7 1 
of the Equinoxes. 
15. The other circumstances as to the figure being the 
same as before, let the straight line GV (Fig. 8.) touch the 
ellipse in G, meet QE in V and CM parallel to GH in M. 
Let GI be perpendicular to OE and meet it in I, and let GH 
meet EQ in T. Then, by a well known property of the ellipse, 
Cl : IT : : EO : its parameter ; and therefore by the nature of 
a parmeter, or three proportionals, Cl : IT : : CE a : CP% and 
IT— - C - ^ — . Hence CT = Cl — IT = Cl — and by 
another well known property of the ellipse, CV = Con- 
sequently CT x CV = CE 2 — CP 2 . Now as MAC is part of 
the straight line drawn from the centre of the sun to that 
of the earth, the angle ACE is the sun’s declination, and as DC 
is perpendicular to AC, the angle ECD is the complement of 
the declination. Let m == the sine of the declination, and 
n — its cosine, and then, radius being 1, CT : CH : : 1 : m, 
and CV : CM or (34. 1 . ) its equal GH : : 1 : n. By multipli- 
cation therefore, CT x CV : CH x GH : : 1 : m 7 i. Conse- 
quenty, using the same notation as in the last article, and 
putting e = CP, as CT x CV = CE 2 — CP 2 , we have a 2 — e % 
:fg : : 1 : mn, and fg = a 2 — t x mn. If therefore X denote 
the area of the ellipse PELO, by the last article, the force of 
all the particles to turn the ellipse is - x a 2 — e x X. 
16. Let PELQ be the same ellipse in Fig. 9, as in the 7th 
and 8th figures. Let the spheroid be cut by a plane parallel 
to PELO, (Fig. 9,) and let the section be the ellipse HKNG ; 
and let this ellipse be supposed to be above the plane of the 
paper on which PELQ is represented. Again, let the spheroid 
be cut by a plane passing through PL, and perpendicular to 
the plane PELO, and let the line of common section of this- 
