The Account of a 
5*6 
ART. IV. PROBLEM. 
Having given the length of a degree of a great circle per- 
pendicular to the meridian, in the latitude whose tangent is t, 
and cosine s, and likewise the length of a degree upon the 
meridian, to find the diameters of the earth, supposing it an 
ellipsoid. 
In fig. 5. let A P A P be the elliptical meridian, passing 
through the point B, the tangent of its latitude being t, and 
cosine s ; and put AC = T, C P = C, D = the length of 
the degree of the great circle, d = that of the degree upon the 
meridian, and r — 9 &c. the degrees in radius. Then, if 
B F, and A F be the ordinate and abscissa to the point B ; 
T 2 
FC = v /PT7^’ 
And<< 
D = 
T a 
r d 
ss/ t* + r c 1 
the great circle, 
C 1 T* 
v/T* + f C 2 
ridional degree. 
= BR, the radius of curvature of 
the radius of curvature of the me- 
These equations give D C* = d s* . T a -f- /*C* ; hence C = 
s T y/ g— ■ d ~-— - ; therefore C : T : : y/ d : ^ D + D — d . t% 
which call as 1 : m ; then r D = — r= -- C ; and C = 5 rDx/mZ + *\ 
ss/m z + t*’ m z » 
therefore T may readily be found. 
