16, A and F may be
made bevel or screw-wheels, without affecting the action or the
analysis; but the train-arm in all cases revolves around the central
axis of the system, that is, about the axis of A, and to this the axis
of F _must_ be parallel, in order to render the deduction of the
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'.
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