"QUOD ERAT FACIENDUM."

To find the cubic contents of the b.u.t.t 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?"

Thus, then--

When I said just a little ago that I had no standard about my person, I spoke the truth only literally. Although not exactly _about_ my person, I had one in my person--I was myself that standard! You will now remember my having submitted myself to a measurement, which showed me to be four feet in length. Of what value that knowledge now proved to me!

Knowing, then, my own height to be very nearly four feet, I could notch off that measure upon one of the sticks, which would give me a measuring-rule of four feet in length.

I proceeded to obtain this result without delay. The process was simple and easy. Laying myself horizontally, I planted my feet against one of the great ribs of the ship, and rested the end of the stick between them. I now stretched myself out at full length, and guiding the rod so as to keep it parallel to the axis of my body, I brought it across my forehead, and beyond. With my fingers I could tell the point that was opposite the crown of my head, and carefully marking this point, I afterwards notched it with the knife. I now possessed a four-foot rule, exact enough for my purpose.

But there were difficulties yet to be encountered. With a four-foot rule, I was but little advanced towards my computation. I might make a nearer approach to the measurement of my diameters, but that would not avail. I must know them _exactly_. I must know them in inches, and even fractions of inches; for, as I have said, an error of half an inch in some of my _data_ would make a difference of gallons in the result.

How, then, was I to divide a four-foot stick into inches, and register the inches upon its edge? How was this to be done?

It seems simple enough. The half of my four feet--already ascertained-- would give me two feet; and the half of that again would reduce the standard to a foot. This again notched in the middle would make two lengths of six inches each. Then I could subdivide those into lengths of three inches, which, if not small enough for my calculation, could be still further subdivided into three equal parts, each of which would be the desired minimum of an inch.

Yes, all this seems easy enough in theory, but how was it to be put in practice upon a piece of plain straight stick, and in the midst of as perfect darkness as that which surrounds a blind man? How was I to find the exact middle--for it must be exact--of even the four feet, much less divide and subdivide till I got down to the inches?

I confess that I was puzzled for awhile, and had to pause and reflect.

Not very long, however; I was soon able to get over this trifling obstacle.

The plan that first suggested itself was to cut a third piece of stick of a little over two feet in length, which I could easily guess at within a few inches. This I could apply alongside of my four-foot rule, beginning at the end, and proceeding as if I was measuring the latter with the former. Of course, on the first application, two lengths would reach from the end of the rule to the notch that marked the four feet length, and perhaps extend a little beyond. I should then shorten the measure and apply it again. This time its end would have approached nearer to the aforesaid notch. Another bit cut off would bring it still nearer; and the process being repeated, by shaving gradually from the end of the stick, I should at last find that two lengths of it would exactly correspond with the length of my four-foot rule. I should then have a piece exactly two feet in length, and by the help of this I could find the middle part of the longer piece, and could mark it with a "nick."

By cutting the short piece into two nearly equal parts, I could then take the larger of them, and, by a similar process, obtain the standard of a foot, and mark it also upon my rule; and so on till I had succeeded in arriving at the inches.

Of course, to do all this would require time, patience, and the nicest precision; but I had plenty of time upon my hands, and it was my interest to be both patient and precise.

Although I regarded not the time, just as I was about to carry out the plan described, another suggested itself that promised to lead me sooner to the issue; it would call for less patience, though an equal amount of precision.

This new plan was a sort of corollary of the former one, the only difference being, that instead of a _stick_ I should perform my subdivision and graduation with a _string_.

The thongs of my buskins came into my mind--the very thing!

I could not have found a better string for the purpose. They were strips of best calfskin, cut with the grain, and could not have been stretched the eighth part of an inch. They would, therefore, measure as accurately as a rule of boxwood or ivory.

One would not be long enough; so I knotted the two together, taking care to make a neat, firm knot of it. They made a string of over four feet, and having laid it along the four-foot rule, I cut it with my knife to that length exactly. I was not satisfied till I had measured it over and over again, each time pulling the thong with all my strength, lest some "kink" might be lurking in it. A slight error would derange my intended scale, though there is less danger in graduating four feet down to inches than in going from the less to the greater standard. In the former, each subdivision naturally lessens the error, while in the latter it is continually doubled.

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 alt.i.tude; 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 b.u.t.t, when full, had contained somewhat above 100 gallons--as near as I could calculate, about 108--and therefore it was in all likelihood an old pipe that had once contained sherry.

CHAPTER THIRTY TWO.

THE HORROR OF DARKNESS.

The result of my calculation was of the most satisfactory nature.

Eighty gallons of water would give half a gallon each day for 160 days, or a quart _per diem_ for 320 days--nearly a whole year! Surely I could subsist on a quart a day?--surely the voyage could not last for so long a period as 320 days? A ship might sail round the world in less time.

I remembered having been told so, and it was fortunate I remembered it, for my mind was now at ease on the score of water. For all that, I resolved not to drink more than a quart a day, and on this allowance I made no doubt that the supply would be sufficient.

There was more danger of running short of food; but, upon the whole, I now felt very little apprehension, as I had fully resolved to diet myself on the most economic scale.

So far, then, as food and drink were concerned, I felt no further uneasiness. It was well a.s.sured that I was not to die either of thirst or starvation; and the very remarkable manner in which both food and drink had been supplied--placed, as it were, before me--naturally led me to the reflection that the hand of Providence had been extended to aid me, and I was still further consoled with the hope that He who had thus mercifully preserved me for the present, would not forsake me in the future.

In this state of feeling I continued for several days, and although it was an irksome life--every hour seeming of itself a day--still I was able to endure it. Sometimes I endeavoured to kill time by counting not only the hours, but even the minutes and seconds; and in this occupation (for I could think of no other) I often pa.s.sed several hours at a time.

My watch enabled me to amuse myself in this manner, and I found companionship in its cheerful ticking. I fancied that it beat louder than I had ever before heard it, and most likely this was so, the sound being magnified by the wooden walls that surrounded my cell. I took care never to let the watch go to the full length of its chain, lest it might run down and derange my reckoning. Not that I cared to know the hour. That was of no consequence. I did not even know whether it was night or day by the watch, nor would it have mattered had I not known the one from the other, as the brightest sun could not have lent a ray of his light to cheer my dungeon. It chanced, however, that I _did_ know the night from the day. No doubt you will wonder how I came by this knowledge--since I had kept no time for the first hundred hours after getting aboard, and there was then, in the complete darkness that surrounded me, no means of distinguishing the one from the other. I had a means of telling, however, and it was this: During all my life I had been trained to the habit of going to bed at a particular hour--ten o'clock at night--and also of rising at six exactly. This was a rule in my father's house, as well as that of my uncle--in the latter, indeed, I was compelled to observe it with a stern exact.i.tude. The consequence of this habit was, that whenever the hour of ten drew nigh, I naturally felt the inclination for sleep; and the habit had grown so fixed, that, notwithstanding the change of circ.u.mstances, it still continued. This I was not slow to observe. I felt the desire to sleep come upon me at regular periods, and I concluded, therefore, that whenever I had this feeling upon me it was about ten o'clock of the night. I had discovered, too, by registering the time with my watch, that I usually slept about eight hours, and then I felt no desire to remain asleep any longer. When I awoke it would be six in the morning; and, in this belief, I regulated my watch to that hour. So convinced was I of these facts, that I felt confident I could have counted the days without the watch; but fearing that some change might occur in my habitual hours of rest, in consequence of the altered circ.u.mstances in which I was placed, I resolved always to keep the time-piece going. Ever before lying down to sleep, I took the precaution to wind it up to the full length of its chain, and on awaking I repeated the operation, so that there might be no danger of even a moment's stoppage.

Though satisfied that I could tell night from day, I have said that it mattered little, or not at all. It was of importance, however, that I should know when each twenty-four hours had ended, for it was only by that means I could have any knowledge of the progress of the voyage. I took especial care to count the hours; and whenever I perceived that the hour-hand had completed two circuits around the dial, I cut a fresh notch in a piece of stick, set aside for this especial purpose. I need not say that my registry was kept with the greatest care. The only part of it on which I could not depend was that referring to the first days after my departure, when I had taken no notice whatever of the time that had pa.s.sed. By guess I had put down four notches against those days and nights, and I afterwards found that my memorandum was correct.

Thus for several days--nearly a week--pa.s.sed I the hours--the long hours--long, and dark, and irksome: ever more or less miserable, at times sadly dejected, but never positively despairing.

Strange to say, my greatest misery arose from the absence of light. I had at first suffered from my cramped position, and also from lying upon the hard oak timber; but I got used to these inconveniences. Besides, for the hardness of my bed I soon discovered a remedy. I had observed that the box which stood upon the other side of my biscuit-house contained some sort of stuff that had the feel of woollen goods. On further examination, it proved to be broadcloth, closely-packed in large webs as it had come from the manufactory. This suggested an idea that was likely to contribute to my comfort; and I set about putting it into execution. After removing the biscuits out of my way, I enlarged the hole (which I had already made in the side of the cloth-box) to such an extent that I was able--not without much labour, however--to detach one of the pieces, and draw it out; and then with less trouble I pulled forth another and another, until I had as much as would serve my purpose. I was two hours in completing this operation, but having got possession of the cloth, and shaken it out of its hard foldings, I procured both carpet and couch soft enough for a king to rest upon; and perhaps as costly, too--for I could feel that I was handling an article that was "superfine." I did not use more of it than was absolutely required to cover the hard oaken planks. Its bulk would have inconvenienced me had I taken much of it from the box; and before spreading it out, I had to clear the way, by returning all the biscuits to their old repository.