The entropy of a system of N oscillators is also shown to be 



163 



Finally, the vibration intensity of black-body radiation is 



1 1 

 I = . 



hv 

 kT 



IJ 



When T = 0, I = 0, but U = — . This "Energierest," or energy residue* 



2 



is independent of the temperature, and is of imjiortance in connection with 



specific heats and radio-active transformations. Planck's radiation formula 



readily follows from the above ecjuation. 



Planck finds the following values for A- and h. k = 1.35 -^ 10""^, and 



h = 6.55 -^ 10 '-' in C. C!. S. units, losing these values together with 



e 



— = 1.77 ^ 10«c, e = 4.09 -=- 10", c, e = 4 6SX18-'»,and c = 3 X 10"', the 



m 



1.46 



mean number of undisturbed vibrations is found to be 1.37 10".)ve ^- , 



14600 



or 1.37 X 10^ e ^' , if X is measured in ^. In the same units the emission 



14600 



munber of an oscillator per second is 2.18 X 10' e ^ , and the mean ac- 



cumulation time is 4.58 X 10-*. X- e '^ . The equations used to obtain the 

 three preceding results are, respectively: 



hv 



Number of vibrations = 



3c '^L 



8tc'-v 



.kT, 



8tc=v- - 



Emission number = e 



3c ^L 



hv 

 kT 



N, 



"Berliner Ber., 5, 1.3, .July, 1911. 

 •.4nn. dor Physik, 26, p. .30, 1008. 



