Example III. Suppose the same three as before, and the common
bets 7 to 4 A against B; 21 to 20 (or 'gold to silver') B against
C; we must state it thus:--7 guineas to 4 A against B; and 4
guineas to L4, B against C; which being reduced into shillings,
the scheme will stand as follows:--
147 A's expectation.
81 B's expectation.
80 C's expectation.
By which it will be 164 to 147 the field against A, (something
more than 39 to 35). Now, if we compare this with the last
example, we may conclude it to be right; for if it had been 40 to
35, then it would have been 8 to 7, exactly as in the last
example. But, as some persons may be at a loss to know why the
numbers 39 and 35 are selected, it is requisite to show the same
by means of the Sliding Rule. Set 164 upon the line A to 147
upon the slider B, and then look along till you see two whole
numbers which stand exactly one against the other (or as near as
you can come), which, in this case, you find to be 39 on A,
standing against 35 on the slider B (very nearly). But as
164/311 and 147/311 are in the lowest terms, there are no less
numbers, in the same proportion, as 164 to 147,--39 and 35 being
the nearest, but not quite exact.