formula, as made by Prof. Willis, and also by Prof. Goodeve, correct,
or even possible.

[Illustration: PLANETARY WHEEL TRAINS. Fig. 17]

This will be seen by an examination of Fig. 17; in which A and B are
two equal spur-wheels, E and F two equal bevel wheels, B and E being
secured to the same shaft, and A being fixed to the frame H. As the
arm T goes round, B will also turn in its bearings in the same
direction: let this direction be that of the clock, when the apparatus
is viewed from above, then the motion of F will also have the same
direction, when viewed from the central vertical axis, as shown at F':
and let these directions be considered as positive. It is perfectly
clear that F will turn in its bearings, in the direction indicated, at
a rate precisely equal to that of the train-arm. Let P be a pointer
carried by F, and R a dial fixed to T; and let the pointer be vertical
when OO is the plane containing the axes of A, B, and E. Then, when F
has gone through any angle a measured from OO, the pointer will have
turned from its original vertical position through an equal angle, as
shown also at F'.

Now, there is no conceivable sense in which the motion of T can be
said to be added to the rotation of F about its axis, and the
expression "absolute revolution," as applied to the motion of the last
wheel in this train, is absolutely meaningless.

Nevertheless, Prof. Goodeve states (Elements of Mechanism, p. 165)
that "We may of course apply the general formula in the case of bevel
wheels just as in that of spur wheels." Let us try the experiment;
when the train-arm is stationary, and A released and turned to the