Piezo-eleciric Property of Quartz. 337 



potentials in air, beside a polished surface of zinc and an 

 oxidized surface of copper, is about '004 of a C.G.S. electro- 

 static unit, provided trie zinc and copper are metallically 

 connected. Hence, if « be the radius of each spherule, we 

 have approximately q = '002 Xu ; because we shall suppose 

 for simplicity that, except the infinitely thin ring on which 

 it is movable, no spherule has any metal within a distance 

 from it of less than two or three times its diameter. Let 

 now N = 10 21 per cubic centimetre ; and let b be a quarter 

 of N~i, that is to say, 5 = |x 10~ 7 of a centimetre. Lastly, 

 to give definiteness to our example, let a = # 2x6. Equa- 

 tion (1) becomes 



fji=86Q$ (2). 



§ 10. From the admirable statement of Messrs. Curie of the 

 result of their measurements quoted in the Appendix of the 

 present paper, I find that a stretching force of 1 kilogramme 

 per square centimetre, in their experiment described in § 2 

 above, produces an electric moment of *063 C.G.S. electrostatic 

 reckoning per cubic centimetre of the crystal. Thus about 

 h of a C.G.S. unit of electric moment per cubic centimetre is 

 produced by 5 kilogrammes per square centimetre of stretching 

 force ; and this, according to equation (2), requires S to be 

 1/2598, which is an amount of change of direction among 

 atoms quite such as might be expected in pieces of crystal 

 stretched by forces well within the limits of their strength. 

 A rough mechanical illustration of the theory of electric 

 atoms to account for the piezo-electric properties of crystals, 

 is presented in an electrically working model of a piezo- 

 electric pile, submitted to Section A in a separate communi- 

 cation at the present meeting of the British Association. 



§ 11. I shall now prove, without any hypothetical assump- 

 tion, the statement at the end of § 3 above. Consider 

 first a simple elongation perpendicular to one of the three 

 pairs of parallel sides of the hexagon in fig. 3, as indicated by 

 the arrow-heads, AAAAAA, in fig. 3. Superimpose now 

 two equal negative elongations, one of them in the direction 

 of the original elongation, and the other in a direction per- 

 pendicular to it. These negative elongations, indicated by 

 the twelve arrow-heads marked C, constitute a condensation 

 equal in all directions ; which produces no change on the 

 electrical effect of the first simple elongation. But it leaves 

 us with a simple negative elongation in the direction perpen- 

 dicular to that of the original positive elongation ; which 

 therefore alone produces the same effect as that which was 

 produced by the original one alone. Thus we see that if 



