from Measuremefits of the Meridian. 435 



actual measurement in the proper latitude ; but we may in 

 some measure be enabled to judge of its exactness by em- 

 ploying the portion of the meridian that has been calculated. 

 Let A' represent the mean latitude between Dunnose and Clif- 

 ton, then 



A = 54° 44' 0" 



A' = 52 2 20 ; 

 and, by means of formula (C), we shall readily obtain, 



D(a')-D(a) = f A e (cos 2 A- cos 2 A'), 



the term containing e 2 being insensible. Now, by dividing 

 the length of the English arc by its amplitude, we get D (A) 

 = 60824 : 1 ; and hence, 



D (A') = 60824-1 + 26*6 = 60850-7, 

 which is only five fathoms less than the exact value of A, and 

 this deficiency is caused by the small error of the arc, which 

 is too short 



It follows, from the foregoing minute examination, that the 

 five arcs are represented with great precision by the elements 

 that have been found ; and further, that each arc, taken se- 

 parately, agrees accurately with the curvature of that portion 

 of the meridian in which it is situated. And there cannot be 

 a more satisfactory way of proving that the meridian of the 

 earth is an ellipsis, than by showing that it coincides with that 

 figure, at the equator, at the mean latitude of 45°, at the pa- 

 rallel of 54° 44' where the curvature is identical to the equa- 

 torial circle, and at the pole. We have briefly endeavoured 

 to accomplish this task as far as the measurements in our 

 possession put it in our power to do so; but the proof would 

 have been much more complete, if we could have confirmed 

 it by the length of the meridian through the whole extent of 

 Britain. 



To the fixt points on the meridian that have already been 

 mentioned, we may add another intermediate 'between the 

 equator and the parallel of 45°. In the expression (C), put, 



Cos 2A = + £, A = 35° 16'; 



then, D(x)=A (1-f - f e 2 ) =A(1- 0- 



At this latitude, which is the complement of 54° 44', the radius 

 of curvature of the meridian is equal to half the polar axis. 

 The length of the degree depends upon the elements of the 

 ellipsis ; and it may serve as a quantity of reference for judging 

 of the consistency of any measurement made near its parallel 

 of latitude. In the present state of this research there is no 

 measurement that can be compared with it. The nearest to 



3 K 2 it 



