As the party walked along, Mr. Twaddleton explained the meaning of the above allusion, with which the reader will be hereafter made acquainted. The children had commenced the sport, and Mr. Seymour informed Tom and Louisa, who were attentively watching the motions of the swing, that its vibrations, like those of the pendulum of a clock, were produced by its effort to fall, from the force of gravity, and its power of ascending through an arc similar and opposite to that through which it has descended, from the momentum acquired during its descent. “Like the bandilor, I suppose,” said Louisa. “Exactly, my dear, that is a very good comparison; for as the bandilor, having descended along the string by its gravity, acquires such a momentum as to enable it to ascend the same string, and thus, as it were, to wind itself up; so does the pendulum or swing, during its descent, acquire a force that carries it up in an opposite arc to an equal height as that from which it had fallen. But tell me, Tom, whether you have not discovered that the motion of your new swing differs from that which you experienced in your former one?” “The ropes of our present swing are so much longer than those which we formerly used, that the motion is much pleasanter.” “Is that all?” said Mr. Seymour. “Have you not observed that you also swing much slower?” “I have certainly noticed that,” said Tom. “It is a law which I am desirous of impressing upon your memory, that the shorter the pendulum, or swing, the quicker are its motions, and _vice versâ_; indeed, there is an established proportion between the velocity and the length, which I shall, hereafter, endeavour to explain to you. Galileo, the celebrated philosopher, and mathematician to the Duke of Florence, accordingly proposed a method of ascertaining the height of the arched ceiling of a church by the vibrations of a lamp suspended from it. The solution of the problem was founded on the law to which I have just alluded, viz. that _the squares of the times of the vibrations are as the lengths_; so that a pendulous body, four times the length of another, performs vibrations which last twice as long. Now it is known that, in the latitude of London, a pendulum, if 39 inches and two tenths in length, will vibrate seconds, or make 60 swings in a minute; by observing, therefore, how much the pendulous body deviates from this standard, we may, by the application of the above rule, find its length; if the distance from the bottom of the lamp to the pavement be then measured, which may be done by means of a stick, and added to the former result, the sum will give the height of the arch above the pavement: but I will show you the experiment the next time we go into Overton church; the vicar can tell us the exact height of the roof, and I will try how nearly I can approach the truth, by observing with a stop-watch how many seconds one vibration of the chandelier continues.”