92 Colonel A. R. Clarke on the Figure of the Earth. 



of RSX from a right angle might, with the value of i we have 

 been supposing, amount to some degrees without going to any 

 hi^h latitudes. 



It appears, then, that it would not do to take the longitude- 

 equations which we have used for the determination of a sphe- 

 roidal figure for the earth also for the determination of an 

 ellipsoidal figure. The only thing that can be done under the 

 circumstances is to take simply the longitude-arc between 

 Bombay and Vizagapatam, as these points are nearly in the 

 same latitude, and to reduce it according to the expression for 

 the length of an arc of parallel on the surface of an ellipsoid, 

 given in the before-mentioned paper on the Figure of the 

 Earth, page 43. 



Then, with fifty-one equations I get the following : — 



u= -0-4903; 



v= +0-2842; 



ic= +0-3599; 



z= -0-1067. 

 From these quantities the following values finally result : — 



a = 20926629; 



5 = 20925105; 



c = 20854477. 



If by the word " ellipticity " of an ellipse we mean the ratio 

 of the difference of the semiaxes to half the sum of the same, 

 the ellipticities of the two principal meridians of the earth are 



1 1 



289-54* 295-77* 



The longitude of the greater axis of the equator is 8° 15' 

 west of Greenwich — a meridian passing through Ireland and 

 Portugal and cutting off a portion of the north-west corner of 

 Africa; in the opposite hemisphere this meridian cuts off the 

 north-eastern corner of Asia and passes through the southern 

 island of New Zealand. The meridian containing the smaller 

 diameter of the equator passes through Ceylon on the one side 

 of the earth and bisects North America on the other. This 

 position of the axis, brought out by a very lengthened calcu- 

 lation, certainly agrees very remarkably with the physical 

 features of the globe — the distribution of land and water on 

 its surface. On the ellipsoidal theory of the earth's figure, 

 small as is the difference between the two diameters of the 

 equator, only 3000 feet, the Indian longitudes are better re- 

 presented than on the spheroidal ; but there is still left at 

 Madras and Mangalore an attraction or disturbance of the 

 plumb-line seawards. 



