the other.

Stability of Equilibrium.

Hence the least inclination of a standing body vir

tually narrows, in one direction, its sustaining base.

40401

Fig. 27.

In G, a ball upon a level plane, the whole mass is supported on a single point as in E (fig. 26), yet the body has no tendency to move, because in every position the centre is at the same height above the sustaining plane, and, in moving, describes the straight level line, a b.

In H, the ball is on an inclined plane, and rolls down because it meets with no resistance in the line of its gravity.

In 1, an oval body resting on a level plane, the centre of gravity has a motion somewhat like that of a pendulum when it is rolled to either side.

K is a true pendulum whose centre of gravity describes the curve shown.

"Stable, unstable, and indifferent equilibrium."

206. The foregoing facts may be summed up in these words :-A body has its equilibrium stable, or does not readily fall, if the height of its centre of gravity be small compared with the extent of its supporting base; it has unstable equilibrium, or is in a tottering condition, if the centre of gravity is high compared with the size of its base; and its equilibrium or balance is indifferent, when any disturbance of the body does not alter the relation of the height of its centre of gravity to its base or support.

207. The importance of considering the position of the centre of gravity, relatively to the sustaining base, will appear in the following instances :

A cart loaded with metal or stone may go safely along a road of which one side is higher than the other, when, if loaded with wool or hay, it would be overturned; because, as shown in figure 28, the low position of the centre of gravity, ‹, in the former case, throws

the vertical line passing through it further from the limit of the sustaining base than in the latter, in which the centre of gravity is at a.

So stage coaches or vans are particularly dangerous when heavy luggage is placed on the top, and lofty vehicles are liable to be overturned by an unevenness of the road.

The centre of gravity being much higher when the crew of a small boat are on their feet than when they are seated, it requires very little to upset the boat in this case; and inattention to this, leads to many serious accidents.

Fig. 28.

Tripods, common chairs, pillar-and-claw tables, candlesticks, table-lamps, and many other articles of household furniture, have stability given to them by widening the base.

208. Any structure, such as a mass of masonry, will stand so long as the vertical line through its centre of gravity does not fall beyond its base; hence the famous tower of Pisa, with a height of 188 feet, though it overhangs sixteen feet, really has its centre of gravity vertically over its base.

A solid hemisphere, or any regular portion of a solid globe, will oscillate like a pendulum till it come to rest in the position shown in the figure, because the height, G A (fig. 29), of its centre of gravity is then less than in any other position.

C

G

A

Fig. 29.

The boy's rocking-horse, the common cradle, and those huge rocking stones called Loggan stones, which are seen in Cornwall and other places, illustrate the same principle.

The common india-rubber toy of a little fat man sitting on a rounded pedestal is loaded with lead to throw the centre of gravity in the lowest position when the figure is upright, so that, on pushing the little man down we are really raising his centre of gravity.

209. The vibratory motion of a pendulum is dependent upon the circumstance of the centre of gravity having been moved from its lowest place, which it again constantly seeks. We may enumerate the following phenomena as being of the same class :

The vibration of the common swing, seen at fairs.

The rocking of a balloon when it first ascends.

The spontaneous shutting of those gates or doors of which the upper hinge is made to overhang or project beyond the lower. Such a gate always returns of itself, from either side to the shut

112

Attitudes illustrative of Centre of Gravity.

position, just as a pendulum returns to the lowest part of its arc : the gate in fact is a sloping pendulum.

Of the same nature also is the rocking or rolling of a ship in a rough sea. When the centre of gravity of a ship is too low, owing to much of its heavy load being placed near the keel, this pendulummotion, in rough weather, becomes excessive and dangerous.

210. The attitudes of animals, particularly of man, illustrate the above remarks with respect to the centre of gravity.

The supporting base in man is the space included between the outer edges of his two feet, and it requires a great many trials to acquire the faculty of poising on this narrow base. On the other hand, quadrupeds, having a broad, supporting base, are able to stand, and even to walk and run, very soon after birth.

In drawing the human figure, the most stable position is given to it by causing a line passing from the junction of the two collar bones with the chest to fall in the centre of the space covered by the two feet. When this line falls near to the outer edges of the feet, it gives to the figure the appearance of instability, and if beyond the space covered by the feet, the attitude is that of falling. Artists are sometimes neglectful of this principle.

The difficulty of the art of walking must be considerably greater to the Chinese ladies, owing to their barbarous practice of preventing the growth of their feet by confining them in small shoes.

Artificial substitutes for legs are most inadequate supports when they consist merely of slender wooden stumps with rounded ends such as are exhibited by the victims of shipwreck and war. The addition of feet to such artificial limbs is not only more pleasing to the eye, but most important, on account of the extension it gives to the supporting base.

211. Surpassing in difficulty is the practice, which is general among the inhabitants of the sandy plains called the Landes, in the south-west of France, of walking on stilts. The Landes afford tolerable pasturage for sheep, but, during one portion of the year, are half covered with water, and during the remainder, are still very unfit walking-ground, by reason of the deep loose sand and thick furze. The natives meet the inconveniences of all seasons by doubling the length of their natural legs, through the addition to them of stilts, which they call échasses. Mounted on these wooden poles, which are put on and off as regularly as the other parts of dress, they appear to strangers a new and extraordinary

Attitudes illustrative of Centre of Gravity.

113 race of long-legged beings, marching over the loose sand, or through the water, with steps of six or eight feet in length, and with the speed of a trotting horse; a possible journey being thirty or forty miles a day. While watching their flocks, they fix themselves in convenient stations, by means of a third staff which supports them behind, and then with their rough sheep-skin cloaks and caps, like thatched roofs over them, they appear like little watchtowers, or singular lofty tripods, scattered over the face of the country.

An example of poising the centre of gravity, even more difficult than that of walking on stilts, is that of walking and dancing on a single rope or wire; or even of keeping the centre of gravity above the base, while standing on the movable support of a galloping horse. A rope-dancer has to carry a long pole in his hand; it is loaded at each end, and when he inclines to one side he throws it a little towards the other side that the reaction may restore his bulance.

Much art of the same sort is shown in the evolutions of the skater; in the supporting of a pole upright on the end of the finger; and in other feats of a like kind.

212. Attitudes, generally, depend on the necessity of keeping the centre of gravity of the body over the base under a variety of circumstances, as in-the straight or upright port of a man who carries a load on his head ;—the leaning forward of one who carries it on his back ;-the hanging backwards of one who bears it between his arms; the leaning to one side of a person carrying a weight on the other side ;—the habitual carriage of very fat people, with head and shoulders thrown back, giving a certain air of self-satisfaction.

When a man walks or runs, he inclines forward, that his centre of gravity may overhang the base; and he must then be constantly advancing his feet to prevent his falling. He makes his body incline just enough to produce the velocity which he desires.

So, in pulling horizontally at a load, he causes his body to overhang its base, that its weight may become a source of power.

When a man rises from a chair, he first bends his body forward or draws his feet backward, so as to place his base under his centre of gravity, and then he lifts his body up. If he rises before *he body is sufficiently advanced, he falls back again.

A man standing with his heels close to a perpendicular wall cannot, without falling, pick up any object that lies before him on the floor; because the wall prevents him from throwing part of his

114

A probable Cause of Sea-sickness.

body backward, to counterbalance the head and arms which have to project forward. For a similar reason, a person, standing with his side close to an upright wall, cannot lift the outside foot without assistance.

When a biped walks, the centre of gravity is brought alternately over the right and over the left foot, as is seen very strikingly in the waddle of a duck. The body advances in a waving line, and this is the reason why persons, walking arm-in-arm, shake each other, unless they make the movements of their feet to correspond, as soldiers do in marching.

213. Sea-sickness is a subject closely related to the present. Man requiring to keep his centre of gravity always over his supporting base, ascertains the requisite position in various ways, but chiefly by comparing the vertical situation of things about him with his own position. Vertigo and sickness are often the consequences of depriving him of his standards of comparison, or of disturbing them.

Hence, on shipboard, where the lines of the masts, windows, fur niture, &c., are constantly changing directions, sickness, vertigo, and similar affections are common to persons unaccustomed to ships. Many persons are similarly affected in carriages, and in swings; or on looking from a lofty precipice, where known objects, being distant and viewed under a new aspect, are not so readily recognised; also in walking on a wall or roof; in looking directly up to a roof, or to the stars in the zenith, because then all standards disappear; on entering a round room, where there are no perpendicular lines of light and shade, as when the walls and roof are covered with a paper which has no regular arrangement of spots; on turning round, as in waltzing, or if placed on a wheel-because the eye is not then allowed to rest long enough on any standard, &c.

People when in the dark, and therefore blind people always, use standards connected with the sense of touch; and it is because, on board ship, the standards both of sight and of touch are lost, that the effect is so remarkable.

No doubt, sea-sickness depends partly also on the irregular pressure of the internal organs among themselves and against the containing parts, the result of their not being rigidly connected.

From the nature of sea-sickness, as discovered in these facts, it is seen why persons unaccustomed to the motion of a ship often find relief by keeping their eyes directed to the fixed shore, where