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same as that which has been described above; and by Problem | D E F on the right of the straight line x Y that passes through XXXVI. in the last lesson (page 49), which teaches us how to draw the eircumference of a circle through any three points that are not in the same straight line, it is plain that we are shown how to describe a circle about any given triangle; for to do this the circle must pass through the three points in which the three straight lines (which form the sides and angles of the triangle) meet.

their centres. The dotted lines G L, H D, D A, and a G show how the tangent may be drawn to the left of the straight line X Y. The straight lines A D, B E, with the arcs A X B, D Y E, show the position of an endless band passing over the wheels or drums A B C, D E F.

B

H

D

In making drawings of machines and machinery, the geometrical draughtsman will find it necessary to know how to draw circles of different A radii touching each other with the utmost nicety externally and internally, and to draw tangents to two circles, as when it is desired to represent in section the course of an endless band or belt of leather which passes round two X wheels or drums, and transmits motive power from one to the other. This brings us to the next two problems. PROBLEM XXXIX.-To draw a circle with a given radius touching another given circle externally or internally in a given point.

N

K

Fig. 58.

M

Let A B C (Fig. 58) be the given circle; it is required to draw two circles with the given radius x, one touching the given circle A B C internally in the given point A, and the other externally in the given point c.

First, let us take the circle that is to touch the given circle internally in the point A. Find D, the centre of the given circle ABC. Join AD, and produce it, if necessary, to meet the circumference of the given circle A B C in the point E. Along A E set off AF equal to the given radius x, and from the centre F, at the distance FA, describe the circle A G H, which touches the given circle A B C internally in the given point a.

To describe a circle with the given radius x, touching A B C externally in the point c. Find D, the centre of the given circle ABC. Join DC, and produce it indefinitely towards K. Set off along C K the straight line CL equal to x, and from L as centre, with the distance L C, describe the circle c M N, which touches the given circle ABC externally in the given point c. PROBLEM XL. -To draw a tangent to any two given circles.

X

Fig. 59.

A straight line may be drawn touching any two given circles either on one side of the straight line that passes through and joins the centres of the circles, or crossing this line. First, let us take the case in which the tangent to the given circles is required to be on one side of the straight line that joins their centres.

Let A B C, D E F (Fig. 59) be the given circles. Draw an indefinite straight line X Y, passing through and joining the centres, G and H, of the given circles, and also passing through the point c in the circumference of the circle ABC, and the point F, in the circumference of the circle D E F. From the point F in the straight line X Y, set off F K equal to G c, the radius of the circle A B C. The remainder K H of the straight line F H, the radius of the circle D E F, is manifestly the difference of the radii of the given circles. With H K as radius, from the point н as centre, describe the circle K L M, and from the point &, the centre of the circle A B C, draw the straight line GM touching the circumference of the circle K L M in the point м. Join H м, and produce it to cut the circumference of the circle D F E in the point E, and through E draw E B parallel to G M. The straight line E B is a tangent to the two given circles A B C, D E F. The same result may be obtained by drawing G B through the point G, parallel to H E, and joining the points B and E. The straight line BE has been drawn as a tangent to the given circles A B C,

Now let it be required to draw a tangent to the given circles A B C, D E F, crossing the indefinite straight line x Y that passes through their centres G and H. From the point c in the direction of Y, set off along c Y the straight line c N equal to F H, the radius of the circle D F E. The straight line G N is then manifestly equal to the sum of the radii of the given circles, being made up of G c, the radius of the circle A B C, and C N, which has been made equal to FH, the radius of the circle D F E. From the centre G, with the radius G N, describe the arc o N P, and from H, the centre of the circle D F E, draw H O touching the arc o N P in the point o. Join G o, cutting the circumference of the circle A B C in the point Q; and through the point o draw Q E parallel to H O. The straight line Q R is a tangent to the two given circles A B C, D E F. The same result may be obtained by drawing H R through the point H, parallel to G o, and joining the points Q and R. The straight line Q R has been drawn as a tangent to the given circles A B C, D E F, crossing the straight line x Y that passes through their centres, from left to right; the dotted lines H P, P G, S T, and T H show how the tangent may be drawn crossing x Y from right to left. The straight lines Q R, S T, with the arcs Q A B S, T DE R, show the position of a crossed endless band passing over the wheels or drums A B C, D E F.

The effect of crossing the endless band is to make the wheels or drums over which it passes revolve in contrary directions. In the first case, when the band forms tangents to the wheels on both sides of the line that joins their centres, the wheels revolve in the same direction, that is to say, by the action of the band the wheels revolve, so that a point в, on the circumference of the wheel A B C, is carried round towards A, and a point E on the circumference of the wheel D E F is carried round towards D, the strap being supposed to move in the direction of the arrows placed near the letters A, D, E, B. In the second case, when the band forms tangents to the wheels crossing the line that joins their centres, a point q in the circumference of the wheel A B C would be carried round towards s, and a point T in the circumference of the wheel D E F would be carried round towards R, the strap being supposed to move in the direction indicated by the arrows placed near the letters Q, R, T, S.

The circles K L M, D E F are called concentric circles because they are described from the same centre, H, and for the same reason the arcs A C B, O N P are called concentric arcs.

Fig. 59 suggests the method of drawing a circle of a given radius to touch two given straight lines. Let LG, M G, produced indefinitely to a and b, represent the two given straight lines, and z the radius of the required circle. In & a take any point u, and through u draw u w at right angles to a a. Bisect the angle a ab formed by the straight lines G a, Gb (produced to meet in a if necessary) by the straight line G Y,' and set off along the straight line u W, U v equal to z. Then through v draw v H parallel to G a, and meeting G Y in H. Then from the point H as centre, with a radius equal to z, describe the circle K L M. This circle touches the given straight lines G a, Gb in the points м and L. PROBLEM XLI.-To draw a tangent through any point in a given arc, when it is inconvenient to determine the centre of the circle of the circumference of which the given arc is a part. Let A B C (Fig. 60)

Fig. 60.

be the given arc, and c the given point through which it is required to draw a tangent to the arc A B C. Through c draw any straight line or chord C A, cutting the arc in the points a and c. Bisect A C in D, and through D draw D Bat right angles to A c. Join B C, and at the point B in the straight line C B make the angle C B E equal to the angle D C Bor E C B. through c draw the straight line XY parallel to B E. straight line x Y is a tangent to the arc A B C, and it is drawn through the given point c, as required.

Then

The

LESSONS IN GERMAN.-XXVI. SECTION XLIX.-VERBS REQUIRING THE DATIVE.

MANY verbs compounded with the particles ab, an, auf, bei, ent, er, nach, ver, vor, zu, and wider; as also, danfen, to thank; brohen, to threaten; folgen, to follow; gehorchen, to obey; schmeicheln, to flatter, etc. (§ 129. 4), govern the dative, as :-Er entfagte dem Glück und der Hoffnung, he resigned (the) happiness and (the) hope. Den besten Menschen kleben Fehler an, faults cleave to the best of men. Der Feldherr gehorchte dem Befehle des Kaisers, the commanderin-chief hearkened to the command of the emperor. Nur ein Sclave schmeichelt dem Herrn-kein Freier vem Freien, only a slave flatters the master-no freeman, a freeman.

Acht, f. outlawry, ban. |
An'gehören, to belong.
An'hangen, to adhere.
Auffordern, to sum-

mon.

Bayern, n. Bavaria.
Bech'ren, to honour.
Bei'kommen, to get at.
Bei'stehen, to assist.
Bei'stimmen, to assent.
Bei'wohnen, to be pre-

sent at.
Besuch', m. visit.
Braten, m. roast meat.
Drohen, to threaten.
Ehre, f. honour.
Entsa'gen, to resign,

renounce.

Erlie'gen, to succumb.
Erwei'sen, to render.
Flichen, to flee.
Fluchen, to execrate.
Fügen, to submit,
conform.
Gebieten, to com-
mand.
Gebre'chen, to want,
need.

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Kriegszug, m. warlike
expedition.
Krone, f. crown.
Lauten, to toll, ring.
Leuchten, to light.
Löwe, m. lion.
Magb, f. servant-girl.
Mislin'gen, to fail.
Nachdem', after.
Ort, m. place.

Troßen, to dare, defy.
Trübe, gloomy.
Ue'belwollen, to wish
ill.

Ueberzie hen, to invade.
Un'umschränkt, para-

mount.
Umge'ben, to beset.
Ur'sache, f. cause.
Verlan'gen,n. demand.
Vernunft', f. reason.
Vor‘haben, n. purpose.
Weg kommen, to get
away, be lost.
Widerstre'ben, to strug-
gle against.
Wunsch, m. wish.
3u'gehören, to belong

to.

Zürnen, to be angry

at one.

9. Doch dem Herzoge, der einem Löwen glich, galt weder Vernunft, noch
guter Rath. 10. Da er bisher alle seine Feinde überwunden hatte, glaubte
er Jedem gewachsen zu sein. 11. Er widerstrebte dem Verlangen, dem
Kaiser die Ehre zu erweisen, die demselben gebührte. 12. Der Kaiser, der dem
Herzoge schon seit langer Zeit übel wollte, und ihm wegen seines Stolzes
zürnte, kam ihm zuvor, und überzog ihn mit Krieg. 13. Der Kriegszug
mißlang vem Kaiser nicht. 14. Der Herzog konnte der feindlichen Macht
nicht widerstehen, und erlag dem Kaiser in der Schlacht. 15. Er mußte
nach England fliehen, und nur seine Familie und einige Freunde folgten
ihm. 16. Hier entsagte er jeder Hoffnung, und fluchte dem Stolze, als der
Ursache seines Elents.
17. Ihrem Wunsche entsprechend, werde ich Ihnen
beim Suchen des Pferdes helfen, das Ihnen weggekommen ist. 18. Gar
leicht gehorcht man einem evlen Herrn, der überzeugt, indem er uns gebietet
19. Dieser Braten schmeckt mir nicht.

EXERCISE 95.

1. I flatter myself that you will honour me with a visit. 2. He would certainly harm me, if he could get at me. 3. The star of hope lights man even in the gloomiest night. 4. I shall assist my friend for the assistance which he has rendered me. 5. The teacher has told me he was contented with his scholars;

they were diligent and anticipated all his wishes. 6. I know

no one who flatters the passions of others as he does. 7. It were to be wished that everybody might assist the poor. 8. Do not flatter your children too much. 9. Napoleon collected around him the best of his generals. 10. After he had made known to them his purpose, they volunteered to assist him. 11. He trusted to his own power, invaded Europe with hostile troops, and defied every danger. 12. According to his own opinion his power was paramount, and he thought not of the difficulties which beset him.

SECTION L.-VERBS REQUIRING AN ACCUSATIVE OF A
PERSON, AND A GENITIVE OF A THING.
Verbs signifying "to accuse, to acquit," and some others (§§
126, 127) govern the accusative of a person, and the genitive of
a thing, as-Gr klagt seinen Diener des Diebstahls an, he accuses his
servant of theft. Der Feind bemächtigte sich der Festung, the enemy
took possession of (mastered) the fortress. Sie beraubten mich
meines Geldes und meiner Ghre, they robbed me of my money and of
my honour. Die Richter sprachen ihn des Mortes los, the judges de-

Rath, m. council, ad- Zuvor kommen, to anti-clared him (spoke him free) innocent of the murder. Er entledigte

vice.

RÉSUMÉ OF EXAMPLES.

Der'jenige, welcher einer bösen Ge
sell'schaft nicht entsa'gen kann,
kann keiner guten an'gehören.
Ihr Freund begegnete mir gestern.
aber mir wollte sein Name nicht
einfallen.

Fürsten entsa'gen nicht so leicht dem
Throne.

Was nüßt es dem Menschen, dem

Schick sale zu widerstreben ?ftets muß er der Macht dessel'ben unterlie'gen.

Traue nicht jetem Menschen, und am allerwe'nigsten denjenigen, die dir schmeicheln.

Die Ermah'nung eines Freundes gilt mir viel, und ich folge ihr gern.

cipate.

He who cannot renounce an
evil company, can belong to
no good one.

sich seines Auftrags mit großer Pünktlichkeit, he delivered his commis-
sion with great punctuality. Der Landmann rühme sich des Pflugs,
the husbandman may pride himself of the plough. Wohl dem,
der sich des Dürftigen annimmt, Pf. xli. 2, Blessed is he that con-
sidereth the poor (needy), Ps. xli. 2.
VOCABULARY.

Your friend met me yesterday, An'schuldigen, to ac- Entledigen, to release,

but I could not remember his
name (his name would not
occur to me).
Princes do not resign the
throne so easily.
What avails it for man to
struggle against (the) his
destiny ?-he must always
succumb to its power.
Trust not every one; and least

of all, those who flatter thee.

The admonition of a friend is
of much value to me, and I
follow it gladly.

EXERCISE 94.

1. Wenn in alten Zeiten ein Mächtiger dem andern feind war, so erklärte er ihm den Krieg. 2. Aus allen Orten, die ihm angehörten, sammelte tiefer mächtige Herr die Männer, die ihm anhingen. 3. Nachdem sie seinem Vorhaben beigestimmt hatten, vervflichteten sie sich, ihm beizustehen, und ihm in den Krieg zu folgen. 4. Solch ein (Sect. XL. 6.) mächtiger Herr war Heinrich der Löwe, Herzog von Bayern, welchem große Länder zugehörten, und Tausente von Kriegern gehorchten. 5. Doch die Krone eines Kaisers schwebte ihm immer vor Augen. 6. Der Herzoghut genügte ihm nicht. 7. Er traute seiner eigenen Kraft und troßte dem Kaiser. 8. Der Kaiser forterte ihn auf, sich seinen Befehlen zu fügen, und drohte ihm mit der Acht.

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RÉSUMÉ OF EXAMPLES.

Des Hoch verraths an'geklagt, entging' Accused of high treason, he
er dem Kerker nur durch die escaped the prison only by
Flucht.
flight.

Beleh're mich eines Bessern, wenn du Teach me (convince me of) a
fannst.

Sie bemächtigten sich des Räubers, der den Kaufmann seines Geldes beraubt' hatte.

Er befann sich eines Bessern, um nicht einer Un'wahrheit bezüchtigt zu werden.

Mein Sohn hat mich alles Gelves
entblößt'.

Enthe bet mich dieser traurigen
Pflicht!

Der Gerech'te erbarmt' sich seines
Biebes.

Grin'nere dich der vielen Wohl'thaten,
die ich dir erwies'.

Geren'ke deines Freundes selbst in weiter Ferne!

Drohe, wie du willst, ich lache deiner.

Nach geschehener Arbeit kann man der Ruhe pflegen.

better, if you can.

They seized the robber who had
robbed the merchant of his
money.

He bethought himself of a
better course in order not to
be accused of an untruth.
My son has stripped me of all
(my) money.

Relieve me of (from) this sad
duty.

The righteous (man) is merciful
to his beast.
Remember the many good deeds
(favours) that I have shown
you.

Remember thy friend even in

remote distance.
Threaten as thou wilt, I will
laugh at thee.

After completed (taken place)
toil, we can indulge in (the)

repose.

acquittal of the innocent, and vouchsafed to them the greatest friendship. 9. The enemy (say, enemies) stormed the town and laughed at the supplicants, who besought them to have pity on them.

KEY TO EXERCISES IN LESSONS IN GERMAN.
EXERCISE 11 (Vol. I., page 68).

2. Yes, he is 3. Have you

1. Is your friend, the captain, still a young man? still young, but his good friend, the Dutchman, is old. a beautiful great dog? 4. No, I have a beautiful great horse. 5. Has your little child my new knife? 6. No, but your good son has your new stick. 7. Has the butcher a fat sheep? 8. Yes, and his good son has a beautiful white lamb. 9. Is your friend, the young Dutch man, rich or poor? 10. He is not rich, but he is contented. 11. A contented man is also rich. 12. A rich man is not always & contented man. 13. Your great house has a steep roof and a deep cellar. 14. From whom have you your new sofa? 15. I have it from a good friend. 16. The pig is a lazy fat animal. 17. A true friend is a strong protection.

EXERCISE 12 (Vol. I., page 94).

and your old friend, the teacher, has the ripe fruit.
1. Have you my ripe fruit? 2. No, I have your silver fruit-knife,
3. Have you my
silver pencil? 4. No, the good teacher has it. 5. Has the old cook
my wooden table? 6. No, the joiner has it, but the cook has a
marble table. 7. Has he also a wooden cask? 8. Yes, and this dili
gent scholar has a beautiful leaden inkstand. 9. Has he also a silver
cup? 10. Yes, and he has also a copper kettle and an iron mortar.
11. Have you my young friend's new knife? 12. No, I have a new
knife from the good merchant. 13. Has this diligent scholar the old

Biele rühmen sich großer Thaten, die Many boast themselves of great friend's good book, or his good cousin's silver pencil? 14. He has

fie niemals vollbracht' haben.

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deeds which they have never
accomplished.
Exempt me from the necessity
of punishing thee.
Before I had expected a blow,
I was already felled (lay
stretched) to the ground.
He was so proud that he did

not vouchsafe to me a look.

EXERCISE 96.

1. Sie erinnern (§ 86. 1, 2) sich wohl noch des jungen Mannes, der im vorigen Jahre des Raubes angeklagt war. 2. Er war beschultigt, einen reichen Vichhändler auf der Landstraße seines Gelves beraubt zu haben. 3. Man konnte ihn jedoch dieses Verbrechens nicht überführen. 4. Er hatte sich bereits aller Hoffnung einer Freisprechung begeben, und sich des Gedanlens entschlagen, für unschuldig erklärt zu werden. 5. Der Richter jet och enthob ihn aller Sorge. 6. Nachdem er den Angeklagten aufgefortert hatte, nur gutes Muths zu sein, und sich alles Kummers zu entschlagen, erklärte a: Ich bin der vollen Meinung, daß man diesen jungen Mann nicht des Raubes bezüchtigen kann. 7. Denn nicht Jeder, der sich des Bettelns schämt, und aller Mittel entblößt ist, wird ein Räuber. 8. Ich kann seines Betragens lobend erwähnen, denn er hat sich immer eines ordentlichen Lebens beslissen. 9. Ich erinnere euch aber an seine Thaten im leßten Kriege, teren er sich mit Recht rühmen kann. 10. Freuet euch seiner Freisprechung, und würtiget ihn eurer Freundschaft. 11. Spottet seiner nicht, weil er im Kerker war, sondern erbarmt euch vielmehr seiner, und gedenket seiner Leiden. 12. Jeder, der seiner lacht, schäme sich seines eigenen Betragens. Alle Anwesenden freuten sich dieser Rede, und man entlerigte augenblicklich en Angeklagten seiner Fesseln. 14. Lehre uns deine Wege, o Herr! und beraube uns nicht deiner Gnade! 15. Ich bin Willens (§ 128), im näch. ften Sommer ein Bad zu besuchen. 16. Ich kann durchaus nicht der Ansicht sein, daß man nach Tische der Ruhe nicht pflegen sollte. 17. Wer sich des Lebens freut, soll sich auch des Sterbens erinnern. 18. Als General Tilly sich der Stadt Magdeburg bemächtigt hatte, lachte er der Flehenden, welche ihn baten, sich ihrer zu erbarmen.

EXERCISE 97.

neither a good book nor a silver pencil-he has only a wooden pencil. 15. Where is the cook's copper kettle? 16. The poor man has only an iron kettle.

EXERCISE 13 (Vol. I., page 94).

1. Hat sie mein reises Obst? 2. Der alte Koch hat meinen filbernen Bleistift. 3. Hat er auch ein neues Messer? 4. Der gute Kaufmann hat einen alten marmornen Tisch. 5. Er hat weder ein golkenes Obstmesser, noch einen silbernen Becher. 6. Der Sommer ist eine goldene Zeit. 7. Der fleißige Tischler hat den eisernen Kessel des Kochs.

EXERCISE 14 (Vol. I., page 94).

1. Is this young lady's young sister in Germany? 2. No, she is in France, but her brother is in America. 3. Where is my new gold pen? 4. Your young friend Miss S. has it. 5. Has your mother the beautiful silk of your aunt? 6. Yes, and also the beautiful fine linen. 7. Where are [ift] your gold spectacles? 8. I have no gold spectacles. 9. Have 11. Is it a you a silver or gold watch? 10. I have a silver watch. 13. Where is your good watch? 12. Yes, but it is not very beautiful. watch? 14. It is in my watch-pocket. 15. Has your sister a gold watch? 16. Yes, and she has also a beautiful gold chain. 17. Where are my new scissors? 18. I have them, but they are not very sharp. 19. Where is your sister? 20. She is with her mother in the library. 21. Where is my glass lamp? 22. I have it. 23. Who has my new opera-glass? 24. I have it, and your new spectacles.

EXERCISE 15 (Vol. I., page 94).

1. Die Mutter dieser Dame ist in Frankreich. 2. Hat die schöne Tochter 3. Mein fleißiger Bruder hat weder der guten Tante eine goldene Uhr? 13. eine goldene Uhr noch ein gutes Opernglas. 4. Meine gute Schwester hat feine feine Leinwand, aber sie hat eine neue gläserne Lampe. 5. Mein Better mit der goldenen Brille ist bei meinem schönen Bruder in ter Bibliothek.

1. In former times the people knew not how to read, much less to write. 2. I am willing to visit next summer the baths of Homburg and Laubach. 3. When Louis Philippe, King of the French, had abdicated his throne, he went with his whole family to England. 4. Some kings have little reason to boast of their reigning. 5. The Emperor Charles V. gave up his crown and went into a convent. 6. It becomes a man better to be studious of his actions, than to boast of his abilities. 7. I will relieve my self of all business, and enjoy a quiet life. 8. He rejoiced at the

EXERCISE 16 (Vol. I., page 102).

1. Has the Frenchman the German's wine? 2. Yes, and the Ger-
man has the Frenchman's cloth. 3. What has the Russian? 4. He
has the country of the Pole. 5. This Greek is no friend of the Turk.
6. Who has the sharp knife of this boy? 7. The friend of this Greek
has it. 8. Have you your nephew's writing-desk? 9. No, I have my
father's writing-desk. 10. Have you this boy's book, or his nephew's
paper? 11. I have the boy's book, and my niece has the nephew's
paper. 12. Is our friend, the captain, a Frenchman or a Greek? 13.
14. Is this
He is a Frenchman, and a great enemy of the Russian.
15. No, he [it] is the
lively countenance is not always the sign of a quiet conscience. 17.
Have you the count's book? 18. No, but the prince has the book.
19. The life of a soldier is fatiguing and unsafe. 20. Have you a
monarchy or a republic? 21. America has no prince, but liberty.
22. I have a gold watch, and you have a silver pencil.

child a son of our neighbour, the merchant?
son of a Jew, and his father is the neighbour of a Christian. 16. A

OUR HOLIDAY.

GYMNASTICS-VIII.

THE HANGING-BAR, OR TRAPEZE. THIS is an apparatus of which most of our readers have heard, but few who are unacquainted with the gymnasium know its precise nature or value in bodily training. The Flying Trapeze is associated in the popular idea with the feats of Leotard and others-feats dangerous to execute, and unpleasant to witness, from the risk obviously incurred by the performer. But the Trapeze of the gymnasium-although the same thing in the principle of its construction-is an apparatus the use of which need not excite any alarm in the minds of those concerned in the safety of the young gymnast. No doubt the same amount of care, and of abstinence from the attempt to perform feats which are simply daring, but otherwise unmeaning and unnecessary, is required in the practice with this contrivance, as with any other; but such exercises as those we shall have to describe may be performed in perfect safety.

The Hanging Bar is, in principle, very much like the Rack, which was described in a former lesson (Vol. I., page 175), and is intended for a somewhat similar series of exercises. In the case of the Rack a horizontal bar is fixed upon two supports let into the ground. In the Trapeze a similar bar is suspended from the ceiling by two ropes, one at each end, as shown in our illustration (Fig. 25). The length of the bar should be about three feet; its thickness, about an inch and a half, sufficient to support the weight of the gymnast, and at the same time to be readily grasped by the hands. Its height from the ground, as it hangs when out of use, should be such that the learner can just reach it; its distance from the ceiling or the cross-beam from which it is suspended need not be more than eight or ten feet, unless the gymnast is sufficiently expert and experienced to be entrusted with a greater power of movement.

The ropes, we need hardly say, must be strong and well secured; and if they are attached to pulleys or any other contrivance by which they may be raised or lowered at will, it will be found an advantage. The first of the exercises to be practised on the Hanging Bar bear a close resemblance to those on the Rack; and for these we advise the reader to consult the lesson before referred to, in which we have described the various modes of hanging by the hands, rising and sinking, etc. But there are other exercises peculiar to the trapeze, among which may be mentioned

Fig. 25.

THE HANGING BAR.

1. Rising to the seat.-Stand crossways below the bar (that is, with the bar endways before you; when you are looking between the two ropes, you are said to stand sideways); take one end of the bar in both hands, the right hand in front; then, by a forward swing, raise the right leg over the bar, grasping the bar in the hock. You now remove the hands, one after the other, to the rope nearest you, and can then work yourself up into the seat on one thigh without difficulty. To gain the seat on both thighs, you throw both legs over the bar in the first movement, and hold the bar in one hand, and the rope in the other. Another but more difficult way of attaining the seat is by rising into the rest, as in the Rack movement.

2. Having reached the seat, you can next stand upon the bar, by grasping a rope in each hand, and raising the body gradually by the purchase thus acquired. Standing upon the bar, you may swing gently backward and forward, and practise a firm hold upon the bar with the feet, which will prepare you for the next exercise.

3. The Hammock.—Standing on the bar, you grasp the ropes firmly at about the height of the hips; you then lean forwards, keeping the feet steadily on the bar, and thus come into the position shown in Fig. 26. You may next perform the same movement by taking a higher grasp of the ropes, about the level of the head, and, as you throw yourself forward, the body then describes almost a semicircle. These exercises may be varied by leaning backwards instead of forwards, thus reversing the position of the body as it appears in the illustration.

4. Turning over may be done in various ways, among which may be mentioned the mode of "circling the bar," which was

:

described in the Rack exercises. Another method is the following lie upon the bar in the position shown in Fig. 27, holding the ropes firmly, but with sufficient ease to give freedom to the wrist. Then turn gradually over backwards, by lowering the head and raising the feet, which are kept close together, and pass between the ropes. You then come into position hanging below the bar, and with the face directed to the ground. Afterwards you can try to return to the lying position by reversing these movements; but you will find this much more difficult than the backward turn from the bar.

5. Squatting on the bar is a position which is practised in order to obtain a facility in changing the seat, or returning to it from the standing posture. Sitting sideways upon the bar, you grasp the rope on your right hand a little above the level of the head, and then, resting the other hand upon the bar itself, you draw up the knees and raise the body from the bar, thus remaining in the sitting position, but partly suspended in the air.

Fig. 26.-THE HAMMOCK,

6. Change of seat is performed readily from the squatting position, by moving the hand which grasps the bar along its surface, and turning the body round until you face the reverse way to that from which you started. At the moment of sitting, you shift the bar-hand from the bar to the rope, while the other hand is passed to the rope on the opposite side. In this change the whole movement takes place between the ropes; but you may also change the seat by passing round and outside either rope, as follows:-Grasp the bar, as you sit, with one hand close to the rope; and let the other hand take firm hold of the same rope a little above the head. Thus, if you intend to pass round the rope which hangs on your right hand, you take hold of the rope with your left hand while the right remains upon the bar. You now raise yourself from the bar, extending the legs horizontally forward, and turn the body round the rope, until you are in position to resume the seat, but facing the other way. Your right arm, which has remained upon the bar, must assist you in preserving the balance of the trapeze, until you can quickly transfer it to the rope which now hangs at the right hand of you.

7. The exercise called the Rest is something like the Hammock, which has already been described; but it requires a little more practice with the trapeze to perform it steadily. You kneel upon the bar, taking hold of the ropes at about the height of your shoulders; you next draw your legs along the bar until the insteps are resting upon it, and then drop the body downwards and forwards. The weight of the body is divided between the hands which grasp the ropes, and the insteps resting on the bar, but is thrown chiefly upon the former.

Fig. 27.-THE TURN OVER

8. Hanging by the legs and hands together upon the bar may easily be accomplished from the sitting position. Raise the legs and draw them backward until the bar is between the hocks, and held firmly; then shift the hands from the ropes to the bar, either outside of or between the knees and lean backwards. You may thus swing in perfect safety, and can raise yourself to the sitting position at pleasure.

Many other exercises are practised upon the Trapeze, such as hanging solely by the hocks or by the insteps, swing and turn, etc., but those we have described are quite sufficient for all beneficial purposes, and we do not advise any of our readers to attempt the daring class of feats. Even in the simpler exercises, care must be taken to guard against a slip or a fall, for to obtain a perfect command of the Hanging Bar, as well as of year own movements upon it, requires practice. It is a widely dif ferent thing to perform gymnastic exercises on a bar in a fixed position, like the Rack, and to attempt them on one that is swaying in the air; and a corresponding degree of caution is required.

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who may be seeking a seat in a merchant's counting. house, a clear idea of the kind of writing suitable

for mereantile correspondence, while the

Dear Sir,

house of business is closed for the evening; while the latter exhibits in an equal degree unmistakable signs of the deliberation, method, and thoughtfulness that should always be exercised by the bookkeeper or accountant, to prevent errors and the disfigurement of the fair page neatly ruled in red and blue for the

the have the pleasure

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reception of facts and figures, by the use of the pen-knife or eraser to remove any mistake that may have unfortunately been made by undue haste on the part of the writer, or want of

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to mark the difference between the general character of the handwriting suitable for the business letter, and that which is better calculated for records of mercantile transactions. Although it must be conceded that both specimens of penman

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task on which he isengaged. The reader will notice that while the loops and tails of letters in the specimens of business handwriting in this page are a little longer than those in the specimens of official handwriting given in previous

lessons (see pages 33, 48), they are not carried above or below the body of the letter to the extent that was formerly insisted on in commercial handwriting, and that there is a total absence of all that obnoxious flourishing and redundancy of capital letters,

San: 1 - For transfer of amount of

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SPECIMEN OF BUSINESS HANDWRITING.-NO. 2.

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ship are perfectly satisfactory, as far as neatness and legibility are concerned, the former is marked by the ease and freedom that a good writer naturally imparts to his handwriting, when, with ready thought and practised hand, he uses the pen rapidly to get through the mass of business correspondence that must be cleared off and sent to the nearest post-office before the

which were once considered as combining to form the height of perfection in the penmanship of the commercial clerk. For business correspondence and the records of mercantile transactions, as well as for official handwriting, a plain, clear hand, devoid of flourishes and ornamentation of capital letters, is the most desirable, and will always command the preference of practical men.

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