[Illustration: PLANETARY WHEEL TRAINS. Fig. 18]

A favorite illustration of the peculiarities of epicyclic mechanism,
introduced both by Prof. Willis and Prof. Goodeve, is found in the
contrivance known as Ferguson's Mechanical Paradox, shown in Fig. 18.
This consists of a fixed sun-wheel A, engaging with a planet-wheel B
of the same diameter. Upon the shaft of B are secured the three thin
wheels E, G, I, each having 20 teeth, and in gear with the three
others F, H, K, which turn freely upon a stud fixed in the train-arm,
and have respectively 19, 20, and 21 teeth. In applying the general
formula, we have the following results:

n 20 n' - a 1
For the wheel F, --- = ---- = ---------, [therefore] n' = - ---- a.
m 19 -a 19

n n' - a
" " " H, --- = 1 = --------, [therefore] n' = 0.
m -a

n 20 n' - a 1
" " " K, --- = ---- = ---------, [therefore] n' = + ---- a.
m 21 -a 21

The paradoxical appearance, then, consists in this, that although the
drivers of the three last wheels each have the same number of teeth,
yet the central one, H, having a motion of circular translation,
remains always parallel to itself, and relatively to it the upper one
seems to turn in the same direction as the train-arm, and the lower in