_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 manœuvre: 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
A B, 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 B D, this fact will be rendered more apparent,
and you will perceive that the angle A B D is equal to the angle C B D:
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.”
[Illustration: Diagram showing the physics of rebounding.]
“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 A B
would certainly be resolved into two others, viz. one in the direction
F B, and another in that of D B; “because,” continued he, “these lines
are the adjacent sides of the parallelogram, of which A B 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 D B will of
course be destroyed by the wall, and that represented by F B, 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 D B will be exchanged for one in an opposite
direction, B D.”
“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 B D, B E, which will, of course, drive the ball down the
diagonal B C.”
“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.”
[Illustration: Diagram showing more physics of rebounding.]
“Clearly so; the force D B must be exchanged for an equal one B D, or
else the angle A B D cannot be equal to the angle D B C; 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 A B.--The force will of course
be resolved into two others, viz. into D B and F B; the force D B,
however, instead of being replaced by the opposite one B D, will now be
represented by the shorter line B G; or that of B H or B I, according
to the degree of elasticity. If we, therefore, complete the
parallelogram, B C, B K, or B M will be the diagonal path of the body;
making, as you perceive, the _angle of reflection_ D B C, greater than
that of _incidence_ A B D; and where the body is perfectly inelastic,
the force D B will be wholly destroyed, and, the force B E alone
surviving, the body will be carried along the line B E. 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,
“‘He who would scan the earth, and ocean’s bound,
And tell the countless sands that strew the shore,’
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.
[Illustration: Two balls, labeled A and B, hanging by strings from a
rod and bouncing against each other.]
“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.”
[Illustration: Six balls hanging by strings from a rod and bouncing
against each other, but with only the two balls on the ends moving.]
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.”
[Illustration: Two suspended, inelastic balls, labeled D and E ,
showing positions after D collides with E]
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.
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[Illustration: Two boys causing havoc by upsetting a washerwoman.]