The Boy Tar

by Mayne Reid

I drew out the stopper, and tasted the water. I had not thought of noticing its flavour before. It appeared to me to be sherry; but as I have said, it might be Madeira, which would make a difference of sixteen gallons—an important item in a calculation such as I was desirous of making. I therefore could not trust to my judgment to make this the basis of a computation, and I had to think of some other device.

Fortunately in my school arithmetic there were a few hints upon mensuration, and the good master had instructed us in these.

I have often wondered that the simple but useful problems of this branch, of science are so much neglected, while the most useless and irrational rhymes are hammered into the heads of poor unfortunate boys. I have no hesitation in giving my opinion, that a knowledge of simple mensuration, which may be obtained in a week’s study, is of more value to an individual—or to the whole human race, if you will—than a perfect scholarship in all the dead languages of the world. Greek and Latin! These have been very barriers to the advancement of knowledge!

Well, I was saying that my old teacher had taught me a few simple problems in mensuration; and fortunately I still held them in my memory. I could tell the solid contents of a cube, of a parallelopipedon, of a pyramid, of a globe (nearly), of a cylinder, and of a cone. The last was the figure that now interested me.

I knew that a barrel was a pair of cones—that is, truncated cones or frustums—with the bases resting against each other. Of course, when I was taught how to measure a cone, I was also instructed to do the same with the frustum of one.

To ascertain the capacity of my butt, therefore, it was only necessary for me to know its length—or its half-length would do as well—its circumference at either end, and also its circumference around the thickest part or “swell.” These three measurements given me, I could tell to a quart how much water would fill it—in other words, I could calculate how many cubic inches of water it should contain. Knowing this, I should simply have to divide by 69 and a small fraction over, and this would give me the number of quarts, which another simple division of 4 would reduce to gallons, if I required to use this standard.

I perceived, therefore, that if I could get the three measurements, I could soon tell the capacity of my butt; but therein lay the difficulty. How were these measurements to be obtained?

I might have obtained the length, for that was before me from end to end; but how should I get the circumference either of the middle or of either end? I could not reach over the top, nor around the ends. Both directions were blocked up against me.

Another difficulty stared me in the face. I had nothing wherewith to measure them—neither rule nor tape—no standard by which I could determine the number of feet or inches; so that even had all sides been free to me, I should still have been in a dilemma.

I was determined, however, not to yield the point until I had given it a good thinking. The occupation would help me to pass the time; and, as I have already hinted, this was a matter of primary importance. Besides, that faithful old schoolmaster had many a time impressed upon us the valuable truth, that perseverance often finds success where success appears impossible. Remembering this bit of admonition, I resolved not to regard the thing as impracticable, until I had exhausted all my powers of contrivance.