(E) 



86 Colonel A. E. Clarke on the Figure of the Earth 



a minimum, the resulting equations in u and v are 

 0= +56-6615 +301-7624w + 126-9252v, 



0= - 16-1)677 + 126-9252 u + 221*4307 v ; 

 .-. w= -0-2899; v- +0-2428. 

 From these we have, in feet of the standard yard, 

 a = 20926202, 

 ^ = 20854895, 

 c__ 292-465 

 a 293465' 



And this is the spheroid most nearly representing the mean 

 figure of the earth. 



But the Indian observations are not well represented by this 

 figure. The southern station of the arc requires a large ne- 

 gative correction of —3" '14, and the northern station a still 

 larger negative correction of — 3 //# 55. Among the longitude 

 stations, there is left at Bombay a westerly deflection of 

 4"-05, and at Madras an easterly deflection of 4 //# 50. The 

 longitudes, in fact, require a larger value of a and a larger 

 value of the ellipticity : while the form of the meridian-arc 

 requires a smaller equatorial radius and a smaller ellipticity. 

 In other words, so far as the observations we have at present 

 to consider indicate, the surface of India does not seem to be- 

 long to a spheroid of revolution : if it does, we must admit 

 large deflections towards the sea at Cape Comorin, at Bombay, 

 and at Madras. 



But we may obtain more strictly the form of the Indian arc 

 from the sixty-six latitude stations it contains. Not to confine 

 the arc to an elliptic form, let it be such that its radius of cur- 

 vature in latitude <£ is expressed by the equation 



p = A' + 2B'cos 2£ + 2C'cos 40, 



a curve which includes the ellipse as a particular case. In 

 order to determine A, B, C, we must apply symbolical correc- 

 tions to the observed latitudes, and make the sum of the 

 squares of these corrections a minimum. As the result of a 

 very long calculation, the actual equation is found to be 



p = 20932184-l-167963-6 cos 20 + 28153-2 cos4(/>. . (E') 



The correction to the latitude of the southern point is +1 //, 61, 

 and to the northern — 0"*81 ; and, generally, the residual cor- 

 rections or apparent local attractions are free from any appear- 

 ance of law, so that the above equation may be taken as very 

 closely representing the form of the sea-level along the meri- 

 dian of India. The geodetic operations give us the/orm of the 



