Electrolytic Theory of Dielectrics. 469 



at right angles ; the number of lines passing across it from a 

 particle on either side being, on the average, one sixth of the 

 whole number emanating from that particle. If q be the 

 charge per particle, and d the distance from centre to centre 

 of adjacent particles, the average number of lines crossing the 



surface per sq. cm. = -r4 ; and the mechanical tension across 



it per sq. cm. is therefore approximately 



This quantity represents the cohesive force of the mass, and 

 is consequently equal to the internal pressure per sq. cm. of 

 the particles due to their heat-motions. 



Pairing of the particles will, however, reduce the cohesion ; 

 for it will strengthen some bonds at the expense of others, and 

 the cohesion depends on the strength of the weakest part. On 

 the other hand, the above formula is only accurate if the 

 closeness of the lines of force cutting the imaginary surface is 

 constant all over it. This will not be strictly the case ; and 

 want of uniformity will increase the cohesion, as the latter is 

 proportional to the mean square of the field strength, while 

 the calculated value is in terms of the square of the mean 

 field. These two causes of error thus tend to compensate — to 

 what extent it is impossible to say, but sufficiently, in all pro- 

 bability, to allow of a determination by the formula of the 

 order of magnitude of q. Applying it to the crystals already 

 discussed, we have therefore 



jL- ~ cohesion per sq. cm. = internal pressure per sq. cm. 



Now, of the value of the internal pressure in a solid it is only 

 possible to obtain the very roughest idea, by applying Boyle's 

 law and assuming that the unoccupied space in a solid is three 

 fourths its apparent volume. The volume of a substance in 

 the form of vapour is, on this assumption, about 1700 times 

 as great as the unoccupied space within it when in the solid 

 form ; from which the internal pressure comes out by Boyle's 

 law to be about 2 X 10 9 dynes per sq. cm. Of course this is 

 the merest approximation to the true value, but it serves as a 

 guide to a better determination in the following manner : — 

 When tension is applied to a rigid body, the internal pressure 

 along the line of pull is reduced, the sum of these two forces 

 (tension and pressure) being now balanced by the cohesion. 

 The maximum possible tension (i. e. the tenacity of the sub- 

 stance) must therefore be less than the internal pressure in the 



