3 2 
Colonel Lambton’s corrections applied 
With respect to the dimensions of the earth, and the length 
of the quadrantal arc of the elliptic meridian, let (l) /=i3°34'44"; 
m' z=. 60493,42 fathoms, e = — ■ — = ,0032226 ; then s e 
=,0096678 ; 3e • sin 2 / 1 V= ,0005329. Then if m be the 
degree on the meridian at the equator, where sin. / is 0, m = 
— = _^£ 49 Mf_ __ 60461,2 fathoms, and therefore 
60461,2 • - = 60850,17 fathoms, the measure of the de- 
gree on the equatorial circle (see the different equations in 
the Philosophical Transactions for 1818, Part II.) 
Put A = 57 0 , &c. the arc equal rad : then A m = 348645 7,9 
and therefore 2 x 3486457,9 = 6972915,8 fathoms for the 
diameter of the equatorial circle ; equal the major axis of the 
elliptical meridian, which call a. Then if the minor axis be 
designated by b, we have b= (1 — e) a = 6950442 fathoms 
for the polar axis of the spheroid, supposing it to be an el- 
lipsoid. But 3,14159, &c. x 6972916 = 21906074 the cir- 
cumference of the circumscribing circle. Then if d=. 1 b — 
=,0064355 ; we have 1:1— ( ) : : 21906074: 
21871024, the length of the elliptic meridian. Hence — T 024 
= 5467756 is the length of the quadrantal arc, which, reduced 
to inches, and multiplied by 10,000000 we get 39,3677 in- 
ches for the metre at the temperature of 62°, which falls short 
of the French metre by ,0032 inches, when reduced to the 
same temperature. 
This conclusion is very satisfactory, and I hope that equal 
success will attend my operations to the northward. I have 
already measured another section, which extends to latitude 
