1911-12.] The Molecular Theory of Magnetism in Solids. 229 
If, on the other hand, we put /3' = 0, y = "0, a =1, etc., we find 
„-L' 0 = ^(2A'-B'-C'), 
P 3 
? L'„=^(-A' + 2B'-C'), - . . . 
P 
y L' 0 =M(-A'-B' + 2C') > 
P 3 
(16) 
which correspond exactly to (8), and exhibit a =1, /T — 0, y'~0; a =0, 
/3'= 1, y' = 0; a —0, /3' = 0, y— 1 ; as the three principal directions of the 
internal field. If we take A' B' }> C', we see that, except in special 
cases, is negative; pLf 0 is negative if B' — A' < C' — B', positive if 
B' — A' > C' — B'; and yL' 0 is positive. By (13) these axes are given by the 
pure strain 
a = a + fiZ + y Y , 
/3' = aZ -f /3 + yX , 
y' = aY + /3X + y. 
Their direction ratios are a = 1, /3 = (X Y — Z)/(l — X 2 ), y = (XZ — Y)/(l — X 2 ); 
and so on, the others being got by cyclical interchange of a, f3, y, and 
X, Y, Z, simultaneously. It is important to remark that these direction 
ratios of the principal axes for the internal field depend only on the angles 
between the crystalline axes, and not at all on the scale of spacing of the 
centres of magnets in any direction. 
The component L' 0 , parallel to the magnetisation, now vanishes when 
a 2 = /3' 2 — y' 2 = 1/3. These conditions give 
a{ 3 - 2(X + Y + Z) - (X 2 + Y 2 + Z 2 ) + 2(X Y + YZ + ZX) } 
= x/3{l+Y + Z + X(X-Y-Z)}, 
/3 and y being got by cyclical interchange. These give, as we see they 
should from the condition aa' + /3/T + yy' = 1, the result a + /3 + y= J3. 
In the case of the transverse component in the clinic systems, the 
equations (7) are replaced by 
a[a\’ + P(pjL)’ + y (qy)’\ 
rrV g M V > A. 
" 0 /o 3 ^ ’ +pix{jyx)' qv(qv)'Y' 2 
(aX + P(pit)' + y(qy)')'- } etc. 
X - a(Xa/ + ffl* . ? + qv + qv y } , ^ 
rrV _nMy 
or A 0 r sZj • + PfX (p /ll y + q v (q v yy/2 
■ (17) 
= “ aa ' 2 ) - q 2 v 2 ay' 2 ](\\' + pp(pfi)' + qv(c[v)) 5/2 
ur 
= + /3Z + yY)(l - a 2 - a/3Z - ayY) - B'a(aZ + fl + yX) 2 
-C'a(aY + /?X + ) 2 ], 
replacing (11) with similar expressions for ^T'o and V T' 0 . 
