182 The Rey. S. Haueuton on the Equilibrium and 
are in every respect similar in each of the eight regions into which the three 
planes drawn at any point divide the body. It is easily seen that in such a me- 
dium the coefficients (a; Bis Y» 4; Bos Yo. %» By» Y;) of the function v, are all zero 
(11), and that consequently v, is reduced to the form, 
2Y, == (4 (=)+ “(+ (3) \+ + (Lv + mv’ + nw’) 
dyn dé dé dt dé dy 
+2(1 Wyte dade De ae i) 
We shall also have the aes (26) reduced to 
ee ae Be Bi, 9s Hes fis) 
GE is “dad ly dadz 
ay ne n ay an ae CE a 
Sgt ae Up ae ae a(1 aja see (42) 
Ee OG ae ae dé dy 
“de — “de? nant dx® ate dye 2(m dadz ce dydz -) 
The equation of the surface of wave-slowness will still be represented by (31), in 
which we must now give to (P, Q, R, F, G, H) the following values, 
p= Av + ny? + Mz F = 2Lyz 
Q=By +12 + Nz G = 2maz (48) 
R = eg?-+ Ma?+ Ly? H = 2nay 
and its traces on the principal planes of symmetry are given by the following 
equations : 
(ry? + ma®—1) [(aa’?+ ny’—1) (By? + Nax’—1) — 4n°a*y?] = 0 
(x2? + L2?—1) [(cz? + ma?—1) (a2? + mz*—1) — 4u’a?2*] = 0 (49) 
(mz? + ny?—1) [(By? + L2’—1) (2 + Ly’—1) — 41%/*2"] = 0 
for it appears immediately from the equation of the surface, that its traces are 
(r—1) [(p—1) (e—1) — HW] = 0 20 
(e—1) [(p—1) (R—1)—@] =O y=OdO 
(e—1) [(e—1) (r—1) — F*] =0 2=0 
