of an Arc of the Meridian. 
44A 
under one point of view for future use, we shall have the fol- 
lowing 
Arcs. 
Feet. Miles. 
1. Clifton and Dun nose - 10 3^337 — 196,27 
а. Dunnose and Arbury Hill - 586320= 111,05 
3. Dunnose and Greenwich - - 313696 = 59,4,1 
4. Clifton and Arbury Hill - 450017= 85,23 
5. Clifton and Greenwich - - 722641 = 136,86 
б. Arbury Hill and Greenwich - 272624= 51,63 
Remark. 
In calculating the distance between the parallels of latitude 
of two places, connected by means of a trigonometrical opera- 
tion, regard must be had to their difference in longitude. If the 
triangles run nearly north and south, in which case stations 
must lie both east and west of the two meridians, it is suffi- 
ciently correct to proceed on the supposition of the earth's 
surface being a plane ; but if, on the contrary, the triangles 
wholly diverge from the two meridians, or even partly do so, 
first running off obliquely and then returning again, a different 
of the degree oblique to the meridian j or, putting i — s* for c 4 , and r for p — m, 
it will be — 
p — rs* 
Corol. If d be the length of the oblique degree, then, since d r= we have 
p — and m ;r And, if D be put for the length of another oblique 
degree at the same point, and S and C the sine and cosine of its inclination to the 
meridian, we shall get m — ^r ~ C \ X Dd, and p = SV ‘~^ 1; X D d, the meri- 
S 8 D — s* d r c* d — C*D 
dional and perpendicular degrees, exhibited in terms of the oblique degrees combined 
with the sines and cosines of their inclinations to the meridian. Therefore, an ellipsoid 
may be determined from the lengths of two oblique degrees in the same latitude. 
We may likewise remark, from the nature of radii of curvature, at the same point 
G, that the expression ---ff-— will also give the oblique degree on different spheroids. 
