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

n n'
For the wheel H, --- = 1 = ----, [therefore] n' = -a;
m -a

n 20 n' 20
For the wheel K, --- = ---- = ----, [therefore] n' = - ---- a,
m 21 -a 21

which corresponds with the actual state of things; all three wheels
rotate in the same direction, the central one at the same rate as the
train arm, one a little more rapidly and the third a little more
slowly.

It is, then, absolutely necessary to make this modification in the
general formula, in order to apply it in determining the rotations of
any wheel of an epicyclic train whose axis is not parallel to that of
the sun-wheels. And in this modified form it applies equally well to
the original arrangement of Ferguson's paradox, if we abandon the
artificial distinction between "absolute" and "relative" rotations of
the planet-wheels, and regard a spur-wheel, like any other, as
rotating on its axis when it turns in its bearings; the action of the
device shown in Fig. 18 being thus explained by saying that the wheel
H turns once backward during each forward revolution of the train-arm,
while F turns a little more and K a little less than once, in the same
direction. In this way the classification and analysis of these
combinations are made more simple and consistent, and the