THE EQUILIBEIUM OF ELASTIC SOLIDS. 33 



Having assumed the proportionality of pressure to compression, he proceeds 

 to define his coefficients. "Let -AS be the pressures corresponding to a uniform 

 linear dilatation 8 when the solid is in equilibrium, and suppose that it becomes 

 mAS, in consequence of the heat developed when the solid is in a state of rapid 

 vibration. Suppose, also, that a displacement of shifting parallel to the plane 

 xy, for which Sx = kx, Sy = -ky, and Sz = 0, calls into action a pressure -Bk 

 on a plane perpendicular to the axis of x, and a pressure Bk on a plane 

 perpendicular to the axis of y ; the pressure on these planes being equal and 

 of contrary signs; that on a plane perpendicular to z being zero, and the tan- 

 gential forces on those planes being zero." The coefficients A and B, thus 



defined, when expressed as in this paper, are A = 3p., B = 



m 

 ~2 ' 



Professor Stokes does not enter into the solution of his equations, but gives 

 their results in some particular cases. 



1. A body exposed to a uniform pressure on its whole surface. 



2. A rod extended in the direction of its length. 



3. A cylinder twisted by a statical couple. 



He then points out the method of finding A and B from the last two cases. 



While explaining why the equations of motion of the luminiferous ether are 

 the same as those of incompressible elastic solids, he has mentioned the property 

 of plasticity or the tendency which a constrained body has to relieve itself 

 from a state of constraint, by its molecules assuming new positions of equi- 

 librium. This property is opposed to linear elasticity ; and these two properties 

 exist in all bodies, but in variable ratio. 



M. Wertheim, in Annales de Chimie, 3 e Sdrie, XXIIL, has given the results 

 of some experiments on caoutchouc, from which he finds that K= k, or p. = f TO ; 

 and concludes that k = K in all substances. In his equations, /A is therefore 

 made equal to f m. 



The accounts of experimental researches on the values of the coefficients 

 are so numerous that I can mention only a few. 



Canton, Perkins, (Ersted, Aime, Colladon and Sturm, and Kegnault, have 

 determined the cubical compressibilities of substances ; Coulomb, Duleau, and 

 Giulio, have calculated the linear elasticity from the torsion of wires ; and a 

 great many observations have been made on the elongation and bending of beams. 



VOL. I. 5 



