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d dx* dy' dz' In the particular case, here considered, dy where , PA, The above are the known general equations of fluid motion, which must be satisfied for all the internal points of both fluids; but at the surface of separation, the velocities of the particles perpendicular to this surface and the pressure there must be the same for both fluids. Hence we have the particular conditions d_dfr 1 dx~ dx L (where x = 0), As = A js, j neglecting such quantities as are very small compared with those retained, or by eliminating s and we get The general equations (1) and (2), joined to the particular conditions (A) which belong to the surface of separation (yi), only, are sufficient for completely determining the motion of our two fluids, when the velocities and condensations are independent of the co-ordinate 2, whatever the initial disturbance may be. We shall not here attempt to give their complete solution, which would be complicated, but merely consider the propagation of a plane wave of indefinite extent, which is accompanied by its reflected and refracted wave. Since the disturbance of all the particles, in any front of the incident plane wave, is the same at the same instant, we shall have for the incident wave <]>=f(ax + by + ct), retaining b and e unaltered, we may give to the fronts of the reflected and refracted waves, any position by making for them = F (a'x + by + ci), Hence, we have in the upper medium, \$ =f{ax + by + ct) + F (dx + bv + ct) (4), and in the lower one + + (5) These, substituted in the general equations (1) and (2), give ^==^(a'+br)y