AECHDEACON PEATT ON THE INDIAN AEG OF MEEIDIAN. 
591 
14. The numerical values of SR at the end of § 3 show that the Indian Arc, as 
represented by the first and second of the four measures I have enumerated, is slightly 
flatter than the mean ellipse in the corresponding parts ; but as represented by the third 
and fourth, is somewhat more curved*. 
15. The calculations of the Survey bring to light, with considerable exactness, the 
errors in the amplitudes, or differences of latitude of the stations, but do not at all 
help us to discover what the total deflections at the stations are. These can be found 
only by a direct calculation of the effect of the causes, such as I have given in my 
former papers. If these are not determined and allowed for, the latitude of a place 
determined by an observation of the sun or other heavenly body must always be erro- 
neous to the extent of the deflection of the plumb-line at the place of observation. 
Thus, if the estimate of the hidden cause of disturbance in the instance of the Indian 
Arising from the Mountains . . 27'98 
Arising from the Ocean . . . . 6T8 
Arising from the Hidden-cause . —7 '87 
Totals 
26-29 
three stations 
are — 
// 
12-05 
6-79 
9-00 
10-44 
'0-00 
7'61 
21-05 
24-84 
* In this Paper only the two northern portions of the Arc are considered. In this note I will give tlie 
results of a comparison of the three great divisions of the whole arc from Kaliana to Punnoe near Cape 
Comorin. The Curve of the Sea-level — for this is, of course, what we mean by the Arc, as it is this which 
the Survey calculates — is defined by the angles between the normals (that is, the plumb-lines) at the extre- 
mities of its three divisions, the lengths of the intervening arcs in feet, and the middle latitudes. The 
data are as follows: they are taken from p. 757 of the Volume of the British Survey lately published. 
They differ slightly from those given at p. 427 of Colonel Eveeest’s Volume of 1847 : the results of the 
first comparison below therefore differ slightly from those in the text of this Paper, in the first of the four 
measures of the Indian Arc enumerated in § 2. 
Astronomical 
amplitude. 
Arc I. Kaliana to Kalianpur (X ) 5 23 37‘060, 
Arc II. Kalianpur to Damargida ... (x') 6 3 55'970, 
Arc III. Damargida to Punnoe (X") 9 53 44T60, 
Putting these in the formulte 
s 
a — h 1 X 
__ 
«-f 5 X 
Length in feet. 
{s ) 1961138, 
{s' ) 2202905, 
(s") 3591784, 
S I S' 
cos 2m' — — , cos 2m 
X' 
Twice the middle 
latitude. 
(2m ) 53 38 0 
(2m') 42 10 27 
{2m") 26 12 46 
and 
we obtain 
' 3 cos 2m' — cos 2m 
cos 2m' — cos 2m 
JE=i(Ja-f seci X^ -|-i(J«— W)^l— cos X secix^ cos 2m, 
Mean ellipse. 
20926500 
Arc II. Arc III. 
20943697, 20893936, 
20863963, 20841164, 20855400 
111 
262 396 294 
17197, -32564 
8563, -14236 
— 4'6 feet, -4-4 feet. 
These results are exhibited in the following diagram. ABCD is the actual arc or sea-level curve connecting 
Arc I. 
a =20983139 feet, 
h =20875011 feet, 
= — 
194 
56639 feet, 
19611 feet, 
—5-8 feet, 
Sa = 
Sb = 
JE= 
