on Change of Temperature. 
297 
Arc. 
Variation. 
10-2(5 
- 77-83 
20-30 
- 96-66 
30-40 
-103-84 
40-50 
- 98-49 
50-60 
- 81-26 
60-70 
- 54-23 
70-80 
- 20-66 
80-90 
+ 15-40 
Are. 
Variation 
100-110 
+ 77-83 
110-120 
+ 96-66 
120-130 
+ 103-84 
130-140 
+ 98-49 
140-150 
+ 81-26 
150-160 
+ 54-23 
160-170 
+ 20-66 
170-180 
- 15-40 
This table also serves as a numerical example of Prop. XI. /, 
which states that to this approximation the quantities in the 
second and fourth columns are equal in magnitude but oppo- 
site in sign. 
To proceed to the next degree of approximation we must 
calculate the value of the expression tan -0 1 cot Pa, and substi- 
tute in the formula 
tf^^ + tan 2 ^ cot Pa. 
The smaller term calculated for every 10° is given in the 
following table in seconds : — 
•• 
tan 2 0, cot Pa. 
Pa. 
tan 2 X cot Pa. 
Pa. 
tan 2 X cot Pa. 
c 
10 
+007 
70 
+U-56 
o 
130 
-0-23 
20 
+0-22 
80 
+0-29 
140 
-041 
30 
+0-42 
90 

150 
-003 
40 
+0-62 
100 
-023 
160 

50 
+0-74 
110 
-0-34 
170 
-0-01 
60 
+0-72 
120 
-0-33 
: 180 

The second term is thus a positive maximum for a pole 
between 50° and 60°; a negative maximum for a pole between 
110° and 120°, and also for a pole between 160° and 180°; 
the largest maximum being the one first mentioned. 
We find from Prop. YIII. that the exact distances of these 
poles from a are respectively 
53° 49' 21"% 113° 49' 27"-2 ; 173° 49' 27"-2; 
and the largest maximum will be 
~ sin 3 107° 38' 54"-4 
= // -80. 
