November 2, 1917] 



SCIENCE 



423 



The corresponding mass of one particle is 



2 e" 

 ™' = 3c-^' 



where R is the radius of the electron ; so 



ato _ ZR 

 Ml d ' 



In the application of this last equation, 

 R is to be taken as the radius of the positive 

 electron, since it is assumed that it is the 

 seat of practically all of the mass of the 

 atom. In order to produce a decrease of 

 mass equal to 0.77 per cent., which is the 

 average decrease in weight as calculated 

 from the atomic weights, the two electrons 

 should approach until their distance is 400 

 times the radius of the positive electron. 

 Thus a packing effect of 0.77 per cent, 

 would be produced by a moderately close 

 packing of the electrons in the nucleus. 



The packing effect for oxygen, which has 

 been taken as the basis for our modern 

 atomic weights, is exactly equal to the aver- 

 age value given above. If the number rep- 

 resenting the atomic weight of hydrogen on 

 the oxj'gen basis, 1.0078 is decreased by 

 this percentage amount, it becomes equal to 

 1.000, so the oxygen system of atomic 

 weights may be considered as a hydrogen 

 system, with hydrogen taken as 1.000, but 

 where the weight of the hydrogen atom is 

 taken after it has been subjected to the 

 average packing effect of 0.77 per cent. 

 Thus in going over from the hydrogen to 

 the oxygen system of atomic weights, the 

 chemists who made the change were, with- 

 out knowing it, making allowance for the 

 average packing effect, for, while the 

 atomic weight of hj'-drogen is 1.0078, the 

 atoms heavier than hydrogen have atomic 

 weights which are near what they should 

 be if they were built up of units of weight 

 very close to 1.000. On the other hand, this 

 unit of mass must be somewhat variable to 

 give the atomic weights as tliej' are, even 

 although a part of the variation, in some 



cases, may be due to the inaccuracy with 

 which the atomic weights are known. This 

 leads either to the supposition (1) that the 

 atoms are built up of some unknown ele- 

 mentary substance, of an atomic weight 

 which is slightly variable, but is on the 

 average extremely close to 1.000, and which 

 does not in any case deviate very far from 

 this value, or to the idea (2) which is pre- 

 sented in this paper, that the nucleus of a 

 known element is the unit of structure. 

 The atom of this known element has a mass 

 which is close to that of the required unit, 

 and it has been proved that the decrease of 

 mass involved in the formation of a com- 

 plex atom from hydrogen units is in accord 

 with the electromagnetic theorJ^ The 

 adoption of the first hypothesis would in- 

 volve much more complicated relations. It 

 would necessitate the existence of another 

 elementary substance with an atomic 

 weight close to that of hydrogen, it would 

 involve a cause for the increase of weight 

 in the formation of some atoms, and a de- 

 crease in other cases, and it would also in- 

 volve the existence of another unit to give 

 the hydrogen atom. 



It may be well to consider here the proh- 

 aiility that the elements from helium to 

 cobalt, atomic numbers 2 to 27, may have 

 atomic weights as close to whole numbers 

 as they are on the oxygen basis, entirely by 

 accident. For example we may calculate 

 the chance that each of the atomic weights 

 should be as close as it is to a whole num- 

 ber, and we find that there is one chance in 

 five thousand billion billion. Another 

 probability is that the sum of the devia- 

 tions from whole numbers shall not exceed 

 the sum found experimentally. This gives 

 the result that there is one chance in fifteen 

 million. Thus, in the words of Laplace as 

 applied to a calculation of probability in 

 connection with an astronomical problem, 

 that the atoms are built up of units very 

 close to one, "est indiquee avec un pro- 



