C 1 
By this means then, the latitude of the place and 
the angle PME (contained between the meridian 
PMN and the great circle AMB) being given, the 
length of the Arc ME will likewife be given, with 
great exadtnefs. But f muff obferve, that as the 
angles PEM and PME mull be taken by the obfer- 
vation of fome ftar near the pole, they will be lefs 
accurate, when reduced to the plain of the horizon, 
than at the pole, in the proportion of the Sine of the 
diftance between the pole and zenith, that is the Col', 
of the latitude, to the R, which with the proportion 
juft mentioned of the Tan. of the latitude to the R, 
makes the accuracy of this method upon the whole, 
when compared with that of the meafurement of a 
degree of the meridian, in the proportion of the Tan. 
multiplied into the Cof. of the latitude, to the lquare 
of the R. very nearly; but the Tan. of any angle into 
its Cof. is equal to the Sin. into the R. whence this 
proportion is the fame as the Sin. into the R. to the 
lquare of the R. and dividing both by the R. fimpiy 
as the Sin. of the latitude, to the R. as above. 
Having got the length of the arc ME, of a great 
circle, in degrees, &c. together with the diftance of 
the two ftations M and E, it is eafy to conclude from 
thence the length of a degree of the parallel of lati- 
tude, at the place of oblervation, which will be the 
fame, without fenfible error, as it would be, fuppofing 
the earth was an exadt fphere, to the fame fcale, with 
the degree of a great circle juft found. 
For in Fig. 8. let APB reprefent a fedlion 
of the earth through its axis PCH; A C B an 
^equatorial diameter; AD the radius of curvature at 
the point A ; and PH the radius of curvature at the 
Vol. LVI. R point 
