In train A'--F':

n' n' n'
--- = 1 = --------; m' = 0, [therefore] ---- = 1, or n' = -t;
m m' - t -t

In combining, we have in the latter train m' = 0, t = -a, whence

n n' n'
--- = 1 = -------- gives ---- = 1, or n' = a, as before.
m m' - t +a

Now it happens that the only examples given by Prof. Willis of
incomplete trains in which the axis of a planet-wheel whose motion is
to be determined is not parallel to the central axis of the system,
are similar to the one just discussed; the wheel in question being
carried by a secondary train-arm which derives its motion from a wheel
of the primary train.

The application of his general equation in these cases gives results
which agree with observed facts; and it would seem that this
circumstance, in connection doubtless with the complexity of these
compound trains, led him to the too hasty conclusion that the formula
would hold true in all cases; although we are still left to wonder at
his overlooking the fact that in these very cases the "absolute" and
the "relative" rotations of the last wheel are identical.

[Illustration: PLANETARY WHEEL TRAINS. Fig. 21]