towards a Dynamical Theory of Solutions. 37 



dielectric capacities which form the conspicuous exceptions 

 to the law of! Maxwell. Let e be the charge of % and \>, and 

 let s be their distance apart in J|? which forms each of the 

 three bonds in (H 2 0) 3 or of the two in (H 2 0) 2 . On the 

 average the directions of the moments are uniformly distri- 

 buted, so that we may replace each in imagination by one of 

 electric moment es/2 at right angles to any electric intensity 

 X which is applied. The force on an electron is eX, which 

 is equivalent to a tractive force e'X/Aa 2 per un ; t area, if 8a 3 

 measures the share of space, or the domain, of £[>. If iv is 

 the rigidity of the molecule under this type of traction, each 

 average pair of moment es/2 has its axis sheared through an 

 angle d = e~K/±a 2 w, so each electron at distance s/± from the 

 centre of the pair is moved through a distance 0.s-/4 and the 

 electric moment produced by X is eds/4i equivalent to an 

 intensity of electrization eQs/32a?, which is often written kX. 

 with the relation iirk + l=K. Hence 



K-l=4ark=irfs/a2a*w. . . . (26) 



I shall apply this equation first to the case of ice with the 

 simplifying assumption that w is equal to the rigidity of ice 

 at its melting-point. In " The Molecular Constitution of 

 Water " it has been shown that the melting of ice is not an 

 ordinary melting at all, it is the sudden breaking down of 

 (H 2 0) 3 into a solution of (H 2 0) 3 in (H 2 0) 2 . It is reasonable 

 to assume then that the rigidity of ice at 0° C. is partly the 

 rigidity of each (H 2 0) 3 due to the bonds £[?, and may be 

 roughly taken for iv. The Young's modulus of ice was 

 found by Reusch acoustically to be 23632 kg. weight/cm. 2 , 

 and by Hess {Ann. d. Phys. viii. p. 405, 1902) on the average 

 2-54 xlO 10 c.G.s. So we assume 3w = 2«5 X 10 10 . If we 

 take 8a 3 as the sum of the values of H 2 and 0, namely 

 10- 24 (2-17 3 + 2*71 3 /2)and e=4'65x 10" 1 ; with K-l=80, 

 we get s/2a = 0'5, that is to say, that our simplifying assump- 

 tions make s of the order of magnitude of 2a the diameter 

 of H 2 0. This result shows that our general principle of 

 accounting for the large K of ice and water by the electric 

 moment es is probably sound. We expect 5 to be actually 

 only a fraction of 2a, a result which we should have obtained 

 if we had assumed w to be only a fraction of the rigidity of 

 ice, which is more likely to be true than our assumption that 

 id is equal to the rigidity of ice. As K is nearly the same in 

 water and in ice, we obtain the interesting result that on 

 account of the bonds $\) in (H 2 0) 3 and (H 2 0) 2 each molecule 

 of water has a rigidity of its own. 



We can carry the inquiry a step farther by treating the 



