AECHDEACON PEATT ON THE INDIAN AEG OE MEEIDIAN. 
583 
the form of the Indian Arc, making use of the observed data. He shows* that the 
following quantities must be added to the obseiwed latitudes of the three stations to 
make the arcs measured by the Survey fit an ellipse of which the axes are given by 
“-^=3A(i-1o^+5v)20890000. «+S=2(i-Io^) 20890000 feet, 
\iz. for Kaliana . . . 0*403+ 4'125lM4-2’7756!;+a? 
Kalianpur . . — 4*085+2*1831w+l‘6203v+a^ 
Damargida oc 
He finds for the mean ellipse of the whole earth w= — 0"*3856, ^;=l"•0620, 
a’=0"*050, and therefore the corrections of the observed latitudes are, by the above 
formulae, 1"*810, — 3"*156, 0"*050. Hence the amplitudes thus determined are 4"*966 
in excess, and 3" *2 06 in defect of the observed amplitudes. 
The form of the local ellipse can be determined from the data by putting the correc- 
tions for the latitudes equal to zero. This gives 
4*125lM+2*7756t;= -0*403, 
2*1831zt+I*6203«= 4*085, 
which give 
-19*2015, i;=28*3920, 
and thence 
«=20984066feet, 5=20876151, 6=:^. 
X i/O 
These results agree well with those of Colonel Eveeest noticed above. 
HI. The third measure is that determined by a comparison of the two arcs, the ampK- 
tudes being corrected for mountain and ocean attraction. Let s, s', A, X', m, m' be the 
lengths, amplitudes, and middle-latitudes of two arcs, of which the amplitudes are not 
large — as in this instance. Then 
s a-\-h 
2 
cos 2ni, 
s s' 
a — h 1 
2 3 cos2?«'— cos 2m’ 
s' a + h ^a — b „ , 
-,= “2 3^ COS 2to', 
s ^ f s' 
, - cos 2m' i cos 2m 
a + b_X a' 
2 cos 2m' — cos 2m 
By what I have stated in paragraph 2, the increase to be made to the amplitudes to 
correct for mountain and ocean attraction is 13" *11 and 3"* 82. The values of X and X' 
are therefore 
X=5° 23' 37"+13"=5° 23' 50", x'=6° 3' 66"+4"=6° 4' 0", 
also 
5 = 1961157 feet, 5'=2202926t. 
These lead to 
a=20906792, 5=20843795, g=^* 
* See Ordnance Survey, pp. 737, 741, 767. 
t See Colonel Eyeeest’s Volume, 1847, p. 427. 
