18 Mr. William Sutherland on the 



to solids in which the molecules are monatomic or composed 

 of equal atoms, as in the case of the elements, all the atoms 

 being treated as separate spheres. The corresponding equation 

 for compound solids is sketched in section 9 of the " Kinetic 

 Theory of Solids " (Phil. Mag. ser. 5, xxxii. p. 550), but in a 

 form which is not correct unless a strained interpretation is 

 put on certain symbols ; but we can easily establish the 

 correct form now. There would be no need to establish a 

 separate form of equation for solid compounds if we knew 

 that the molecules move as wholes ; but, on the contrary, we 

 have evidence that the atoms in the molecule move almost 

 independently of one another, for according to Joule and 

 Kopp's law the molecular specific heat of solid compounds is 

 the sum of the atomic specific heats of the atoms in the mole- 

 cule. In a certain sense a solid compound is like a mechanical 

 mixture of its atoms : in the act of combining the atoms have 

 produced mutual changes in their sizes and attracting-power 

 and other properties, and the solid is like a mechanical mixture 

 of these changed atoms. Now in the establishment of equa- 

 tion (3) for elements, the first term 2D/3e 2 {e — E) is calculated 

 as the collisional pressure per unit surface, that is the force 

 transmitted across that surface by the collisions of molecules, 

 or rather atoms, of diameter E, average distance e from next 

 neighbour, and kinetic enegy D, while the term £?'</>(?') /6<? 3 

 is the resultant attraction which equilibrates this collisional 

 pressure. Let N be the number of atoms in unit volume, 

 then e 3 =l/N, and the collisional pressure can be written 

 2DN/3(1 — E/e). Now if we have N molecules of a compound 

 solid in unit volume, and if each molecule contains n\ atoms 

 of an element A 1? n 2 atoms of an element A 2 , and so on, then 

 the collisional pressure due to the n x atoms of A x in unit 

 volume is , m 1 u 1 2 Nw 1 /3(l — Ej/^j), and similarly for the other 

 atoms, the total collisional pressure being their sum, so that 

 we have the equation 



N/ n 1 m l v x 2 n 2 m 2 v 2 2 \ U ... /1m 



denoting the mean distance of two neighbour molecules from 

 one another by e : thus we get for a compound solid free 

 from external force the equation 



We cannot assign the values of 1 — E^ for atoms in com- 

 pounds in the present state of our knowledge ; but as it was 

 shown that for the metals 1 — E/<?=7&0, where b is the 

 coefficient of linear expansion and 6 the absolute temperature, 



