584 
AECHDEACON PEATT ON THE INDIAN AEC OE MEEIDIAN. 
IV. The fourth measure of the arc is one proposed by Captain Claeke in the volume 
of the Ordnance Survey. He suggests that by the principle of least squares the ellipse 
should be found which departs least from the mean ellipse in form, and at the same 
time gives deflections of the normal from the normal of the mean ellipse most in accord- 
ance Avith the calculated deflections. He finds this ellipse, taking account of mountain 
attraction only; the amount of ocean-attraction not having then been ascertained. 
The following recalculation, according to Captain Claeke’s method, takes account of 
both. 
Let ?i, 4? 4 be the latitudes of the three stations referred to the mean ellipse. Then 
/i — 1"’81, /2+3”T6, Z3 — 0"’05 are the observed latitudes (see the calculation under H.}. 
Let Zi+^i, 4+^3 be the latitudes of the three places referred to any other ellipse, 
the axes being given by the formulce in u and v under II. Then ei + l"-81, 3"T6, 
e3-l-0"‘05 are the corrections which must be added to the observed latitudes to make them 
accord with this ncAv ellipse. The dimensions, then, of this ellipse are determined by 
solving these equations : — 
0-403+4-125H^+2-7756?;+^, 
e2-3-I6 = -4-085-l-2-183Hi+l-6203i;+.r, 
^3+0-05=^. 
These equations give 
w=_0-3856+2-5946e,-4-4446^2+l-8500e3, 
l-0620-3-49586i-f6-6056e2-3-1098e3. 
Suppose di, d^, d^ are the angles of deflection caused by the mountains and ocean. Then 
the most probable ellipse to measure the curvature of the Indian Arc (supposing there 
are no other causes of deflection of the vertical) is that AAdiich makes 
(€l--d^y-{-(e2 — (? 2 )^+(^ 3 — (hy 
+(2-5946^.-4-4446^2-fl-8500^3)H(3-4958ei-6-6056e2+3-1098^3)^ 
a minimum. By diflerentiation with respect to e^, and we obtain three equations, 
which after transformation become 
0-76873t?,-f0-35716fZ2-0-12584fZ3, 
^3= 0-35716fZ. + 0-341996^2-l-0-300864 
e3=-0-12583(Z, + 0-30087fZ2+0-82493f?3. 
These give 
M=-0-3856fl-0-17432f7,-0-03671(Z2-0-13760(73, 
V = l-0620+0-06325(Z,+0-07484fZ2-0-13808cZ3. 
The values of the calculated deflections (Zj, d^^ d^ are 34"T6, 21"'05, 17"‘23. When 
these are substituted in the above formulae, we have 
e,=31"-61, e3=24"-58, e3=16"-25, ^=2-4255, ?;=2-4189. 
Hence the errors in the observed latitudes as afiected by deflection (or 62“3T6, 
