«248 PHILOSOPHICAL TRANSACTIONS. [aNNO 1787. 



With regard to the 1st ellipsoid, supposing the earth to be homogeneous, it 

 is well known, that the ratio of its semi-diameters may be found, by comparing 

 with each other the lengths of the pendulums that vibrate seconds in different 

 latitudes ; which lengths are deduced from the seconds of acceleration, that the 

 pendulum, so adjusted, and unalterably fixed as to length, at the equator, would 

 perform in 24 hours, on being successively transported to different latitudes, as 

 far as the pole, where the force of gravity being the greatest, the acceleration 

 would likewise be the greatest. The calculations for this purpose were first made 

 soon after Lord Mulgrave's return from his voyage towards the north pole in 



1773. \ 



And it appears, that the arithmetical mean of 75 comparisons between Spitz- 

 bergen and the equator gives the ratio of the semi-diameters 179.O47 to 178.047. 

 On this hypothesis the arc mp should contain 27350 fathoms. The error on 

 the total arc m Perpignan amounts to 2078 fathoms. M. Bouguer's degree at 

 the equator being adhered to, the 45th of latitude will exceed the truth 2l6, 

 and that at the equator 148 fathoms. 



The ratio of the semi- diameters of the 2d ellipsoid, has been obtained by the 

 comparison of such measured lengths of the degrees of the meridian in differ- 

 ent latitudes, as have been found to be most consistent with each other. Our 

 countryman, Mr. Norwood, was the first, of late times, who made any attempt 

 of this sort. But the measurement, executed by him in the year l633, between 

 London and York, has no pretence to exactness, since he himself tells us, that 

 when he did not measure, he paced ! Besides, his degree is as great, or even 

 greater, than that in Lapland;* and these are surely sufficient reasons for re- 

 jecting it from the comparison. The degree measured by M. Liesganig in lati- 

 tude 45° 57', in that part of Poland lately fallen to the share of the Emperor 

 and annexed to Hungary, being so much shorter than degrees to the southward 

 of it, gives grounds to suspect, that some error had crept into that operation, 

 or that the plummet had been affected by the attraction of neighbouring moun- 

 tains, and therefore is not used on the present occasion. M. De La Caille's de- 

 gree at the Cape of Good Hope, being in south latitude, and so much greater 

 than those of the same height in northern latitudes, is also improper to be 

 brought into the comparison, lest the difference may have arisen from a dissimi- 

 larity in the two polar sides of the ellipsoid. The degree measured in the north 

 of France, compared with that in Austria, coming out absurd, it has been 

 judged best to take a mean between them for a mean latitude. In like manner 

 the latitudes of the two Italian degrees differing but little from each other, a 

 mean length has been taken between them for a mean latitude. Accordingly 



* That in Lapland however has since been found to be very erroneous. 



