316 BELL SYSTEM TECHNICAL JOURNAL 



Yet strange as it may seem, this failure of atomic masses to be 

 integer multiples of either the mass of H' or one-sixteenth-the-mass-of- 

 O^^ is no detriment to theory, but rather the reverse. There is a very 

 general hypothesis which may be phrased as follows: if a number of 

 elementary particles cling together in a stable cluster, the mass of 

 the cluster M is less than the sum 2w of the masses which the particles 

 would have if they were free, and the difference (Sm — M) is the 

 energy "of binding," the energy which would have to be given back 

 to the particles of the cluster to disperse them again into freedom. 

 I say "the difference of masses is energy," thus invoking Einstein's 

 principle of the equivalence of energy and mass. By this principle a 

 mass amounting to m grammes is an energy amounting to mc^ ergs 

 (c standing as usual for the speed of light in vacuo, 3- 10^") and an 

 energy amounting to E ergs is a mass of Ejc^ grammes, whether it be 

 kinetic energy or light or whatsoever other form.^ If a nucleus be a 

 cluster of, say, electrons and protons, then its mass must be less than 

 the sum of their separated masses, for otherwise it would have no 

 cohesion and would fall apart of itself; and its deficiency of mass is a 

 measure of its stability. 



At this point I ought to give some idea of the orders of magnitude 

 involved. Nothing has been said thus far about the mass in grammes 

 of any kind of atom, but we now require some such value in order to 

 make the translations between energy expressed in ergs or in electron- 

 volts, and mass expressed in terms of our standard one-sixteenth-of-0^^. 

 The masses of atoms in grammes are not known nearly so well as 

 their ratios to each other, but the three significant figures assured for 

 oxygen are sufficient for our purpose. The mass of the oxygen atom 

 is 2.64- 10~^^ g, and it follows that one million electron-volts of energy 

 amount to .00107 of one of our units of mass. Now the mass of the 

 electron is .00054; the mass of the proton is that of the H^ atom less 

 that of its orbital electron, or say 1.0072; the mass of the O^^ nucleus 

 is that of the O'^ atom less that of its eight orbital electrons, or say 

 15.9957. If we make the hypothesis that the O^^ nucleus is a cluster 

 of sixteen protons and eight electrons, the separate masses of these 

 twenty-four particles add up to 16.1195, and there is a discrepancy of 

 0.1238 units; but this is perhaps no real discrepancy, but simply the 

 energy which the twenty-four particles yielded up when they gathered 

 into the cluster, and which must be restored to them if they are ever 



' In the special case of a system of electrified particles acting on one another 

 strictly according to the laws of classical electrodynamics, the equivalence of mass m 

 and energy mc^ can be derived from these laws; i.e. it can be deduced that two 

 configurations of the system differing in energy by E differ in mass by Ejc^. How- 

 ever, such particles could not form a stable cluster; so that one is compelled to 

 postulate Einstein's general principle, after all. 



