“But suppose,” said Tom, “it were possible to make the experiment a thousand miles above the earth, would not the diminished effect of gravity be discovered in that case?”
“Undoubtedly,” replied his father, “indeed it would be sensible at a much less distance: for instance, if a lump of lead, weighing a thousand pounds, were carried up only four miles, it would be found to have lost two pounds of its weight.” [(2)]
“This discussion,” observed Mr. Twaddleton, “reminds me of a problem that was once proposed at Cambridge, to find the elevation to which the Tower of Babel could have been raised, before the stones would have entirely lost their gravity.”
“Its solution,” said Mr. Seymour, “would require a consideration which Tom could not possibly understand at present, viz. the influence of the centrifugal force.”
“I am fully aware of it,” replied the vicar, “and in order to appreciate that influence, it would, of course, be necessary to take into account the latitude of the place; but, if my memory serves me, I think that under the latitude of 30°, which I believe is nearly that of the plains of Mesopotamia, the height would be somewhere about twenty-four thousand miles.”
Mr. Seymour now desired Tom to inform him, since all bodies fall with the same velocity, what that velocity might be.
“Sixteen feet in a second, papa;--I have just remembered that I had a dispute with a school-fellow upon that subject, and in which, thanks to Mrs. Marcet, I came off victorious, and won twelve marbles.”
“Then let me tell you, my fine fellow, that unless your answer exclusively related to the first second of time, you did not win the marbles fairly; for, since the force of gravity is continually acting, so is the velocity of a falling body continually increasing, or it has what is termed an ‘accelerating velocity;’ it has accordingly been ascertained by accurate experiments, that a body descending from a considerable height falls sixteen feet, as you say, in the first second of time; but three times sixteen in the next; five times sixteen in the third; and seven times sixteen in the fourth; and so on, continually increasing according to the odd numbers 1, 3, 5, 7, 9, 11, &c. so that you perceive,” continued Mr. Seymour, “by observing the number of seconds which a stone requires to descend from any height, we can discover the altitude, or depth, of the place in question.”
Louisa and Fanny, who had been attentively listening to their father’s explanation, interchanged a smile of satisfaction, and, pulling Tom towards them, whispered something which was inaudible to the rest of the party.
“Come, now,” exclaimed Mr. Seymour, “I perceive by your looks that you have something to ask of me: is Louisa sceptical again?”