Pyro-electricity and Piczo- electricity of Crystals. 457 



springs are specially designed and constructed to annul this 

 effect. 



§ 9. Solve now the electrical problem of finding the change 

 of electric moment of each molecule of the homogeneous 

 assemblage, produced by the change of configuration de- 

 scribed in § 8, when the potential is zero throughout the 

 surface-layer. To avoid tampering with the separate insula- 

 tion of all or any of the molecules, and to conform our ideas 

 to the realities of experiments on the electric properties of 

 crystals, I suppose this equality of potential to be produced 

 not by temporary metallic connexion between the molecules 

 as in § 3 (2), but by a metal coat enclosing our model, and 

 having its inner surface everywhere very near to the 

 boundary of the assemblage; for example, everywhere 

 within a distance of less than 2h or 2>h in our model, or of 

 less than 10 R x h if we are dealing w r ith a real crystal in a real 

 experiment. 



§ 10. To find experimentally the solution of the mathe- 

 matical problem of § 9, divide the metal coat into two parts ; 

 one of them (corresponding to Coulomb's " proof-plane ") 

 we shall call for brevity E. It may be either so small that 

 it is sensibly plane, or it may be a portion of the coat 

 covering a finite plane part of the boundary of the assem- 

 blage. Commence now with the crystal in its natural 

 undisturbed state, and having the metal coat on it with E 

 insulated from the rest of the coat. Produce a change of 

 configuration as in § 8 ; and then measure how much 

 electricity would need to pass from E to the rest of the coat 

 to equalize the potential between them. This is wholly and 

 exactly what MM. Curie do in their admirably designed 

 measurement with their " quartz piezo-electrique," avoiding 

 all need for consideration of the essentially transcendent 

 problem of the distribution of electric potential at the surface 

 of an uncoated crystal when there is either pyro-electric or 

 piezo-electric disturbance of its interior. 



The quantity of electricity thus measured, divided by the 

 area of E, is equal to the component perpendicular to E of 

 the interior electro-polarization when E and the rest of the 

 coat are metallically connected. 



§11. In conclusion, following Voigt in his Allgemeine 

 Theorie, already referred to, we see' that there are essentially 

 18 independent coefficients for the piezo-electricity of a 

 crystal in general ; in three formulas expressing the three 

 components of the electric moment per unit of its volume 

 each as a linear function of the six components of the geo- 

 metrical strain of the substance. To each of these expressions 

 I add a term for the component of the electric moment due 



