B. Galitzine on Radiant Energy. 123 



perature depends directly on the sum total of all electrical 

 displacements, and the fourth power of the absolute tempera- 

 ture is directly proportional to the sum of the squares of all 

 the electrical displacements, these latter being calculated for 

 vacuum. 



The equation (22) enables us to solve another problem. If 

 we differentiate it with respect to T 1? we have 



T 3 = const. [ f ^p 4>(n)dn +/K,T) <f>(n m ) J] . 



If the function / is known, that is if we know completely 

 the distribution of energy in the spectrum, we are led to an 

 equation of the form 



d&> i:V T\ 



^r^I(«, 1), 



from which the unknown function co can be determined. 



The converse problem unfortunately cannot be solved ; that 

 is to say, a knowledge of the function a> tells us nothing con- 

 cerning the distribution of energy in the spectrum, because 

 "df(n, T)/dT cannot be equated to zero*. 



§ 4. Relation between the Radiating Power and the Surrounding 



Medium. 



Let us now imagine our radiation-cylinder to contain some 



* Cf. on tills subject the following references : — Draper, Phil. Mag. 

 [3] xxx. p. 345 (1847) : Knoblauch, Pogg. Ann. lxx. pp. 205, 337 

 (1847) : Jaques, Inaugural Dissertation Johns Hopkins University 

 (Baltimore, J. Wilson & Son, 1879) ; Beibl iii. p. 805 (1879) : Stefan, 

 Wien. Ber. lxxix. p. 423 (1879) : Oroya, Ann. de Chim. et de Phys. [5] 

 xix. pp. 472-550 (1880) : Langley, Comptes Rendus, xcii. p. 701 (1881); 

 xciii. p. 140 (1881), and later papers : Desains, Comptes Rendus, xciv. 

 p. 1144 (1882) ; xcv. p. 433 (1882) ; xcvii. pp. 689, 732 (1883) : Lecher, 

 Wied. Ann. xvii. p. 477 (1882); Christansen, Wied. Ann. xix. p. 207 

 (1883) : ScHLEiERMACHERjWied. Ann. xxvi. p. 287 (1885): Bottomley, 

 Beibl. x. p. 569 (1886) : H. Weber, Wied. Ann. xxxii. p. 250 (1887) ; 

 Math.-naturw. Mitth. uus den Sitzunqsber. d. Berl. Akad. xxxix. pp. 933, 

 565 (1888); Beibl. xiv. p. 897 (1890): Koyesligethy, Wied. Ann. 

 xxxii. p. 699 (1887) ; Astr. Nachr. Nr. 2805, p. 329 (1887) ; Abh. der ungar. 

 Akad. de?- Wiss. xii. Nr. 11 ; Math. u. natumo. Ber. aus Uhyarn, iv. p. 9 

 (1887) ; v. p. 20 (1887) ; vii. p. 24 (1889) ; Beibl. xii. p. 346 (1888) ; xiv. 

 p. 116 (1890) : W. Micheeson, Jouni. d. russ. phys.-chem. Get. [4] xix. 

 p. 79 (1887) ; [6] xxi. p. 87 (1889) ; Journ. de Phys. [2] vi. p. 467 (1887) ; 

 Beibl. xiv. p. 277(1890): Emden, Wied. Ann. xxxvi. p. 214 (1889): 

 Graetz, Wied. Ann. xxxvi. p. 857 (1889) : Lord Rayleigh, Phil, Mag. 

 xxvii. p. 460 (1889): Ferrel, Sill. Journ. [3] xxxix. p. 137 (1890); 

 Beibl. xiv. p. 981 (1890) : Edler, Wied. Ann. xl. p. 531 (1890) : VlOLLB, 

 Comptes Rendus, cxiv. p. 734 (1892) ; Journ. de Phys. [3] i. p. 298 (1892). 



