surfaces with one hand, you bring the other near the second other, but one of them communicates with the frame by means
surface, the recombination will take place through the arms of a small piece of tin which bends over at A, fig. 403, in such
and body, and a shock will be experienced, the violence of
which will be proportional to the size of the surface of the con-

Fig. 403, denser and the strength of the electric charge.

Volta's Condensing Electrometer,--This is nothing else than the gold-leaf electrometer already described, with the addition of two condensing disos, The copper rod which bears the pieces of gold leaf, instead of terminating above in a brass ball, ends in a brass disc, on which is placed a piece of glazed taffeta, fig. 401, rather larger than the disc, and serving to isolate it from a second diso of a similar sort, but furnished with a glass handle and placed above it. To render even small quantities

of electricities perceptible by this electrometer, bring the
body whose amount of electricity you wish to determine
into communication with one of the plates, which is then
called the collecting plate, and the other plate in communication a manner that it touches the thumb of the person who holds
with the earth, by touching it with the finger slightly wetted, the instrument in his hand. To charge the fulminating square,
fig. 402. The electricity of the body on which you are experi- bring the isolated tin-foil—that is, the tin-foil which does not

communicate with the wooden frame--near an electrical
Fig. 401,
Fig. 402.

machine. As the other sheet of tin-foil is brought into com-
munication with the earth by the hand, the two sheets act
exactly like the plates of the condenser of (Epinus, and a
great quantity of contrary electricities is collected on the two

The fulminating aquare, like the condenser, is discharged
with the simple exciter. For this purpose, hold the square in the
hand, and apply one of the balls of the exciter to the extremity
A of the little strip of tin belonging to the lower tin-foil. Then
turning the exciter on its hinges, bring the other ball near the
upper tin-foil, when a bright spark will appear accompanied
by a report, owing to the recombination of the two electricities

; but the experimenter will feel no shock, because the recombination takes place entirely through the metallic exciter. If, on the contrary, while holding the apparatus in the same manner, you first touch the isolated tin-foil, you will experience a violent shock, as the recombination will take place through the arms and body,

The Leyden Jar, so-called from the place where it was invented, is ascribable to Musschenbroeck, a Dutch philosopher (some say his pupil, Cuneus), who discovered it accidentally in 1746. Having fixed a metallic rod in the cork of a bottle fall of water, he brought it near an electrical machine, intending to electrise the liquid. Now the hand which held the bottle performing the office of one of the plates of the condenser,

while the water inside represented the other, positive fluid menting then spreads over the surface of the collecting plate, colleeted on the inner surface of the bottle, and negative fluid and acts through the taffeta on the second plate and on the on the outer surface in contact with the hand. Consequently

, hand, so as to repel the electricity of the same kind to the having brought one hand near the metallic rod while the other earth and attract that of a contrary sort. The two fluids there- grasped the bottle, Musschenbroeck received so violent & fore collect on the two plates just as in the condenser of shook that, as he afterwards wrote to Reaumur, he would not Epinus, but without any divergence in the pieces of gold leaf, have it again for the whole kingdom of France. However, this since the two electricities are rendered latent. The apparatus experiment being once known, attempts were made in all being thus charged, you may first withdraw your finger, and quarters to repeat it. The abbé Nollet, professor of natural then the source of electricity, without as yet obgerving any philosophy at Paris, first replaced the water in the bottle by divergence. But if you take up the upper plate, fig. 401, the crumpled sheets of tin-foil, copper, silver, or gold. An English electricity is no longer latent, and that of the second plate philosopher had already discovered that, by covering the being distributed equally over the rod and over the pieces of exterior with tin-foil, the shocks might be rendered much gold

leaf, these diverge very much. The divergence may be more violent. The Leyden jar then took the form it still greatly increased by fitting to the foot of the apparatus two retains, but the theory of it was not understood till Franklin copper rods terminating in balls of the same metal, for these explained it by showing that, like the fulminating square, it is balls being electrised by the influence of the picces of gold really a condenser, leaf, react upon them. The sensibility of the apparatus may As represented in fig, 404, at the moment of discharge, the be still further increased by removing the taffeta and separat

Fig. 404. ing the two plates by nothing more than a very thin layer of gum-lac varnish upon them. Lastly, instead of taking the upper plate for the collecter, as in our figure, it is better to take the lower plate, because it is always the plate which communicates with the source that is most charged. Like all electric aparatus, the condensing electrometer requires to be carefully tried and even warmed before experimenting.

The Fulminating Square is a condenser more simple than that of Epinus, and better adapted to produce lively sparks and violent shocks. It consists of an ordinary square of glass with a wooden frame round it. On the two surfaces of the glass are stuck two leaves of tin-foil opposite each other, and leaving border of about two inches between each and the frame ali round. The leaves of tin-foil do not communicate with each


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Leyden jar consists of a thin glass bottle, varying in size Jars with Moveable Armatures. The jar with moveable according to the quantity of electricity which is required to be armatures serves to show that in the Leyden jar and in all collected. The inside is filled with gold or copper leaf. The condensers it is not solely upon the armatures that the two outside and the bottom are covered with tin-foil B, which, latent electricities are collected, but chiefly on the surfaces of however, terminates at a considerable distance from the neck the glass that separates them. This jar, the several parts of of the bottle. Through the cork passes a copper rod bent into a hook, and terminating in a knob A. Inside, this rod commu

Fig. 406. nicates with the gold or copper leaf which fills the bottle, and is called the internal armature, the tin-foil B being called the external armature,

The Leyden jar is charged, like the condenser of Epinus and the fulminating square, by making one of the armatures communicate with the earth and the other with the electric source. For this purpose, hold it in the hand by the external armature, and present the internal armature to an electrical machine, the positive fuid then collects on the gold leaf, and the negative upon the tin-foil. The contrary would take place if, while holding the jar by the hook, you were to present the external armature to the machine. The theory of the Leyden jar is the same as that of the condenser. Like the condenser, it is discharged slowly or instantaneously. To discharge it instantaneously, hold it as in fig. 405, and bring the two


rie. 405.

which are capable of separation, consists of a large conical glass vessel B, fig. 407, an external armature c of tin plate, and an internal armature D of the same material. These portions being placed one in the other, as represented in fig. A, form a complete Leyden jar. After having electrised it, like the common jar, and isolated it on a cake of resin, fig. 4, remove the internal armature with the hand, then the glass vessel, and lastly the external armature, and arrange them all in a row as represented in the figure. Now the two armatures are evidently thus brought to the natural state. But if you put back the armature c on the cake of resin, and put the glass vessel in it, and again the armature d in this, you again form a Leyden jar, which gives a spark almost as strong as if you had

not discharged the two armatures. Hence we infer that the armatures into communication by means of the simple exciter, two latent electricities, yielding to their mutual attraction, taking care first to touch the armature held in the hand, leave the two armatures in a great measure and go to the otherwise a shock will be felt. To discharge it slowly, isolate surfaces of the glass. it on a cake of resin, and touch, first the internal armature, Cascade Charge. This name is given to an electric charge with the finger or a metal rod, and then the external armature, which is transmitted from one Leyden jar to another, when and so on continually, eliciting each time a feeble spark. To they are arranged one above another as follows. The first is render the slow discharge more perceptible, arrange the attached by its hook to the conductor of an electrical machine, Leyden jar as represented in fig. 406. The rod is straight then the hook of the second passes through a metallic ring and furnished with a small bell. Near the jar is a metallic fastened to the external armature of the first; a third is rod with a second bell like the first, and a small electric pen- attached to the second in the same manner, and so on to the dulum consisting of a copper ball attached to a silk thread. number of five or six, the external armature of the last comThe jar not being fixed to the board B on which it is placed, municating with the earth by a metallic wire. As soon as the take hold of it by the external armature and charge it by first jar is charged, it reacts upon the neutral fluid of the bringing it near an electrical machine, and then put it on the second and decomposes it, then this reacts in the same way board. The internal armature now containing an excess of upon the neutral finid of the third, and so on throughout tiil positive electricity not neutralised, the pendulum is attracted all the jars have the same fuid as the machine, and the and knocks the bell of the jar. It is then repelled immediately, contrary at their external armatures. These jars can be disand goes to the second bell, to which it communicates its charged one after the other, or all together, by making the electricity. But on returning to a neutral state it is again internal armature of the first communicate with the external attracted by the first bell, and so on for several hours, if the armature of the last. air is dry and the jar large.

Electric Jars and Batteries.-An electric jar is a large Leyden

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jar with a neck wide enough to enable one to stick tin-foil all external armatures of the jars. The tin-foil also lines the round the inside for the internal armature. The rod which goes sides of the box as far as the two metallic handles. The through the cork is straight, and terminates below in a metallic battery is charged, as seen in the figure, by bringing the chain, which puts it in communication with the tin-foil that internal armatures into communication with an electrical forms the internal armature. A battery is a collection of seve- machine, and the external armatures with the ground by the ral jars in a wooden box, fig. 408, communicating together, wood of the box and the table on which it rests, or, still better

by a metallic chain attached to one of the metallic handles.
Fig. 408.

An electrometer with a dial fixed to one of the jars, serves to
indicate the charge of the battery. In spite of the large
quantity of electricity collected in the apparatus, the electro-
meter diverges only slowly and a few degrees, which ought
not to occasion surprise, since the divergence arises solely
from the difference in the tension of the two armatures. The
number of jars is generally four, six, or eight. The larger and
more numerous they are, the more time is required to charge
the battery. To discharge it, bring the two armatures into
communication by means of the exciter, taking care to touch
the external armature first. We must in this case use the
glass-handled exciter, and take every precaution to avoid
shock, otherwise with a strong battery serious consequences
might result. When we wish to strike down an animal, or any
object whatever, we make use of the universal exciter repre-
sented in fig. 409. It is a small wooden box with two glass
columns, on which copper rods are hinged. Between these
columns is a glass support with a small plate, on which is
placed the animal or object upon which we wish to experi-
ment. The two copper rods being directed towards this object,
one of them is made to communicate with the external arma-
ture of the battery, and the other with one of the balls of the
glass-handled exciter. Then bringing the other ball of the
exciter near the internal armature, a spark appears between

this ball and the armature, and another between the branches internally by means of metal rods, and externally by tin-foil of the universal exciter. It is the latter spark that strikes the which lines the bottom of the box, and is in contact with the object.

Fig. 409.

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cannot prevent the formation of habits of some kind or other.

Still, a man has much in his power as it regards the kind of

habits which he forms, and is highly accountable for the Habits differ from principles, or constitutional desires, independ very much on the character of his habits

. Yes, ..

exercise of this power.' A man's happiness and usefulness that they are adventitious. Every habit is acquired by man's moral character derives its complexion, in a great repeated acts. The human constitution possesses a wonderful degree, from his habits. In this place, it is not necessary to susceptibility of forming habits of every kind. Indeed we go into the philosophy of the formation of habits. Our object


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is to consider habits and habitual actions as they partake of a But the whole plausibility of their arguments depends on the
moral character, or as they are the object of moral approbation pre-established connexion between happiness and a virtuous
or disapprobation. If we should remove from the list of moral course of life. That true happiness is the natural effect of
actions all those which are prompted by habit, we should cut virtue, falls entirely short of proving that the essence of virtue
off the larger number of those which men have agreed in judg- consists in the tendency of certain actions to the person's true
ing to be of a moral nature.

interest; whereas, when we perceive an action to be virtuous,
That there are virtuous habits and vicious habits, will we are conscious that it is not from any view of the connexion
scarcely be denied by any considerate person. A habit of of the action with our own happiness thnt we approve of it; but
lying, of swearing, of slandering, of cheating, of irreverence, of our judgment is immediate, founded on a moral character per-
indolence, of vainglory, with many others, are, alas ! too ceived in the act itself. And in many cases virtue requires us
common. There are also virtuous habits, such as of industry, to deny ourselves personal gratification for the sake of others,
temperance, kindness, veracity, diligence, honesty, etc. To be A man supremely governed by a regard to his own interest,
sure, these virtues commonly flow from principle, but the is never esteemed a virtuous man by the impartial judgment of
practice of them is greatly facilitated by correct habits. Two mankind. According to this theory, the only thing censurable
considerations will show that men are properly accountable for in the greatest crimes is, that the guilty person has mistaken
those actions which proceed from habit. The first is, that in the best method of promoting his own happiness. Upon this
the formation of his habits man is voluntary. The acts by principle, man is at liberty to pursue his own interest at the
which they are formed are free acts, and the agent is respon- expense of the happiness of thousands, and if he is persuaded
sible for all their consequences. The other consideration is, that any action will tend to his own interest, he is at liberty to
that habits may be counteracted and even changed by the force | do it, whatever may be the consequences to others.
of virtuous resolutions and perseverance. Where habit has Dr. Paley adopts the principle that all virtue consists in a
become inveterate, it may be difficult to oppose or eradicate regard to our own happiness, taking into view the whole of our
it; but the strength of moral principle has often been found existence. His definition is, however, a very complicated one,
sufficient to counteract the most confirmed habits. When it is and deserves to be analysed.
asserted that men long enslaved by evil habits cannot make a Virtue," says he, " is the doing good to mankind, in obedi-
change, it is on the ground that no principle of sufficient ence to the will of God, for the sake of everlasting happiness,"
power exists in the mind of the agent; but for that deficiency according to which definition the good of mankind is the object,
the man is responsible. Yet a power from without may intro- the will of God the rule, and everlasting happiness the motive
duce a new principle potent enough to overcome evil habits. of human virtue. If the question be asked, why we should
The importance of possessing good habits is admitted by all seek the good of mankind, the answer is, from a regard to our
moralists. Aristotle makes the essence of virtue to consist in everlasting happiness; and if the question be, why should we
"practical habits, voluntary in their origin," and agreeable to make the will of God the rule of our conduct, the answer must
right reason. Dr. Thomas Reid, in his Essay on the Active be the same ; so that really all virtue is resolved into a regard
Powers," defines virtue to be “the fixed purpose to act accord- to our own happiness.
ing to a sense of duty," which definition Dugald Stewart Now every man desires to promote his own happiness, and
modifies, by observing, “It is the fixed purpose to do what is according to Dr. Paley's theory, the only difference between an
right, which evidently constitutes what we call a virtuous dispo- eminently good man and one of the opposite character is, that
sition. But it appears to me that virtue, considered as an the one pursues a wiser course than the other ; but they are
ay tribute of character, is more properly defined by the habit both actuated by the same motives.
which the fixed purpose gradually forms than by the fixed This theory loses sight of all intrinsic difference between
purpose itself.” Dr. Paley lays it down as an aphorism, that moral good and evil, and admits the principle that happiness is
"mankind act more from habit than reflection." "We are,” | the only conceivable good, and that anything is virtuous the
says he, "for the most part, determined at once, and by an tendency of which is to promote our greatest happiness.
impulse which has the effect and energy of a pre-established

A theory the opposite of that which makes a regard to private
habit.” To the objection, “If we are in so great a degree interest the ground of virtue, is the one which makes all virtue
passive under our habits, where is the exercise of virtue, or to consist in a regard to the public good. This is the theory
the guilt of vice?" he answers, " in the forming and contracting of Bishop Cumberland in his work, De Legibus, and is not
of these habits.” “And hence,” says he, "results a rule of essencially different from the scheme of those who make all
considerable importance, viz. that many things are to be done virtue to consist in disinterested benevolence, No doubt,
and abstained from solely for the sake of habit.”

much that deserves the name of virtue consists in good will to THE NATURE OF VIRTUE.

others, and in contributing to their welfare; but it is not

correct to confine all virtuous actions to the exercise of beneThe theories on this subject have been numerous, and con- volence. We can conceive of benevolence in a being who has trary to one another. It is now proposed to mention some of no moral constitution. Something of this kind is observable the principal of them. . We shall first mention the theory of in brute animals, and atheists may exercise benevolence to Mr. Hobbes and his followers, who deny that there is any their friends. The indiscriminate exercise of benevolence to natural distinction between virtue and vice, and maintain that creatures, without any respect to their moral character, might by nature all actions are indifferent, and that our ideas and appear to be an amiable attribute, but it could not properly be feelings on the subject of morality are altogether the effect of called a moral attribute. A prudent regard to our own welfare education and association. Mr. Hobbes did indeed maintain and happiness is undoubtedly a virtue. It has been considered that men are bound to obey the civil government under which so by the wisest of men, and we know that prudence was one they may happen to live, and

to conform to the religion estab- of the four cardinal virtues of the heathen. As the whole is
lished by law, however contrary to their own private judgment. made up of parts, it is evident that if it is a virtue to promote
All moral duty, according to this theory, was resolved into the the well-being of the whole, it must be so of each of the parts.
authority of the law of the land. As no natural moral rule The pursuit of our own happiness where it does not infringe
existed, it was held that, except so far as a man was restrained on the rights of others, has nothing evil in it, but is approved
by civil authority, he had a right to do what he pleased; and by every impartial mind. Some who maintain that all virtue
while he confined himself within these bounds, he need feel no consists in benevolence, admit that we may seek our own
concern about the consequences of his conduct.

happiness just as we seek that of our neighbour; but the
Perhaps the most extraordinary system of virtue every pro- human constitution is not formed to exercise that abstract im-
mulgated was that of Mandeville, who maintained that all partiality. While we are bound to promote the welfare of
pretensions to virtue were mere hypocrisy, which men assumed our neighbour and of strangers, our obligation is still stronger
from the love of praise. This writer forgot that hypocrisy to endeavour to secure our own happiness; and if a friend and
assumes it as true that that which is counterfeited is an object a stranger stand in equal need of a benefit which we have it in
of esteem and approbation among men. That virtue consists our power to bestow, it is evidently our duty to consult first
in the mere pursuit of pleasure, or of our own interest, is a the welfare of our friend, other things being equal.
system as old as Epicurus, and has had many abettors up to What Bishop Butler has said on this subject in his short

treatise on "Virtue," is worthy of consideration : “ It deserves

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this time.


to be considered whether men are more at liberty in point of as a radical principle of his whole system. It will not there.
morals, to make themselves miserable without reason, than to fore be necessary to make any distinct remarks on President
make others so; or dissolutely to neglect their own greater Edward's theory,
good for the sake of a present lesser gratification, than they are
to neglect the good of others whom nature has committed to
their care. It should seem that a due concern about our own
interest or happiness, and a reasonable endeavour to secure and LESSONS IN ARITHMETIC.No. XXXII.
promote it, is, I think, very much the meaning of the word
prudence in our language--it should seem that this is virtue, PERIODICAL, OR CIRCULATING DECIMAL.
and the contrary behaviour faulty and blameable; since in the
calmest way of reflection, we approve of the first and condemn DECIMALS which consist of the same figures or set of figures
the other conduct, both in ourselves and others. This appro- repeated, are called PERIODICAL, OR CIUCULATING DECIMALS,
bation and disapprobation are altogether different from mere

The repeating tigures are called periods, or repotends. If one desires of our own and their happiness, and from sorrow in figure only repeats, it is called a single period, or repetend ; as missing it."

Il111, etc. ; .33333, etc.
Again: "Without inquiring how far and in what sense virtue

When the same set of figures recurs at equal intervals, it is is resolvable into benevolence, and vice into the want of it, it called a compound period, or repetend; as :01010101, etc.; may be proper to observe that benevolence and the want of it,

•123123123, eto. singly considered, are in no sort the whole of virtue and vice.

If other figures arise before the period commences, the For if this were the case, in the review of one's own character, decimal is said to be a mixed periodical; all others are called or that of others, our moral understanding and moral sense, pure, or simple periodicals. Thus - 42631631, etc., is a mixed it would be indifferent to everything but the degrees in which periodical; and :33333, etc., is a pure periodical decimal. benevolence prevailed, and the degrees in which it was wanting.

1. When a pure circulating decimal contains as many figures That is, we should neither approve of benevolence to some

as there are units in the denominator less one, it is sometimes
persons rather than others, nor disapprove of injustice and false called a perfect period, or repetend. Thus, 1 = "142857, etc.,
hood, upon any other account, than merely as an overbalance and is a periect period.
of happiness was foreseen likely to be produced by the first, calied the terminate part of the fraction.

2. The decimal figures which precede the period, are often
and misery by the second. But now, on the contrary, suppose
two men competitors for anything whatever which would be

Circulating decimals are expressed by writing the period
of equal advantage to each of them; though nothing indeed once with a dot over its first and last figure when compound;
would be more impertinent than for a stranger 10 busy himself and when single by writing the repeating figure only once
to get one of them preferred to the other, yet such endeavour with a dot over it. Thus *46135135, etc., is written ·46135
would be virtue, in behalf of a friend or benefactor, abstracted and 33, etc., 3.
from all consideration of distant consequences; as that exam-
ples of gratitude and friendship would be of general good to

Similar periods are such as begin at the same place before
the world. Again, suppose one man should by fraud or violence or after the decimal point; as •i and 3, or 2:31 and 3:76,
take from another the fruit of his labour, with intent to give it
to a third, who, he thought, would have as much pleasure from

Dissimilar periods are such as begin at different places; as
it as would balance the pleasure which the first possessor •i23 and ·42325.
would have had in the enjoyment and his vexation in the loss ; Similar and conterminous periods are such as begin and end in
suppose that no bad consequences would follow, yet such an the same places ; as 2321 and 1634,
action would surely be vicious. Nay further, were treachery,
violence and injustice not otherwise vicious than as foreseen
likely to produce an over balance of misery to society, then, if

in any case, a man could procure to himself as great adyantage Case I.---To reduce pure circulating decimals to cominon frie-
by an act of injustice as the whole foreseen inconvenience tions.
likely to be brought upon others by it would amount to, such a
piece of injustice would not be faulty or vicious at all.” The circulating decimals, or the manner of obtaining them. For

To investigate this problem, let us recur to the origin of
fact then appears to be, that we are constituted so as to condemn
falsehood, unprovoked violence, and injustice, and to approve example, ) = 11111, etc., or 'i; therefore the true value of
of benevolence to some rather than others, abstracted from all 1•111), etc., ori, must be ) from which it arose. For the same
consideration of which conduct is likely to produce an over-
balance of happiness or misery.”

reason •22222, etc., or óż, must be twice as much or 3; •33333,
The danger of this theory is not by any means so great as etc., or •3 = }; :4 = #; = $, etc.
that of the selfish scheme, because it comprehends a large part

Again, bb = .010101, etc., or öl; consequently .010101 ·
of actions which are truly virtuous. But all definitions of
virtue which are not so comprehensive as to embrace the whole etc., or .0i = t; •020202, etc., or '02 = ; .030303, etc., or
of moral excellence, are injurious ; not only by leaving out of | .03 = '; .070707, etc., or •07 = d, etc. So also at -
the catalogue of virtues such actions as properly belong to it, -001001001, etc.

, or -voi; therefore ·001001, etc., or ·001 = odei
but by leaving men to form wrong conceptions of what is right
and wrong, by applying a general rule, which is not correct, to

·002 = t; etc.
practical cases. When it is received as a maxim that all virtue

In like manner { = .142851; and 142857
consists in seeking the happiness of the whole, and when a multiplying the numerator and denominator of by 142857,
particular act seems to have that tendency, men are in danger we have it. So z is twice as much as }; three times
of overlooking those moral distinctions by which our duty as much, etc. Thus it will be seen that the value of a pure
should be regulated. This effect has been observed in persons periodical decimal is expressed by the common fraction whose
much given to theorise upon the general good as the end to be numerator is the given period, and whose denominator is as
aimed at in all actions.
President Edwards has a treatise on Virtue, in which he many 9s as there are figures in the period. Hence,

To reduce a pure circulating decimal to a common fraction,
enters very deeply into speculation on the principles of moral

Make the given period the numerator, and the denominator will
His definition of virtue has surprised all his
admirers ; it is, “ the love of being as such." When, however, be as many 9s as there are figures in the period.
this strange definition comes to be explained, by himself and

Ex. 1. Reduce :3 to a common fraction.
his followers, it amounts to the same as that which we have
been considering, which makes all virtue to consist in disinter-

2. Reduce 6 to a common fraction.
ested benevolence.

3. Reduce is to a common fraction.
Dr. Samuel Hopkins, who was his pupil, and well understood
his principles, gives this as his definition of virtue, and has it! 4. Reduce 123 to a common fraction.

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= 393333; for,

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Ans. ], or s.
Ans. %, or

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