propofed trigonometrical Operation . 209 
The feventh or la ft ellipfoid, being that of the leaft flattening, 
has for the ratio of its femi-diameters 540 to 539. The arc MP 
fhould contain 27206 fathoms. The 45th degree of latitude 
being adhered to as the ftandard, the arc M Perpignan would 
only exceed the truth by 46 fathoms ; but, on the other hand, 
the degree at the equator erring in excefs 124^ fathoms, and 
that at the polar circle being defective near 303 ; therefore, in 
the firft cafe, the error on 8°f would be 10 37, and in the laft 
2524 fathoms. Hence it is obvious, that the arcs of an ellip- 
foid, however great or fmall the degree of its obiatenefs may 
be, will not any way correfpond with the meafured portions of 
the furface of the earth : for if we retain the length of M. 
Bouguer’s degree at the equator as the ftandard, and make the 
ellipfoid extremely flat, as in N’ 1. the figure will become too 
prominent in middle latitudes, that is to fay, the curve will 
rife above the real furface of the earth, and, in proportion to 
the excefs of the radius, will always give degrees that exceed 
the meafured length. On the contrary, if We give the ellip- 
foid a fmall degree of flatnefs, as in N J 7. and adopt the mea- 
fured length of the 45th degree as the ftandard, the meafured 
and computed arcs will nearly agree in middle latitudes ; but at 
the equator the curve will rife very confiderably above the fur- 
face, and will thereby give degrees that are too great ; while at 
the polar circle it will fall below it, and give degrees that are 
too little in the proportion of about 1 \ to 1 compared with 
the error at the equator. From all which we may conclude, 
that the earth is not an ellipfoid. 
The tw r o columns towards the right-hand of the table, 
contain the arcs of two fpheroids differing from the ellipfoid. 
The firft is that adopted by M. Bouguer as his firft hypo- 
thecs, where the increments to the degrees of the meridian 
Vol. LXXVII. £ e above 
