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.