434 Mr. Ivory on the Figure of the Earth, as deduced 



Here the factor on the right-hand side is but slightly affected 

 by the terms containing s, which reduce it to 12*37; and 

 D (45°) is found equal to 60757, the same value derived from 

 the two elements, and very nearly the same that results from 

 the actual measurement without any assumption about the 

 figure of the earth*. It is therefore certain that the elements 

 which have been found represent with great exactness both 

 the whole arc between Dunkirk and Formentera, and also its 

 mean curvature. I have likewise found that the same elements 

 represent, with small errors, the partial arcs between Dunkirk 

 and Montjouy, and Montjouy and Formentera. But it is well 

 known that the four sections of the arc between Dunkirk and 

 Montjouy are very irregular ; and the causes of the irregu- 

 larity have not been very well explained. Whatever these 

 causes may be, they extend their influence to the measure- 

 ments that have been made in England. Unless I have been 

 misinformed, a re-measurement between Greenwich and Paris 

 has lately been executed, the results of which, when made 

 public, will probably help to clear up the perplexing anoma- 

 lies that occur in the comparison of the partial arcs. 



We may now compare the Swedish, or most northerly, arc 

 with the curvature at the pole. We have, 



A = D(90°) x (1-s); 



and, by substitution, we get, 



98870 = D (90°) . (1-622022-0-7842 . s-0'860 . s 2 ). 



From this equation, taking the foregoing value of e, D (90°) 

 will be found equal to 61051, or only three fathoms less than 

 the value deduced from the two elements; and even this dif- 

 ference will disappear, if we take into account the error of the 

 arc itself. 



If in the expression (C) we make 



Cos 2 A = - £, A = 54° 44', 



we shall get cos 4 X = — ^, and 



D(X) = A(1 -fi«) = A. 



It appears, therefore, that a degree of the meridian in Britain, 

 very nearly midway between York and Edinburgh, is equal 

 to a degree of the earth's equator. Although the Trigono- 

 metrical Survey has been extended between the extreme north 

 and south points of the island, yet, as far I know, the calcula- 

 tions have not been completed except for a small part of the 

 meridian between Dunnose and Clifton. We cannot there- 

 fore verify what has just been shown by comparing it with any 



* Phil. Mag. and Annals for May, pp. 346, 347. 



actual 



