and the Partition of Energy in Continuous Media. 231 



walls. Let the constitution of this stream of energy be 

 supposed given by the formula 



f{\ T)d\ (2) 



It is commonly argued or assumed * that the constitution 

 of the energy in this experiment must be the same as in the 

 preceding imaginary experiment. If so, the functions F and 

 / must be identical. 



5. Assuming the legitimacy of using the theorem of Equi- 

 partition of Energy, the function F can be calculated at once 

 from this theorem. It is found f that 



F(\, T) = 8ttRTx- 4 , (3) 



where R is the universal gas-constant. 



The function /can be determined experimentally. Planck % , 

 with the help of a mathematical argument, with the details 

 of which we are not here concerned, arrives at the formula 



/(X , T) = ^_I_ .... (4) 



a form which agrees well § with experimental readings, pro- 

 vided c and k may be treated as adjustable constants. 



The values of c and k which Planck arrives at by comparing 

 formula (4) with experiment are 



c=l-965 x lO" 16 , £=1-346 x 10~ 16 . 



On the other hand, Lorentz ||, using the form SwkXr^T, to 

 which formula (4) reduces for long wave-lengths, obtains 



£=l'07xl0- 16 



as the value of h given by experiments on light of great 

 wave-length. According to Planck's analysis, the constant k 

 ought to be identical with the gas constant R, of which the 

 value is known to be ft=l()- 16 to within a few per cent. 



* The assumption is tacitly involved in the common employment of the 

 expression "radiation appropriate to a given temperature." ICf. Proc. 

 Roy. Soc. A. lxxvi. p. 306, 1905.) 



f Rayleigh, Phil. Mag. [5] xlix. p. 539 (1900), and Nature, lxxii. 

 pp. 54, 243 (1905). Also J. H. Jeans, Phil. Mag. [6] x. p. 91 (1905). 



X Vorlesungen ilber W&rmestrahlungen (1900)7 pi 157, and in earlier 

 papers. 



§ Planck, Vorlesungen itber Wiinnestrahlungen, p. 158, and Paschen, 

 Annalen d. Pki/sik, iv. p. 277. 



|| Koninh. Akad. van Wetenschappen (Amsterdam), April 24, 1903, 

 p. 678. 



R2 



