December 7, 1917] 



SCIENCE 



569 



atomic weights against square roots of atomic 

 weights. Although the values for successive 

 elements vary somewhat irregularly, if aver- 

 ages are taken for successive groups of ten or 

 twelve elements each it appears that there ex- 

 ists an approximate general linear relation of 

 the form 



==0.520 — 0.0088VTF. 

 W 



(1) 



N is the atomic numher, and W is the atomic 

 weight. The average deviation in N/W from 

 this straight line, regardless of sign, is 0.008. 

 Hydrogen alone was not included in this aver- 

 age. 



The relation between N/W and any other 

 power of Wj such as WJ or TFa, is not so nearly 

 linear. Furthermore, if values of N/W are 

 plotted against V W for the odd-numbered and 

 even-numbered elements separately, it is found 

 that a number of curious and nearly exact 

 linear relations exist. Unless these are acci- 

 dental, equation 1 must express no mere em- 

 pirical relation, but an actual tendency of 

 atoms. 



If atoms have the structure called for by 

 Rutherford's theory, equation 1 must repre- 

 sent a property of the atomic nucleus. If the 

 nucleus is built up of positive and negative 

 electrons, equation 1 can be accounted for if it 

 has a surface shell of positive charge and a vol- 

 ume distribution of negative charge. The 

 values of the coefficients in (1) seem to indi- 

 cate that the negative electrons in the nucleus 

 are packed together like solid spheres; to each 

 negative electron on the surface of the nucleus 

 two positive electrons are attached, on the 

 average. (A positive electron is very much 

 smaller, and hence much more massive, than 

 a negative electron. This is a common as- 

 sumption in electron theory.) If the number 

 of positive electrons (hydrogen nuclei) in the 

 nucleus is p, and if p is numerically equal to 

 Wj then n, the number of negative electrons in 

 the nucleus, is 0.4S0 17 + 0.0088 W,. (It was 

 this three to two ratio of the exponents of W 

 that suggested the assumed structure of the 

 nucleus.) The first term in the equation just 

 given may be supposed to equal the number of 



negative electrons in the surface layer of the 

 nucleus; then the second term is the number 

 of negative electrons crowded inside. The lat- 

 ter are held together by the external positive 

 shell; it is assumed that this shell tends to 

 contract, perhaps under electromagnetic forces. 



In very heavy atoms the number of negative 

 electrons inside the nucleus is so large that 

 they can not be held together by the positive 

 contractile shell against their mutual repul- 

 sions. Hence there is an upper limit to atomic 

 weights, and immediately below this limit 

 atoms are unstable. 



The nucleus-model described also is capable 

 of illustrating isotopism. Those elements 

 which have atomic weights not whole numbers 

 may, as has been suggested by Harkins and 

 Wilson,! each be a group of isotopes — in which 

 case their atomic weights are averages. (This 

 suggestion was first made by Soddy.) For 

 those atomic weights at which the number of 

 negative electrons inside the nucleus increases 

 by unity one might expect that two stable sys- 

 tems could exist. Such atomic weights, as 

 calculated by the equation for n given above, 

 are 23, 37, 49, 59 ; for these values the number 

 of negative electrons inside the nucleus is 1, 

 2, 3, 4, respectively. These values of W, then, 

 should be critical values near which isotopes 

 can exist most readily. It is at least interest- 

 ing to note that, of the four atomic weights 

 less than 60 which differ from integers by more 

 than 0.16, the values of three are 24.32, 35.46, 

 58.68 (Mg, CI, ISTi), while Si = 28.3. It is 

 known, moreover, that isotopes occur at neon, 

 with atomic weights 20 and 22. 



The atomic weights of elements heavier than 

 nickel show no tendency to approximate to 

 whole numbers, according to Harkins and Wil- 

 son. This is to be expected; because for those 

 elements the number of negative electrons in- 

 side the nucleus increases more rapidly with 

 the atomic weight, so that almost every heavy 

 element is near a " critical " value of W. 



JoHx Q. Stewart 

 Palmer Physical Laboratory, 

 Princeton University 



1 Harkins and Wilson, J. Am. Chem. Soc, 

 XXXVII., pp. 1383-1396, 1915. 



