/ ' ' ' - 
so8 Gen. Roy’s Account of a 
The ratio of the femi-diameters of the fourth ellipfoid 222.55 
to 221.55 is the fame, as may be feen by referring to the table, 
with that adigned by M. Bouguer to his firft fpheroid, where 
the increments to the degrees of the meridian above that at 
the equator are as the fecond power or fquares of the fines 
of the latitudes. It was intended chiefiv to (hew how fmall - 
J 
the difference is between the magnitudes and nature of the 
curves of the two figures. The arc MP (hould contain 27294. 
fathoms. The arc M Perpignan errs in excels 1 177 fathoms. 
The 45th degree exceeds the truth 116 fathoms; and that at 
the polar circle falls fhort of the meafured length 21 fathoms: 
M. Bouguer’s degree at the equator being adhered to as the 
fcandard. 
The ratio of the femi-diameters of the fifth ellipfoid, 230 
to 229, is that afligned to the earth by Sir Isaac Newton. 
On this hypothefis the arc MP (hould contain 27241 fathoms. 
The arc M Perpignan only exceeds the truth 202 fathoms, 
becau(e the 45th degree of the meridian is here adhered to as 
the (fandard length. But then the degree at the equator falls 
(hort of the meafurement 102 fathoms, and that at the polar 
circle 146! ; wherefore, an arc of 8"f, in the firft cafe, would 
be defective 850, and in the laft 1220 fathoms. 
The ratio of the femi-diameters of the (ixth ellipfoid, 310.3 
to 309.3, is obtained by adhering to the meafured lengths of 
the degrees at the equator and 45th of latitude. The arc 
MP (hould contain 27220 fathoms. The arc M Perpignan 
only exceeds the truth 131 fathoms; but on this hypothefis^ 
the degree at the polar circle would be defective near 217 fa- 
thoms, and confequently on 8°j the error would be 1807 
fathoms. 
7 
The 
