 we must multiply the quantity E, not by 2/V, but by 4/V. 

 (Cf. Introduction.) 



If P is the pressure exerted on the base B, we have 



e B, we have 



p = T| --^-dT—e 

 J TdT dl e ' 



First Proof. 



Let the piston B be in contact with A, and keep A at 

 temperature T. Now let the piston B be moved as slowly as 

 possible through a distance h. The amount of heat Q im- 

 parted to the system, assuming the masses of A &c. to be 

 infinitely small, is given by 



Q = eh + ?h. 



All quantities of heat are expressed in mechanical units. 



If, now, we gradually reduce the temperature of A to zero, 

 all the energy will be transferred from the cylinder to other 

 bodies. When this has been done, let B be pushed back again 

 to A without expenditure of work. The process is reversible, 

 and as A's mass is infinitely small the second law of thermo- 

 dynamics gives us the following equation:. — 



dQ 



Q_C T dQ 



, de 



f T dT 



* = J -JJ^r, (4) 



or 



de 



P=tC ^dT-e, 



(5) 



which was to be proved. 



This formula differs, however, from that of Boltzmann by a 

 constant factor. For, substituting for e its value from (3), 



F-J[T0g«-.], ...<«, 



