458 Pyro-electricity and Piezo-electricity of Crystals. 



to change of temperature when force acting on the surface 

 prevents change of volume or shape. Thus we have in all 

 21 independent coefficients for piezo-electricity and pyro- 

 electricity ; to be determined for a real crystal by observation. 

 It is interesting to see how our model can be constructed to 

 realize the piezo-electric and pyro-electric phenomena in 

 accordance with any given values of these 21 coefficients, by 

 experimental solution of as much of the mathematical problem 

 of § 4 as is necessary for the purpose. 



§ 12. Choose any convenient shape, spherical or not wildly 

 different from spherical, for each molecule. Divide the 

 whole surface into 22 parts (not wildly unequal nor extrava- 

 gantly different from squares or equilateral equi-angular 

 hexagons), and number them 0, 1, 2, .... 2 1 . Construct a 

 trial molecule with part always of copper ; and with, for 



first trial, part 1 of zinc, and parts 2,3, 21 of copper, 



Take a large number of such molecules and make of them a 

 Bravais homogeneous assemblage with any arbitrarily chosen 

 values for the six edges of the fundamental acute-angled 

 tetrahedrons. Connect the molecules homogeneously by 

 springs of non-conducting material in the manner described 

 in § 2 above. To provide fully for pyro-electricity, without 

 hypothesis, we must now take care that these springs are 

 such, that when the temperature is changed, and the border 

 molecules are held fixed, all the interior molecules shall be 

 caused to rotate round parallel axes through equal angles 

 proportional to the difference of temperature. For this 

 purpose the springs must be of two or more different 

 materials ; and when set in their proper positions between 

 the molecules they must be under stress, some of them 

 pushing and some pulling, in the undisturbed condition of 

 the assemblage. 



§ 13. Subject now the assemblage successively to six 

 different geometrical strain-components, e,f,g, a, h, c ; and 

 to one change of temperature, t, with the boundary mole- 

 cules held fixed. With each of these seven configurations, 

 measure, by three separate measurements conducted according 

 to the method described in § 10, the three components of 

 the sum of the electric moments of the molecules in unit 

 volume. 



§ 14. Repeat the same 21 measurements with part 2 of 

 the surface of each molecule zinc, and all the rest copper : 

 next with part 3 zinc, and all the rest copper : and so on. 

 Thus w T e have 21 2 distinct measurements, each giving inde- 

 pendently one of the 21 2 multipliers [#, e, 1], [#, e, 2], &c, 

 which appear in the following 21 equations : — 



