Mechanism of Radiation. 437 



spherical surface. Writing A for -: — - ~^(v sin 61) + -yr? the 

 r ° sin 6 do v y d <£' 



tangential dilatation, we see that the two spectrum-series 

 corresponding to any single shell may be associated with the 

 most general distribution of u and A which is possible over 

 the surface of the shell in question. Combining the series 

 from all the shells, we find that we can now associate a free- 

 period with every degree of freedom implied in the possibility 

 of giving arbitrary values to u and A at every point of every 

 shell. The remaining degrees of freedom can be accounted 

 for by adding to the foregoing distribution of u and A a dis- 

 tribution of displacement for which u = and A = everywhere. 

 These are the tangential degrees of freedom of the first class, 

 for which p 2 = Q. 



Numerical Calculation of the Size of an Atom. 



§ 21. From equation (25) we can form an estimate of the 

 size of atom which would be required in order to give vibra- 

 tions comparable in frequency with those of light. 



As regards order of magnitude, we may take p 2 = 10 31 

 pj(T = ejm= +10 7 , /3 2 (l-f Ji) +(T 2 £ 2 = p 2 ; and these values sub- 

 stituted in (25) give p = 10' 23 , as regards order of magnitude. 

 The charge on a single negative ion is 6 x 10~ 10 , so that the 

 number of ions per cub. centim. is of the order of 2 x 10 32 . In 

 an atom of atomic weight n, the number of ions is of the order 

 of 10 3 m, so that the radius of the atom will be n%10~ 9 cm. 



The Spectrum of a Real Atom. 



§ 22. It will be convenient at this stage to examine to 

 what extent it is possible to deduce the spectrum of a real 

 atom (as we are imagining it to be) from the spectrum of the 

 ideal atom which has so far been the subject of investigation. 



Let us consider a real atom I consisting of a finite number 



of ions A, B, C We are going to compare this with 



an ideal atom I', consisting of a finite number of elements of 



volume A', B', C These elements can always be chosen 



(since the whole structure of I' is, up to the present, at our 

 disposal) so that the total charge in the element A' is all of 

 the same sign, and equal to the charge of the ion A. In this 

 case, since we shall suppose the ratio of the charge to the 

 mass to be numerically equal to the same constant for both 

 atoms, the mass of the element A' will be equal to the mass of 

 the ion A'. 



The position of the element A' is as yet undetermined ; but 

 the more closely the atom I approaches to spherical symmetry 

 of structure the more nearly will it be possible to arrange the 



Phil. Mag. S. 6. Vol. 2. No. 11. Nov. 1901. 2 G 



