230 Proceedings of the Royal Society of Edinburgh. [Sess. 
The various equations show that the internal field is distorted from its 
symmetrical disposition when the crystalline axes are inclined, while 
retaining its general features relative to them. 
In the subsequent sections, crystalline arrangements referable to 
rectangular axes will alone be considered. 
13. The term of next order in the parallel component of the internal 
force is 
L'j = 2M^[35 cos‘0 - 30 cos 2 0 + 3](A 2 h- 
With cos 0 = (a A + j3 . pju + y . qv)/(\ 2 V 2 + g V) 1/2 > this becomes 
L'j = ?^- 2 [(Da 4 + E/3 4 + Fy 4 ) + 2(Ga 2 /3 2 + H/3 V + W) - (V« 2 + B 2) 8 2 + C 2 y 2 ) + J] ; 
P 
( 18 ) 
which, if we consider the cubic system, reduces to 
L' s = ?^f[D(a 4 + /3 4 + y 4 ) + 2G(a 2 /3 2 + /3 2 y 2 + y 2 a 2 ) - A 2 + J] 
2Ma 2 
[(D - G)(a 4 + /3 4 + y 4 ) + G - A 2 + J] 
where 
(A 2 + /l 2 + v 2 ) 9 
3 
(A 2 + /X 2 + v 2 ) 5/2 
We readily deduce 3A 2 = 10J, 2G + 3D = 35/3 . J. Hence, finally, 
l' 2 =^!(g-d) 
^-2(a 4 + /3 4 + y 4 ) 
. (19) 
The corresponding term in the transverse component is 
T' 2 = sin 0 cos 0 (70 cos 2 0 - 30)(A 2 +p 2 //, 2 + q V) _5/2 , 
and the component of this in the direction of the A-axis is (cf. § 7) 
rjv _Ma 2 y [A - a(aA + p/3(j. + qyv)~\ ( 70(aA + p/3/L + gyi/) 8 30(aA + pfi/x 4- qyv) > 
2 p 5 ^ (A 2 +p 2 /x 2 + g 2 v 2 ) 3 j (A 2 +p 2 /x 2 + g 2 v 2 ) 3/2 (A 2 +p 2 /x 2 + q 2 v 2 ) 1/2 J ’ 
In the cubic system this becomes 
, Mr? 2 "\ 
\T 2 = 2 ~ (G - D)a[(a 4 + j8 4 + y 4 ) - a 2 ] , 
/r 2 - 2^(G - D)/3[(a 4 + /3 4 + y 4 ) - /3 2 ] , ■ 
V T' 2 |2Ml 2 (G-D) y[(a 4 + /3 4 + y 4 ) - y 2 ] . 
P b 
SO 
. ( 20 ) 
