Not very long, however; I was soon able to get over this trifling
obstacle.
The plan that first suggested itself was to cut a third piece of stick
of a little over two feet in length, which I could easily guess at
within a few inches. This I could apply alongside of my four-foot rule,
beginning at the end, and proceeding as if I was measuring the latter
with the former. Of course, on the first application, two lengths would
reach from the end of the rule to the notch that marked the four feet
length, and perhaps extend a little beyond. I should then shorten the
measure and apply it again. This time its end would have approached
nearer to the aforesaid notch. Another bit cut off would bring it still
nearer; and the process being repeated, by shaving gradually from the
end of the stick, I should at last find that two lengths of it would
exactly correspond with the length of my four-foot rule. I should then
have a piece exactly two feet in length, and by the help of this I could
find the middle part of the longer piece, and could mark it with a
"nick."
By cutting the short piece into two nearly equal parts, I could then
take the larger of them, and, by a similar process, obtain the standard
of a foot, and mark it also upon my rule; and so on till I had succeeded
in arriving at the inches.
Of course, to do all this would require time, patience, and the nicest
precision; but I had plenty of time upon my hands, and it was my
interest to be both patient and precise.
Although I regarded not the time, just as I was about to carry out the
plan described, another suggested itself that promised to lead me sooner
to the issue; it would call for less patience, though an equal amount of
precision.
This new plan was a sort of corollary of the former one, the only
difference being, that instead of a _stick_ I should perform my
subdivision and graduation with a _string_.
The thongs of my buskins came into my mind--the very thing!
I could not have found a better string for the purpose. They were
strips of best calfskin, cut with the grain, and could not have been
stretched the eighth part of an inch. They would, therefore, measure as
accurately as a rule of boxwood or ivory.
One would not be long enough; so I knotted the two together, taking care
to make a neat, firm knot of it. They made a string of over four feet,
and having laid it along the four-foot rule, I cut it with my knife to
that length exactly. I was not satisfied till I had measured it over
and over again, each time pulling the thong with all my strength, lest
some "kink" might be lurking in it. A slight error would derange my
intended scale, though there is less danger in graduating four feet down
to inches than in going from the less to the greater standard. In the
former, each subdivision naturally lessens the error, while in the
latter it is continually doubled.
When convinced that I had got the thong to the precise length, I placed
its two ends together, and then drawing it with a firm pull through my
fingers, I creased it exactly in the middle. Holding it taut upon the
blade of my knife, I cut through at the crease, and thus divided it into
two moieties of equal length, each two feet long. The part with the
knot I laid aside as being no longer needed, and the remaining half I
again doubled, and cut into two. This gave me two pieces each a foot in
length.
One of these I next folded in triple, and creased for cutting as before.
This was a delicate operation, and required all the skill of my fingers
to accomplish, for it is much easier to divide a string into two equal
parts than into three. I was a good long time before I could get it
trebled to my satisfaction; but I succeeded at length, and then severed
the parts.
My object in thus cutting into three, was to get the pieces in even
fractions of four inches each, in order that by two more doublings I
might arrive more accurately at the inch.
And in two more doublings I found it.
To make sure that I had committed no error, I took up the knotted piece,
which I had laid aside, and after placing the other fragments where they
could be got at, I reduced the second half of the string as I had done
the first.
To my gratification, the inch I obtained from both exactly corresponded.
There was not a hair's breadth of difference.
I was now in possession of a guide to the true graduation of my
measuring-stick. I had pieces of one foot, of four inches, of two, and
of one; and by the help of these I proceeded to mark my rod after the
manner of a draper's yard-stick.
It occupied some time, for I worked with care and caution; but my
patience was rewarded by finding myself in possession of a measure upon
which I could rely, even in a calculation involving the question of my
life.
I was not much longer in deciding the point. The diameters were now
measured by feet and inches, and the _mean_ of the two taken. This was
reduced to surface measure by the usual method of squaring the circle
(multiplying by eight, and dividing by ten). This gave the base of the
hollow cylinder, which would be equal to the frustum of a cone of like
altitude; and another multiplication by the length produced the entire
cubic content.
Dividing by sixty-nine, I got the number of quarts, and so gallons.
The butt, when full, had contained somewhat above 100 gallons--as near
as I could calculate, about 108--and therefore it was in all likelihood
an old pipe that had once contained sherry.