Philosophy in Sport Made Science in Earnest / Being an Attempt to Illustrate the First Principles of Natural Philosophy by the Aid of Popular Toys and Sports

CHAPTER IX.

Trap and Ball.--Gifts from the Vicar.--An Antiquarian History of the Ball.--The See-saw.--The Mechanical Powers.--The Swing.--The Doctrine of Oscillation.--Galileo’s Discovery.--The Pendulum.--An interesting letter.--Mr. Seymour and the Vicar visit Major Snapwell.

Mr. Seymour, having observed his children busily engaged at the game of Trap and Ball, determined, as usual, to make it subservient to scientific instruction. With this view he hastily sketched a diagram, and proceeded with it to the scene of sport.

“Now, Tom, let me see how far you have profited by our late conversation. I have some questions to ask you about the action of your Trap and Ball,” said his father.

“I do not suppose there is much philosophy in the game,” observed Tom.

“Of that we shall judge presently.--Can you tell me the direction which the ball takes after it flies from the spoon of the Trap, in consequence of the blow of the bat upon the trigger?”

“It flies upwards, to be sure, and allows me to strike it with my bat,” answered the boy.

“Very true; but at what angle?--I see you hesitate, look therefore at the diagram I have prepared, and attend to my explanation of it.”

Mr. Seymour produced the sketch which we here present to our readers.

Sketch of Trap.

“AB represent the spoon and trigger in their quiescent position. Upon striking the end B with the bat, they are brought into the position CD. The spoon will thus have described the small arc AC, when it will be suddenly stopped by the end of the trigger D coming into contact with the shoe. The motion of the ball, however, will not be arrested, and it will consequently be projected forward out of the spoon.”

“Exactly,” exclaimed Louisa, “in the same manner as the shilling flew off the wine glass, or a person on a galloping horse would be thrown over the head by its suddenly stopping.”

“I thank you, Louisa; your memory, I perceive, has not suffered from the drenching you received from the water-cart;^[25]--but can you tell me,” continued Mr. Seymour, “the direction which the ball will take after its release from the spoon?”

This was a step beyond Louisa’s knowledge, and her father, in order to assist her, begged her to consider in what direction it was moving before it left the spoon.

“You have just told us,” said Tom, “that it described an arc, or portion of a circle.”

“Very well,” said Mr. Seymour; “and did not the philosophy of your sling teach you that, when a body revolving in a circle is suddenly disengaged, it will fly off in a right line in the direction in which it was moving at the instant of its release?--the ball therefore will describe the tangent CE.”

“It is all clear enough to me now,” said Tom, evidently vexed that he had overlooked a principle which had been so lately explained to him by the action of his sling.

“I now see, too,” added Tom, “why the ball seldom flies off at the same angle in every trap.”

“That,” said his father, “must of course depend upon the extent of the arc described by the spoon, and which will of course vary in different traps.”

“Before we conclude the subject, let me ask you whether there is not some one point in the bat, at which you can most effectually strike the ball?”

“To be sure,” answered Tom, “in the same way tha there is a point in my hoop-stick at which I can give the strongest blow--and that point is termed the Centre of Percussion.”

“Enough,” said Mr. Seymour; “see, here comes the vicar.”

True to the hour appointed, did Mr. Twaddleton make his appearance, just at the conclusion of the discussion above described; and, as he approached the party, Louisa observed that he was carrying a canvass bag in his hand.

“What have you there?” asked Mr. Seymour. “A sack of sugar-plums?”

“No, no; spheres of larger diameter. Here,” said the vicar, as he opened his bag, “is a foot-ball for you, Tom; and here is a hand-ball for you, Louisa.” He then presented each of the other children with a similar present, exclaiming--

‘Nemo ex hoc numero mihi non donatus abibit.’^[26]

as Virgil has it.”

“Perhaps,” said Mr. Seymour, “you will enhance the value of this favour, by giving us an antiquarian history of the ball, which will be very acceptable to us at this time, as we have just concluded a philosophical enquiry upon that subject.”

To this request the vicar readily assented, and proceeded as follows:--

“The Greeks appear to have played with four kinds of ball: viz. the little ball, the great ball, the empty ball ( sfa??a ?e?? ), which was blown up with air, like our foot-ball, and the leathern ball ( ??????? ), which was suspended from the ceiling, and stuffed with bran or sand, as those who tossed it were robust or delicate. The Romans,” continued the vicar, “had also four kinds of pilÆ, or balls. The follis, a large ball made of leather and blown up with air, like our foot-ball; the larger kinds of which were struck with the arm, the smaller ones with the fist. Suetonius tells us that Augustus CÆsar greatly delighted in the amusement; and in truth it was a glorious sport, an exercise equally adapted for the young and old; or as Martial has it,--

‘Folle decet pueros ludere, folle senes.’“^[27]

“And yet,” said Mr. Seymour, “neither Horace nor Virgil played at it; do not you remember the lines in the fifth satire?--

‘Lusum it MÆcenas, dormitum ego Virgiliusque;

Namque pilÂ lippis inimicum et ludere crudis.’”^[28]

“Many thanks, Mr. Seymour, many thanks for brushing up my recollection; but I am a little doubtful about the game at which MÆcenas played at Capua: I have, by-the-by, lately read^[29] an account of a peculiar game of ball for which the city of Sierra is celebrated, and it is supposed to be that referred to by Horace--‘It is played in the foss, which has a very high wall, and it is not unlike a tennis-court; the ball is very large, and appears to be inflated with air; the arm is defended by a wooden guard or shield; at certain periods of the game, one of the players runs down a spring-board, and throwing the whole of his weight, momentum, and strength upon the ball, as it is thrown towards him, he strikes it to an astonishing distance.’ The second kind of ball,” continued the vicar, “was termed trigonalis, which is conjectured to have been nearly the same as our tennis-ball. It derived its name from the position of the three persons who played with it; they were placed in a triangle, and alternately caught and tossed the ball, and he who first let it fall to the ground was the loser. The third kind of ball was the paganica, as being much used in country villages. Some authors state it to have been constructed of leather and stuffed with feathers, while others conjecture it to have been a large kind of follis. The fourth was the harpastum; a small ball, so called because the gamesters endeavoured to snatch it from each other.”

“It seems,” observed Louisa, “to be a sport better adapted to boys than girls.”

“In that supposition you are quite mistaken,” replied the vicar; “on the contrary, the hand-ball would seem to have been originally a female sport, for Homer has restricted the pastime to the princess and young maidens of Corcyra; at least, he has not mentioned its ever having been practised by the men.

‘O’er the green mead, the sporting virgins play,
Their shining veils unbound; along the skies,
Toss’d and re-toss’d, the ball incessant flies.’”[30]

Mr. Seymour said that, as the vicar had satisfied them of the high antiquity of the ball, he hoped he would now afford them some information respecting its use in England.

“The game of hand-ball,” said the vicar, “called by the French palm-play, because the exercise consisted originally in receiving the ball, and driving it back again with the palm of the hand, was formerly a favourite pastime among the youth of both sexes; and in many parts of the kingdom it was customary for them to play at this game during the Easter holidays for tansy cakes. In ancient times, the mayor and aldermen of Newcastle used to go in state at the feasts of Easter and Whitsuntide, to a little mall of the town, to witness this game. It was originally played with the naked hand; then with a glove, which in some instances was lined; afterwards, cords and catgut strings were bound upon the hand to make the ball rebound more forcibly.”

“That custom,” observed Mr. Seymour, “doubtless, gave origin to the racket.”

“It did,” replied the vicar; “and the places where this game was played were called tennis-courts, and the game itself obtained the name of tennis, from the French word tenez^[31] (take it, hold it), frequently used during the exercise. The pastime, I believe, was introduced amongst our ancestors about the year 1222, the sixth year of Henry III, by persons of superior rank and family, who erected courts or oblong edifices for the performance of the exercise.”

“I long to hear something about foot-ball,” exclaimed Tom.

“That is a pastime,” said the vicar, “which was formerly in great vogue in England, but of late years it has fallen into disrepute. It derives its name, as you may suppose, from the circumstance of the ball being driven with the foot, in preference to the hand. When a match is made, two parties, equal in numbers, take the field, and stand between two goals, which are placed at the distance of eighty or a hundred yards from each other. The ball, which is commonly a blown bladder, cased with leather, is delivered in the midst of the ground, and the object of either party is to drive it through the goal of their opponents, by which the game is won. The abilities of the performers are best displayed in attacking and defending the goals, whence the pastime is more frequently called a goal, than a game at foot-ball. In this attack and defence, the exercise becomes exceedingly violent; the players kick each other’s shins without the least ceremony; and this occasioned James I. to speak of foot-ball as ‘meeter for laming than making able the users thereof.’”

“I believe,” said Mr. Seymour, “that the ancient game of goff is still much practised in Scotland.”

“It is,” replied the vicar. “In the reign of Edward III. the Latin name cambuca, a crooked club, or staff, was applied to this pastime, because it was played with such an instrument. The bat was also styled a bandy, from its being bent; and hence the game itself is frequently called bandy-ball.”

“And how is it played?” asked Tom.

“It is played on a smooth common, by driving forward two small hard balls, with the bandy I have just described, into very distant holes in the ground, about a foot deep, and nine inches over: and the party whose ball is driven into these holes with the fewest strokes, is the victor.”

“But come,” said Mr. Seymour, “it is high time to think of our dinner; the children must require some refreshment. I am not, my dear vicar, one of those philosophers who believe that play was invented by the Lydians^[32] as a remedy against hunger; nor do I subscribe to the opinion of the elder Scriblerus, that it was on such an account wisely contrived by Nature, that children who have the keenest appetites should, at the same time, be those who are most addicted to sport.”

“Whether you believe or not that the Lydians invented sports shall not be a subject of contest between us,” said the reverend antiquary; “but,” continued he, “one thing is quite certain, that the Lydian games were at first called Lydi by the Romans; and afterwards, by corruption, Ludi; a presumption I must needs say in favour of the Lydian claim; but enough of this: to what do you propose we should next turn our attention? I doubt not you have some new sport for our recreation as well as our instruction,” added the vicar.

“We will, if you please, attend the children to their see-saw, which the gardener has lately constructed for them,” said Mr. Seymour.

The party accordingly walked to the grove, in which a plank had been placed across a wooden post: and upon which Tom and John had been riding for some time in the earlier part of the morning. The boys again mounted their new hobby; and, after amusing themselves for some minutes, Mr. Seymour desired them to stop, in order that Tom might explain the principle upon which the see-saw acted. Tom replied, that he was not aware of any principle which could apply to riding on a plank.

“Have I not often told you, my dear boy, that the principles of Natural Philosophy may be brought to bear on the most trivial acts of life? Listen, therefore, and you shall find that your present amusement teems with instruction. You are already well acquainted with the nature and operations of the centre of gravity; tell me, therefore, whereabouts it lies in the plank upon which you are riding.”

“I should think,” replied Tom, “that in this instance, the centres of gravity and magnitude must coincide, or be very nearly in the same point.”

“The centre of gravity must, as you say, be very nearly in the middle of the board; and if that be the case, you will allow that, supposing those who ride upon it are of equal weight, the plank must be supported in the centre to make the two arms equal; but you and John are of unequal weight, so that you perceive the plank must be drawn a little farther over the prop to make the arms unequal; and John, who is the lightest, must be placed at the extremity of the largest arm. Thus arranged, you will exactly balance each other; and as each of you, on your descent, touches the ground with your feet, the reaction affords you a spring, which destroys the equilibrium, and enables you to oscillate in arcs about the centre of motion.”

“Do we then describe the arcs of a circle as we ascend and descend?”

“Undoubtedly you must. Look at this diagram,” said Mr. Seymour, “and you will see at once that the plank can only move round its centre of motion; for how could you rise, or your brother fall, perpendicularly in a straight line? You must, in rising, and he, in descending, describe arcs of your respective circles. It is equally evident that his velocity must be very superior to yours; for, if you could swing quite round, you would each complete your respective circles in the same time.”

“It would really appear so,” said Tom; “and I have myself observed, that the lighter person has the better ride, as he moves both farther and quicker, and I now understand the reason of it; it is because being farther from the centre of motion, he describes a larger arc.”

“The greater velocity with which your little brother moves, renders his momentum equal to yours. You have the most gravity, he the greatest velocity; so that, upon the whole, your momenta are equal: for you, no doubt, remember that momentum is weight multiplied into velocity.^[33] You have here then a striking instance of mechanical advantage gained by opposing motion to matter, or velocity to weight; for I think you will readily admit, that without the aid of the plank, your little brother could never have raised you from the ground.”

“That is clear enough,” said Tom.

“The plank, then, thus arranged,” continued his father, “constitutes what has been termed a mechanical power, to which the name of lever has been given; it is not, however, my intention at present to enter into the history of these powers, of which there are six distinct kinds; the one presented to you, in the instance of the see-saw, is perhaps the most simple, and not the least important of them.”

“It is very curious,” observed the vicar, “to reflect upon what a simple, and apparently trifling fact, the powers of civilized man may be said to depend. The single truth you have just announced, of making velocity a compensation for weight, has supplied his weak arm with the means of controlling the very elements.”(23)

“It is very true,” said Mr. Seymour, “and we might go so far as to say that, had it been the will of the Almighty Creator of the universe to have withheld from matter that property which we have been discussing, man must have remained the most helpless and forlorn of his creatures. I now propose,” added Mr. Seymour, “to accompany the children to their swing; the present is a suitable opportunity for giving them some idea of the doctrine of oscillation, or the theory of the pendulum.”

“Let us proceed, then, to the Icarian Game,” exclaimed the vicar.

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.”

“But, papa, why surely the duration of its vibration must depend upon the force which you may happen to give to the chandelier?”

“Not in the least; and this brings us at once to the consideration of the most curious and important fact in the history of the pendulum, and for a knowledge of which we are also indebted to Galileo.^[34] It is termed isochronous^[35] property, or that by which all its vibrations, whether great or small, are performed in exactly the same period of time; but that you may be better able to comprehend this subject, attend to the diagram which I have prepared for your instruction.

Drawing of a pendulum and its movements.

Suppose that the swing or pendulum AB be raised to C, it will, in effect, be raised the perpendicular height EC, and in falling will describe the arc CB; and, in the point B, it will have that velocity which is acquired by descending through CB, or by a body falling freely through the perpendicular CE. This velocity will be sufficient to cause it to ascend through an equal arc BD, to the same height from whence it fell at C; and since the times of ascent and descent are equal, it will describe both these arcs in exactly the same space of time. Having lost all its motion at D, it will again begin to descend by its own gravity; and in the lowest point B it will acquire the same velocity as before, which will cause it to reascend to C; and thus, by ascending and descending, it will perform continual vibrations in the circumference CBD; and, were it not for the resistance of the air, and the friction at the centre of motion A, the vibrations would never cease: but from these obstructions, though small, it happens, that the velocity of the mass of matter at B is a little diminished in every vibration; and consequently it does not return precisely to the same points C or D, but the arcs described continually become shorter and shorter, till at length they grow insensible; and yet the very same time is required for the performance of the shorter as the longer arcs; for, although in the one case the body passes over less space, still its velocity is proportionally decreased. You perceive, then, that in an attempt to ascertain the height of a ceiling by the vibrations of a chandelier, the extent of its swing cannot alter the time which may be required for its completion. And, if you will place your little brother in the swing, you will perceive that he will return to your hand in nearly the same space of time, whether he describes a large or small arc; although this experiment must be considered as extremely rude, since there are many disturbing causes for which the theory cannot possibly make any allowance. I must, moreover, warn you that where the arc described is very considerable, the difference in the time will be greater; for, in order to ensure this property of vibrating through unequal arcs in equal times, it is necessary that the path of the body should describe a peculiar curve, called a cycloid(24), and not the segment of a circle; at present, however, it is not possible for us to enter into this difficult branch of science, although I trust that at some future period I shall be justified in an attempt to explain it.”

Mr. Seymour having concluded his lecture, was about to return to the Lodge, when Mrs. Seymour approached the party, carrying in her hands a letter, which the smile on her countenance announced to contain agreeable intelligence.

“I have just received,” said Mrs. Seymour, “a letter from Miss Villers, whom you must all remember as a most delightful person. I am informed that she is about to be married to the nephew of a gentleman who is at present in our neighbourhood in search of a country residence.”

“Does she mention the gentleman’s name?” inquired the vicar.

“Mr. Henry Beacham,” said Mrs. Seymour.

“The nephew of Major Snapwell, I declare,” exclaimed the delighted vicar.

The whole party participated in the pleasure which their excellent friend expressed at this discovery, and Mr. Seymour immediately accompanied Mr. Twaddleton to Ivy Lodge, to congratulate the major, and to make such arrangements as might expedite the purchase of Osterley Park, and the consequent introduction of a family into the neighbourhood of Overton, from whose society the Seymours anticipated the highest satisfaction.

At the same time Mrs. Seymour hastened to dispatch a letter to Miss Villers, in order to solicit her immediate presence at Overton Lodge.

25.See page 65.

26.“Not one amongst you shall depart without a gift from me.” Æn. v. 305.

27.Lib. xiv. epig. 43.

28.

“MÆcenas goes to tennis, hurtful game
To a weak stomach, and to tender eyes,
So down to sleep with Virgil, Horace lies.”--Francis.

29.“Two Hundred and Nine Days,” or “The Journal of a Traveller on the Continent,” by Jefferson Hogg: London, 1827.

30.Pope’s Odyssey, lib. v.

31.This etymology has been disputed, and it has been said that the holding or keeping possession of the ball is no part of the game; for, during the play, the ball is in continual motion, or passing from one to another. Others seek the etymology of the name, and the origin of the game, in a place in France called Tennois; or, by a change of one letter, Sennois, in the district of Champagne, where balls were first made, and the game, as it is said, first introduced.

32.Herodotus speaks of the inhabitants of Lydia having successfully had recourse to gaming as a partial substitute for food, during a famine of many years’ continuance.

33.See page 61.

34.This discovery was published at Paris, in a treatise called “L’Usage du Cadran, ou de l’Horloge Physique Universelle,” in the year 1639; from which may be dated the invention of the pendulum.

35.Compounded of the Greek words ?s?? equal, and ?????? time.

Three people looking at a diagram drawn on the ground.

Clyx.com