We have here a compound train, consisting of two simple planetary
trains, A--F and A'--F'; and its action is to be determined by
considering them separately. First suppose T' to be removed and find
the motion of F; next suppose F to be removed and T fixed, and find
the rotation of F'; and finally combine these results, noting that the
motion of T' is the same as that of F, and the motion of A' the same
as that of T.

Then, according to the analysis of Prof. Willis, we shall have
(substituting the symbol _t_ for _a_ in the equation of the second
train, in order to avoid confusion):

n n' - a
1. Train A--F. --- = 1 = --------; m' = 0,
m m' - a

n' - a
whence -------- = 1, n' = 0, = rot. of F.
a

n n' - t
2. Train A'--F'. --- = 1 = --------; m' = 0,
m m' - t

n' - t
whence again -------- = 1, t = 0, = rot. of F'.
-t

Of these results, the first is explicable as being the _absolute_
rotation of F, but the second is not; and it will be readily seen that