114 B. Galitzine on Radiant Energy. 



against the pressure of light, viz. P . 47rR 2 . SR, must be equal 

 to this, and hence 



P _2Q 

 V" 



This conclusion appears to me to be wrong, although the 

 result obtained by a different method of reasoning differs 

 from Bartoli's formula only by a constant factor. Our 

 system consists of the inner black sphere and the space 

 between the two spheres, which also possesses a portion of 

 the energy*. On reducing the outer sphere work is done ; 

 not because the energy of the absolutely black body is thereby 

 increased — for all the energy gained by the inner sphere is 

 taken from the space between the spheres — but because the 

 whole energy of the system passes from a lower to a higher 

 temperature. 



Boltzmann t has also attacked the same question. Let E 

 be the heat radiated from unit surface in unit time (Boltzmann 

 denotes it by </>(0) \ then he finds for the pressure P of light 

 against a perfectly reflecting wall the expression 



dE 



p=^[tJ-^t-e] 



or 



cm 



P-JlJrf-g-4 



T being the absolute temperature. He writes the constant of 

 integration equal to zero. This formula enables us to calcu- 

 late the pressure P numerically for any assumed law of 

 radiation. The method by which Boltzmann obtains his 

 formula is quite a legitimate one, but I differ from him as to 

 the value of the numerical factor. The subject may be treated 

 in a more simple manner, as I shall proceed to show. 



In conclusion 1 may draw attention to a paper by Lebedew J, 

 who has made a very interesting application of the Maxwell? 

 Bartoli theory, by comparing the force of repulsion due to 

 radiation with universal gravitation §. 



§ 2. Deduction of the Formula for the Pressure of 

 Light P. 



. Imagine an empty cylinder A B, of length h, whose walls 



* Cf. Thomson, Phil. Mag. [4] ix. p. 36 (1855). 



i Wied, Ann. xlv. p. 292 (1892). % Tom. cit. 



§ Cf, also Kolacek, Wied. Ann xxxix. p. 254 (1890). 



