474 ADDEESS DELIVERED AT A MEETING OF 



method ; and he has determined the form of the function which 

 enters the general equation of Lagrange (and which depends upon 

 t.he internal forces acting at any point of the medium), from the 

 assumed principle, that the molecules of solid and fluid bodies act 

 on each other only in the direction of the line joining them, and with 

 forces which depend on the magnitude and direction of that line. 

 This function is easily shown to consist of two parts, one of them 

 depending on the first power of the displacement, and the other 

 upon its square ; the former of these is assumed to relate to perfect 

 fluids, and the latter to solids, while both must be taken into account 

 in imperfect or viscous fluids. The form of this function, in the case 

 of solids, bears some analogy to (although it is quite different from) 

 that of the function employed by Professor M'Cullagh in his- 

 dynamical theory of light ; and the author deduces, from that dif- 

 ference, the important physical consequence that the molecules of 

 the luminiferous ether do not, according to that theory, act on one 

 another in the direction of the line joining them. 



The differential equations of motion cannot be integrated gene- 

 rally ; but the values of the three component displacements which 

 correspond to the case of plane waves are manifestly particular in- 

 tegrals ; and the equations of condition, which result from the sub- 

 stitution of these values in the general equations of motion, lead to 

 a remarkable geometrical construction for the three possible direc- 

 tions of molecular vibration, and the corresponding velocities of the 

 plane waves, by means of six fixed ellipsoids. 



The author then determines the equation of the surface of icave- 

 slowness (or the reciprocal polar of the wave-surface), the nature 

 and properties of which are analogous to those of the surface of the 

 same name in the theory of light. This surface is of the sixth de- 

 gree, and has three sheets, corresponding to the three velocities of 

 wave propagation ; and, like the corresponding surface in the theory 

 of light, it serves to determine the direction of the refracted waves, 

 in passing from one medium to another, as well as the laws of pro- 

 pagation in the same medium. In the most general case consi- 

 dered by the author, namely, when the molecules of the medium 

 are arranged symmetrically round three rectangular planes, it is 

 shown that this surface has four nodes, at which the tangent plane 

 is a cone of the second degree ; and thence arises a conical refrac- 

 tion in Sound, similar to that discovered theoretically by Sir Wil- 

 liam Hamilton in the case of Light. 



