﻿912 Mr. C. GL Darwin : A Theory of the 



each substance a row is devoted to the parameter (for 

 particles from RaO). In some cases it appears very small, 

 but this is implicit in the experiments, which show a great 

 difference in the characters of the various velocity curves. 

 In the case of hydrogen (9) is insoluble for the two larger 

 values of a. This means that with these values the relation 

 between the air velocity curve and that of hydrogen is such 

 that the latter is a more abrupt curve than would be one 

 with an infinite parameter. The first part of the table gives 

 the data used for the solutions. In addition to the atomic 

 constants a and w, I also calculated for comparison with 

 experiment the equivalent of the film at a third velocity. 

 Within narrow limits this came out the same for all six 

 columns, which means that an enormous change must be 

 made in a before any appears in Ax z . This shows that 

 it would be impossible to get measurements of sufficient 

 accuracy to determine the radius of the air atom in addition 

 to the other constants, the theoretical possibility of which is 

 indicated above. 



The table shows that n is proportional to the atomic weight 

 for the heavier substances. Hydrogen is in conformity with 

 this, when the solution exists. It is clear, however, from 

 the great difference between a for surface and a for volume 

 distribution (which, when there is only one electron in the 

 system, cannot correspond to any very great physical dif- 

 ference) that our analysis cannot be regarded as holding for 

 systems containing a very small number of electrons. It is 

 probably the assumption that the a. particle exerts no force 

 except when inside a sphere round the centre, which breaks 

 down. Since the result with regard to a is certainly unsatis- 

 factory, it is very doubtful how much significance is to be 

 attached to the value for n. The absence of the hydrogen 

 solution for larger values of a- for air may also be due to the 

 inapplicability of our analysis to the case of a very small 

 number of electrons. If this larger value of a for air is 

 adopted, then for air and the metals n will be about half the 

 atomic weight and hydrogen will be exceptional ; if the 

 small value of a be taken, then n will be equal to the atomic 

 weight and hydrogen (as far as the analysis is to be trusted 

 for it) will be regular. In this case helium will be excep- 

 tional, for the whole hypothesis depends on the assumption 

 that for it n = 2. Great importance thus attaches to the case 

 of helium, because there is only one adjustable constant cr 

 instead of two, a and n. Unfortunately no measurements of 

 equivalence have been made, but only a determination of the 

 whole range *. If the value found for this be put in (7) 

 * E. P. Adams, Physical Review, vol. xxiv. p. 108 (1907). 



