IN PHYSICAL ASTRONOMY. 
37 
_ f o r . - 11640w,a’\ 20 
-i“ r3 + ri 2849^0/ /I7 
^ 40 3 a 3 
5 ~ ~ 37 .43 pa 3 
If ^ = J ^. 72 J, as Newton finds, Principia, vol. iv. p. 2, Glasgow edit., 
r,= -007208 r 3 = -16923 r 5 = - *008437 z 147 = -03896 
A,= -010244 X 3 = -40409 X 5 = - -22501 s 147 = z 147 + r x = -04617 
These values being substituted in the developments of S R, l d R &c. given 
in this paper, more accurate values maybe found from the differential equations 
by a new integration. It would be shorter, but perhaps not quite so satis- 
factory, to assume the values of X 3 , &c. given by M. Damoiseau in these 
substitutions. 
Converting the coefficients of the arguments of longitude into sexagesimal 
seconds; 
A=s 21 1 3" sin 2* + 4571 "-3 sin (2 t - x) - 779"-3sinz 
2370 458S-61 673-7 
The numbers underneath are the values according to M. Damoiseau. 
The coefficient of the variation thus obtained (2113" or 35' 13") agrees 
within three seconds with that found by Newton, vol. iv. p. 10, which is 35' 10". 
The approximation is in fact of the same order as that of Newton. Newton 
does not appear to have succeeded in determining the evection, the most con- 
siderable of all the lunar inequalities after the equation of the centre. The 
value assigned by him to the annual equation is 1 1' 51" or 71 1" (corresponding 
to e ( = •0169166) ; he has not however given the method by which it was 
obtained. 
The equation 
r , „ , m' f a 3 , , 
{l-3r 0 }-l+ — + 
7)1 f Qp t Qp *1 
since r ° = ~^\ 2 a} &3 >° — 2 a* ^ 3 ’ 1 j (See Phil. Trans. 1831. p. 50.) 
• „ , , m. f a 3 , 5 a 2 , 1 
gives c = 1 + -'{ ^63.0 - 4 —A>} 
If A jl + 2r 0 | =n Or »{l + 2r 0 } S sn 
« = nL ^ *b 90 + l* bai ll 
[ u la/ 3(0 a/ 31 a 3 3,0 4 a/ 3,1 J J 
