456 Lord Kelvin on the Theory of 



part of the boundary of the assemblage ; and this whether the 

 molecules are spherical, or of any other shape not too wildly 

 different. We see also that for all molecules not nearer than 3h, 

 or perhaps 4/i, or bh, from any part of the boundary of the as- 

 semblage, the distribution of electricity is similar. That is to say, 

 the whole assemblage within a thin surface-layer (of some such 

 thickness as 3A or 4/z) is homogeneous, not only geometrically 

 and mechanically, but also electrically. The problem of 

 finding, with moderate accuracy, the distribution of electricity 

 on each molecule of the homogeneous assemblage thus con- 

 stituted, is comparatively un-laborious if the shape of each 

 molecule is spherical. 



§ 7. We also see, by the known elements of electrostatics, 

 without solving the problem of finding the quantity of elec- 

 tricity on each molecule of the surface -layer in the circum- 

 stances described in § 6, that the sum of the quantities on all 

 the molecules of this layer, per unit of the surface, is equal to 

 the component, in the direction normal to the surface, of the 

 electric moment per unit-volume of the homogeneous assem- 

 blage within the surface-layer. 



§ 8. The condition of the whole assemblage, surface-layer 

 and homogeneous assemblage within it, at which we have 

 arrived in §§ 6 and 7, may be regarded as representing the 

 natural undisturbed condition of a crystal. Let now any 

 homogeneous change of configuration of our assemblage be 

 produced either by proper application of force to the mole- 

 cules of the surface-layer, or by uniform change of tempera- 

 ture throughout the interior, or by both these causes acting 

 simultaneously. We need not exclude the case of no change 

 of shape or bulk of the boundary ; that is to say, the case of 

 no change of the relative positions of corresponding points 

 of the molecules ; and our " change of configuration " 

 only an infinitesimal rotation of each molecule. The in- 

 clusion of this case is important to guard against a 

 tendency which I find in the writings both of MM. Curie 

 and of Yoigt : — a tendency to a hypothetical assumption 

 unduly limiting the pyro-electric property to identity with 

 the piezo- electric effect produced by force causing the same 

 change of shape or bulk as that which is produced by the 

 change of temperature. In nature, we may -expect as a 

 general possibility, and as a probable result in some cases, a 

 bodily electro-polarization produced by change of tempera- 

 ture, even though change of bulk and shape are prevented 

 by force applied to the surface. And, in our model, changes 

 of forces of the springs would certainly cause rotation of the 

 molecules, and so produce electro-polarization, even when 

 the molecules of the boundary are held fixed, unless the 



