On the Intimate Structure of Crystals. 279 



It will be observed that in every case the ratio is smaller the greater 

 the difference between the size of the component atoms. 



It may next be pointed out that there exists a very important 

 limitation to our power of arranging pairs of atoms or diatomic 

 molecules in the manner we have suggested ; the two atoms of the 

 molecule may be equal in size, or they may be unequal, so long as the 

 inequality does not exceed the value of 1 : 0*7286.* 



I owe to the kindness of Professor Miers the following method of 

 finding the value of this limit. Let the centres of the spheres 

 be referred to three edges of the cube, meeting at one corner, as 

 the axes x, y, and z. The coordinates for the centre (Ci) of the 

 larger sphere are A B, B, B, and for the centre C 2 of the smaller 

 sphere r, r, r. Then 



(CA) 3 = (A-B-r) 2 +2(B-r) 2 . 

 In the limiting case, when the two larger spheres are in contact, 



A = B(2+ v / 2), 



.*. (CA) 2 = B 2 (5 + 2 v /2)-2Br(3+ v /2)3r 2 . 

 Also (CA) 2 = (B + r) 2 , 



.*. B 3 (4 + 2 v /2)-2Br(4+-v/2)+2r 8 = 0. 



BV B 5'4142 1 



=2-. 1 = 0. 



rj r 6'8284 3'4142 



.'. B/r = 0-7929 d=\/0-3358 = 1*3724 = l-*-0'72865. 



When the smaller spheres fall below the limiting value 0'729 the 

 tangent planes to the spheres no longer define a cube, but a figure 

 which is a hemimorphic form of the rhombohedral or hexagonal 

 system ; and in all cases that I have yet examined of diatomic salts, 

 belonging to a homologous series crystallising in the cubic system 

 with cubic cleavage, I find that directly one of the atomic volumes 

 falls below this limit the salt passes out of the cubic system and 

 presents itself under hemimorphic hexagonal forms. This is the case 

 with silver iodide, which is fully discussed in the second part of this 

 communication. That the substances to which we have at present 

 restricted our attention consist of pairs of atoms which lie within 

 the prescribed limit is shown by the following table, in which the 

 ratios of the diameters are 



* If the centres of the spheres be situated on the nodes of a cubic lattice, the 

 value of this limit will be changed. 



