IN PHYSICAL ASTRONOMY. 
357 
h ,2 sin 2 cos (3 nt - njt + 3 s - e,— 2 v,) 
1 1 
Cl 
1 1 
— m, ^ 3>3 sin 2 y cos (2 nt — 4 ra/ + 2 s — 4 s, + 2 v) 
[73] 
bs > 3 sin2 g- cos (4»/ — 2 w/ + 4 8 — 2 s, — 2 
[74] 
In the development of R, I have supposed / = 0, so that t t is the angle con- 
tained between the orbits of the planets P and P ( , or Pj and P 2 ; in the ge- 
neral case, when / x , and / 2 , are retained, cos = cos ^ cos / 2 + sin i l sin < 2 cos 
(<i — / 2 ), /j and / 2 , being the inclinations of the orbits of the planets P t , P 2 to 
any plane xy , of which the direction is arbitrary, 
r r] sin (X v — \]) = r x r 2 1 cos 2 cos 2 ^ sin (X x — X 2 ) 
— sin 2 cos 2 sin (X x + X 2 — 2 + sin 2 ~ cos 2 sin (A 2 -|- X 2 — 2 v 2 ) 
— sin 2 ^ cos 2 sin (A x — X 2 - 2 + 2 v 2 ) j 
r r ; ' | cos (X v — X,') + s s t = r Y r 2 | cos 2 cos 2 cos (X 2 — X 2 ) 
+ sin 2 cos 2 cos (X x -j- X 2 - 2 ^) + sin 2 cos 2 cos (X x + X 2 - 2 v 2 ) 
+ sin 2 sin 2 cos (X x - X 2 - 2 ^ + 2 v 2 ) 
+ sin sin i 2 cos (X 2 — X 2 — ^ + v 2 ) — sin sin i 2 cos (X x -f X 2 — v 1 — v 2 ) £ 
Errata. 
In page 330, for i and v, read i t and v r 
