422 



SCIENCE 



[N. S. Vol. XLVI. No. 1192 



to he whole numbers. Though this is not 

 quite true, it is seen that the packing effect 

 for oxygen is 0.77 per cent., which is the 

 average packing effect for tlie twenty-one 

 elements considered (elements of low atomic 

 number). Therefore these elements, which 

 have packing effects equal to that of oxy- 

 gen, will have whole numbers for their 

 atomic weights. Since, too, the packing ef- 

 fect is very nearly constant, all of these 21 

 elements will have atomic weights close to 

 whole numbers. 



While according to our ordinary experi- 

 ence mass and weight seem to be additive, 

 the question may be raised whether in the 

 formation of atoms, which is a process 

 which is, up to the present time, outside 

 our experience, this is true. There are 

 three remarkable facts to be explained: 

 first, the atomic weights of the lighter ele- 

 ments on the hydrogen basis approximate 

 whole numbers ; second, the deviations 

 from whole numbers are negative, and 

 third, these deviations are practically con- 

 stant in magnitude. 



It has been already stated that accord- 

 ing to the work and calculations of Dar- 

 win, and of Geiger and Marsden, the nu- 

 cleus of the atom is extremely minute in 

 comparison with the size of the atom, so 

 that in the nucleus the mass, if the deter- 

 mined dimensions of atoms and their nu- 

 clei are at all correct, is many thousand 

 billion times more concentrated than in the 

 atom. If the nucleus is complex, the elec- 

 tromagnetic fields of the charged particles 

 would be extremely closely intermingled in 

 the nucleus, and it would seem reasonable 

 to assume that this would affect the mass, 

 so that the mass of the whole nucleus would 

 not be equal to the sum of the masses of its 

 parts. 



Let us take an extremely simple case for 

 calculation, and find how closely packed 

 the charged particles in a nucleus would 

 have to be to cause the observed decrease in 



weight (0.77 per cent.) which is found for 

 most of the atoms. In making such a cal- 

 culation, as a guide for our assumptions, 

 we have the observed fact that radioactive 

 atoms shoot out both positively charged 

 alpha particles and negative electrons at 

 such high speeds that it seems probable 

 that they come from the nucleus of the 

 atom. The observed relations between the 

 products of the radioactive changes sup- 

 port this idea very strongly indeed. Thus 

 there seem to emerge from the nuclei of 

 complex atoms both positively and nega- 

 tively charged particles, and the negatively 

 charged particles are found to be negative 

 electrons. This point should be empha- 

 sized, since many workers on atomic theory 

 have endeavored to construct their imagi- 

 nary nucleus of positively charged par- 

 ticles alone. 



The simplest case for calculation^ would 

 then be for a nucleus consisting of one 

 positive and one negative particle. Let the 

 distance between the particles be d, the 

 charges respectively e^ and e„, let the ve- 

 locity of the particles be along the straight 

 line connecting them and equal to u. Then 

 if c is the velocity of light, the particles 

 have a longitudinal momentum which dif- 

 fers from the momentum calculated by 

 ordinary mechanics for electrically neutral 

 particles possessing mass by an amount 

 equal to 



" c2 ■ d ■ 



This may be called the mutual electromag- 

 netic momentum of such a system of par- 

 ticles. The mutual electromagnetic mass 

 corresponding to this is 



A?ni = 



2 6162 



2 e^ 



since e\ =6%. 



2 For this calculation see the following papers by 

 Harkins and Wilson: Proo. Nat. Acad. Sciences, 1, 

 277-78 (1915) ; /. Am. Chem. Soc, 37, 1373-78 

 (1915), and Phil. Mag., 30, 725-28 (1915). 



