60 THE ROYAL SOCIETY OF CANADA 



It is interesting to make a comparison of the values obtained from 

 various considerations for the radii of atoms. Richards^ has shown 

 that the assumption of definite spherical atoms gives consistent results 

 for the compressibilities of substances. This has led him to a cal- 

 culation* of the size of the alkali and halogen atoms, making use of 

 data on compressibility and contraction during chemical combination. 

 These values for the halogens are given in Table IV. 



Rankine^ has built up theoretical models from which he has been 

 able to calculate the atomic dimensions from viscosity measurements. 

 Thus with chlorine he constructs a molecule by combining two argon 

 atoms with centres 2 . 05 A.U. apart, as found for chlorine by Bragg 

 from X-ray measurements. The theoretical viscosity of this molecule 

 agrees qwantitatively with the measured viscosity of chlorine. By a 

 similar process with the other halogens he is able to deduce that the 

 diameters of the atoms of the alkali metals and the halogens may be 

 assumed to be the same as those of the atoms of the nearest inert 

 gases, as obtained from viscosity measurements. 



Born and Lande"' have been able, by mathematical studies, to 

 determine the dimensions of lattices of positive and negative ions, 

 such as sodium and chlorine, held together by electrostatic forces. 

 In this way they have developed a theory of atomic structure which 

 gives the proper value of the compressibility of the salts. Bohr's 

 theory of coplanar orbits gives a structure for the salt with twice the 

 proper value of the compressibility. Lande is able to calculate the 

 diameters of some atoms and his values for the halogens are included 

 in Table IV. 



Finally, W. L. Bragg' ^ has made a careful and thorough analysis 

 of the data obtained by different experimenters by X-ray analysis 

 of different substances. His conclusion is that the experimental 

 values can be well represented by assuming the atoms to be spheres 

 of definite diameter, packed closely together. Bragg's values and 

 Davey's'^ are also in Table IV. 



It will be seen that the agreement among the values is remark- 

 able, especially in view of the many different methods and hypotheses 

 involved in their calculation. The author's results for the halogens, 

 which were, no doubt, purer and freer from iron impurity than the 



^Richards, Jl. Amer. Chem. Soc. 36, 2417, 1914. 

 «Richards, Jl. Amer. Chem. Soc. 43, July, 1921. 

 sRankine, Proc. Roy. Soc, Feb., 1921. 

 "Born and Lande, Zeits. f. Physik, 1, 191, 1920. 

 "Bragg, W. L., Phil. Mag. 40, 169, 1920. 

 '2Davey, Phys. Rev. 18, 102, 1921. 



