860 



LORD KELVIN. 



assemblage; and it supplies us with a perfect explanation of the piezo- 

 electric quality to be inferred from the brothers Curie 1 s expérimental 

 discovery, and Yoigt's mathematical theory. 



§ 42. Look at the diagram in §39 ; and remember that it indicates a 

 vast homogeneous assemblage consisting of a vast number of parallel 

 plane layers of atoms on each side of the plane of the paper, in which 

 seven atoms are shown. The quartets of electrions were described as ail 

 similarly orientée!, and each of them equilateral, and having its geome- 

 trical centre at the centre of its atom ; conditions ail necessary for 

 equilibrium. 



§ 43. Let now the assemblage of atoms be hoinogeneously stretched 

 from the plane on both sides to any extent, small or great, without any 

 component motions of the centres of the atoms parallel to the planes of 

 the layers. First let the stretch be very great; great enough to leave un- 

 disturbed by the other layers the layer for which the centres of atoms 

 are, and the geometrical centres of the quartets were, in the plane of the 

 paper. The geometrical centres of the quartets are not now in the plane 

 of the paper. The single electrions on the near side seen in the diagram 

 over the centres of the circles are drawn towards the plane of the paper; 

 the equilateral triangles on the far side are also drawn nearer ; to the 

 paper and the equilateral triangles are enlarged in each atom 

 by the attractions of the surrounding atoms. The contrary inward mo- 

 vements of the single atoms on one side of the plane, and of the triplets 

 on the other side, cannot in gênerai be in the proportion of three to 

 one. Hence the geometrical centres of gravity of the quartets are now 

 displaced perpendicularly to the plane of the paper to far side or near 

 side ; I cannot tell which without calculation. The calculation is easy but 

 essentially requires much labour; involving as it does the détermina- 

 tion of three unknowns, the length of each side of the equilateral triangle 

 seen in the diagram, the distance of each of its corners from the elec- 

 trion on the near side of the paper, and the displacement of the geome- 

 trical centre of gravity of the four to one side or other of the plane. 

 Each one of the three équations involves summations of infinte conver- 

 gent séries, expressing force components due to ail the atoms surroun- 

 ding any chosen one in the plane. À method of approximation on the 

 same gênerai plan as that of the footnote to § 9 above would give a 

 practicable method of calculation. 



