CONTEMPORARY ADVANCES IN PHYSICS 319 



by much the largest) part of the procession they fall below their nearest 

 integers. There is a minimum or greatest-negative-value of the 

 difference {AI — A) near A = 110, and a minimum of the packing- 

 fraction near A = 60. It may seem paradoxical that the two minima 

 do not coincide, but the apparent paradox is easily understood. 



If all the packing-fractions were negative, and all the atomic masses 

 lay just below their nearest integers, we should infer that all the nuclei 

 consist of particles having one sixteenth the mass of O^^ when free, 

 and that all the differences (M — A) are losses of mass due to clustering 

 or packing. The policy of plotting packing-fractions is open to 

 criticism because it leads, or rather misleads, to that untenable idea — 

 untenable, because so many of the nuclei show positive values of 

 (M — A). One is obliged to argue that the protons and neutrons 

 which are presumably packed into nuclei undergo an average shrinkage 

 in mass from 1.008 or 1.007 to 1.000, and in addition an extra change 

 either positive or negative of which {M — A) /A is a sort of a measure. 

 This viewpoint has certain merits, but I think that the best thing to do 

 with a packing-fraction is to retrace the steps whereby it was originally 

 calculated, and thus obtain the mass of the atom in question, which 

 then may be compared with the masses of adjacent atoms, or those 

 of the elementary particles of which one supposes it built, or indeed 

 with anything else whatever. ^^ 



The sort of reasoning that then is possible can best be shown by 

 illustrations. 



We start with H^ nuclear mass 1.0072, and go ahead to H^, nuclear 

 mass (by Bainbridge's latest measurement) 2.0131. As Z = 1 for 

 this latter nucleus, it might conceivably be either a cluster of two 

 protons and an electron, or a proton and a neutron. Here the principle 

 of the interrelation of mass and energy may prove important: if for 

 either of these models the sum of the masses of the separated particles 

 should be smaller than 2.0131, it would be necessary to discard either 

 that model or the principle. There is no difficulty with the former 

 model, the sum being 2.0149. As for the latter, not even the indirect 

 estimates of the mass of the neutron are sufficiently close to permit 

 the test. One may turn the argument around and deduce that if it 

 is ever shown by other evidence that the H^ nucleus is a proton plus a 

 neutron, the mass of the latter when free must be more than 1.0058. 



Many a search has been made for nuclei of mass-number 3, but all 

 in vain ; the non-existence of such kernels may be as significant to the 



^2 The same remark goes for the so-called "mass-defect," which for a nucleus of 

 mass-number 4w -[- i (w = any integer, b = any integer less than 4) is computed by 

 adding the masses of n alpha-particles and b protons, and taking the difference 

 between their sum and the actual mass of the nucleus. 



