CONTEMPORARY ADVANCES IN PHYSICS 327 



divisible by four. There is evident, in Fig. 6, a relative scantiness 

 of atoms for which (A — Z) is, or would be, odd; this would be even 

 more obvious if the dots, instead of being all alike, were proportioned 

 in size to the relative abundances of the isotopes within the elements. 

 It seems unlikely that in the inaccessible parts of the earth and the 

 stars these atoms should be so over-abundant as to restore the balance. 

 Except for this unlikely possibility, we must infer that nuclei for which 

 (A — Z) is odd are not easily formed or else that they break up easily. 

 Such nuclei, if imagined as clusters of protons and electrons, would 

 have odd numbers of electrons; if imagined as clusters of protons and 

 neutrons, they would have odd numbers of neutrons. 



In comparing the relative abundances of the different isotopes of a 

 single element, one feels on surer ground. It is a general rule (violated 

 only by the radio-active elements, their end-products, possibly a few 

 others) that these quantities are the same for every sample of a given 

 element, wherever out of the earth's crust or even out of meteorites it 

 may have been taken. It looks then as though the mixing of the 

 isotopes within each element had been pretty thoroughly accomplished 

 in the beginning of time, and as though the ratios of their relative 

 amounts might have universal value. 



Mostly the ratios are deduced from the darkness of the spots which 

 the isotopes imprint upon mass-spectrum plates. The difficulties of 

 inferring from the aspect of a spot the number of the particles which 

 made it are like those which occur in photography, and are overcome 

 in much the same way. The charges being exactly and the masses 

 nearly the same for the isotopes of a heavy element, one may pretty 

 safely suppose that equal numbers of atoms of such isotopes produce 

 equal effects; but with very light elements this is not so sure. In 

 occasional experiments the total charge which the ionized atoms bring 

 with them is measured, and this is in principle the neater method. It 

 may be carried out acceptably with apparatus not designed for making 

 exceptionally accurate measurements of mass. Bleakney has em- 

 ployed it with hydrogen and neon. 



About a couple of hundred abundance-ratios of isotopes in individual 

 elements have now been measured, mostly by Aston. No rule has 

 so far emerged from all these data, excepting the partial one about 

 elements of odd atomic numbers which I cited earlier. There has, 

 however, been a useful and entertaining set of by-products, in the 

 form of revisions of the standard values of the chemical atomic weights. 

 Obviously "physical" values for these can be obtained, if one can 

 measure the masses and the relative abundances of all the isotopes. 

 The highest attainable accuracy of this scheme in the most favorable 



