Spectra and Planck's Law. 433 



they cannot, even when combined with the condition that at 

 great distances the electric force must be expressed by Qe/r 2 , 

 afford sufficient data to determine uniquely the law of force, 

 and, in fact, we can find, without difficulty, different expression 

 for R which would yet give the same series of spectral lines. 



The quantity c, which occurs in the expressions for R and 

 B inside the atom, is of the dimensions of a length, and if it 

 were a universal constant, i. e., the same for all atoms, there 

 would be some standard length occurring either in all the 

 atoms or in the medium surrounding them. In this case, 

 since c would not vary from atom to atom, the frequency of 

 the vibration would be proportional to Q, the positive charge 

 in the atom. Moseley's experiments on the wave-length of 

 the characteristic Rontgen radiation given out by the different 

 elements, if taken in conjunction with the assumption that 

 the positive charge is proportional to the atomic number, 

 show that the frequencies are proportional to the square, and 

 not to the first pow r er of the positive charge. For this 

 reason we must suppose that Q/c is proportional to Q 2 , so 

 that c = c'/Q where c' and not c is a universal constant. 



Since c is of the dimensions of a length multiplied by a 

 charge of electricity, it represents the moment of an electric 

 doublet, and if it is taken as a universal constant we must 

 suppose that electrical doublets with constant moments form 

 a part either of the atoms of all the elements or else of the 

 medium which surrounds them. 



We can calculate the value of c or c' if we know the 

 amount of work required to move an electron from one of 

 its positions of equilibrium to an infinite distance from the 

 atom. For we see by equation (2) that if the position of 

 equilibrium of the electron is that corresponding to a? = 7r/2, 

 this work is equal to 



or if the work is expressed as Ye, where V is the potential 

 through which the charge e must fall to acquire this amount 

 of energy, 



V 



\ 7T7 C 



If we take the ionizing potential as the measure of V, then 

 for the atom of hydrogen V = ll volts, and Q = e, we find, 

 putting * = 4-7 x 10" 10 , V = 11/300, 



c = 7-7xl0" 9 , 

 and 6'' = cxQ=3-6xlO- 18 . 



Phil. Mag. S. 6. Vol. 37. No. 220. April 1919. 2 H 



