TOL. LXXVII.] PHILOSOPHICAL TKANSACTIONS. 249 



the latitudes and the measured lengths of the degrees which, in the 2d ellipsoid, 

 have been compared together, will appear as below : 



Observers names. Countries. Latitudes. Measured lengths. 



Bouguer, Peru, 0° 0' 60484.5 



Mason and Dixon, . . Maryland, 39 12 6o628.5 



Boscovich, Italy, 43°0'1 ^9 / ^^725.5 1 ^ 



Beccaria, Piedmont, 44 44 J ^"^ ^^ 1 6082 1.3 / ^^' '"^'^ 



Cassini, &c Middle of France, 45 60777.6 



Liesganig, Austria, 48 43 ) «?/ ^0839-4 1 /Cnoo, « 



Cassini, &c North of France, . . 49 23 j ^^ "^ 1 60826.6 / ^«»33.0 



Maupertuis, &c Lapland, 66 20 6l 194.3 



Now these 6 degrees, being successively compared with each other, 15 results 

 are thence obtained, the arithmetical mean of which gives for the ratio of the 

 semi-diameters of the ellipsoid that of 192.483 to 191.483. Hence the arc mp 

 should be in length 27331 fathoms. The arc m Perpignan exceeds the truth 

 1758, the 45th of latitude 180, and that at the polar circle near 88 fathoms. 



The ratio of the semi-diameters of the 3d ellipsoid 2l6.o6 to 215.06 is ob- 

 tained by adhering to the measured lengths of the degrees at the equator and 

 polar circle. According to this hypothesis the arc mp should contain 27301 

 fathoms. The arc m Perpignan exceeds the truth 1288, and that at the 45th of 

 latitude more than 128 fathoms. 



The ratio of the semi-diameters of the 4th ellipsoid 222.55 to 221.55 is the 

 same as that assigned by M. Bouguer to his first sphferoid, where the increments 

 to the degrees of the meridian above that at the equator are as the 2d power or 

 squares of the sines of the latitudes. The arc mp should contain 27294 

 fathoms. The arc m Perpignan errs in excess II77 fathoms. The 45th degree 

 exceeds the truth 1 1 6 fathoms ; and that at the polar circle falls short of the 

 measured length 2] fathoms ; M. Bouguer's degree at the equator being adhered 

 to as the standard. 



The ratio of the semi-diameters of the 5th ellipsoid, 230 to 229, is that as- 

 signed to the earth by Sir Isaac Newton. On this hypothesis the arc mp should 

 contain 27241 fathoms. The arc m Perpignan only exceeds the truth 202 

 fathoms, because the 45th degree of the meridian is here adhered to as the 

 standard length. But then the degree at the equator falls short of the measure- 

 ment 102 fathoms, and that at the polar circle 1464-; therefore an arc of 8^-i- 

 iii the first case, would be defective 850, and in the last 1220 fathoms. 



The ratio of the semi-diameters of the 6th ellipsoid, 310.3 to 309.3, is ob- 

 tained by adhering to the measured lengths of the degrees at the equator and 

 45tli of latitude. The arc mp should contain 27230 fathoms. The arc m Per- 

 pignan only exceeds the truth 131 fathoms; but on this hypothesis, the degree 



VOL. XVI. - K K 



