414 Mr. L. Fletcher on the Dilatation of&'ystals 
whence 
s 
^ 1= sin£> 
z x = —scot/3. 
For Y, ifOY=*, 
#=(), y=*, s = 0; 
whence x , ^ 
£cotC 
A 'l = = — a~> 
sm p 
t 
* yi smasmC 
^ 1= = £(cot/3cotC ;— tiI* 
V sm (J/ 
IV. Find the coordinates (#/ ?// 0/) of each of the points 
X', Y' at the second temperature relative to the oblique axes 
oa', oiy, oc. 
For X', 
, A' A' s 
* 1= A^ = AsnT/3' 
*/=<>, 
p-2l= — tt scot/3 
For Y' 
C 
r 
A' £ cot C 
A l A sin/3 
B' B' t 
yi= tj^i = 
B ^ B sin a sin 
01 = TT ^1= TTM COt /3 Cot r- 73 I. 
(J C V sm (J/ 
V. Find the coordinates a/, ?/, e' of each of the same points 
X', Y' relative to the rectangular axes OX, OY, OZ. 
In just the same way as in § II. we find that 
x' = x{ sin @ r +y x f sin a.' cos (7, 
y'=y 1 'sina / siii C, 
/ = 0/ cos f + yx cos a' + z{. 
Substituting in these equations the values of #/, y/, 2/ deduced 
in § IV., we find 
