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has informed me of his design; Pythagoras called those who love figure in the lower line;" whereas 1, in my original conception, wisdom, philosophers; a man eager for glory often turns aside when I borrowed 1 (as old men and old writers call it), I reduced the from the way of virtue'; what slave is more aniached to his master figure in the upper line by unity, and this I found on mature ressonthan a dog ? a good man adheres to good resolutions; the are of ing to be pilosophically correct. Mr. Augustus De Morgan in his Cicero was fruitful in virtues; the prison is filled with traffickers; Principles of Arithmetic "gives a reason for the popular method, a life without friends is full of snares and fear; Italy was formerl; but it secms to want originality. "To put the less line under the full of Pythagoreans; Gaul abounded in men and the productions greater" should be discarded altogether. "In multipli ation, you of the earth; he is without human aid; he declared that he was must place the multiplier under the multiplicand, you must begin the third person who was destined by fate to hold supreme power | with the unit figure of the multiplier,” &c. I will now work an in the state; it is clearly ascertained 10 me that you are able to example in the different ways, in which every one of these rules gain the kingdom; beasts are devoid of reason and speech; all is violated. who are posseused of virtue are happy; anger cannot govern itself; whaterer any one erjays is his own (enjoyment is possession);

1st method.

2nd mcthod. Tarquia had a brither (by name) Aruns, a man of a mild character; the flert of Xerxes consisted of one thousand two hundred ships;


6721296 he accused him of flight and fear; ( free ther, Oson, from


43927 blame; he is a man of no importance; the little field was worth two thousand sesterces; your letter wis of value to me; of what


60191664 account is that glory of men? Sextilius highly valued money


302158320 obtained legally; depraved men are wont to value their own


181471992 property little, and to long for others' property ; it is very base to


308688961392 value more highly what appears useful than what appears honour

47019072 aple; Canius bought the gardens at the price which Pythius wished; I sell my corn for not more (pluris) ihan the rest, perhaps

303698961392 even for less; I do not care a rush for those nefarious men; let us account of no consequence the tales of ill-tempered old men;

3rd method. you do not value me a farthing; how much do I value you? not a rush; this slave is worth nothing ; be allows her to play as she

6721296 likes, and does not regard her at all; what is of very great import

45927 ance is often considered a necessity; Julius Caesar adapted the year to the course of the sun, so that it had three hundred and

55112+ sixty-five days; Claudius took very little sleep; the state of the

4108992 Serons is very strong and of great weight among the Gauls ; an

30362944 orator ought to be a man of good judgmeut and of very high ability; thou also wilt become one of the celebrated fountains; any min

308088961392 may err, but none except a fool will persist in error; it is the mark of a dull understanding to follow the streamlets and not to visit

I do not mean to say that every example in multiplication is so the fountains ; nothing is so much the token of a narrow and well adapted for contractions as the one I have chosen, but I do deprared mind as to love riches; all these things, except the capitol say that many are so; In the first method, it may be observed and the citadel, were in the enemy's hands ; you know that by that the sum of the 1st and 2nd, as well as of the 4th and 5th this time I am altogether Pompey's; to put many persons in partial products of the multiplicand, is equal to the middle. In the danger of their lives seems the act of a cruel man, it man he may second method, the first partial produet is that of 9 times the mulbe called; to yield to necessity has always been considered the tiplicand, for 900; the second partial product is that of 6 times the mark of a wise man ; Popilius got the keys into his own possession ; times the first, for 27; hence, the total product is that of 45,000,

former, for 45,000 ; and the third partial product is that of three that you should come as soon as possible greatly concerns your 900 +27=45927. In the third method, the first partial product domestic interests; your being in good health greatly concerns you and me; it is not of so much consequence in what disposition times the former, for 96; the third is that of 7 lines the second for

that of 12 times the multiplier, for 1,200; the second is that of 3 a thing is written as in what it is taken; that in no way concerns me; 11.7t concerns them more than himself ; letters were devised 672,0000; hence, the total product is that of 672,000+1,200--96+3 that we inight inform the absent of anything which it concerned us

6721296. or (aut)them to know; your being the commander is for the common In division, we are told that “the product of the divisor by the safety; it is of no consequence how many books you hare, but of quotient figure must be less, or at least rot more, than the diviwhat kind they are ; Caesar was accustomed to say that his safety dend;" even this is not absolutely necessary, although I admit that concerned not himselt so much as the commonwealth; he is sick it is, generally speaking, the most convenient. But in the finding of at heart; he is very much attached to (very fond of) you; he wewt the greatest common measure it may frequently be dispensed with away with a confused and un'etermind mind.

to great advantage. The olden writers seem to insist that in the Rule of Three the first and third terms must be of the same kind; but the moderns, upon wbom new light has broken in, all say, with.

out doubt correctly, that "the first and second must be of the same CORRESPONDENCE.

kind.” With me it has been always a matter of indifference, and

in a strict numerical sense there is really no difference. Another ARITIIVETIC.

hindrance to the young tyro is the mysterious language in which

the rules of arithmetic are enveloped.' Every new enunciation of Mo. 1:ITOR,-Yesterday, for the first time, the Porular EDUCA- the application of its fundamental principles is dignified with the Ton was put into my hand. At page 224, 1 find “Garçon Embar. appellation of a new rule; hence, the question commonly put: rasse." rishing for a solution of a certain question ; but whether to

"low far can you cipher?" "What rule are you now in ?" For clear up.is own mind, or to embarrass the mirds of others, we are my own part, I never could discover but two rules, Addition and not strico y told. But however this my be, I would infurm him subtraction ;'or, for the sake of conformily, if you please, four. that he n. ay find it clegantly solved in Professor Davics' “ Key to Our old mathematicians liked to be accounted conjurers, and the Ilution's Mathematics," page 191.

present ones evince a desire to mystify their knowledge, or to let it dit. Editor, I perceive you have afforded a niche to arithmetic out as slowly as possible. Hence, youths are suffered to believe in your popular journal; perrait me, therefore, as an old arithme. that they are about to learn a certain species of magic, that figures tician, to give a les hints relating to that science. Altlıough I am

are tools selected for this purpose, and ibat a configuration of inese old and fast falling into the back-ground before my youthful, more tools, according to unexplained rules, gives them the mastery over highly gifted. more highly favoured, and rapidly improving country- secrets otherwise unattainable. They are left to think that io add men, yet mv arithmetic, as yet, is in tolerable repute, because whole numbers, and to add vulgar fractions, are different operaperhaps it is original. I was a very poor boy, brwught up in the tions; and thus they stumble at every step. There is no man, most servija drudgery at the plough; no school, no teacher, I had however illiterate, but he can add and subtract; from this, thereto glean fer kuowledge by the way side, and that, too, then (more so fore, it is evident that arithmetic is the easiest of all than now; in a very barren land. But by some kind inatinet I Why, then, should we embarrass a science founded on common know the principles of the fundamental rules in arithmetic before sease with so many unnecessary difficulties? Yours, &c. I knew their names. As years came on, and I began to see the

THOMAS GUNDRY.' work of others, I became a critic. A few of my pertinent remarks on tearhers and writers on arithmetic I will lay before you. I quarrelled first with the word must either expressed or implied: llucl Vor, near IIeiston, Cornwall, "In subtraction you must when you borrow 1, carry ten to the next

Sep, 19, 1853.




Thirteen thirty-sirths of the whole, the Wolf finish'd, Twenty-one thirty-sixths, the Tiger diminished, Leaving only two thirty-sixths, full to the King, . The portion eaten up, by himsell, at a spring. llaving found out these answers, apart from all men, I beg to subscribe myself, A. U., Rutherglen,

[This question was also correctly solved by J. W., Reading; W Parker, Busk; H. R. R.; Josephus, Gravesend; R. Brown, Leren H. C. P., Bristol; and others.]

G, A., jun. (Liverpool): We don't know the French dictionary he speaks'of.
Cassell's French Dictionary has the pronunciation wherever there is any
difficulty.-S. E. (Sheffield): We think our own system the best.

G. M. (Aldersgate) informs us that quillet glass may be easily had under
The name of tube glass, and that it may be purchased at Mr. Gibbon's glass
and bottle warehouse, Jerusalem-passage, Clerkenwell, where spirit-lamps
and other chemical apparatus may also be had.

A SUBSCRIBER (Brimley) recomiends such of our subscribers ns call spare the money to do themeelves the pleasure of presenting rol. i. of the P. E. to some promising, aspiring young friend! He seems to think that bis this means many would be greatly encouraged in the work of Self-Impropement, and at the same time be induced to buy the whole series. He has tried the plan himself, and expects gord results.-PIULO (Nottingham: The instruments he mentions will be described in future numbers.

ALPHA (Thornton Le Clay): The term instinct is generally applied to the reasoning power of the loner animals, and is considered to be an instan'a. neous faculty of judging of what is right and wroig as regards their welfare, conferred on them by God. The term reasin is applied to that faculty with which God has endowed man, to enable hin to judge of what is right and

wrong as regards his welfare; conscience is no other than this faculty properly Sir, I beg leave to send you a sketch of a balance which I have instructed, or made aware of what is right and wrong, and of their case designed, with a riew to bring such an instrument within the reach wencesHence, the man who has received the bighest moral ar.d reizi, us

When the conscience in seu.ed by of any student of chemistry; the expense to an ingenious person neglecting its warning, the possessor of it becomes worse than the line would scarcely exceed a shilling. The balance is composed of a ignorant sarage, and hig actions faits lower than the brute creat . We penknife blade, easily procurable at any cutler's for a few pence, recommend all our readers, by all means, to cultivate a tender conscience, fixed in a stand of wood; the beam, made of a bit of polished' brass and one void of offence towards God and man.

The penny edi jan of the wire, is formed to rest on the edge of the blade as shewn in the and in good condition, on paying the difference in price.

P. E. may be exchanged for the three-halfpenny edition, if it be quite clean sketch; and the pans are watch glasses borne by silk threads; on the top of the loop in the beam, I have soldered an index which can mial Theorem in the le*s018 in Algebra as soon as we cau. --J. 5. (Dartford) be adjusted (the balance being at perfect rest; by a card with a Go on improving.-F. RICHARDS (Selly): We don't know it.-1. zero point drawn on it, sliding in a groove on the top of the wooden EDWARDS Swinton-st.): Thauke-R. J.R.: We quite agree with his persirke stand. This balance will be found inexpensive, and sufficiently

on Prop. Ili. Book 1., but we have dwelt already too long on the initial prosensitive for all usual purposes, weighing grains with accuracy. Í positions; we must now advance with m re poed. am, &c.,


OMEGA : We think that the Latin Dictionary by E. A. Andrews, which is

a translation of Dr. Freund's Latin Dictionary published in Germany, is 114, Great Britain-street, Dublin.

most likely to be the best As to the study of Latin, get all the knowlede Sep. 17, 1853.

you can by hook or by crook.–J. E. S. A. is too flattering to us; we shall consider his suggestions.

. E. (Oldham), STUDENT IN FRENC II (Lecds): Yes.---JAMES JONES

(Morriston): Apply and go ahead, — CONSTANT ADMIRER (Torquar) SOLUTIONS.

deserves our sincerest thath's; but many men, many minds.- WARIN E 3: Dereham): Ah! my friend, beware! there are sad Hawe in Legendre's lico

metry ; don't forsake old Euclid; he has stood 2,000 years! The secnd case pliction of the Question proposed in No. 75, page 344, Vol. III., of of Prop. VII. won't do, neither will the demonstration of Prop. XV!.. the Popular Educator."

JENOBIA (Brighton): The Historical Educator" is a substitute for the

lessons in History in the P. E.-J. THOMPSON (Leicester): We are not Here, the wolf would eat } of the sheep in 20 minutes, and certain. the tiger would eat of the sheep in 10 minutes ; therefore, ingenious; many thanks for his kind endeavours on our behalf.-E. HART:

J. F. ENTWISTLE (Wigan): His tables for the Octary Scale are very both would eat ở of the sheep in 20 minutes. Consequently For a list of French books, write to any of the foreign booksellers in London, there would be of the sheep to be eaten together by the wolf, as D. Nutt, Strand; Dulan ant Co., Soho-square, &c.

The best library in tiger, and lion.

London for scientific and all other books is that of the British Museum;

admission is free, but you must have a recommendatory letter from some Now, the wolf would eat 1 sheep in 1 hour; the tiger would gentleman who is well know, addressed to the chief librarian.-A SCESCE; eat 3 sheep in 1 hour; and the lion would eat 2 sheep in 1 BER (Westminster) need be under no alarm about omissions of sectlone in any hour; therefore, all would eat 6 sheep in 1 hour. In what make very considerable progress in leatuing before he thinks of the milis. time, then, would they eat of a sheep? Here we have try; mere spouting won't do. 6 sheep : } sheep :: 1 hour : 13 minutes for the time taken by the 3 animals to eat the whole sheep, from the commencement of the operation.

LITERARY NOTICES. Lastly, we have 60 minutes : 213 minutes :: 1 sheep: 13, the part the wolf ate ; 20 minutes: 114 minutes :: 1 sheep : 38, the part the tiger ate; 30 minutes : 13 minutes :: 1 sheep: , the The Third Volume of CASSELL'S CLASSICAL Libary will contain the part the lion ate. Whence, 18+1+1=39=1 sheep, proof.

Acts of the Apostles in the original Greek, according to the text of Augustus

Hahn; with grammatical, historical, and expository Notes ; followed bits G. ARCHBOLD, St. Peter's. revised and corrected. This work is well adapted for the ure of Schools


Colleges, and Theological seminaries, and will supply our Greek students [The following rythmical answer may please some readers.] with excellent materials for practice in translation. Mister Autodidactos, I've look'd o'er your rhyme,

LATIN, And propose now to tell you exactly the time

The first volume of CASSELL'S CLASSICAL LIBRARY is now ready, Which the Wolf, with the Tiger and Lion combined,

price Is. 6d., containing Latin extracts for translation on the folowing Took to eat up the Sheep, and leave nothing behind.

subjects-Easy Fables, Mythology, Biograp's, The History of Rome, and Twenty-one and *wo-thirds are the MINUTES, you see,

Ancient Gengraphy; with a suitable Dictionary. The second volume, That the sheep was in eating among them all three.

which is publishing in weekly numbers price 20. each, will consist Then as to the portion to each one allotted,

of useful Latin Exercises, or English sentences, to be translated into Latin,

with numerous references to Andrews and Stoddart's Latin Grammar, : This may, in the followiag words, be just noted :

valuable treatise now in the pre-s.


Fig. 12,


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Ist unit of time is 1, and the spaces described in 2, 3, 4, 5, &c., No. V.

units of time, are 4, 9, 16, 25, &c., it follows that the space

described in the 2nd unit of time is 4 less 1, that is, 3; in the LAWS OF FALLING BODIES, INTENSITY OF 3rd unit it is 9 less 4, that is, 5; in the 4th unit, 16 less 9, that GRAVITY, &c.

is, 7; and so on. Hence, the spaces described in the 1st, 2nd, Falling Bodies.-The three laws of Falling Bodies are the 3rd, 4th, &c., units of time are successively 1, 3, 5, 7, &c., following, which are only strictly accurate when the conside according to the series of odd numbers. From this it is evident ration of the resistance of the air is omitted ; or, in other that the spaces described increase by equal quantities in equal words, when the bodies fall in a perfect vacuum.

times, which is in accordance with the definition already given to the earth's surface, at the same place. This law is proved in a vacuum, and from heights in the atmosphere differing 2st Law; All bodies, large or small, fall with equal rapidity of uniformly accelerated motion.

The laws of falling bodies are only true when the bodies fall by the following experiment, called the guinea and feather expe; little from each other in comparison with the radius of the riment. Take a tube of glass of about two yards in length, and a convenient diameter, fig. 11, closed at one of its extremities, carth. When the bodies fall in the air, ihese laws are modiand furnished at the other with a brass stop-cock; put into this fied by the resistance of the atmosphere; and when they fall tube, placed vertically, with the closed end lowest, any two from very unequal heights in the atmosphere, the force of bodies of different densities, such as lead and cork, gold and gravity is not strictly the same. paper, &c., and make a vacuum in it with

Galileo, an Italian philosopher and Florentinc nobleman, Fig. 11,

an air-pump ; then quickly invert the was the first who made the discovery of these laws, and tube, by placing the closed end uppermost, where he was professor of the mathematics in 1611 A.D.

announced them to the students of the university of Pisa, and keep it in the vertical position; you will now see the light body and the heavy Inclined Plane. - Various apparatus have been invented for body, such as the guinea and the feather, the purpose of proving the laws of falling bodies ; Galileo both fall to the other end of the tube employed the inclined plane in an original manner; Atwood with the same velocity. Readmit a little invented the machine known by his name; and M. Morin, air by opening the stop-cock, invert the director of the “ Conservatoire des Arts and Metiers" at Paris, tube in the same manner as before, and constructed an apparatus first proposed by M. Poncelet. you will see the light body falling more

An inclined plane is one which makes with a horizontal slowly than the heavy one, in proportion plane any angle less than a right angle. In proportion to the to its comparative weight. Lastly, re- smallness of the angle between these planes, so is the decrease admit the air completely, perform the of the velocity of a body which descends along the inclined same inversion, and you will find that plane. Thus, let a B, fig. 12, represent an inclined plane, ac the light body falls still more slowly than the horizontal plane, and b c a perpendicular to the horizontal before, in consequence of the greater effect of the resistance of the air when fully admitted into the tube. The conclusion from these experiments is, that if in the ordinary circumstances of the atmosphere bodies fail to the ground with unequal velocity, the cause of this is the resistance

Q of the air, which is more sensibly observed on the lighter bodies, and not from any difference in the action of gravity upon different substances, for it acts alike upon all substances, making them fall from the plane drawn from any point 3 in the inclined plane. It any same height in the same time in a vacuum. body m rest upon this inclined plane, its weight p acting verMoreover, under equal volume, all bodies tically may be resolved into two torces Q and F, the one acting experience the same resistance of the air in in a perpendicular and the other in a parallel direction to the fulling; but the force with which they are inclined plane a c. The first force, a, will be completely attracted overcomes this resistance in pro-counteracted by the resistance of the inclined plane which acts portion to their mass.

in the direction Qg, and the other force r only will act on the The resistance of the air to falling mass of the body n in order to make it descend along the plane. bodies is particularly evident in the case

In order to ascertain the value of the force F, take on the of liquids. When ihey fall in the air, line up a length the number of whose units represents the they separate and fall in drops ; but when weight P, and complete the parallelogram D GEH; then the they fall in a vacuum, they fall like a solid force will be represented by the number of units of length mass, without separating into drops. This in Gd. But the triangles 1 GH and Apc are similar, because phenomena is proved by the apparatus their angles are equal (Cassell's Euclid, Book VI., Prop. IV.); called the water-hammer; this is a tube whence we have of glass of about an inch in diameter,

GH: DG :: AB: B C, or and about a foot or sixteen inches long,

:: AB : BC; nearly half filled with water and hermetically sealed, after the air has been expelled that is, the force r will be less than the weight P, in proportion by raising the water to the boiling point. as the height B C of the inclined plane is less than its length a c.

then this tube is quickly inverted, the Thus we can make the force r as small as we please, by water in falling strikes against its lower end with a smart makes with the horizon, and thus slacken the motion of the dry sound like that of the collision of two solid bodies.

2nd Law. The velocity acquired by a body falling in a moveable body M, so as to be able to take account of the
vacuum is proportional to the time of falling. Thus, at the described in one, two, three, &c., seconds, and
end of 2, 3, 4, &c., times a given unit of time, the velocity altering the laws of the motion, since the
acquired will be 2, 3, 4, &c., iimes the yelocity acquired in or constant. By such experiments as this

that the spaces described increased as that unit.

times, 3rd Law. The spaces described by a body falling in a vacuum, are proportional to the squares of the times of falling. Atwood's Machine, -The laws of fall Thus, if the times of falling be 1, 2, 3, 4, 5, &c., times a given were more clearly demonstrated expe unit of time, the spaces described will be 1, 4, 9, 16, 25, a machine invented by Mr. Atwood, F &c. times the space described in that unit.

the University of Cambridge.

This a Since, according to the third law, the space described in the narrow wooden pillar, about seven VOL, IV.



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THE POPULAR EDUCATOR. having on the top a glass case, in which is placed a brass pulley the weight m to fall by itself, now puts in motion this weight R, fig. 13. Over this pulleypasses a silken thread, so fine that its and the two other weights m and ar'. The quantity of motion, weight need not be taken into account, and having two equal or momentum, will therefore be still the same. If we denote

weights M and a' sus- the velocity of the mass at the end of a second hy , the Fig. 13.

pended at its extremities. momentum will be (m+2m)x ; and by putting this equal to the The axle of the pulley, momentem of m, when it falls alone, we have the equation instead of resting on two

mg fixed bearings, is sup- (m+221) .=mg; whence x =

Thus, if the weights ported on the circumfe.

M+2 rences of four moveabie x and ' were each 16, the weight m being unity or 1, we wheels. By this arrangement the axle of the should have x = ; that is, the velocity of the mass would

33 pulley transmits its motion to the four wheels, be only one thirty-third part of the velocity which it would and the sliding friction have if it fell freely in the air. By this means we can more of fixed bearings is con- easily ascertain the nature of the force which causes bodies to verted into the rolling fall, and also render the resistance of the air imperceptible. friction of the wheels, a

The first experiment performed by this machine proves that contrivance by which the the spaces described by a falling body increase as the squares friction of the axle is very of the times. The pendulum p being at rest, and the second much diminished.

index being beyond zero, the weight m' is placed on the platB

On the pillar is fixed a form 1, and is loaded with the additional weight m, the whole clock-movement w, which being kept in the horizontal position by the extremity of the regulates a seconds' pen- lever , and corresponding to zero on the scale. Removing dulum p by means of an then the hollow stage B, and preserving only the final stage A, anchor escapement. This place the latter, by trials, at such a distance from the zero escapement is shown on point at I, that from this point to the stage A the weights # the dial-plate above the and u take only one second in falling, the fall commencing at swing-wheel which occu- the instant when the pendulum having

been put in molim M

pies the centre. This the index reaches zero on the dial-plate; for at this point the
escapement oscillates with lever p is put in motion by the eccentric, and the platform 1 is
the pendulum, and in overturned, setting the weights m and m at liberty to fall.
left alternately at each the space descended in a second, to be seven divisions of the

Suppose now that we have found the height of the fall, or

tooth of the swing-wheel stage a to a distance from the zero point 1, equal to four time
to escape. The axis of the preceding distance, that is, to the 28th division of the
this wheel carries at its scale, and it will be seen that this space is described in
anterior extremity an in.
dex marking seconds, and

exactly two seconds by the two weights m and a'. In like at its posterior extremity,

manner it will be found that at a distance nine times the first behind the dial-plate, an in three seconds; and so on. The third law is, therefore,

or at the 63rd division of the scale, the space will be described eccentric, shown at E on verified by experiment. the left of the pillar. This eccentric mores with the recollected that in accelerated motion the velocity at a githa

In order to verify the second law by experiment, it must be

index, and presses on a instant is that of the uniform motion which follows upon the
motion, overturns a small what Taw the velocity of a falling body varies, we have only
platform 1, employed to
support the mass m'.

to measure the velocity of the uniform motions which immeParallel to the pillar, two, three, &c., seconds of the full.

diately follow the accelerated motions successively after one, is a wooden scale of nearly ratede motion is obtained by means of the stage 3. This is

The determination of the uniform motion after the acceleinto inches and tenths of placed just at the distance from the zero of the scale which the an inch, used for the in the first experiment; then, the additional weight m being purpose of measuring the stopped in its descent by the stage , the weight ar continues spaces described by the falling body. On this

to descend alone, until it be stopped' by the stage a, which is screws can be adjusted to any required height. The stage to ne motion is uniformly accelerated, and from 3 to a it is scale are two stages A and 1, which by means of tangent occupy only one second in passing from 3 to A. Now, from A is intended to receive the weight i' at the end

of its course ; uniform ; for the weight m being stopped by the stage bir and the stage B, which is hollow, allows this weight to pass through it, and is used only to stop the progress of the addi- gravity no longer acts from B to a, and the motion is only tional weight m which rests upon it at starting. The use of number of the

divisions of the scale passed over by the weight Atwood's machine is to diminish the velocity of a falling mo from the one stage to the other will then represent the body, and to produce at pleasure a uniform motion, or a velocity acquired by the two weights m and x' at the end of motion uniformly accelerated. In order to understand the nature of this machine, suppose

one second. that a small piece of brass m, which in the engraving rests on a distance that the two weights m and x' take two seconds to

In repeating this experiment, the stage B is lowered to such the stage B, falls alone ; let its velocity at the end of a second descend from the point I to the stage B; the stage A is then then be denoted by mg. If this piece of brass m be placed on the first experiment. Thus, the two weights fall during two the weight s', when at the top of the scale, it will descend and secords in a state of uniformly

accelerated motion; then reach communicate part of its motion to the two weights m and m'; ing the stage B, the weight w'

alone passes over the interval for previously to this, the two weights being equal were in between the stage 3 and the stage 1. The velocity acquired equilibrium, the action of gravity in each being mutually at the end of two seconds is therefore double of that acquired alanced. It is plain that the same force which would cause at the end of one second. Similar experiments being made fol


three, four, &c., seconds, it will be found that the relocities to guide a long wooden ruler which is applied to the cylinder, acquired are three, four, &c., times the velocity acquired at the and is used to trace on its surface two kinds of cquidistant end of the first second ; and thus the second law is verified.

lines, the one in planes perpendicular to the axis of the M. Morin's Apparatus. - In this apparatus, or continued cylinder, and the other vertical. indicator of mou.cn, the uniform rotatory motion of a cylinder The cast-iron piece, or monkey, M, guided in its descent by covered with paper is combined with the motion of a falling two straight iron wires, F and G, firmly fixed at their extremi. body, in such a manner that by means of a pencil properly ties, is placed at first in a catch at D), which can be opened at adjusted for the purpose, it describes on the paper a curve pleasure by drawing the wire 1. To this monkey u is which represents the law of the motion. In fig. 14, the cylin- lastened at R the pencil which describes, during its descent, der A, which is covered with paper, is about 9 feet in height, the curre se on the cylinder as it revolves. From the form and about 16 inches in diameter; this cylinder is set in motion of this curve the laws of motion arc deduced. by a weight P, and this motion is communicated by means of a For the space passed over by the pencil at the end of any cord to the drum B; this drum, by means of two hevelled given time, is at the point mof the curve equal to the portion wheels, communicates the motion to a rod u and to a wheel am of the vertical traced on the surface of the cylinder. But and pinion 1 and o, which put the cylinder A in motion. the motion of the cylinder being uniform, we can take for the

'The weight p having a tendency to accelerate its motion duration of the fall, when the moveable has descended 10 m, during its descent, M. Wagner, the maker of the apparatus, em the arc h ", between the point m and the vertical which is

Fig. 14.

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ployed, for the purpose of regulating the motion of the drum x, drawn through the point at the origin, or the beginning of the à regulator of which the mechanism is concealed in the figure. motion of the pencil. In like manner, at any other point m, It is known in mechanics, however, by the name of the diffe- of the curve, the space passed over is represented by a' me" rential motion, and it depends both on the motion of a pendulum and the time by h' m'. Now, by comparing the lengths a m c, and of a fly furnished with leaves, which moves with great and a' m' with the arcs h m and i' m', we find that the lengths rapidity. This fly is contained in a drum T, which rises or distances a m and a' m' are to one another as the squares of or falls according to the velocity of the apparatus. When their corresponding arcs ; thus it is clearly demonstrated that the motion is accelerated and the pendulum oscillates too the spaces passed over are to one another as the squares of rapidly, the drum rises, and the leaves of the fly then meeting the times of passing over ; and we therefore conclude that with the resistance of the air, the motion is retarded. On the the motion of falling bodies is one uniformly accelerated. other hand, when the velocity diminishes, the drum is lowered, The ratio which is found to subsist between the arce hm, and the fly then meeting with less resistance from the air, the l'm', &c., and the verticals a m, a'm', &c., show that the curve motion is accelerated. Thus a motion sensibly uniform is S R is a parabola whose axis is parallel to the generatrix of the obtained ; and for this purpose the descent of the weight p | cylinder; and this is at once demonstrated by unfolding on a for about 20 inches is sufficient,

plane the paper cover of the cylinder on which the curve is The wheel n, fixed on the axis of the cylinder, is employed ) traced by the pencil.

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