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. I persevered, therefore, and in less time than I must take in describing it, I hit upon a plan for "gauging" the butt. CHAPTER THIRTY. MY MEASURING-RULE. The details of my plan suggested themselves in the following order:--