Theory of Spectrum Emission. 57' 



of the approximate perturbation method is based thereupon).. 

 But how small or how large this fraction may be, is difficult 

 to say. If, for the moment, 2a is taken to be the diameter 

 of the nucleus, then for the few gases involved in Rutherford's 

 scattering experiments, a is certainly as small as 10 -11 or 

 10- 12 cm., that is to say, a of the order 10" 3 or lO" 4 *. But 

 for other elements, and especially for the heavy ones, a may 

 be much larger than this. Then, tc containing many units,. 

 7 may become quite a conspicuous fraction of unity. In 

 short, there is a wide range of values which y can assume. 

 If it is near its lower limit we shall still have a Balmer 

 series, although slightly shifted and with fine structure of its 

 members ; but if it mounts up, say to ~ or only ^, the very 

 type of the series may cease altogether to resemble the 

 Balmerian one. Within these wide limits, it would certainly 

 be useless to attempt to prejudice the value of a or of 7 for, 

 say, the atoms of copper or of iron. On the contrary, one 

 would have first to re-examine carefully and to try to- 

 disentangle the spectra of such elements and base the guesses 

 about the appropriate value of 7, and thence of a, upon the 

 observed features of their spectrum " series." 



Having thus dealt sufficiently (for the present state of our 

 knowledge) with the numerical aspect of the coefficient 7, 

 let us pay some attention to the equation (21) itself, together 

 with (21-2) and (21*3) . 



It may be well to write that equation in a form exhibiting 

 directly the ratio of a to the dimensions of the orbit, so as 

 to have before our eyes the assumption of its smallness, upon 

 which the validity of the equation rests. Such a form is 

 easily obtained when it is remembered that (21) is but the 

 developed form of 



W_«. 2 Rf F) 



eh ~ n 2 \ i+ W l 



Now, TF = *VW(1 — e 2 )/2p 2 , and, as in (18), 

 the symbol g(i, e), 



whence 



F K 2 e*m' 2 a?g 



W - p± • 1-e 2 ' 



* If, as Sir E. Rutherford is inclined to assume, the mass of the nucleus 

 (and therefore, practically, of the whole atom) is purely electromagnetic, 

 then, for k = 1 say, a would be about ^ 00 of the radius of an electron or 

 «=^10- Vj cm., and therefore, ot = ^.10- 8 . But such an assumption 

 is by no soeans necessary. There is, in fact, no evidence whatever for 

 the existence of pure positive charges. 



