650 VHILOSOPHICAL TRANSACTIONS. [aNNO 17U5. 



of a degree on the meridian in lat. 50" 41', in order to show how far the varyin^T 

 the length of that degree, will affect the comparison between the measured and 

 computed degrees on the first ellipsoid: and those in the 7th are determined by 

 using 60851 fathoms for the degree on the meridian, and SllQl fathoms for that 

 of the great circle perpendicular to it; which last degree is obtained by taking 

 the angle at Dunnose, equal to 81° 56' 53".5, instead of 81° 56' 53". 



Now this comparison between the measured and computed degrees, sufficiently 

 proves that the earth is not an ellipsoid, since the differences are, excepting 2 

 instances, constantly minus; this however presupposes that the degree of the 

 great circle perpendicular to the meridian in lat. 50° 41', as we have found it 

 and likewise the degree on the meridian arising from the measured arc between 

 Greenwich and Paris, and their difference in latitude, are nearly right. Also, 

 were it of Mr. Bouguer's figure, the degree of a great circle in lat. 50° 41' 

 would be 61270 fathoms, which is 88 fathoms greater than we have derived it ; 

 we may therefore safely infer, that his hypothesis is more ingenious than true; 

 since it cannot be supposed that the degree, resulting from these observations, 

 is 88 fathoms in defect; but whether the earth be a figure formed by the revolu- 

 tion of a meridian round its axis, on which the length of the degrees increase 

 according to any law, or one whose meridians are formed by the combination of 

 many different curves, it appears to be certain, that we may consider 6ll82 fa- 

 thoms as nearly the length of a degree of a great circle, in latitude 50° 41', by 

 which we are enabled to settle the longitudes of those places whose situations 

 have been determined in this operation. 



The length of the degree as given by General Roy, from the directions of the 

 meridians at Botley Hill and Goudhurst, is 6 1248 fathoms, which is 66 fathoms 

 different from this result: but this is not to be considered as extraordinary, since 

 the distance between those places is not more than 23 miles, and the direction 

 very oblique to the meridian. It is an indispensable requisite, that the stations 

 chosen for this purpose be nearly east and west; because if both places were on 

 the same parallel of latitude, the horizontal angles would give the difference of 

 longitude, without adverting to the principle of the sums of the angles on a 

 sphere and a spheroid being nearly equal, when the places on each have corres- 

 ponding latitudes, and the same difference of longitude. Were a degree of a 

 great circle perpendicular to the meridian measured in some jilacc remote from 

 the latitude of 50° 41', the diameters of the earth, supposing it an ellipsoid, might 

 be determined; for if / = the length of a degree of a great circle perpendicular 

 to the meridian, in the latitude whose sine is s and cosine c, and l = the length 

 of the degree in lat. 50° 41', a and b being the sine and cosine of that latitude; 

 then will the ratio of the axes be that of \/ (/V" — l'"Zi-) to \/ (h'a- — /V). It 

 is therefore much to be wished, that such measurements were made in the 



