-a = a - m', or m = 2a.

The other view of the question is, that F turns once backward in its
bearings during each forward revolution of T; whence in Eq. 2 we
have--

n' n
-------- = --- = -1, n' = -a,
m' - a m

-a
[therefore] -------- -1, which gives -a = a - m', or m' = 2a,
m' - a

as before.

It is next to be remarked, that the errors which arise from applying
Eq. I. to incomplete trains may in some cases counterbalance and
neutralize each other, so that the final result is correct.

[Illustration: PLANETARY WHEEL TRAINS. Fig. 20]

For example, take the combination shown in Fig. 20. This consists of a
train-arm T revolving about the vertical axis OO of the fixed wheel A,
which is equal in diameter to F, which receives its motion by the
intervention of one idle wheel carried by a stud S fixed in the arm.
The second train-arm T' is fixed to the shaft of F and turns with it;
A' is secured to the arm T, and F' is actuated by A' also through a
single idler carried by T'.