2i 2 Gen. Roy’s Account of a 
Befides thefe two fpherpids of M. Bouguer, I had com- 
puted the arcs of another between the two, where the incre- 
ments to the degrees of the meridian were in the ratio of the 
fractional power of the fines of the latitudes. Thus the 
computed agreed accurately with the meafured dimenfions in 
three principal parts of the earth’s circumference, namely, at 
the equator, 45 0 and 66° 20' of latitude,- at the fame time that 
the arc MP contained 27257 fathoms ; but the labour of com- 
putation being hereby greatly augmented, and the error on the 
total arc between M and Perpignan amounting to 290 fathoms 
in excefs, this fy ffem did not feem to me to deferve to be put 
in competition with the fimplicity of that of M. Bouguer, who 
indeed, for the fame reafon, preferred the fourth to the frac- 
tional power ^l-iths, which he tells 11s was that which hill 
came nearer the truth. In fhort, it muff be from the refults 
of future operations executed in very high latitudes, and the 
meafurement of degrees of longitude on the equator, that we 
can hope to have fufficient authority for any correction or a 
melioration of the fyftem of M. Bouguer. 
Differences of longitude . 
Hitherto there has been no particular reference to fome lines 
at the bottom of the table, containing the computed lengths of 
degrees of longitude on each hypothecs, in three different lati- 
tudes, namely, the equator, 43 0 32^ and 5i°28 / 4o // . No 
meafurements of degrees of longitude, as far as I know, have 
ever been executed with fufficient care and accuracy, except 
that in the fouth of France, as mentioned in the 105th and 
106th pages of M. Cassini’s book, which was determined by 
the 
