While examining the cask, to find if there was not some means of
ascertaining its different diameters, I discovered the very way itself.
All I wanted was a straight rod or stick, of sufficient length to reach
quite across the butt at its thickest part. It was plain to me, that by
inserting such a stick into a hole in one side of the cask, and passing
it on till it touched the staves on the other side, at a point
diametrically opposite, I could thus obtain the exact measurement of the
diameter of that part of the vessel, since the portion of the rod
reaching from side to side would be the diameter itself. The diameter
once obtained, it needed only to multiply by three to get the
circumference. But in the calculation which I was desirous of making,
it was the diameter itself I wanted to find, and not the circumference.
I only thought of the latter, because, under ordinary circumstances,
when a cask is bunged up, it is easier to measure the circumference of
the swell than its diameter. In no case does it signify which, as the
figure three will always reduce the one to the other, near enough for
most practical purposes, though not mathematically exact.
Now, it so chanced that one of the holes I had cut through the staves
had been made in the very middle of the swell, where the butt was
thickest. Therefore a straight stick passed into this hole, and pushed
on till it touched the opposite side, would give the greatest diameter
of the cask.
You may imagine that this might have been obtained by simply planting
the stick in a vertical position _outside_ the butt, and notching it at
a point on a level with the top of the vessel. True, this might have
been done had I been operating with a barrel lying upon a plain surface,
with nothing around it to obstruct me, and plenty of light to observe
the true level. Even thus it would have been rough guess work, and not
to be depended on when a calculation was to be made involving life or
death in its consequences--for such it really did involve--at least, I
supposed so. But the butt was so placed, resting upon the timbers of
the ship, with its swollen side sunk between them, that I could not have
measured it in this manner. Even though I might have marked a rod on a
line with its top, I could not have planted the other end so as to be on
a level with its base.
There seemed no other way to get at the thing than by inserting a
straight stick into the hole, and thus measure the diameter; nor did I
trouble myself about any other, as this appeared to be the best plan I
could adopt.
Where was I to find my stick--my measuring-rule? That is your question,
is it not?
It is easily answered. The deal board that had formed part of the
biscuit-box would supply me with the material, and out of that I could
soon make one. No sooner thought of than I set about it.
The board was but a little over two feet in length, and of course not
long enough to reach across the great cask, which at its thickest part
appeared four or five. But a very little ingenuity sufficed to overcome
this obstacle. I should only have to split off three thin pieces, and
by splicing their ends together, I should get a stick of length
sufficient.
I did so. Fortunately, the deal was cut nicely with the grain of the
wood; and in splitting it, I guided the blade of my knife so as not to
let it run out at the edges.
I succeeded in getting three pieces of the thickness I wanted; and,
after shaving off their angles, and making them clean and trim, I cut
their ends with a slant for the splice.
The next thing was to obtain two pieces of string, and this was the
easiest thing in the world. I wore upon my feet a pair of little
"buskins" that laced up to the very ankle. The laces were thongs of
calfskin, each of them a full yard long. They were just the thing; and,
drawing them out of the holes, I completed the splicing, and now held in
my hands a straight stick full five feet in length--quite long enough, I
conceived, to reach across the thickest part of the butt, and slender
enough to go into the hole--which I had already widened a little to
receive it.
"So far good," thought I; "I shall now insert the measuring-stick, and
find my diameter."
I rose to my feet to carry out this design, but I need not describe the
mortification I felt on perceiving that the first of these operations,
which would appear to be the simplest of all, could not be performed.
At the first trial I saw that it was quite impossible. It was not
because the hole was too small, or the stick too large. I had made no
mistake about this; but my miscalculation was in regard to the space in
which I had to work. Lengthways my little chamber was nearly six feet,
but crossways little more than two; and up where the hole was--in which
I intended to insert the measuring-rod--it was still less. Of course to
get the stiff piece of stick into the cask was plainly impossible--
without bending it, so that it must break--for the dry deal would have
snapped through like the shank of a clay pipe.
I was a good deal chagrined at not having thought of this before; but I
was still more vexed at the idea of being obliged to abandon the design
of making the measurement I had intended, for before reflecting I
believed that this was to be the result. A little further
consideration, however, helped to a new plan, proving the importance of
not arriving too hastily at conclusions. I discovered a way of getting
in the stick to its full length, without either breaking or bending it.
This could be effected by taking it to pieces again, then first
inserting one of the pieces, and holding it till the second could be
spliced on to its end, and then pushing both into the cask, and joining
the third piece in a similar fashion.
About this there appeared no difficulty, and the result proved there was
none; for in less than five minutes after conceiving it, I had carried
the design into execution, and the measuring-rod stood inside the
barrel, with one end projecting some inches on the outside.
Holding this end carefully in my hand, I caused the other to play about
on the opposite side, until I felt convinced that it touched the point
that was exactly _vis-a-vis_ with the aperture; and then steadying the
stick, I notched it with my knife, on a level with the outer surface of
the stave. To calculate from this notch would not be correct, as it
would be more than the diameter of the cask--that is, in reference to
what it would contain--but I had no intention of doing so. I should
make allowance for the thickness of the stave, and that would give me
the measurement I wanted.
Having made my mark, I drew forth my measuring-rod, piece by piece, as
it had been plunged in. I took care as I did so to notch both the
splices, so that I might be able to put them together again in the exact
place where they had been while making the measurement. All this
attention to such minute particulars was of importance, and I knew it to
be so, for the mistake of even a quarter of an inch in the length of my
diameter would cause a difference of many gallons in the result. Most
certainly, then, was it of consequence that I should be precise in my
_data_.
I now had the diameter of the swell; the next thing was to get that of
the head, or end. About this there was less difficulty--in fact, not
any. It was obtained in a few seconds.
Though I could not myself get round either of the ends of the butt, nor
even my arm, I could pass the rod around them, and in this way measure
them. Even had there not been space to admit the measuring-stick, I
should have found a means--by simply drilling another hole with my
knife, close to either end, and gauging as before. But this would have
occupied time, and it was not necessary to do so, since the stick passed
along the head of the butt without any obstruction, till its end rested
against the projecting rim on the opposite side. I had nothing to do
but assure myself that its point was fair in the middle, and then make
my mark as before.
The length of the butt was yet to be ascertained; and this, though
apparently a simple operation, cost me a good deal of consideration,
before I could get at it with any degree of exactness. You may fancy
that it would have been easy enough to get at the length, by just
placing the stick parallel to the cask, and notching it square with the
ends of the latter? And so it might be easy enough, with plenty of
light around you to see when it _was_ square, and a level surface upon
which to rest your measure. But as I had the advantage neither of light
nor level ground, I encountered great difficulty in this operation. I
could not tell when the ends lay even with each other, merely by the
touch. I had to pass my fingers from one to the other, and could not
grasp both at one time--that is, the rim of the cask and the end of the
rod--since they must needs be several inches apart. The stick, too, lay
unsteady, and by the feel I could not be sure when its end was exactly
"flush" with the head of the cask. The mistake of an inch--it might be
several--would falsify all my computations, and render them of no use.
It would not do to proceed upon such a conjectural basis, and for a
while I was puzzled, and had to pause.
This was an unexpected obstacle, for I had from the first regarded the
diameters as the only difficulty; about the possibility of obtaining the
length, I had never entertained a doubt.
But my wits again came to the rescue, and I soon discovered a plan that
would effect the end in view. I had to make another rod--by splicing
two more lengths split from the board--and with this I was able to
determine the point.
I managed the matter thus: The old rod I pushed along the head of the
cask quite beyond its outer edge, so that it rested at both ends against
the projecting rim. Thus placed, it was exactly parallel with the plane
of the barrel's head, while a foot or more projected outward and towards
me. Holding the end of the second rod against this projecting part, and
at right angles, I gave it a direction along the side of the cask, and I
was able to mark the point, where the middle part of the swell came in
contact with the second rod. This, of course, after deducting the depth
of the rim and the presumed thickness of the head, gave me half the
length of the interior of the cask, and that was all I wanted, since two
halves make one whole.
I was now in possession of the _data_ of my problem; it only remained
for me to seek the solution.