199 



The late Mr. Green, of Cambridge, applied the same method to the 

 more difficult dynamical question of the movement of the mole- 

 cules of the luminiferous ether ; in which application he was 

 followed, but with more success, by the distinguished mathemati- 

 cian, whose name is imperishably connected with the records of this 

 Academy. 



Mr. Haughton has judiciously adopted the same mathematical 

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

 enters the general equation of Lagrange (and which depends upon 

 the 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 which 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 func- 

 tion, in the case of solids, bears some analogy to, although it is 

 quite diflerent from, that of the function employed by Professor 

 Mac Cullagh in his dynamical theory of light ; and the author 

 deduces, from that difference, 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 

 integrals; and the equations of condition, which result from the 

 substitution of these values in the general equations of motion, lead 

 to a remarkable geometrical construction for the three possible 

 directions of molecular vibration, and the corresponding velocities 

 of tlie plane waves, by means of six fixed ellipsoids. 



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

 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 



