190 The Rev. S. Havcuton on the Equilibrium and 
slowness, which will evidently become a surface of revolution round the axis of z. 
There will be no conical refraction for any direction of wave-transmission ; but, 
since two sheets of the surface touch each other on the axis of z, there will be 
only two velocities of waves parallel to (x, y), while there will be three velocities 
in every other direction. 
Ill. If the medium be perfectly homogeneous and uncrystalline we shall still 
use the equations (47) with the additional relations, 
AB Ce iM ING A ONy 
which reduce them to the following form : 
QE (awe Pt Pe ae 
Ta =*(855 a = a at? (a ye ie) 
ad’n _ ay dy , ay ae 
i saul (a ote (Ge a dx a) Ca ‘i ica) (50) 
A oa(oth a (Bhs Del fe+ fb) 
These are the differential equations of motion of a solid homogeneous and un- 
crystalline body, and were given first by Navier in the memoir already alluded to. 
Referring to the general form of v,, it will readily appear that, for the case at 
present considered, it becomes 
av, = 9(3(Sa+ gat + St" + v?-+ w’) 
dy dg dé dg dé dy 
+2(Fr. “dz + da ‘dz Zs dx’ =) (51) 
which will give the corresponding equations, 
wan(set Tes) sas(Z4+7) 
ups v(3a+ o+5) p=s($+5) (52) 
2=eQE+E+R) 2="Gte) 
