Vlll PREFACE. 



ing the propagation of transversal vibrations through the 

 luminiferous ether, it becomes necessary to investigate the 

 equations of motion of an elastic solid. It is here that Green 

 for the first time enunciates the principle of the Conservation 

 o work, which he bases on the assumption of the impossibility 

 of a perpetual motion. This principle he enunciates in the 

 following words: "In whatever manner the elements of any 

 material system may act upon each other, if all the internal 

 forces be multiplied by the elements of their respective direc- 

 tions, the total sum for any assigned portion of the mass will 

 always be the exact differential of some function." This func- 

 tion, it will be seen, is what is now known under the name of 

 Potential Energy, and the above principle is in fact equivalent 

 to stating that the sum of the Kinetic and Potential Energies 

 of the system is constant. This function, supposing the dis- 

 placements so small that powers above the second may be 

 neglected, is shewn for the most general constitution of the 

 medium to involve twenty-one coefficients, which reduce to nine 

 in the case of a medium symmetrical with respect to three 

 rectangular planes, to five in the case of a medium symmetrical 

 around an axis, and to two in the case of an isotropic or un- 

 crystallized medium. The present paper is devoted to the 

 consideration of the propagation of vibrations from one of two 

 media of this nature. The two coefficients above mentioned, 

 called respectively A and B, are shewn to be proportional to 

 the squares of the velocities of propagation of normal and 

 transversal vibrations respectively. It is to be regretted that 

 the statical interpretation is not also given. It may however be 

 shewn (see Thomson and Tait's Natural Philosophy, p. 711 (m.)) 

 that A-%B measures the resistance of the medium to com- 



