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statics, and hydrodynamics. Statics treats of the equilibrium, and dynamics of the motion of solids. Hydrostatics treats of the equilibrium, and hydrodynamics of the motion of fluids.

The magnitude of forces producing equilibrium is measured by comparing their effects with those of known weights or pressures. The direction of a force is the direction in which it moves, or tends to move the body on which it acts. To estimate the effect of a force, we must know its magnitude, direction, and point of application. When any number of forces act on a body in such a manner as to produce an effect which might have resulted from the action of a single force, that single force is termed the resultant of the several forces, and the several forces considered in relation to the resultant are termed the components. The magnitudes and directions of the components determine the magnitude and direction of the resultant.

Several forces acting simultaneously on a body may all act on the same point. A large bell is rung by separate ropes meeting in a thicker rope attached to the bell. The forces may be applied at different points of the body. A carriage, for instance, is drawn by a pair of horses abreast. The forces may have the same or different directions. In the case of the carriage they are the same, but in that of the bell they are different.

When any number of forces act at the same point, and in the same direction, their resultant is equal to their sum. If a weight of six pounds is suspended from a hook, and from the bottom of this weight another weight of ten pounds is suspended, the whole force exerted on the hook is equal to a weight of sixteen pounds, and the two weights might be replaced by one, without altering the strain on the hook. If the weights are attached to the hook by separate strings, and the string connected with the lesser weight is made to pass upwards over a pulley, the two forces then act in opposite directions; the force of six pounds acting upwards, and that of ten pounds acting downwards. In this case, the lesser weight neutralises six pounds of the greater, so that the hook only sustains four pounds, acting downwards. If the greater weight is made to act upwards, and the

lesser one downwards, the force on the hook would be four pounds, acting upwards. In each case the resultant is equal to four pounds, and acts in the direction of the greater weight. When, therefore, any number of forces act on a point, some in one direction, and the rest in the opposite direction, their resultant is equal to the difference between the total force acting in these opposite directions, and has the same direction as the greater amount of force.

When two or more forces act on a point in directions which are inclined to each other, the direction of their resultant is not so evident as in either of the above cases. The following example illustrates this:-If a ship at sea is acted on simultaneously by a wind blowing southward, and a current running eastward, it will evidently follow neither the course of the wind, nor that of the current, but proceed a little southward, and a little eastward at the same time, and thus take a south-easterly direction, just as if it were influenced by one force acting in that direction. So, also, if a single force were acting on the ship it might be removed, and two other forces substituted in its place, which might act at some angle of inclination to each other. The same holds good whether the body thus acted on be in motion or not. The case here presented of the composition and resolution of force is termed the parallelogram of forces, the general truth of which may be stated as follows:-If two forces, acting on a point, be represented in magnitude and direction by two adjacent sides of a parallelogram, their resultant will be represented in magnitude and direction by that diagonal of the parallelogram which is drawn from the vertex of the angle formed by these two adjacent sides. the components are equal, the resultant bisects the angle at which they act; but if they are unequal, the direction of the resultant lies nearer to that of the greater force.

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Forces which act on different points, and in parallel directions, have their resultant always equal to their sum. When there are only two forces, and these of the same magnitude, the resultant is midway between them. Thus, when a pound weight is put into each pan of a pair of scales, the weights produce the same effect on the scale beam as if two pounds were suspended from its centre. If the forces

are unequal, the resultant lies nearer the greater force, and the nearer in proportion as the one force exceeds the other. If two men carry a weight of thirty pounds suspended from a pole six feet long, the ends of which rest on the shoulders of the men, the weight is divided between them, equally or unequally, according as it is situated in the middle of the pole or nearer to one end. If the weight is situated two feet from one end, and four from the other, the man nearest to it will support twenty pounds, and the other ten pounds; but if it is one foot from one end, and five from the other, the man nearest to it will then support twenty-five, and the other only five pounds.

LESSON XXIII.-WEDNESDAY.

EXCELSIOR.

The shades of night were falling fast,
As through an Alpine village pass'd
A youth, who bore, 'mid snow and ice,
A banner, with the strange device,
"Excelsior!"

His brow was sad; his eye beneath
Flashed like a falchion from its sheath;
And like a silver clarion rung

The accents of that unknown tongue,
"Excelsior!"

In happy homes he saw the light
Of household fires gleam warm and bright;
Above, the spectral glaciers shone,
And from his lips escaped a groan,
"Excelsior!"

"Try not the pass !" the old man said,
"Dark lowers the tempest overhead,
The roaring torrent is deep and wide!"
And loud that clarion voice replied,
"Excelsior!"

"O stay!" the maiden said, "and rest
Thy weary head upon
this breast!"

A tear stood in his bright blue eye,
But still he answered, with a sigh,
"Excelsior!"

"Beware the pine-tree's withered branch!
Beware the awful avalanche!"

This was the peasant's last "good-night!"
A voice replied far up the height,
"Excelsior!"

At break of day, as heavenward
The pious monks of St. Bernard
Uttered the oft-repeated prayer,
A voice cried through the startled air,
"Excelsior!"

A traveller, by the faithful hound,
Half-buried in the snow was found,
Still grasping in his hand of ice
That banner, with the strange device,
"Excelsior!"

There in the twilight cold and gray,
Lifeless, but beautiful, he lay,
And from the sky, serene and far,
A voice fell, like a falling star,
"Excelsior!"

Longfellow.

LESSON XXIV.—THURSDAY.

ENGLISH HISTORY-PLANTAGENET LINE.

The accession of Henry II., A.D. 1154, was hailed with joy by the English people, who looked to him as their deliverer from the anarchy to which they had been a prey during the late reign. Henry was young, brave, and the most powerful prince of his time, inheriting, from his mother, England, Normandy, and Maine; from his father, Anjou and Tou raine; and, in right of his wife, the provinces of Guienne and Poitou. His French territories included the whole Atlantic coast, and extended over a fifth part of France.

The first measures of Henry were vigorous and wise. He forced Stephen's Flemish mercenaries to quit the kingdom, demolished or resumed their castles, annulled all the acts of his predecessor, and confirmed the charter of Henry I. He accepted a fee, or sum of money, from each knight instead of

service, and with the revenue thus procured he maintained an army of mercenaries. Geoffrey, his younger brother, claimed Anjou; Henry forced him to relinquish it for a pension. The regency of Brittany next fell into his hands, during the minority of the infant heiress, his daughter-inlaw. The rich earldom of Toulouse then excited his cupidity. His attainment of this was prevented by the king of France, and a treaty was made between them.

In these turbulent times, amidst the strife of rival sovereigns and the ignorance of the people, the Church of Rome had been steadily extending her temporal as well as spiritual powers. The superstition of the age enabled her to encroach upon the liberties and independence of nations, until her usurpations became at length too galling to be endured, and general resistance was provoked. In this great contest Henry took a part. He had appointed to the see of Canterbury his favourite, Thomas à Becket, previously chancellor. Becket, though educated a churchman, had been a soldier and a courtier; was brave, able, learned, and inordinately ambitious. Having attained the dignity of archbishop, he renounced the luxury and splendour of his former life, and assumed a character of severe and self-denying sanctity. His garb, his food, his attendance, were mean and scanty, and he bent the whole force of his powerful mind to the augmentation and inviolability of the power of his Church. The crimes and immorality of the clergy demanding prompt repression, Henry required that, if found guilty before the bishop, they should be given up to the secular power. This Becket refused. The king then summoned a council, which passed the laws known as the "Constitutions of Clarendon." Becket openly violated them, and escaped from the anger of Henry to the Continent, where he was protected by the king of France and the Pope. At length a reconciliation was effected, and Becket returned to his see. No sooner had he entered it, than his insolence and assumptions renewed the quarrel. The exasperated king is said to have expressed a wish to be rid of him by any means, and four barons, acting upon this hasty speech, assassinated Becket before the altar of his own church at Canterbury. He was canonized as a martyr by the Pope, and Henry did penance at his tomb.

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