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THE ROYAL SOCIETY OF CANADA 



radii of the various orbits have been assumed to be in the ratios of 

 P: 2^: 3^: 4^:, etc., neglecting any shrinkage of the rings due to the 

 repulsion of the electron rings, and, since the orbits are coplanar, the 

 total area of the electronic orbits of an atom can be readily evaluated 

 in terms of the radius of the innermost ring of electrons. But in 

 Langmuir's model the radii of the shells are supposed to be in the 

 ratios of 1:2:3:4, etc., and the arrangement of the electrons is spatial 

 about the nucleus. To allow for this the radii of the orbits of the 



various electrons have been assumed to be on the average ^= times 



V- 



the distance of the electron from the nucleus. This will be quite 

 accurate for those shells containing 8 electrons and approximately so 

 for those containing a larger number of electrons. The distribution 

 of the electrons in the various rings or shells of the two models is 

 indicated by the following table of the inert gases. 



The results of the calculations are compiled in Table III. There 

 are twenty-six diamagnetic elements which lend themselves to this 

 analysis. When once the radius of the innermost ring or shell of 

 electrons is known it is a simple matter to obtain the value of the 

 atomic radius, by multiplying by the proper factor, i.e., n^ in Bohr's 

 model or n in Langmuir's model, where n is the number of rings or 

 shells supposed to exist in the atom. In the last three columns are 

 given the data regarding the spacings of the atoms of the elements, as 

 derived from X-ray crystallographic measurements. The values in 

 the last column are those obtained by W. L. Bragg, from the analysis 

 of chemical compounds, and thus presumably denote the radius of the 

 ion. It will be noted that it is considerably less than the distance 

 between atoms, given in the preceding column, which was obtained 

 by analysis of crystals of the pure element. As regards the values 

 obtained from considerations of magnetism it will be seen that they 

 are of the right order in all cases and with many elements the agree- 

 ment is more than fair, especially in view of the fact that the measure- 

 ment of these feeble diamagnetic susceptibilities cannot pretend to the 

 accuracy of crystal analysis, and, moreover, an error of 1 per cent, 

 in k means a 12 per cent, error in the value of (1 — m)- 



