On the Calculation of Series in Spectra. 563 



gold atoms deduced by Sir Ernest Rutherford from the 

 scattering of the a rays. 



The difficulties of this hypothesis of the mechanism of 

 radioactive transformations are obvious. The chief of them 

 is probably the question as to where the energy of the 

 80 positive particles comes from, which changes from 

 element to element as the substance disintegrates. This 

 difficulty arises of course, perhaps in a slightly milder form, 

 in any theory of radioactive transformations. On the other 

 hand, the 80 independent factors seem almost unavoidable 

 for X is undoubtedly determined by a question of probability, 

 and experiments show it to be of the form E 80 . In view of 

 the further numerical agreement with Sir Ernest Rutherford's 

 measurements of the diameter of the nucleus, it would seem 

 most desirable to re-examine the original formulae of Geiger 

 and Nuttall, and to attempt to extend them to elements which 

 emit f$ particles. 



Conclusions. 



It is shown that the well known formula connecting the 

 life and the range of radioactive elements may be developed 

 from a few simple and plausible assumptions. 



It follows that the explosion of an atom necessitates the 

 fortuitous coincidence of some 80 independent events. A 

 calculation of the radius of the nuclei of radioactive atoms 

 on the above assumptions leads to a value of the order 

 3'9 . 10~ 13 , in fair agreement with the accepted dimensions. 



Farnborough, 



Julv 4th. 1915. 



LVIII. On the Calculation of Series in Spectra. 

 By H. G. Savidge and Prof. J. W. Nicholson*. 



SERIES in spectra are usually isolated by the spectro- 

 scopist as the result of a preliminary search throughout 

 the spectra for pairs and trios of lines whose distances apart, 

 when expressed in wave numbers, are constant. If such 

 trios or pairs can be found, there is usually a probability that 

 they are successive members of two interlacing series, one 

 of the diffuse and one of the sharp type, whose calculated 

 limits should be identical. But in practice, spurious doublets 

 and triplets — the result of chance — find their way into the 

 list, and cause the necessary calculations to be very long and 

 tedious. For in order to determine whether three lines are 

 * Communicated bv the Authors. 

 202 



