Centre of Gravity illustrated by Vegetable Forms, &c. 115

visible; or by lying down on their backs, between supports, and shutting their eyes.

214. As no form or condition of matter escapes from the great laws of nature, we find the attitudes and general state of vegetable as well as of animal bodies, characterized by the necessity of having the centre of gravity supported over the base. Left to the guidance of nature, the springing pine rears its structure, alike on the level plane and on the rocky mountain side, straight up to the zenith as accurately as if directed by a plummet. On a smaller scale, the grasses and corn-stalks of our fields illustrate the same truth. And whenever, in tree or shrub, accident or peculiar nature causes a deviation from the vertical, additional strength and support are provided.

215. Beauty of form or position is often felt to belong to bodies, merely because they possess the shape and support required, that the centre of gravity may be stable.

In architecture, how displeasing to the eye of an observer is a wall or pillar that is not quite upright; or a column with too small a base; or a very tall narrow house; or a long slender chimney! On the other hand, how beautiful in a lofty edifice is the suitable succession of columns, from the massive Doric of the basement, supporting the whole superstructure, to the light Corinthian or kindred forms seen above! The Chinese pagoda is a fine example of the union of the requisites for stability, namely, perpendicularity and expanding base, with the other qualities of perfect symmetry, graceful proportion, and fanciful ornament. When seen in its own country, crowning a rising ground in a wooded island, or springing up from the centre of any rich landscape, it forms perhaps as beautiful an object as fancy has imagined.

216. Beauty of attitude and grace of carriage in the human figure may in great part be referred to the same principle.

The postures of opera dancers might pass as intentional illustrations of the number of ways in which the centre of gravity may be kept above a narrow base, by counteracting one disturbing motion or extension of a limb by some opposite and corresponding motion, The common statue of the god Mercury on tiptoe is a permanent familiar illustration of such a beautifully balanced attitude.

Grace of carriage includes a perfect freedom of motion, with a steady bearing of the centre of gravity over the base. It is usually possessed by those who live in a hilly country, taking much and varied exercise, or who make gymnastics a part of their discipline.

116

Beauty of Structure-of Carriage.

Great is the contrast between the gait of the active mountaineer and that of the mechanic or shopkeeper, whose confinement to the cell of his trade soon produces in his body a shape and air corresponding to it :--and in the softer sex what a difference there is between that strong and graceful fair one who recalls to us the fabled Diana of old, and that other sedentary being, who having scarcely trodden but on smooth pavements or carpets, carries her person, under any new circumstances, as if it were a load new and foreign to her.

217. The centre of gravity is the centre of mass, and therefore of any action or force which is uniformly distributed through the

mass.

When a person lifts a uniform rod or bar by its middle, the gravitation of both ends being equal, he overcomes it equally, and raises them evenly together. When he lifts by a part nearer to one end there will be a turning motion of the rod round the support, proportioned to the excess of weight in the greater side.

b

a

Ө

If a weight of three pounds, a (fig. 30), be affixed to one end of a rod, and a weight of only one pound, b, to the other, the two will be equally raised if lifted by a point of the rod, c, three times nearer to the centre of the large weight than to the centre of the small one, that is, at the centre of gravity of the two masses, a and b. (For the sake of simplicity, the weight of the connecting rod itself is neglected.)

Fig. 30.

218. The centre of gravity, it is to be noted, is also the centre of centrifugal force.

For if the balls, a and b, of the last figure were made to spin round a common centre, as by turning upon a pivot at c, the centrifugal forces balance on each side of c, because the less velocity of a is compensated by its superior mass, and the smaller mass of b is aided by its greater velocity. It is on this account that the axis of a millstone, or of a great fly-wheel, or of the balance-wheel of a watch, must pass through the centre of gravity or mass, to prevent its being more worn on the one side than on the other.

Though we commonly say that the earth revolves round the sun, or that the moon revolves round the earth, it must be borne in mind that in all such cases, both bodies are revolving round their common centre of mass. In the case of the sun and the earth, the former is about a million times larger than the latter; thus, their common centre of mass is a million times nearer to the centre of the sun

Centre of Centrifugal Force-Centre of Percussion. 117

than to the centre of the earth, and is therefore within the body or circumference of the sun.

219. The centre of gravity in a body moving evenly is also its centre of percussion. If the centre of gravity of a body be moving in a straight line, all its parts will be moving in parallel straight lines; and, the momentum being equally diffused through the whole, is as if condensed in this point. So that, if such centre come against an obstacle and is brought to rest, all the parts of the body will be brought to rest together; while if any other part than this centre be hit, the body loses only a part of its momentum, and then turns round the obstacle as a pivot or centre of motion, that side advancing on which the greater mass happened to be.

In a hammer, or in a pendulum, the momentum is not equally diffused through the whole, for the velocity of different parts is different, being greatest far from the centre of motion; thus, the centre of percussion in these cases is farther from the centre of notion than the centre of gravity or mass is, and if an obstacle meet either at its centre of gravity, the momentum would not be wholly given up.

220. The exact place of the centre of percussion in many cases is easily ascertained by calculation. In a uniform bar or rod swinging as a pendulum, for instance, it lies at the distance of one-third of its length from the lower end; and in a pendulum this is called the centre of oscillation.

If a man use a stick, or a bar of iron, to strike with, he must take care to make it strike the object by its centre of action or percussion, which will depend on the velocity given to the further end of the stick or bar. If, wielding the rod like a hammer, he were to strike an object by the centre of gravity of the rod, his own hand would receive a part of the shock, because the centre of percussion lying beyond the obstacle would tend to make the bar move round the object as a pivot. A very heavy mass thus carelessly used will seriously strain the wrist. In a common hammer, as the chief part of the mass is at the end, and the greatest velocity is given to it too, the centre of percussion is there, and no precautions are

necessary.

In cricketing, the art of making a good hit depends on knowing by experience the proper spot of the bat with which to meet the ball.

With proper manipulation, a weaker man, or an inferior blow, may suffice to put the ball to a much greater distance than a

118

The Centre of Percussion.

stronger one. The "sting," with which all cricketers are acquainted, is caused by the ball meeting with great force the bat either within or beyond the centre of percussion; and it must be remembered that the more swiftly the batter wields the further end of his bat, the nearer to that end is the centre of percussion, and therefore is the proper spot to "take" the ball.

SECTION II. THE SIMPLE MACHINES.

ANALYSIS OF THE SECTION.

By a combination called a MACHINE, a force of small intensity may be made to act through a considerable space, and become transformed into one of increased intensity, acting through a proportionally diminished space, the substitution in the form of Energy being of great consequence to man in the accomplishment of his manifold purposes. The SIMPLE MACHINES are those which in this way transform molar energy or the energy of visible masses, and they are commonly enumerated as the LEVER, the WHEEL AND AXLE, the INCLINED PLANE, the WEDGE, the SCREW, the PULLEY. From an erroneous idea of the principles involved, these were formerly designated the MECHANICAL POWERS; but there is no reason but old usage why the title should be confined to them, any arrangement of parts which connects or exchanges different intensities of force being equally worthy of the name.

The action of all machines is either (i.) to effect such transformation of intensities of energy directly, or (ii.) to do it by the cumulative principle, as in slings, brakes, fly-wheels, &c., or (iii.) to effect merely a directive change of motion, as of horizontal into vertical, of rectilinear into rotatory, or of rotatory into rectilinear motion, the last being an important conversion, though troublesome to effect by rigid mechanism, as is proved by the many futile attempts to obtain a PERFECT PARALLEL motion.

In all machines due account must be taken (i.) of the resistance among the moving parts owing to FRICTION, which wastes Energy to no purpose, and (ii.) to the STRENGTH OF THE MATERIALS of which the machine is made, as well as to the forms and positions of the structure which have to be adjusted to the strains that the different parts have to bear.

The Simple Machines.

221. The Energies or forces of nature at our command for the accomplishment of the thousand kinds of work to be done are few in number, as has been seen; and, in many situations, we are confined to one. This one may be unsuited to our purpose in the form in which nature gives it. For example, a waterfall is unfit to grind corn; and horse-power is unadapted to spin wool or draw water