Motion of Solid and Fluid Bodies. 181 
tion being given, we have to determine three refracted and three reflected 
vibrations ; the directions of these are known by means of the surface of wave- 
slowness, and the quantities which are to be determined are the six intensities of 
the reflected and refracted vibrations. Now we have six conditions to determine 
these six quantities; these conditions are—the conservation of the real vibration 
in passing from one medium into another—the conservation of the perpendicular 
component of the first transversal—and the conservation of the second transversal 
parallel to the plane of separation: the equations of condition given by these 
considerations are, 
ves a, Ae 
Ne 5. waa (46) 
If the vibration pass from a homogeneous solid into one of crystalline struc- 
ture, there will be three refracted and two reflected waves; and the unknown 
quantities will be the five intensities and one direction in the homogeneous body, 
which is not given by the wave-surface ; or, vice versd, if the vibration pass from 
the crystalline into the homogeneous body, there will be three reflected and two 
refracted waves, and the six unknown quantities will be the same as before. Also, 
if two homogeneous bodies be superposed, it will be shown that there are two 
reflected and two refracted waves, and the unknown quantities are four intensities 
and two directions. In fact, whatever be the nature of the superposed bodies, 
the unknown quantities will be six in number, so that they can be completely de- 
termined by the six equations of condition. 
We have hitherto considered the differential equations arising from v, expressed 
in its most general form, and although the relations (15) might have been intro- 
duced, yet the simplification produced by them would be very slight ; the prin- 
cipal effect of these equations being to modify the equation of wave-slowness, and 
it appears very difficult to obtain any other relations among the coefficients ef v,, 
which should simplify to any important extent the equations of motion. 
I shall now discuss a few particular cases of solid bodies, in order to show the 
manner in which the general equations already found should be modified when 
applied to such cases. 
I. Let us suppose the solid to have its molecular constitution such, that it is 
symmetrically arranged round three rectangular planes, i. e. the molecular forces 
