Marbles.--Antiquity of the game.--Method of manufacturing them.--Ring-taw.--Mr. Seymour, the Vicar, and Tom, enter the lists. The defeat of the two former combatants; the triumph of the latter.--A philosophical explanation of the several movements.--The subject of Reflected Motion illustrated.--The Vicar’s apology, of which many grave personages will approve.

In our last chapter we left Mr. Seymour and his reverend friend on their way to Ivy Cottage; it is only necessary to state that the major received them with that satisfaction and gratitude which the nature of their visit could not fail to produce. Plans were proposed, and arrangements concluded for the furtherance of the object we have announced; in short, in the brief space of an hour, the major had determined the course of his future life, and had framed schemes of happiness, and visions of domestic peace, which he impatiently sought to realize. The vicar was detained by the major, but Mr. Seymour quitted Ivy Lodge and returned to his family. He found the children engaged in playing at marbles. Tom was displaying to his sisters many instances of his adroitness and skill in shooting at and hitting marbles.

“Why, Tom!” exclaimed Mr. Seymour, “how came you possessed of such a multitude of marbles?”

“By luck; good luck, papa; I won them all before the holidays; and I can assure you that my school-fellows acknowledge me as one of the best players at ring-taw in the school.”

“Justly, then, has your merit been rewarded,” said the father. “Have you not read of the skilful Roman, who could blow peas through a quill, and deposit them with such nicety on the point of a pin, placed at some distance, as rarely to miss his aim?”

“And what was his reward?” asked Tom.

“A bushel of peas, my boy, which the emperor commanded to be presented to him. But do not misunderstand me, far be it from my wish to disparage your skill; whatever we undertake, we should endeavour to accomplish; I am, therefore, well pleased to find that you can play at marbles with so much success.”

“I wonder who invented marbles?” said Tom.

“That question, my dear, must be addressed to Mr. Twaddleton, who, I have no doubt, will immediately answer it.”

Scarcely had these words been spoken, when the vicar appeared on the lawn. Mr. Seymour informed him of the subject of their conversation, and added, that he had just told the children he was sure he would readily answer their question.

“Not so readily as you may imagine,” replied the vicar; “but I will tell you all I know upon the subject. It appears to be a very ancient game; for it is stated by Suetonius, that Augustus, when a youth, spent many hours in the day in playing with little Moorish boys ‘cum nucibus,’ that is, with nuts, which appear to have been then used in the very way in which you now play with your marbles. In later times, round stones, picked out of gravel, were introduced for this purpose. The marbles which you now hold in your hand are substitutes of still more modern invention. The best of them are imported from Holland, where, as I have been informed, they are manufactured by grinding fragments of alabaster and of other stones, in an iron mill of a peculiar construction, in which there are several partitions furnished with rasps, which turn with great velocity, by means of a stream of water; and thus, having rounded the stones, project them out of different holes for which their size may adapt them. Thus manufactured, they are brought down the Rhine, and from thence dispersed throughout Europe; immense quantities are also exported to India and China. There are, however, as you well know, inferior kinds, which are of home manufacture, and consist of potter’s clay covered with a glaze, and burnt in a furnace.”

“I have often wondered what is the meaning of the words taw and ally,” observed Tom.

“Why, your taw is a brown marble, and your ally, if I remember rightly, a very white one; is it not so?” asked the vicar.

“To be sure,” said Tom.

“Very well, then,” said the vicar, “the words are clearly abbreviations of tawny and alabaster.”

“Now then,” said Mr. Seymour, “for a game; what is it to be, Tom?”

“Ring-taw for ever!” cried Tom; “it is the only game of marbles worthy of being played.”

“It is really so long since I left school,” observed his father, “that I must beg you to refresh my memory, and give me some instructions about this favourite game of yours.”

“I will tell you all about it. We must first draw a circle, on which each player is to put a certain number of marbles to be previously agreed upon; we then make a mark at some distance, which is called the offing, and from which we are to shoot at the marbles in the ring.”

“That is all very intelligible,” observed his father; “and I suppose the object of the player is to shoot a marble out of the ring, which not only gives him that marble, but entitles him to shoot again at another, and so on, until he misses, or all the marbles are won.”

“That is right, papa.”

“And a good marksman,” observed the vicar, “who has the first shot, may easily win the game, before any other player can gain the opportunity of shooting at a single marble.”

“I see that clearly,” said Mr. Seymour; “he may strike out a marble from the circle, and then shoot at another, and in this manner traverse the whole ring; I therefore conclude, that good players will always demand a large ring, or else there would not be much chance for any one, except for him who played first.”

“That is the game; but I must tell you,” said Tom, “that if the player should leave his own marble in the ring, he is at once put out; and should it be within a certain distance on the outside, an adversary may shoot at it, and by hitting it, put him also out of the game.”

“I believe that I am now a perfect master of the subject,” said Mr. Seymour; “what say you, vicar?”

“I understand it; and it appears to me to be capable of some scientific calculation; but the practical results must, of course, differ very widely from the theory, for the unevenness of the ground, and the inaccurate construction of the marble, are circumstances which never can be duly estimated.”

“Certainly not,” replied Mr. Seymour; “these difficulties even exist at the game of billiards(25), where the table is smooth and perfectly horizontal: but we do not require perfect accuracy, an approximation to it will be sufficient for the purposes of illustration; we will, therefore, if you please, proceed at once to the game, and I will endeavour to point out to Tom the nature and direction of the several forces by which each marble will be influenced.”

Tom, accordingly, like the son of Cornelius Scriblerus, converted his legs into a pair of compasses, and described, with the toe of his shoe, the necessary circle upon the ground. Each party, by agreement, placed two marbles upon the ring, and it fell to the lot of the vicar to open the campaign. Mr. Twaddleton then advanced, and with the assumed air of a true knight-errant, approached the ring, exclaiming with a loud voice, and with a gesture of inexpressible drollery, “I demand gracious leave that I may be delivered of my vow, and forthwith combat in the lists;” so saying, he unfurled his red banner, and sounded a trumpet; or in more humble phraseology, he extracted his hand-kerchief from his pocket, and applying it to his nasal organs, produced a loud and thrilling blast, which frightened every sparrow from its resting-place. After this preliminary ceremonial, he marshalled his limbs into the most appropriate attitude, and thrusting one hand behind the exuberant tail of his coat, he, with the other, shot forth his missile at the largest marble opposite to him. His taw faithfully delivered its errand, and inflicted such a blow upon the paunch of his antagonist, that although nearly twice the size of its assailant, like a true bully, it skulked off, and retreated several feet beyond the lists; but, alas! the little marble of the vicar, unlucky wight! was so stunned by the operation, that it staggered, and reeled backwards into the ring, and thus, according to the established law of the field, completed by one act the total defeat of its luckless commander.

“Your marble is left in the ring!” exclaimed Tom, with a shout of triumph.

“I see how it happened,” said Mr. Seymour; “the vicar struck the marble plump, or ‘played a full ball,’ as we say at billiards, and the result easily admits of explanation. You already know that a marble possesses elasticity; when, therefore, the one in the ring was struck, it went off with a velocity equal to that with which the striking marble approached it, while the latter, in return, received a blow equal to that it gave, which destroyed its motion. When we go back into the library, I will exhibit a very pretty experiment in farther elucidation of this philosophical truth.”(26)

It was now Mr. Seymour’s turn to enter the lists. He carefully applied his knuckles to the ground, and taking aim at a little marble which he had selected as his victim, gallantly shot the missile from his thumb and finger; but, alas! alas! the goddess, whatever may be her name, who presides over this species of tournay, doubtless saw the impending fate of her favourite, and, after the example of Venus, who turned aside the weapon from Æneas, assumed the shape of a small pebble, and thus arrested the fatal course of the marble, and gave it a new direction, which sent it curveting through the ring, without committing one single act of devastation.

“Bravo! bravo!” exclaimed Tom, “it is now my turn.”

The boy, according to the usage of the field, might at once have won the game by striking his father’s marble; but he was too magnanimous to take such an advantage, and too eager to display his own skill, to cut the game short by a manoeuvre: he had determined to win his laurels by hard fighting and generalship. He accordingly proceeded to strike a ring marble; in effecting which he had, like the vicar, challenged a gigantic knight as his antagonist; but, instead of striking it plump, he struck its upper quarter, so that it was rolled out of the ring, while the striking marble, imparting only a portion of its momentum, continued to move forward after the impact. This course was greeted with the acclamations of Mr. Seymour and the vicar, the latter of whom declared it to have been “nobly run,” and gallantly accomplished; and extracting a sixpence from his waistcoat pocket, exclaimed, after the manner of chivalry, “Largesse, largesse, glory to the sons of the brave! glory to the invincible knight of the taw!”

The boy had not only struck the marble out of the ring, but he had, at the same time, contrived to place his own marble in the most favourable position for his future operations; and, indeed, it may be here observed, that in this consists the art of playing the game. It is almost unnecessary to add that Tom won every marble in succession.

Mr. Seymour then proceeded to explain the laws of impact, by which the movement of each marble was directed. He observed, that the subject embraced two propositions, viz. the direction of the object marble after having been struck, and that of the striking marble after the stroke. He said that, if a straight line were drawn between the centres of the striking and object marbles, it would necessarily pass through their point of contact, and, if continued, would represent the path of the latter after the blow. In order to find the direction of the striking marble after the shock, he told him that he must imagine a tangent to the path of the object ball drawn from its centre, and then a line parallel to it, from the centre of the striking marble; the latter of which would be the required path.

Mr. Seymour now inquired whether there was any other game of marbles at which they could amuse themselves.

“The game which we call ‘lagging out,’” replied the boy, “is amusing enough. It consists in striking your marble against the wall, and making it rebound, so as to hit any other marble that is placed at a certain distance from it, or to come within a span of it.”

“I understand,” said his father, “and, like ring-taw, it may be made subservient to our purpose of illustrating the doctrine of forces; although I think that the principle of reflected motion may be more readily explained by the rebounding ball.”

Mr. Seymour here took the elastic ball, and threw it obliquely against the wall, from which it rebounded in an opposite and equally oblique direction. He then sketched the annexed figure, and proceeded as follows:--“When I threw the ball against the wall B, in the direction AB, having struck it, it glanced off, making an angle, in its passage back again, equal to that which it made in its approach to the wall. If I draw the perpendicular BD, this fact will be rendered more apparent, and you will perceive that the angle ABD is equal to the angle CBD: the former is termed the angle of incidence, the latter the angle of reflection; and these angles, remember, are always equal, provided the ball under experiment be perfectly elastic.”

“Do you mean to say,” asked Tom, “that the more obliquely I throw the ball against the wall, the more obliquely it will rebound?”

“Exactly; that is my meaning: and see whether you cannot explain the fact, for it depends on the composition and resolution of the forces, a subject which I should hope you thoroughly understand.”

Tom pondered for some time over the drawing, and at length observed, that there was one difficulty which he could not immediately surmount.

“State your difficulty,” said Mr. Seymour.

He proceeded to observe, that the force acting in the direction AB would certainly be resolved into two others, viz. one in the direction FB, and another in that of DB; “because,” continued he, “these lines are the adjacent sides of the parallelogram, of which AB is the diagonal; and I well know that whenever a force strikes obliquely, it is thus resolved.”

“That is all very well explained,” replied his father; “pray proceed.”

“Now comes the difficulty,” continued Tom; “for the force DB will of course be destroyed by the wall, and that represented by FB, which is the only one that can remain, would carry the ball to E.”

“It certainly would do so,” answered his father, “if the ball were perfectly devoid of elasticity; but remember that, in consequence of this property, the force DB will be exchanged for one in an opposite direction, BD.”

“I had entirely overlooked the elasticity,” said Tom; “I now see my way clearly, for in that case there must be two forces acting in the directions BD, BE, which will, of course, drive the ball down the diagonal BC.”

“Your demonstration is perfectly correct, my boy; and I think you will now admit that I could not have adduced a more beautiful instance of the composition and resolution of forces; for, in the first place, you resolve the diagonal force into two others, and then you recompound these again to produce another diagonal one.”

“But I think you told us that the angles of incidence and reflection were only equal when the rebounding body was perfectly elastic.”

“Clearly so; the force DB must be exchanged for an equal one BD, or else the angle ABD cannot be equal to the angle DBC; but I will render this fact still farther intelligible by another diagram.

Let B, as in the former case, represent the wall, upon which the imperfectly elastic body impinges in the direction AB.--The force will of course be resolved into two others, viz. into DB and FB; the force DB, however, instead of being replaced by the opposite one BD, will now be represented by the shorter line BG; or that of BH or BI, according to the degree of elasticity. If we, therefore, complete the parallelogram, BC, BK, or BM will be the diagonal path of the body; making, as you perceive, the angle of reflection DBC, greater than that of incidence ABD; and where the body is perfectly inelastic, the force DB will be wholly destroyed, and, the force BE alone surviving, the body will be carried along the line BE. I have now,” continued Mr. Seymour, “explained to you the principal laws which govern those forces by which your ball or marbles are actuated. It is true that in practice you cannot expect the results should accurately coincide with the theory, because, in the first place, you cannot obtain marbles that are of equal density and elasticity, and of true figure; and, in the next, there will be obstacles against which it is impossible to guard. The spinning of the marble will also have a material influence on its motion, as we have already discovered. In the game of billiards, where every obstacle is removed, as far as art can assist, the theory and practice are often strangely discordant. But we have dwelt sufficiently upon the subject; we will, therefore, return to the library, where I intend to exhibit an experiment in farther elucidation of the subject of collision.”

The party accordingly proceeded on their return.

“I hope,” said Mr. Seymour, addressing himself to Mr. Twaddleton, who was walking a few paces before him, “that the maiden ladies have not espied their vicar at a game of marbles; if they should, what a chuckling would there be at their next tea-party!”

“A fig for the spinsters!” exclaimed the vicar, as he hastily turned round, and arrested the progress of the party by his gesture. “You really speak, Mr. Seymour, as though it were derogatory to my character to descend from the more austere pursuits to the simple but innocent amusements of youth. Let me remind you, sir, that the Persian ambassadors found Agesilaus, the LacedÆmonian monarch, riding on a stick.”

“True,” replied Mr. Seymour; “and the ambassadors found Henry the Fourth playing on the carpet with his children; and it is said, that Domitian, after he had possessed himself of the Roman empire, amused himself by catching flies; but these were kings: now I admit that philosophers are monarchs, but monarchs are not always philosophers; you must, therefore, produce some less objectionable authority, if you stand in need of such a sanction. Let me see whether I cannot assist you; there was Socrates, if tradition speaks truly, who was partial to the recreation of riding on a wooden horse, for which, as Valerius Maximus tells us, his pupil Alcibiades laughed at him.”

“I care not who laughs at me,” exclaimed the vicar; “I enjoy the amusements of youth, and agree with Dr. Paley, in regarding the pleasure which they are made to afford, as a striking instance of the beneficence of the Deity; and should you so far relax as to put your plan into execution, of writing a work upon juvenile sports, I hope you will call upon me to compose a eulogy, by way of preface.”

“I shall not forget your offer, depend upon it.”

“Did not Archytas,” resumed the vicar,

as Horace says, invent the children’s rattle?--Toys, my dear sir, have served to unbend the wise, to occupy the idle, to exercise the sedentary, to moralize the dissipated,”--

“And,” interrupted Mr. Seymour, “to instruct the ignorant.”

“I will also convince you,” continued the vicar, “that the tournaments were indebted for their origin to the Troy game (ludus TrojÆ), first introduced into Italy by young Ascanius.”

The foregoing episode having been concluded, the party proceeded, without any farther interruption, to the Lodge. On their arrival, Mr. Seymour produced a piece of apparatus, for the purpose of exhibiting the experiment he had promised, in illustration of the doctrine of the Collision of Elastic Bodies.

“Here are two ivory balls,” said he, “suspended by threads; I shall draw one of them, A, a little on one side; now I let it go, it strikes, you see, against the other ball, B, and drives it off to a distance equal to that through which the first ball fell; but the motion of A is stopped, because, when it struck B, it received in return a blow equal to that it gave, and its motion was consequently destroyed. To extend the experiment, here are six ivory balls hanging in a row; I will draw the first out of the perpendicular, and let it fall against the second; see! see! none of the balls appear to move except the last, which you perceive flies off as far as the first ball fell. I should like to hear you explain this.”

Tom observed, that when the first ball struck the second, it received a blow, in return, which destroyed its motion; and that the second ball, although it did not appear to move, must have struck against the third, the reaction of which set it at rest; that the action of the third ball must have been destroyed by the reaction of the fourth, and so on, until motion was communicated to the last ball, which not being reacted upon flew off.

Mr. Seymour commended Tom for his explanation; but he begged him to understand that such an effect only occurred when the balls were elastic; and he proceeded to exhibit the difference between elastic and inelastic bodies by another experiment. “When you raise one of these inelastic balls, made of clay, out of the perpendicular, and let it fall against the other, E, the action and reaction not being augmented by the force of elasticity, are insufficient to destroy the motion of the former; only part of the motion D will, therefore, be communicated to E, and the two balls will move together to d e, which are less distant from the vertical line than the ball D was before it fell.”

Before we close this chapter, we cannot resist the pleasure of informing our readers that Major Snapwell, in company with his legal adviser, had quitted Overton, for the purpose of making such preliminary arrangements as the purchase of an estate must necessarily require. It is not our intention to accompany them; nor shall we travel over the plains of parchment, nor wade through the rivers of ink, which separate the confines of verbal agreement and legal possession; but claiming the prerogative of authors, we shall dip our wing in the cup of inspiration, and by a single flourish of our feathered talisman, at once put the worthy Major in the undisturbed possession of his newly purchased mansion, and instal him in one of Daw’s most comfortable elbow-chairs, surrounded by all the luxuries of polished life.