210 Gen. Roy’s Account of a 
above that at the equator follow the ratio of the fecond power 
or fquares of the fines of the latitudes, and to which he has 
fuited his firft table of degrees, N° 32. p. 298. This fpheroid 
differs but infenfibly, as has been already mentioned, from the 
fourth ellipfoid. They have both the fame femi-diameters ; 
but the arcs of the fpheroid being fomewhat longer than thofe 
of the ellipfoid, the former thereby becomes, in a trifling 
degree, more prominent in middle latitudes. On this hypo- 
thecs the arc MP fhould be in length 27295 fathoms; M Per- 
pignan exceeds the meafurement 1196 fathoms; and the de- 
gree at the equator being adhered to as the ftandard, the 45th 
errs in excels 118, while that at the polar circle is defective 
only 20 fathoms. 
The fecond fpheroid is that whereon M. Bouguer founded 1 
his fecond hypothefis, which fuppofes the increments to the 
degrees of the meridian, above that at the equator, to follow 
the ratio of the fourth power or fquared fquares of the fines of 
the latitudes, and to which he has adapted his fecond table of 
degrees N° 38. p. 305. It will be perceived, that the ratio of 
the femi-diameters of this fpheroid, viz. 179.410 178.4 differs 
little from that appertaining to the firffc ellipfoid ; but here the 
curve falling confiderably within, that is to fay, being lefs pro- 
minent than the ellipfoid in middle latitudes, the arcs are 
thereby contra&ed in fuch a manner as to agree within 5 fa- 
thoms with the meafu red length of the meridian of France, in 
an extent of about 8°f , comprehended between M near Dun- 
kirk, and Perpignan fituated at the bottom of the Pyrenean 
mountains. By infpeCtion of the table it will further appear, 
that the errors in the feveral feCtions of this arc are not only 
fmall, but they are fometimes plus and fometimes minus, a> 
never failing proof that, as fat as our prefent data will enable 
