"newshound" wrote: No way this is a substitute for Marv's method, but you
could just use a
spreadsheet. Set up a column going from 1 to 100 (more if you want) and
multiply your fraction by each number in turn. It should be quick enough
to
spot the close matches: here's a section

47 7.674113
48 7.837392
49 8.000671
50 8.16395
51 8.327229
52 8.490508
^^^^^^^^^^^^^^^^^^^^^
I came to the conclusion that it is 49/8, using a similar method. I used
the average ratio in Townsend's list, which was .163118, and then set up a
chart assuming thew small gear had 1 tooth, 2 teeth, 3 teeth... etc until I
came to 8 teeth, which gave me 49.04 on the large gear. Continuing the
process, I didn't come to anything close until 16/98.09. This tells me that
it has to be one of those two, or a multiple, which would be out of
reasonable range.

There may be a mathematical reason to get a weighted average from Townsend's
numbers, but what I did produces a pretty solid conclusion.