454 Lord Kelvin on the Theory of 



chemical compound molecule such as H 2 or Si0 2 in a 

 realizable model, which indeed I actually made three weeks 

 ago and described in a communication to the Philosophical 

 Magazine * without knowing that I had been anticipated. 



§ 2. To represent pyro-electric and piezo-electric qualities 

 in a crystal, take as crystalline molecule a rigid body of any 

 shape, bounded by a surface made up of pieces of different 

 metals, soldered together so as to constitute one metallic con- 

 ductor. Arrange a large number of such molecules in order, 

 as a Bravais homogeneous assemblage, not touching one 

 another. Connect every molecule with neighbours by springs 

 of non-conducting material (india-rubber may be taken if we 

 wish to make a practically working model) . We may. for ex- 

 ample, suppose each molecule to be connected with only twelve 

 neighbours ; its two nearest, its two next-nearests, its two 

 next-next-nearests in the plane of those four, and the three 

 pairs of nearests, next-nearests, and next-next-nearests on 

 the two sides of that plane. Thus we have a perfect me- 

 chanical model for the elasticity and the piezo-electricity 

 of a crystal ; and for pyro-electricity also, if we suppose 

 change of temperature to produce either change of the con- 

 tact-electricities of the metals, or change of configuration of 

 the assemblage, whether by changing the shape of each 

 molecule or by changing the forces of the springs. 



§ 3. The mathematical problem which this combination 

 presents is as follows : — 



Given a homogeneous assemblage of a large number of 

 equal and similar closed surfaces, S, each composed of two or 

 more different kinds of metal soldered together, all insulated 

 in a large closed chamber, of which the bounding surface C is 

 everywhere at a practically infinite distance from the assem- 

 blage, and is of the same metal as one of the metals of S, 

 copper we shall suppose, to fix the ideas. 



It is required to find : — 



(1) The potential in the copper of every molecule when 

 the total quantity of electricity on each is zero. 



(2) The quantity of electricity on each molecule wdien all 

 are metallically connected by infinitely fine wire. 



§ 4. The mathematical expression of the conditions and 

 requirements of the problem is as follows : — 



Let/(P) denote a given function of the position of a point 

 P on the surface S of any one of the molecules ; expressing 

 the difference of the potential in the air infinitely near to P. 

 from the potential in the air infinitely near to the copper 



* For October 1893, " On a Piezo-electric Pile. 





