ElimaLtava Mounralrns, 329 
rections, in.order to shew that ilie error’ is really too small to be worth 
attending to. 
8. urs then is the principle, on which the determination of the differ- 
ences of latitude, longitude and Asimuth, of the two ends of an arc of 
distance, on the spheroid, is founded. The whole is reduced by consider- 
ing the matter in this way, to the resolution of a right angled spherical 
triangle. All that is required, being the Radii of curvature of the per- 
pendicular to the meridian, for the points A and B, and the distance of 
their points of intersection in the polar axis D HE. The former are con- 
tained in Table 2, and tle latter in Table 6, calculated from the formula 
2¢ (Sine 4 — sine r) where 2 ¢ means the difference of the axes and 4, ne 
the latitudes of the points BA. It may be more conveniently expressed: 
as follows: : (ees i | 
ds DE=2cdL,sinel CosQ+t dL). 
9. Tux problem being thus simplified and reduced’ to the resolution 
of'a common spherical analogy, we may next inquire whether the received 
formula may not in the cases under consideration, be rendered something 
more convenient in calculation, by eraploying the substitutions and. deve— 
lopments, which the arithmetic of sines offers. 
10. Iw the spherical triangle P A B right angled at B, we have the 
P sides. P B, (Co-latitude B), A B (distance from the me- 
ridian reduced to ° '; and "') to find the third side P A 
(Co-latitude of A), and the angles P (diff. long.) PAB 
Azimuth of B from A.. 
