588 
AECHDEACON PEATT ON THE INDIAN AEG OE JHEEIDIAN. 
Taking the variations with respect to a and 
0<5t~^^)(cos X— cos 2 ot)| 
^/3= ^^)(cos X+cos 2m) j. 
Put X=ll° 27' 11", and 2m=47° 34' 25", 
§a=-0-9196678^a-0-1404082(Sa-§5) 
= -l-0600760^a+0-1404082^J, 
g/3= -0-4053130^5+0-3353533 
— 0-3353533^a-0'7406663^i. 
10. The formula I have thus obtained are as follows: — 
Is - 0-0003397^a-0-0010097^5, 
0-0025536^a-0-0075756^5, 
aa =-l-0600760k+0-1404082a5, 
§/3 = 0-3353533^a-0-7406663^&. 
The values of V) have been found in paragraph 5 for the Four Ellipses. By sub- 
stituting them in these formulee we are able to compare the ellipses with the mean 
ellipse. The results of this substitution are gathered together in the following Table, 
which contains also the semi-axes and ellipticities : — 
Mean Arc. 
Arc I. 
Arc II. 
Arc III. 
Arc rV. 
II II II 
<U 
feet. 
20926.500 
20855400 
1 
294 
feet. 
20985260 
20875737 
1 
192 
feet. 
20984066 
20876151 
1 
193 
feet. 
20906792 
20843795 
1 
332 
feet. 
20919988 
20846981 
1 
287 
II II 
miles. 
1M3 
3-85 
miles. 
10-90 
3-93 
miles. 
-3-73 
-2-20 
miles. 
— 1-23 
— 1-60 
Js = 
= 
Ja = 
= 
— 0-0000761 
— 0-0007445 
— 11-26 
0-88 
— 0-0002654 
— 0-0019379 
-11-00 
0-74 
0-0009542 
0-0071414 
3-65 
0-38 
0- 0011977 
0-0089801 
1- 08 
0-77 
§ 4. The difference between the geodetic and astronomical amplitudes, in the Indian Ai'c 
between Kaliana and Bamargida, arises solely from local attraction affecting the 
plumb-line, and in no degree whatever from any deviation of the curvature of the arc 
from that of the mean arc. 
11. The differences of the length of the four arcs, and of that of the mean arc between 
Kaliana and Damargida, are, by the Table in the last paragraph, 
-0-0000761 mile, -0-0002654, 0-0009542, 0-0011977. 
