Chapter Thirty One.
“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.