296 Mr. L. Fletcher on the Dilatation of Crystals 
(a) From Prop. VII. we have 
k 
sin (f> 
sin fa sin (ca + </>)' 
where we may write 
ca= 80° 32' 37"% 
c a=-80°55'44"-5, 
= -582"-4; 
whence 
&=598"-18 
= -0029001 
in circular measure. Whence, as before only to the first ap- 
proximation, 
^-3= -0029001. 
(b) If 6i be the displacement of a pole P when small quan- 
tities of the second order are neglected, we have 
6± = k sin Pa sin Va. — k sin Pa sin (Pa— aa), 
= k sin Pa (sin Pa + a- 180°), 
= —k sin Pa sin (Pa + a); 
whence in the present instance 
6>,= -598"-18sinPasin(Pa + 18° 31' 38"'3). 
To show the displacements in various parts of the zone, the 
values of 6 X for poles at every 10° from a are given below : — 
Pa. 
y ". 
Pa. 
e-'. 
p, 
e,". 
o 
10 
- 4961 
o 
70 
-561-92 

130 
-23924 
20 
-127-44 
80 
-582-58 
140 
-140-75 
30 
-224-10 
90 
-567-18 
150 
- 59-49 
40 
-32794 
100 
-51757 
160 
- 5-26 
50 
-426-43 
110 
-43974 
170 
4- 15-40 
60 
-507-69 
120 
-343-08 
180 

Perhaps the alteration of the angles in various parts of the 
zone is more clearly shown by taking the differences of the 
above terms, and thus finding the variations of a series of 
arcs each of which is initially 10° in length. 
We then have (still neglecting squares of small quantities): — 
