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Prof. W. J. Sollas. 



we have imagined to exist in the case of common salt, already 

 described, for it can readily be shown, and will presently appear, 

 that the ratio of the volumes of the eight spheres forming a primi- 

 tive cubelet to the volume of the interstices continuously diminishes 

 as the spheres approach equality, or, more precisely, the total volume 

 of the cubelet, including interstices, is to the volume of the con- 

 tained spheres as 1*9099 : 1 when the spheres are all equal, and 

 diminishes from this down to a limit, of which we shall have more 

 to say presently, of 1*7125 when the two kinds of spheres have 

 attained the greatest possible degree of inequality consistent with 

 the arrangement assigned to them. 



Of the different possible modes of packing in the cubic system, 

 the one we have adopted is the only one that gives this result, 

 within the limits of difference in size which we are considering ; every 

 other kind of simple packing leads to an increase in the gross volume 

 when the two sets of constituent spheres depart from equality in dimen- 

 sions. There is but one exception to this statement, and this does 

 not affect our argument, as it is true of one particular ratio only, 

 and is not applicable to the haloid salts of the alkalies. 



Returning now to the imagined cubelet of common salt, we are 

 able to give a value to the diameter of the sodium atom it contains ; 

 thus, the gross volume of the sodium is 11-73, one-half of the gross 

 volume of sodium in the free state ; suppose eight atoms of sodium 

 built up into a cube in the same way that the four molecules of 

 sodium chloride were imagined to be built up, one sphere to each 

 corner of the cube, then the edge of the cube will be equal in length 

 to the sum of the diameters of two sodium atoms. Thus, the gross 

 volume of sodium 11' 73 X 8 = 93*84, the gross volume of eight atoms, 

 and V93*84 = 4' 5443, the length of the edge of the cube ; this 

 divided by 2 gives the diameter of a sodium atom as 2*2721.* But 

 the length of the edge of a cubelet of sodium chloride was found to 

 be 4*7623 ; deducting the diameter of a sodium atom from this, we 

 have 4*76232*2721 = 2*4902, the diameter of an atom of chlorine. 



Using the value found for the diameter of an atom of sodium as 

 a basis, we may proceed to treat all the haloid salts available for 

 examination in the same way as follows : 



Diameters of 

 atoms. 



LiCl 4*3433 



_C1 2*4902 



Li = 1*8531 



Diameters of 

 atoms. 



KC1 5*3216 



-01 2*4902 



K = 2*8314 



* This could of course be directly obtained from the gross volume, which might 

 be regarded as the cube circumscribing the sodium sphere ; but I am anxious to 

 preserve a parallelism in treating the salts and the elements. 



