_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.
[Illustration: Sketch of Trap.]
“A B represent the spoon and trigger in their quiescent position. Upon
striking the end B with the bat, they are brought into the position
C D. The spoon will thus have described the small arc A C, 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 C E.”
“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_ ( σφαιρα κενη ),
which was blown up with air, like our foot-ball, and the _leathern
ball_ ( κωρυκον ), 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.”
[Illustration: Two children on a see-saw, with circles drawn around
them to show their 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.
Suppose that the swing or pendulum A B be raised to C, it will, in
effect, be raised the perpendicular height E C, and in falling will
describe the arc C B; and, in the point B, it will have that velocity
which is acquired by descending through C B, or by a body falling
freely through the perpendicular C E. This velocity will be sufficient
to cause it to ascend through an equal arc B D, 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 C B D; 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.”
[Illustration: Drawing of a pendulum and its movements.]
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.
-----
Footnote 25:
See page 65.
Footnote 26:
“Not one amongst you shall depart without a gift from me.” _Æn_. v.
305.
Footnote 27:
Lib. xiv. epig. 43.
Footnote 28:
“Mæcenas goes to tennis, hurtful game
To a weak stomach, and to tender eyes,
So down to sleep with Virgil, Horace lies.”--FRANCIS.
Footnote 29:
“Two Hundred and Nine Days,” or “The Journal of a Traveller on the
Continent,” by Jefferson Hogg: London, 1827.
Footnote 30:
Pope’s Odyssey, lib. v.
Footnote 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.
Footnote 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.
Footnote 33:
See page 61.
Footnote 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.
Footnote 35:
Compounded of the Greek words ισος equal, and χϱονος time.
------------------------------------------------------------------------
[Illustration: Three people looking at a diagram drawn on the ground.]