d.

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 containe