Ernest.—Twice 32 makes 64; the half of 32 is 16; which added to 64 makes 80 feet.
Father.—Very well. Tell me now, if you recollect the proper term in geometry for the circumference of a circle, or say of a tree, since we are talking of trees.
Ernest.—Oh, you may be sure that I could not forget that it is called the periphery.
Father.—Right. And what is the term for any line which may be drawn from one point of the periphery to another, passing through the centre? Now, Jack, you may show us what a great geometrician you intend to be.
Jack.—I believe it is called the diameter.
Father.—So far right. Next, can you tell me what is the diameter of a periphery of eighty feet, and what distance there is between the extremities of the roots of the giant tree and its trunk?
The boys all began to reckon, and soon one said one number, one said another,—at random; but Fritz called out louder than the rest, that the distance was twenty-six feet.
Father.—You are pretty near. Tell me, did you make a calculation, or was it a mere guess?
Fritz.—No, father, not a guess; but I will tell you. In the town in which we lived, I have often taken notice that the hatter, when he was about to bind the edge of a hat, always measured three times the length of the diameter, and a trifle over, for the quantity of ribbon he should use: thus I had no difficulty in finding that the third of eighty was about twenty-six; and adding a couple of feet for the over measure, we may call it twenty-eight.
Father.—I am glad to see you did not lose such an opportunity for calculation; but a great boy like you, who have advanced in your studies, ought not to be under obligations to the hatter for the answer. But now let us go back to the measure of our trees, which are really of a most extraordinary size. Height from the ground to the branches, sixty-six feet; thickness, eight feet in diameter, and twenty-eight feet distance from the extremities of the roots to the trunk. They really, with propriety, may be called giant trees.