68 PHILOSOPHICAL TRANSACTIONS. [aNNO IJQl. 



Paris will, on such an ellipsoid, exceed the measured arc by a quantity answering 

 to about 21" of latitude. It is evident however, that if we suppose small errors 

 to have taken place in determining the celestial arcs, or differences of latitude 

 in some of the operations (for there is little doubt but the terrestrial mensura- 

 tions in general have been made exact enough,) it will be easy to reconcile most 

 of the results to an ellipsoid. 



The following computations of the longitude are made on a supposition, that 

 the earth is an ellipsoid, for the purpose of comparing the conclusions with what 

 has been inferred from observation. It will be seen, that the ratio of the axes 

 comes out very near the ratio assigned by Sir Isaac Newton, or 229 to 230. It 

 is determined of such a magnitude, by adhering nearly to the measured arc of 

 the meridian between Greenwich and Paris, deduced from the late operation, 

 that the computed meridional degrees differ but little from the measured ones in 

 5 different places in middle latitudes; but the defects at the equator and polar 

 circle are supposed to be nearly equal to each other. This will be seen better 

 by the following comparative view of the measured and computed degrees in the 

 same latitudes. 



According to Lat. Measured. Computed. Excess or defect 



° ' Fath. Path. in measured arc. 



M. Condamine, &c 60481 60344- +137 



Mason and Dixon, 39 12 6o621 6o682 — 54 



Boscovich, &c 43 60725 6073S — 13 



Cassini, &c 45 60778 60768 + 10 



Liesganig, 48 43 60S39 60823 + l6 



r Arc from latitude ~4 



French and English < 48° 50' 14" to > 160656 ]6o662 — 6 



L 51 28 40 J 

 Maupertuis, 66 20 61 194 61057 +137 



In the 5 comparisons, from latitude 39° 1 2' to Greenwich, the greatest error, 

 54 fathoms, answers to about 3" of the celestial arc: neither of the other 4 

 differences amount to 1''. The determination of M. Beccaria is not brought 

 into the comparison, because his measured degree in latitude 44° 44' is longer 

 than the measured one in latitude 45°. 



The longitude of Dunkirk on this ellipsoid is found to be 9"* 29.8' in time; 

 and consequently that of Paris 9'" 20^'; which is about \\^ more than that in- 

 ferred from the value of the measured arc between Goudhurst and the meridian 

 of Botley Hill ; and therefore the sum of the 2 horizontal angles at these 

 stations would, on this ellipsoid, be only about 4" less than those found by actual 

 observation. 



Method of compulation. — On an ellipsoid, where the degrees of the meridian 

 at the equator and polar circle are 60481 and 61 194 fathoms respectively, the 

 degree in latitude 50° 9'^, the middle latitude between Greenwich and Paris 

 will be 6098 1 fathoms, exceeding the measured degree by 140 fathoms; there- 



