Electrolytic Theory of Dielectrics. 465 



great alterations long before the molecules were brought into 

 contact. Nevertheless, the following considerations seem to 

 me to render it probable that if M and k are represented by 

 their normal measured values in the above expression, the 

 resulting number will not be hopelessly different from what 

 it ought to be. 



T is small compared with 0'4 M, as M is almost certainly 

 larger than_ the measured value of M. The expression 

 (0'4 M + T)& therefore reduces itself practically to the inte- 

 gral of the product M.k with alterations in length of the 

 crystal between the limits and 04 cm. Now M and k are, 

 from their nature, closely connected (if the chain hypothesis 

 be true). Whatever alteration one undergoes, the other must 

 undergo a similar one and in the opposite sense. If, for in- 

 stance, at high pressures M increases, it will be due to the 

 fact that the molecules resist being brought together more 

 than they do at low pressures ; but this is only another way 

 of saying that they are more reluctant to impair at high than 

 at low pressures : in other words, that the value of h has di- 

 minished, and to an extent which is roughly comparable with 

 the increase of M. The variations of M and k thus tend to 

 compensate each other, and it therefore follows that the varia- 

 tions in the value of their product will be small compared with 

 those of either factor separately, and that the assumption that 

 Mk is constant over a wide range is probably not very far 

 from the truth. 



Mallock * gives the value of M for tourmaline parallel to 

 the axis as 1*3 x 10 12 C.Gr.S. Hence we may write 



(0-4M+T)£<s 2-8xl0 4 <p. 



As regards the value of n one can only assume that the chains 

 are close together ; i. e. that 



71 = (|xlO- 8 ) 2 = 4zX 1016, 



It is quite possible, and even likely, that the true value is less 



than this, but it cannot be much greater. 



Putting these quantities into the equation for q, we obtain 



for tourmaline, 



>2x2*8xl0 in i9 TTi ci 



<1 = a — -.mft > i'4 x 10" 12 E.S. 



* <4 x 10 lb 



For quartz, q > 1-0 X 10~ 12 E.S. 



The most probable value of the ionic charge of oxygen is 

 10- 11 E.S. 



* Proc. Roy. Soc. xlix. p. 398. 



