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Pyro-electricity and Piezo- electricity of Crystals. 455 



parts of the surface S. This function is the same for cor- 

 responding points of all the molecules. 



Let Y n be the potential at the copper of the molecule num- 

 bered n. 



Let D(P t , P ) be the distance between a point P^ on the 

 molecule numbered ?', and a point P n on the molecule num- 

 bered n. 



Let ^\ds i denote integration over the surface of molecule i, 

 and p. a function of the position of P. on the surface of this 

 molecule ; (the electric density at P 4 ). 



Let 2. denote summation for all the molecules, including 

 the case i — n. 



Let q n be the total quantity of electricity on molecule ??. 



The equation of electric equilibrium is 



D^Tj = /(P » )+V » • • • {a) ' 

 and we have 



It is required to find 



(1) V n , when g n = 0, for every value of n ; 

 and (2) q n , when V tt =0, „ „ 



§ 5. The problem thus proposed is of a highly transcen- 

 dental character, unless the surface S is spherical. In this 

 case it can be solved for any finite number of molecules by 

 mere expenditure of labour ; perhaps the work of the natural 

 working-life of a competent mathematician, if the assemblage 

 is a Bravais parallelepiped of 125 globes in 5 "reseaux" of 

 25 globes each, would suffice to give the solution for each 

 item within one per cent, of accuracy ; and not much more 

 labour would be needed to solve the problem to the same 

 degree of accuracy for each of 125 x 10 21 spherical molecules 

 in a similar Bravais parallelepiped of 5 x 10 7 u reseaux/' if 

 the distance (h we shall call it) between the planes of cor- 

 responding, points of two consecutive " reseaux " of nearest 

 and next-nearest molecules is not greater than about twice 

 the diameter of each molecule. 



§ 6. When this last condition is fulfilled, we can see, from 

 general knowledge of the doctrine of electric screening, 

 without solving the problem as proposed for every individual 

 molecule, that the solution of the second part (2) of the 

 requirements is ^==0, very approximately for every molecule 

 at any distance exceeding two or three times h from every 



