Measurement of three Degrees of the Meridian. 349 
The arc of the meridian, between Greenwich and For- 
mentera, is so fortunately situated, that its middle point is in 
latitude 45 0 . Its whole extent measures 12 0 48' 44'', and the. 
distance between the parallels, in linear measure, was found 
to be 730430,7 toises. Hence the mean degree, correspond- 
ing to the latitude of 45 0 4/ 18", is 57010,5 toises ; and if we 
multiply this number by 90°, we get one-fourth part of the 
meridian of the earth. 
The correction to be deduced for oblateness is 58, 59, or 
61 toises, according as it is assumed to be or 3-i-, 
and if we take the mean of these, we have the fourth part of 
the meridian Q = 513088b toises ; and hence the metre = 
44330867 lines ; so that the value of the metre turns out to 
be almost entirely independent of the elliptical form of the 
earth. 
The radius of the equator is derived from the expression 
log. a = log. (v) + K . d ■ 8 + T& ■ £ ' — 5? . £ ’)> e bein S the 
oblateness, and n the periphery of a circle = 3,1416. 
In order to compare any degrees measured with those ob- 
tained on the elliptic hypothesis, we have a very simple for- 
mula. Let m and m" be the values of two degrees on the 
meridian, of which the mean latitudes are t]/i and ^2 ; in com- 
paring the analytic expressions for these two degrees, deve- 
loping them, and then making tp = 45°, we have m! — m . 
(1 — if- cos. 2^2 . cos. *2^2), m~ 57010,5 toises,/) = 
And then we shall find that the oblateness gives 57075,66 
and 57192,38 toises for the degrees in England and Lapland. 
I shall here subjoin one reflection more, which appears of 
MDCCCX1I. Z z 
