We shall then have, for the train ABF (Eq. I.),
n 60 n' - a
--- = - ---- = -2 = --------, in which n' = 1, m' = 0,
m 30 m' - a'
1 - a 1
whence -2 = -------, 2a = 1 - a, 3a = 1, a = ---.
-a 3
And for the train A'B'F' (Eq. II.),
n 60 n' 1
--- = ---- = 6 = --------, in which a = ---, m' = 1,
m 10 m' - a' 3
n'
whence 6 = -----------, or n' = 4.
1 - (1/3)
That is, the last wheel F' turns _four_ times about the axis LL during
one revolution of the crank H. But according to Profs. Willis and
Goodeve, we should have for the second train:
n 60 n' - a 1
--- = ---- = 6 = --------, in which a = ---, m' = 1,
m 10 m' - a' 3
n' - (1/3)
which gives 6 = -----------, n' - (1/3) = 4, n' = 4-1/3,
1 - (1/3)
or _four and one-third_ revolutions of F' for one of H.
This result, no doubt, might be near enough to the truth to serve all
practical purposes in the application of this mechanism to its
original object, which was that of paring apples, impaled upon the
fork K; but it can hardly be regarded as entirely satisfactory in a
general way; nor can the analysis which renders such a result
possible.
* * * * *