involved in the Formation of Complex Atoms. 125 



as before, and the production of helium in radioactive 

 changes also remains unexplained. 



In a paper presented to the National Academy of Sciences 

 on February 25, 1915 *, the authors gave the outline of a 

 system for the structure of the elements which explains 

 these facts, and which is based upon the atomic weights 

 of the elements and the well established electromagnetic 

 theories of mass and energy. If the atomic weight of 

 hydrogen is taken as 1*0078, and this number is multiplied 

 by 4 for helium, 12 for carbon, 16 for oxygen, and so on 

 for the first 27 elements in the periodic table, the average 

 percentage deviation of the determined atomic weights from 

 these numbers is —0*77. Of these 27 elements, six show 

 a difference of exactly 0'77 per cent. To account for the 

 closeness of the atomic weights to whole numbers, the 

 simplest procedure is to consider that they are made up of 

 hydrogen, but it is evident that this deviation of —0*77 

 per cent, must be accounted for in some way. That is, if 

 helium is made up of four hydrogen atoms, in its formation 

 there must have been a decrease in mass equal to 0'77 

 per cent. 



If mass is considered to be electromagnetic, it may be 

 expressed as a function of the total energy of the system. 

 Any change in the energy of a system would cause a change 

 in its mass. 



Changes in energy might be due to either a change in the 

 kinetic energy of the system, or in the potential energy. 

 While there might be changes in the velocity of the various 

 particles in the formation of one helium atom from four of 

 hydrogen, it seems unlikely that the resultant change in 

 energy would be very great, since practically all of the mass 

 is in the nuclei ; and while in all of the recent theories of 

 the structure of the elements it has been considered that 

 the negative electrons are moving with high velocities, the 

 nuclei are supposed to either be stationary with respect to 

 the atom as a whole, or at least to have only a relatively 

 small motion. In regard to the potential energy, it has 

 been known for some time that the total energy of a svstem 

 of charged particles is not equal to the sum of the energies 

 of its parts if the particles are close enough together so that 

 their fields overlap. The magnitude and sign of this 

 "packing effect" were calculated in the paper mentioned 

 above. The following is a brief summary of the method, 



* Proc. Nat. Acad. Sciences, i. p. 276 ; J. Amer. Chem. Soc. xxxvii. 

 p. 1367. 



