B. G-alitzine on Radiant Energy. 115 



and base B, are perfect reflectors, and in which B can be 

 displaced after the manner of a piston. A is an absolutely 

 black body which may be re- h 



placed, when necessary, by a I 

 perfectly reflecting wall. A 



For simplicity, let the area of 



the cross section of the cylinder be unity. 



Let us denote by e the emissivity of our black body, i. e. 

 the quantity of heat which unit surface of it radiates out in a 

 normal direction every second. In a direction making an 

 angle $ with the normal to the surface the emissivity will 

 be smaller, namely e cos (f>. To obtain the total quantity of 

 heat E radiated from a unit of surface each second we require 

 to evaluate the following integral*: — 



E = 27re I cos<£sin$<i</> = 7re, . . . (1) 

 Jo 

 in which both e and E are functions of the absolute tempe- 

 rature T onlyf. 



JSTow let us calculate the quantity of energy e in unit 

 volume of our cylinder when the black surface A is at tempe- 

 rature T. First of all imagine the cylinder to extend to 

 infinity on the right, and let e' denote the energy contained 

 in unit volume in this case. 

 We have obviously 



e=W (2) 



If the surface sent out all its energy E in a normal direc- 

 tion, we should have 



e = y> 

 or 



2E 



e= -T' 



But in reality a quantity of heat 27re sin <£ cos <£ dcf) is 

 radiated at an angle lying between and $ + ^<£. The 

 velocity V<p with which this energy is propagated in a direc- 

 tion parallel to the axis of the cylinder is, according to the 

 laws of reflexion, equal to V cos 0. The amount of energy 

 in unit volume will thus be greater, and we shall have, as 

 soon as equilibrium is established, 



Q f*/ a sin<£cos<£ ,. 1 2E 



* Cf. Wiillner, Lehrbuch der Rvperimental-Physik. iii. p. 238 (41 h 

 edition, 1885). 

 f Cf. Kirchhoff, Pogg. Ann. cix. p. 275 (1860). 



12 



