on 
Change of Temperature. 
For X', 
s 
A' 
~ A 
sin/3' 
sin/8 
y' 
z' 
s 
= 0, 
A' 
~ A 
cos/3' 
sin/3 
" c 
cos/3. 
sin/3 
415 
and for Y', 
sd _ A' sin /3' cos C B' sin a! cos_C / 
T ~ A sin /3 sin C B sin a sin C ' 
?/ _ B' sin a' sin C 
t ~~ B sin a sin C 
/_ A' cos/3' cos C C cos/3 cos C 
t ~ A sin /3 sin C C sin /3 sin C 
B' cos a 7 C cos a 
B sin a sin C C sin a sin C 
VI. Hence P, the coefficient of expansion of the crystal-line 
OX, is 
x' _ 1 _ A! sin ffi 
7 Aldnl? ; 
Q, the coefficient of expansion of the crystal-line OY, is 
-1: 
y' 1 _ B' sin a! sin C x 
£ B sin a sin C 
and R, the coefficient of expansion of the crystal-line OZ, is 
C 
C L 
Also (fig. 10), if 
D =r 
-Y'OZ, E = X'OX, F=|-Y'OX, 
D=cosZOY' 
_ z' _ A' cos /3' cos C C cos /3 cos C 
t A sin /3 sin C ' C sin /3 sin C 
B' cos a! C cos <x 
B sin « sin C C sin a sin C ? 
E = XOX / 
/ A'cosyS 7 C'cos/3 
~ s ~ A sin/3 C sin/3' 
F = cosXOY' 
_«'_ A' sin & cos C B' sin a' cos C 
— t ~ A sin /3 sin C ' B sin a sin C " 
