328: AN ACCOUNT OF THE 
axisin'E. Join A &, also A B. With the radius B E find the value of the 
angle AE B. Phere are then given in the solid angle PE AB, the two 
plane angles AEB, BE P (Co-lat. B), and the inclination of their 
planes = 90 to find the third angle P EB, and the inclination of Ws 
plane with each of the others. But this is evidently that case of right 
angled triangles, in which the base and per] pendicular are aes to find the 
AS 
pypolenys and the angles. 
7. Iris however to be remarked that though the inclination of the 
planes PAGE; P BE be realty the difference of longitude of A B, yet 
the other results of the spherical analogy Hs not equally answer for the 
spheroid, F or the angle P EB A which is that found by spherical compu- 
tation, is not strictly speaking the Co-latitude of A. ‘The true Co-fatitude 
of this point is the angle formed by the vertical A D with the polar axis, 
that is the angle P DA. The difference of the two angles is D A E, and. 
this is the correction to be applied: in order to haye the true Co-latitude 
in the spheroid.* Likewise is it evident that the inclination of the planes 
PE A, ‘AEB is not the real Azimuth of ‘the point B trom A, this being 
determined by the angle which the vertical plane passing through A, forms 
with the meridian that is to say by the inclination of the planes 4 D B, 
PDA. Itis true, that each of these results may for all practical purposes 
be supposed the measure of the Co-latitade and Axmuth, but it was thought 
necessary to make this remark and to give an expression for the two cor- 
* Itis not to be supposed that this is the only effect which the spheroidal figure has on the 
difference of latitude. It has mach more) vie value of the angle A E B, depending altogethes 
on the degree of ellipticity. 
