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LESSONS IN ARCHITECTURE.-VII.

ROMAN ORDERS OF

ARCHITECTURE-TUSCAN ORDER-COM-
POSITE ORDER.

THE origin of the Tuscan order of architecture is involved in
obscurity. During the era of the kings of Rome, it appears
that this order was followed in the buildings of the Romans;
but it originally belonged to the people of Etruria or Tuscany,
and in that country remains of this order are found which can
be traced to a very remote an-
tiquity. The characteristic
qualities of the Tuscan style
were solidity and grandeur,
features in which it resembled
the ancient Egyptian architec-
ture, with less gigantic but
more graceful forms. To whom
the Etrurians were indebted
for their style of architecture
cannot now be determined, or
whether it originated entirely
with themselves. Some, indeed,
say that they brought it from
the East; but we cannot agree
with those who would deprive it
of all originality, and assert that
it was only the ancient Doric
stripped of its finest features.
The early Romans, who used
this style, did not invent it;
for they were mere warriors and
not artists. They adopted from
time to time the arts of the
nations which they conquered.
Hence, first came the Tuscan
style, and then the Grecian orders,
to be adopted by the Romans.
The Temple of Jupiter Capi-
tolinus-begun by Tarquinius
Priscus, and finished by Tar-
quinius Superbus said to have
been built by workmen from
Etruria, and the tomb of Por-
senna, king of that people, were
splendid early specimens of this
order; but no remains of them
are to be found. The column
of Trajan, built about a century
after the Christian era,
and
which remains to this day, is
considered to be a remarkable
specimen of the Tuscan column.

magnificence, they loaded every member of it with ornaments unknown to the Greeks. In the Composite, sometimes called the Roman order, there was especially a profusion of ornament; and there was scarcely a moulding which was not loaded with decorations. When the particular members could receive no more ornaments, they had recourse to varying the outlines of their edifices (particularly their temples) into every shape that could be produced by the union of circular and triangular figures. Specimens of the Roman style of architecture are to be seen in

the arch of Titus and the baths of Diocletian; and two magnificent capitals are to be seen in the baptistery of Constantine, which belonged to some elder edifice whose history is now unknown. A representation of the Tuscan and Composite orders will be given in the next lesson.

In the decline of the Roman empire, Constantine the Great transferred the capital from Rome to Byzantium, as Constantinople was then called, and attempted to make the latter city rival the former in monumental grandeur by erecting immense public edifices. Here, however, as in Italy, art and science took a retrograde course, and the elegant orders invented by the Greeks rapidly lost their original purity and simplicity. A new style was then grafted on Roman art; the capitals lost their graceful outlines, and assumed cubical forms; the columns were shortened, and the entablature no longer possessed its regular proportions. This style of architecture was called the Byzantine; its ornamentation was no more that of Rome. It again approached the older Greek style, but shorn of the grandeur and magnificence of the whole, and of the exquisite beauty of its details. The Byzantine style lasted during the period of the Eastern empire, and to this day it is employed by the Greeks in their buildings. From the combined influences of that empire, and the memorials which Rome still preserved, in the first ages of the Christian era, of the finest periods of her architecture, a variety of styles arose, of which the oldest was called the Latin style, because it was adopted by the whole of the Latin Church. Numerous examples of this style are to be found in Italy, and some in France; such as the churches of St. Laurence (without the walls) and St. Agnes, at Rome; the ancient baptistery of St. John, at Poitiers, etc. This style, in which may be found all the divisions of an order, was preserved entire until the age of Charlemagne, of which the cathedral of Aix-la-Chapelle, and the porch of the monastery of Lorsch, or Laurisheim, a town of Germany in the grand duchy of Hesse-Darmstadt, are striking proofs. After the reign of this emperor, new innovations and a retrograde movement ir the forms of the orders of architecture led to the Romane style, in which all regular proportion was completely aband while in most of the applications of this style the entab was altogether omitted. From the Romanesque to the p

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PORCH OF THE ABBEY OF LORSCH, OR LAURISHEIM.

After the introduction of the Grecian orders of architecture into their edifices, the Romans chiefly employed Greek artists, and made no alteration in the form of these orders, except sometimes blending them together in the same building. In general, they employed the Corinthian order, as the most elegant; and a modification of this order is attributed to them, as the only attempt which they made at originality in architecture. But some are inclined to believe that even this invention was due to some Greek architect. This new order was called the Composite, because it was, in fact, a compound order, made by the union of the Corinthian and the Ionian orders. The power, the wealth, and the vanity of the Romans led them to increase the number, the magnitude, and the decorations of their edifices to a degree far beyond those of Greece. In the theatre of Marcellus, and in the Coliseum, the Doric and the Ionic styles were both introduced; but the Corinthian style, with its rich ornaments, was most adapted to the tastes of the masters of the world; and as if not left by the inventors in a shape sufficiently expressive of splendour and

VOL. II.

43

style the transition was easy. In the latter, the column departed still more from the rules established by antiquity; it was lengthened out of all proportion, and degenerated into a group of slender pillars. Towards the end of the Middle Ages, the fact of the numerous relations which subsisted between Italy and all parts of Europe, and of the continued existence in that country of the principles and specimens of ancient architecture, led to a return to the established rules of the Greeks and the Romans. This return produced a change in the appearance of architectural monuments in Europe. This epoch, which was called the Renaissance period, brought back the different orders to reasonable and true proportions, and architecture has continued in this state, with more or less variation, to the present day. In a future lesson we shall give a brief account of the various styles of architecture that have prevailed in Great Britain at various periods.

LESSONS IN GREEK.-IX.

THE THIRD DECLENSION (continued).
NOUNS WHOSE STEM ENDS IN A CONSONANT.

c. The Nominative appends r to the stem.

Or this sub-division the first class has a stem which ends in a p sound, or in a k sound; that is, in either β, π, φ, or in y, γγ, *. χ. Observe that σ with a p sound makes y; and with a k sound, makes f.

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1. I avoid a flatterer. 2. Ravens croak. 3. You are delighted 5. They drive the horses by the harp. 4. Dances delight men. with (dat.) a whip. 6. The minds of men are led by the harp. 7. The pipe (plural) delights shepherds. 8. The she-goats are driven to the meadow. 9. The shepherd sings to the pipe. 10. The daughter has a beautiful face, but a bad voice.

Of another class under this head, the stem ends in a t sound, that is, in either δ, τ, κτ, θ, or νθ. The nouns in the ensuing table are ἡ λαμπας (instead of λαμπαδς), a torch; ἡ κορυς (1πstead of κορυθς), a helmet; δ, ή ορνις (ορνιθς), a bird; ὁ αναξ (ανακτs), a king; and ἡ ἑλμινς (έλμινθς), & tapeworm.

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Singular.

Dat.

λαμπάσι.* κορίτσι.* ορνι-σι.* αναξ-ι.* ἑλμισι.*

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ο κοραξ.

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λαμπάδας. κορύθ-ας. ορνίθας. λαμπάδες. κορύθ-ες. ορνίθες.

ανακτίας. ἑλμινθας.

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Gen.

Dat.

λαιλάπος.

λαιλάπι.

κοράκος,

λαρυγγός.

Dual.

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λαμπάδοιν. κορύθ-οιν. ορνίθ-οιν. ανακτ-οιν. ἑλμινθοιν.

The noun δ, ή παις, child, has in the vocative παι. Here belong the adjectives in us and . (gen. -ίδος, εἶτος), 13 δ, ἡ ευχαρις, το ευχαρι (gen. -ἴτος), pleasing, graceful: also those in as (gen. -άδος), as δ, ἡ φυγας (gen. φυγάδος), an exile, or banished person: those, too, in ης (gen. -ητος), as δ, ἡ αργης (gen. -ητος), white: those, moreover, in ως (gen. -ωτος), as 6, ή αγνως (gen. αγνωτος), unknown: and those in us (gen. -ίδος), 33 δ, ή αναλκις (gen. αναλκίδος), without strength; ἡ πατρις (sc. γη, land), gen. πατρίδος, one's native country: finally, those in is (gen. ύδος), 23 δ, ἡ νεηλυς (gen. νεηλύδος), recently come.

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youth.
Νυξ, νυκτος, ή, night.
EXERCISE 27.-GREEK-ENGLISH.

1. Οἱ ορνίθες ᾳδουσιν. 2. Χαρις χαριν τίκτει, ερις εριν. 3. Μακαριζομεν την νεότητα. 4. Απορια τικτεί ερίδας. 5. Πλουσία 6. Ω καλε παι πολλακις την κακοτητα πλούτῳ κατακρύπτουσιν. στεργε τον αγαθον αδελφον και την καλην αδελφην. 7. Ἡ φιλο χρημοσύνη μητηρ κακοτητος άπασης εστιν. 8. Οἱ πενητες πολύ therefore equivalent to our that is, or supply; so here, se. eater means that the verb εστι, is, being omitted by the author, must be supplied by the reader.

• Instead of λαμπαδσι, κορυθσι, ορνιθοι, ανακτσι, and έλμινθι

λακις εισιν ευδαιμονες. 9. Η σοφια εν τοις των ανθρωπων θυμοις | in gold. 4. From a good deed arises glory. 5. We admire the θαυμαστους των καλών ερωτας ανεγείρει. 10. Ο θάνατος τους | good words of the wise. 6. The good deeds of good men are ανθρώπους φροντίδων απολύει. 11. Η φιλία δια δμοιοτητος admired. 7. The soldiers fight with (dat.) spears. 8. I do γίγνεται. 12. Οινος εγείρει γέλωτα. 13. Εν νυκτι βουλη τοις not exchange the wealth of virtue for (dat.) kings. 9. Obey ye σόφοις γιγνεται. 14. Οἱ σοφοι κολαζουσι την κακοτητα. 15. Οι άνθρωποι πολλακις κουφαίς ελπίσι τέρπονται.

EXERCISE 28.-ENGLISH-GREEK.

1. Birds sing. 2. Favour is begotten by favour, strife by strife. 3. By (dat.) wisdom (there) is awakened in men's minds a wonderful love of good things. 4. I am delighted with the song of birds. 5. The songs of birds delight the shepherd. 6. We delight in (dat.) birds. 7. Men follow kings. 8. Men obey the king.

There are neuter nouns which belong to this class. The stem of these neuter nouns ends in r and in κτ, as γαλα, milk, γαλακτος, of milk. As the laws of euphony do not endure a Tor KT at the end of a word, the T and the кT disappear in the nominative, or pass (as in ous, gen. ωτος, an ear) into σ. Thus, το σώμα, σώματος, a body ; το γονν, γονατος, a knee ; το γάλα, γαλακτος, milk, and το ους, ωτος, an ear, are declined as follows:

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Αμάρτημα, άτος, το,

a failing, a fault, sin. Απτομαι, Ι hang on something, I touch. Βαστάζω, I bear, carry. Βοήθημα, άτος, το, help. Γευομαι, I taste. Γυμνάζω, I exercise. Διαμείβομαι, Ι exchange. Εθιζω, I accustom. Θεραπεία, -ας, ή, care, service.

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make a libation.
Σπεύδω, I hasten,
Ταυτολογια, -ας, ἡ,

saying the same
thing again, repe-
tition.

Φαυλος, -η, -ον, radi-
cally bad.
Χρημα, ατος, τo, a
thing for use; in
the plural, goods,
property.

Νύμφη, ης, ή, α
nymph.
Ποικιλος, -η, -ον, va-
rious, variegated.
Πραγμα, ατος, το, α
deed, thing. Χρήστος, -η, -ον, use.
Ρημα, ῥημάτος,
ful, good.
thing spoken, a Χωρισμός, -ου, δ, a
word.
separation.

EXERCISE 29.-GREEK-ENGLISH.

1. Εν χαλεποις πραγμασιν ολίγοι έταιροι πιστοι εισιν. 2. Oi ἱκεται των γονάτων ἁπτονται. 3. Ο θάνατος εστι χωρισμός της ψυχης και του σώματος. 4. Ο πλουτος παρέχει τοις ανθρωποις | ποικιλα βοηθήματα. 5. Μη πειθου κακων ανθρωπων ῥημασιν. 6. Μη δούλευε, ω παι, τῃ του σωματος θεραπεία. 7. Οἱ Έλληνες ταις Νύμφαις κρατηρας γάλακτος σπενδουσιν. 8. Εθιζε και γυμναζε το σώμα συν πονοις και ίδρωτι. 9. Οἱ αδολεσχαι τείρουσι τα ώτα ταις ταυτολογίαις. 10. Την ψυχην εθιζε, ω παι, προς τα χρηστα πράγματα. 11. Οἱ φαυλοι μυθοι των ωτων ουχ άπτονται. 12. 13. Μη εχθαιρε φίλον μικροῦ ἁμαρτηματος | 14. Γεύου, ω παι, του γαλακτος. 15. Οἱ στρατιωται δορατα βασταζουσιν.

Τοις ωσιν ακουόμεν.

Ενεκα.

EXERCISE 30.-ENGLISH-GREEK.

1. Ο young men, exercise your (the) bodies with labour and sweat. 2. We strive after good deeds. 3. Many men delight

* For σωματσι, γονατσι, γαλακτσι, έτσι,

not the words of the bad.

KEY TO EXERCISES IN LESSONS IN GREEK.-VIII.
EXERCISE 21.-GREEK-ENGLISH.

1. Pay respect to the old man. 2. Worship the divinities. 3. Shepherds guard flocks. 4. Avoid the bad man as a perilous harbour. 5. Without the divinity man is not happy. 6. God dwells in the upper air. 7. Often severe cares waste away the minds of men. 8. Follow good leaders, O beloved (O friend). 9. O young man, get out of the way of the aged. 10. Often the people have an unjust disposition (as their) leader. 11. God is the punisher of those who are too elated. 12. Have a sound mind. 13. Ο God, bestow good fortune on old men. 14. Huntsmen capture lions.

EXERCISE 22.-ENGLISH-GREEK.

1. Οι αγαθοι παίδες τους γέροντας θεραπεύουσι. 2. Οι γεροντες θεραπεύονται ύπο των αγαθών παίδων. 3. Οι σωφρονες νεανίαι εικουσι της όδου τους γερουσι. 4. Έπεσθε, ω φιλοι, αγαθῷ ἡγεμονι. 5. Εχομεν αγαθους ἡγεμόνας. 6. Ο λέως πολλακις έπεται κακοῖς ἡγεμοσι. 7. Ο Θεος παρέχει ευτυχίαν τοις σωφροσι, 8. Οἱ λέοντες θηρεύονται ύπο των θηρευτων. 9. Το θείον σεβόμεθα.

EXERCISE 23.-GREEK-ENGLISH.

1. Love your father and your mother. 2. Be not thou a slave to the belly. 3. Rejoice, Ο dear youth, in thy good father and thy good mother. 4. Consult not with a bad man. 5. There were many beautiful temples to (in honour of) Demeter (Ceres). 6. The good daughter 7. Good men are admired. willingly obeys her dear mother. 8. Often a bad son is born of a good father. 9. I hate the bad man. 10. Shining glory follows good men. 11. Persephone (Proserpine) was the daughter of Demeter (Ceres). 12. Ο dear daughter, love thy mother. 13. Virtue is an honourable prize for a wise (skilful) man. 14. Good sons love their fathers and their mothers. 15. The Greeks worship Demeter. 16. Ο dear youths, obey your fathers and your mothers. 17. Ο dear father, gratify thy beloved daughter.

EXERCISE 24.-ENGLISH-GREEK.

1. Ω νεανίαι, στεργετε τον πατέρα και την μητέρα. 2. Αἱ αγαθαι θυγατέρες τοις πατρασι και ταις μητρασι πείθονται. 3. Οἱ πολίται την Δημητερα σεβονται. 4. Τη Δημητρι έπεται ή Περσεφόνη. 5. Τον αστέρα θαυμάζομεν. 6. Ω θηρευται, μη δουλεύετε τη γαστρι 7. Αγαθη μητηρ αγαθην θυγατέρα στέργει. 8. Ω μητέρ και πατέρ, στέργετε τους παίδας. 9. Ο ανηρ εχθαίρεται. 10. Τον ανδρα εχθαίρουσι. 11. Τοις σοφοις ανδρασι πείθονται. 12. Τη Δημητρι έπομαι. 13. Πολλάκις εξ αγαθου πατρος και μητρος γιγνονται κακοι νέοι,

men.

ESSAYS ON LIFE AND DUTY.-IX.

FIDELITY.

Men can

THE whole fabric of society is cemented together by the
principle of faith. Mutual trust is the very life of nations and
Commerce can be carried on by consignor to consignee,
across the Atlantic and Pacific, only by confidence in the
honesty and integrity of others. Breaches of trust shake the
financial foundations of the strongest empire when failures are
connected with large and influential national undertakings;
and in the personal relation of man to man there is nothing
more disastrous in its results than fractured faith.
regain much in material things, but in a moral sense it takes a
long time to restore the lost confidence of others. He who has
lost the glory of fidelity cannot make amends for its absence by
the excess of any other virtue. To take the lowest ground,
Gdelity is a most valuable market commodity. One who can be
trusted, not only with untold gold, but with the honourable seerets
and interests of others, is sure not only to be esteemed highly,
but to take a high position in the world of duty. It is the
faithful servant that is honoured, rewarded, and loved the best.

There are many testing seasons of fidelity, alike in the
affections of youth and in the enterprises of manhood. There
are times when self-pleasing and self-aggrandisement strongly
tempt to fickleness. It may be that some temporary advantage
stares us in the face if we will give up our friend, or some
immunity from the stress of persevering toil if we will change
our pursuit; and at such times we are tempted to be n
to our long-cherished friendship, or our present wei
sibility. But success gained by fickleness is p
material gain can make up for the loss of r

MAY

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atness and Then conme sphere r scoures of life, sed, and whose thfulness of others. rward for infidelity; in miation to religion. working of daily life as cannot consent to confine rua: it is essentially appliccase who acts contrary to it. mere belief, a convincing proof that wierate errors of conduct vaava. This ought not so to be, for faithin the life are certainly as obnoxious sts at the creed.

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ven when seen in the lower creation. as lare con proved faithful unto death. The a mai hod at the loss of its mate, and the dog Nem vunë euro saugà to plunge into the wild surf of the verse she tervest attacks of robber-bands, to How much more beautiful, however, is tay had in moral and responsible beings; in the pa si prosa wà cà misfortune cannot change; in the love and deco which time cannot weaken and oceans cannot The volanoy to principle which temptations to emolumeat and bour cannot shake, and in respect for the just cla mia of otheam, which no amount of self-seeking can set aside. Picity down not, however, imply absence of alteration in in lamint or poduct. So far from this, fidelity to conviction Messitato a marked alteration of our course, and a Now light is ever being cast upon drenge of pH updutons, the poth of us ch ludividual life; and no man, unless he is either delt, will affirm that it is impossible for him to Thuck e mu obherwise than he does at the then present time. Extolite ab much a season may indeed be most painful to us; it HOT = He from old companionships, and take from us their But nothing can make amends for the loss of mamy they have which fidelity to the present truth brings to every Fully be nuk monfined to great occasions or lofty matters; it to make for a process of fidelity in small affairs that we the able or wishful to do our duty in matters of Fidelity is a matter of heart and conscience, wicked mocked of mere detail. It is the spirit of life itself, tud toonhund to any one department of mundane affairs. kad buded that, fidelity may often hinder material prosFiber Bus, and that it may bring anxiety and pain to ok it is certain to more than compensate for all by the great gain of a present easy conscience, and * ty kuonoured name. It would be invidious to draw d to say that women are, on the whole, more thman; but it cannot be forgotten that, in the Adance and the persistency of devotion, they the noblest examples of fidelity in every age

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boy who would succeed in life-in commercial enter4 in professional duties-will find fidelity a kind #ently a stern one. Pupils from this school take ps in our merchants' counting-houses, rise to i pistes of emolument, and win the highest prizes of City • poplave to manifold affairs; to family confidences, to 14 afterorizes to religious principles, to social affecties; and the secret of many disasters is to be found in unfaithfulness. by outward position as by inward ral principle has its sphere of ensed with without endangering

Faithfulness has its prominent mer-stones of the temple, and woe foundations, or removes it from its

MECHANICS.—XVII.

PROOF OF THIRD LAW OF MOTION-LAWS OF FALLING BODIES-ATWOOD'S MACHINE.

In our last lesson we stated and explained the third law of motion, which teaches that when pressure produces motion in a body, the momentum generated in a unit of time is proportional to the pressure. We deferred, however, the proof of it, and therefore proceed now to look at some experiments which show its truth.

The apparatus usually employed consists of what is known, after its inventor, as Atwood's machine. It consists essentially of a fine cord, which passes over a wheel or pulley, and to each end of which equal weights are fastened.

In Fig. 96, A represents the wheel over which the cord passes, a small groove being turned on the edge to receive it. In order to reduce friction, which would materially interfere with the accuracy of the results obtained, this wheel does not turn in bearings, but its axle rests upon the rims of four others, called friction wheels. These turn with the axle, and so far diminish friction that its effect is scarcely noticed. One of the pillars which support these wheels is accurately graduated to inches and iractions of an inch.

B

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H

A hollow ring, D, and a stage or table, E, are also fixed to clamps Fig. 96, sliding on this pillar, so that by means of small thumb-screws they can be adjusted at any height and distance from each other that may be desired.

A pendulum of such a length as to tick seconds, with a small dial to register the number, is fixed on another support at H. A catch is also fixed above D, to hold w till it is allowed to fall. There are several minor details of construction which have to be attended to, but they need not be explained here.

Since w and w' are equal they will balance each other, and no motion will ensue; but if we now take a small bar of metal, F, and lay it across the top of w, it will cause it to overbalance w', and to descend with an accelerating velocity until it reaches the ring D, when, the bar being too long to pass through, will rest upon it, and w will continue to travel onwards with the momentum it has acquired. Now the weight moved is clearly the sum of the weights of w, w', and F, and the moving force is the weight of F; and by a series of experiments it is found that the velocity with which w descends is always in the propor tion of the weight of F, divided by the total weight moved. For instance, make w and w' each to weigh 71 oz., and F a quarter of an ounce: the velocity will be represented by, the mass moved being 16 oz., or 64 times the moving force. Now diminish each of the weights to 7 oz., and make F half an ounce. The mass moved will remain the same as before, but the moving force will be as large again as it was, and we shall find the velocity will be represented by, that is, it will be twice as great as it was. In other words, if the mass remain the same, a double pressure is required to produce a double velocity, a triple pressure three times the velocity, and so on.

Now let the mass be doubled, the moving force remaining the same. Make w and w' 153 oz. each, and F half an ounce, the velocity will now be, or the same as it was at first. So that, if the mass be doubled, a double pressure is required to produce the same velocity. We see, then, that whether the mass or the velocity be increased, the pressure must be increased in the same proportion, and therefore that the pressure is proportional to the mass multiplied by the velocity, i.e., to the momentum, and this is what the third law of motion asserts.

MOTION OF FALLING BODIES.

We are now in a position to examine the laws of motion of falling bodies. At first sight, however, this appears a difficult matter, since different bodies fall with different degrees of

velocity. If we take a stone and a piece of thin paper, and let them fall at the same time, the stone will reach the ground before the paper. Most people would say the reason was that the stone was heavier than the paper, but this clearly is not the true reason, for if we take two stones of different weights and let them fall, both will take the same time. The fact is, that they are not falling through an empty space, but through the air, and this offers a resistance to their fall, which increases with the surface they present. If we take a piece of gold, and letting it fall from any height, notice how long it takes to reach the ground, and then beat it out into a thin leaf, its weight will not be at all diminished, yet it will fall with much less speed on account of its increase of surface. The most conclusive proof that this is the real reason is afforded by what is called the guinea and feather experiment, as shown in Fig. 97.

A brass cap is made to fit air-tight on to the top of a tall glass cylinder, from which the air can be exhausted by an air-pump.

Through this cap a small rod passes, by turning which two small flaps can be allowed to fall. Now let a guinea or other piece of money be laid on one and a feather on the other. If the rod be turned both will fall, but the gold will outstrip the feather and reach the ground first, because it meets with less resistance in proportion to its weight.

Now replace the guinea and the feather

Fig. 97.

on the flaps, as at first, but this time carefully exhaust the air from the receiver; on turning the rod and watching, both will be found to fall in exactly the same time.

All bodies, then, fall at the same rate, and acquire the same velocity in falling, except so far as they are impeded by other

causes.

A balloon, if we could make it strong enough not to burst, would in a vacuum fall in exactly the same time as a ball of lead.

If we take a number of balls made of different substances and arrange them side by side in a box, the bottom of which turns on a hinge, and allow it to fly open, the balls will travel in a straight line and all reach the ground together. A little consideration shows that it is very natural that it should be so. If we have a number of equal balls, made, for instance, of lead, each will fall in the same time. Now let two or more be rolled into one, and the large one will fall in the same time that the small ones composing it did, though it is heavier, for there is obviously no reason why the mere change of shape should alter the speed.

We want to know now what is the actual velocity with which a body falls; and this is often a useful thing to know, for by it we can ascertain the height of a tower or the depth of a well. We have only to drop a stone from the top, and notice how long it takes to reach the bottom, and from this we can calculate the height.

A falling body is acted on by the attraction of the earth. Now after any given time-say, for instance, one second-it has acquired a certain velocity with which it would continue to move if the attraction ceased. It does not cease, however, and hence the body must fall with a constantly increasing velocity. This we can calculate by means of Atwood's machine. We can, by diminishing the weight of the par, decrease the velocity in any proportion we like, and thus are able to measure the space passed over.

If the bar weighs as much as the weights do, then the moving force is one-half of the mass moved, and the velocity with which it descends is one-half of the velocity it would have were it free to fall from its own weight alone. But to make the speed more easily measurable, let us further diminish the weight of the bar as compared with the weights. If we make w and w' to weigh 7 oz. each, and the bar, F, oz., we shall have as convenient a proportion as we well can. The total mass moved will in this case be 1 pound, and the moving force oz., or of the mass; the velocity with which w falls will therefore be of that of a falling body.

Now raise w with the bar on it to the catch, and allowing it to start at one tick of the pendulum, note how far it falls before the next. The easiest way of doing this is to fix the ring a

little way under w, and, by shifting it up and down, ascertain the place at which the second tick of the pendulum occurs at exactly the same time as the sound of the bar striking on the ring. This distance will be found to be 3 inches. Of course, you must measure from the height of the under side of the bar, for that is the part which strikes the ring. This, then, is the space passed over in the first second, and if we multiply this by 64, we find that 16 feet is the space a body, left free, will by its own weight fall through in the first second. More exact experiments show that the amount is 16 feet, but we may take 16 as near enough for most practical purposes. We have thus found the distance w passes in one second; but we want to know what momentum it has acquired, that is, what space it would, from the velocity it has received, pass over in the next second, supposing gravity were to cease to act altogether. As it falls with an accelerating velocity, it must be moving more quickly at the end of the second than at the beginning, and thus its velocity at the end must be greater than 3 inches. To ascertain this we leave the ring as before, 3 inches under the bar. Now when w passes through the ring, the bar rests on it, being too long to pass, and therefore w falls from its own momentum alone. If, then, we fix the shelf, E, at such a distance under D that the weight strikes upon it at the third tick, the distance between D and will be that which w passes over from its momentum, and this space we shall find to be 6 inches, or just double that passed over in the first second.

Now if the ring had been removed, and the bar left on during this second, it would, by the second law of motion, have caused w to fall through an additional 3 inches. It ought then to fall through 6 inches from its own momentum, and 3 inches from the force of gravity, making in all 9 inches; and if we place the stage 12 inches below the catch, we shall find that such is the case. Thus it passes 3 inches in the first second, and 3 times 3 inches, or 9 inches, in the second. By again arranging the shelf and ring, we shall find that the momentum acquired after two seconds is double that acquired after one, for it will carry w through 12 inches in the third second.

Similarly in this second it will move 12 inches from momentum, and 3 inches from gravity, making in all 15 inches, or 5 times 3, and its momentum at the end will be 18 inches.

Now if we arrange these results in a tabular form, we shall find some simple laws which regulate them. Instead, however, of putting down 3, 6, 9, etc., we will use 1, 2, 3. The proportion is just the same, and if we had made the bar instead of of the mass, these are the distances in feet which would have been moved over.

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3.

4.

41.

16

16

5.

Now we saw that the space any body falls through in the first second is 16 feet. Hence in the second it is 48, or 16 x 3, in the third 80, or 16 x 5. Generally, then, if we multiply the numbers in the above table by 16, we shall have those applicable to the case of falling bodies. This may be more clearly represented by Fig. 98. In this diagram vertical height represents the time in second breadth, the velocity; and area the total space pas At the end of the first second it shows the space

6.

Fig. 98.

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