"QUOD ERAT FACIENDUM."
To find the cubic contents of the butt in feet or inches, and afterwards
reduce them to liquid measure--to gallons or quarts--would have been
easy enough, and only required a simple computation in figures. I knew
that I was arithmetician enough to make this computation, even though I
possessed neither pen nor paper, slate nor pencil; and if I had, there
was no light by which I could have used them. "Ciphering," therefore,
in the ordinary way, was out of the question; but I had often practised
myself in casting up accounts by a mental process, and I could add and
subtract, multiply or divide a considerable series of figures without
the aid of either pen or pencil. The problem I had before me would
involve but a limited number of figures, and I felt satisfied I could
easily manage it, so far as that was concerned.
I have said that it _would have been_ a simple and easy computation to
find the contents of the cask in cubic feet or inches. _Would have
been_ supposes that there was a difficulty--and there _was_ one. An
important preliminary matter had to be settled before I could enter upon
any calculation--a very important one; and that was, that I had not yet
reduced my measurements--neither the diameters nor the length--to feet
and inches! I had measured the cask with plain pieces of stick, and had
registered the dimensions in simple notches; but what of this? I knew
not what distance these notches might be from the end, or from each
other--how many feet or inches! I might make a rude guess, but that
would be of no service to me; so that after all my pains I had as yet no
_data_ to go upon, nor could I have any until I had first _measured my
measuring-rods themselves_!
Apparently, here was a difficulty not to be got over. Considering that
I had no standard of measurement within reach--neither yard-stick, nor
foot rule, nor graduated scale of any kind--you will naturally conclude
that I must have abandoned the problem. A computation founded on the
mere length of the stick would have been absurd, and could have given me
no information whatever upon the point about which I wanted to be
informed. To find the cubic and liquid contents of the cask, I must
first have its length, with its largest and shortest diameters,
expressed in _standard_ terms--that is, either in feet or inches, or
some other divisions of a scale.
And how, I ask, was this to be ascertained, when I possessed no standard
of measurement about my person? None whatever. I could not make one;
for in order to do so, I should have required another for a guide. Of
course, I could not _guess_ the length either of feet or inches.
How, then, was I to proceed?
Apparently, the difficulty was not to be got over. The thing seemed
impracticable.
To you it may seem so, but it did not to me. I had thought of this
before. I should not have proceeded as far as I had done--taking so
much pains and trouble with the splitting and splicing of my sticks, and
making my measurements so exact--had I not foreseen this difficulty, and
thought of a way to surmount it. All this had been prospectively
arranged. I knew before-hand that I _could measure_ my sticks, and tell
their linear dimensions to the exactness of an inch.
"How?"