On the Intimate Structure of Crystals. 295 



Professor Miers. The ratio of sine and cosine for this angle is 

 0'41 : 1*0, which gives the relation that should subsist by hypothesis 

 between the coefficient of expansion along the axes a and c at 

 15 C. Fizeau's observations fail us here, and I look forward 

 with interest to fresh determination^ of these constants, which 

 Mr. Tutton has kindly promised to make for me. It is now 

 possible to trace out the series of changes which silver iodide un- 

 dergoes as it falls in temperature from 150 downwards ; at 146 

 (Mallard and Chatelier) or 142 (Rodwell) it possesses cubic symmetry, 

 because the atoms of iodine are out of all proportion so much 

 larger than those of silver, that the latter cease to be operative as 

 elements in the crystalline structure ; the iodine atoms are arranged 

 to form cubes which we may picture to ourselves as rhombohedra 

 with an angle of 90 j every iodine atom is chemically united 

 with an atom of silver which depends from it into the central space 

 within a rhombohedron ; as the iodine atoms become smaller, with 

 loss of energy, this space becomes too small to contain the silver 

 atom which is consequently forced outwards or upwards ; as it passes 

 out of the rhombohedron of 90 the vertical parameter of the latter 

 is necessarily lengthened, while its horizontal parameters are 

 shortened ; the change in dimension of the vertical parameter, 

 which occurs as soon as the centre of the atom of silver begins to 

 move above the plane containing the centres of three surrounding 

 iodine atoms, is excessive as compared with that of the horizontal 

 parameter, but the difference is diminished by the diminishing ratio 

 between the diameters of the two different kinds of atoms ; at 15 the 

 difference of the two coefficients is probably nearly as 3 : 1 ; it will dimi- 

 nish rapidly with further cooling, and, before the atoms of silver assume 

 a position in which the radius vector drawn from them to the iodine 

 atoms, about which they revolve, makes an angle of 45 with the 

 parameter Oa, the expansion along the vertical axis will cease and 

 be replaced by contraction, unless, indeed, as this crisis is approached 

 the diameters of the atoms should fall within the ratio of 1 : 0*729, 

 when the crystal would once again become cubic. 



In the study of molecular volumes we hold the key which is 

 destined to unlock the secret of crystal structure so long concealed. 

 We shall eventually discover by its means, in connection with other 

 studies, the relative and absolute dimensions of all the elementary 

 atoms, and probably not only this but also their true forms for it 

 is possible that they are not all spheres. 



