100

The Correlation of Physical Forces.

the particles; as with the pendulum at the turning point of its arc of vibration, there is a moment of pause, after which the cohesive attraction restores the former actual or visible Energy in a contrary direction, and the ball rebounds at the same rate at which it fell.

Were there no air and no friction to impede the swing of a pendulum, and cause its visible Energy to pass into heat-motion, we know that it would go on oscillating for ever. As it is, the returning velocity is always less than the advancing one. So in reality we find no body perfectly elastic; there is always more or less conversion of the impinging Energy into heat-vibration between the particles, and therefore never complete restoration of the impact by the force of cohesion. There is loss of visible Energy and production of this heat-motion in proportion as the body is inelastic; but there is no annihilation of Energy.

Friction is but the transferring, through impact of surface protuberances, of visible or molar energy into molecular or invisible heatvibration. If it be sufficiently continued, the minute quiver of heat may rise to such a degree that it again becomes visible, as when the brake of a railway train is heated until it catches fire.

The motive power of a flowing river may be converted into useful work by turning a hundred mills in its course, or it may all be allowed to run to waste in the shape of friction against its bed, diffusing an invisible quiver throughout its own particles and those of the earth against which it rubs.

So, could we utilize the ceaseless surge of the ocean, it would be a powerful source of Energy; as it is, it is allowed to be expended merely in heating the ocean waters and the rocks on which they lash.

The penetrating power of the cannon or musket ball is but the combined atomic energy of the gunpowder, set loose by the application of a spark, just as a huge boulder on the face of a rock may have its Energy of position transformed by the removal of a trifling obstacle.

Nor is this connection between different kinds and forms of Energy a mere vague assertion of cause and effect. Not only is the chemical Energy the cause of the projectile force of the ball, but the mechanical force of the ball is really the identical chemical Energy in another form.

A railway train is stopped, as we know, by the application of the brake and by friction against the rails; but the heat developed by

The Mechanical Equivalent of Heat.

ΙΟΙ

friction is not a mere invariable accompaniment of the stoppage of the train, for it is the actual motive Energy transformed into another shape, just as the original momentum of the train was the heatmotion derived from that of the steam (derived in its turn from the oxidation of the carbon in the coal, that again being derived from the primeval energy of the sun); and, could we recover or measure exactly all the heat generated by friction in the stoppage of the train, we should have exactly the same amount as that expended in setting it in motion.

192. Some general ideas on the subject of this mutual relation between forces or Energies had been long entertained before any definite facts had been established. By the labours of our countrymen, Joule and Thomson, as well as by those of several continental philosophers, an exact numerical relation or equivalence was proved to exist between the amount of heat produced by friction and the amount of mechanical force expended in producing it. And this establishment of the Mechanical Equivalent of Heat, as it is termed, was the first experimental step towards the modern doctrine of Energy.

By a series of ingenious and careful experiments, Joule succeeded in establishing that the force resulting from the fall under gravity of one pound of matter through the space of 772 feet is just sufficient to heat one pound of water by the amount of 1° Fahr., if converted by impact or other means entirely into heat. That is to say, the molar motion of one pound, generated by this extent of fall, is converted into an intensely rapid quiver of the molecules of the water, which we measure by saying it raises one pound of water by one degree of Fahrenheit's scale.

Thus, 772 foot-pounds is denominated the mechanical equivalent of heat.

Between the other forms of Energy-such as Heat and Chemical or Electrical Force-similar definite correlations have also to some extent been established; but the practical determination of them is much complicated through the impossibility of insuring the conditions that Energy may pass from one form into another pure and simple-such as electricity only into heat only--and the detecting and measuring of all the forms of Energy simultaneously produced, is the problem that has to be solved before such correla tions can be fully and absolutely asserted.

6

102

The Conservation of Energy.

Conservation of Energy.

193. The conclusions from these experiments have been carried one step farther. They have shown that not only may one kind or form of Energy be translated into another, but also that in the translation nothing is lost, and that there is every reason to believe that the destruction of Energy is, equally with that of matter, impossible. There is, throughout the universe, nothing but the transformation of Energies; no loss of Energy is possible. Its disappearance in one form is owing to its change or conversion into another; and had we a machine or engine capable of reversion like the simple pendulum, for kinetic and potential Energy, we might see the oscillation of Energy between the two forms of mechanical and heat Energy, for example, just as we do that of the pendulum between kinetic and potential.

There may be an ebb and flow between the relative amounts of the various Energies, but the sum of them all is constant and invariable throughout our universe. There may, indeed, be a tendency of all the present Energies of nature ultimately to pass into one uniformly diffused heat-quiver : it may be indeed that, in some incalculably remote age, all the changes will have been rung upon the present distribution of the forms of Energy, and that the vitality of all nature will exist merely as a universal pulse. Yet the grand generalization of modern times constrains us to believe that in that pulse will be found the exact representative of every motion and form of Energy at present operating around or within us, that, in fact, Energy is coeternal with matter. We cannot say that we know fully the nature of the different Energies—such as magnetism, heat, electricity, and chemical affinity; but the principle of the Conservation of Energy, with which alone the facts discovered by modern experiment appear reconcilable, justifies us in regarding them all either as some species of actual motion, or as some sort of potential Energy inherent in definite arrangements of those minute particles which form the foundation of the material universe.

PART II.

SECTION 1.-CENTRE OF GRAVITY,

ANALYSIS OF THE SECTION.

As the earth's attraction, acting equally all round its centre, has a resultant or combined effect radiating from that centre, so the conjoint effects of the weight or gravitation towards the earth of all the particles of any body balance about a point within the body, which is known as the CENTRE OF GRAVITY. The situation of this point, in a body of uniformly distributed mass, may be determined by calculation from its figure; and, in bodies of regular shape, is identical with the centre of the figure. In bodies of irregular shape or distribution of mass, its position may often be found most readily by experiment. It is of great importance to consider the effect of the position of the centre of gravity in bodies and structures relatively to their supporting bases; as the conditions of stability or instability depend upon this relative position.

The centre of gravity is also the CENTRE OF ACTION of any force distributed uniformly, as gravity is, through any mass.

"CENTRE OF GRAVITY."

194. If a uniform beam or rod be supported by its middle, like a weighing beam, the two ends will balance each other, because there is just as much similarly situated matter on the one side of the support as on the other, and therefore no reason why the attraction of the matter on one side should overpower that on the other. If equal weights be afterwards placed in corresponding situations on the two arms of the beam, the balance will not thereby be disturbed; and the operation of adding weights that counterpoise, above and below, and near and far from the centre, may be continued, until a bulky mass is built up upon the beam, yet the whole will remain perfectly supported and in equilibrium about the original centre. Now, in every body or mass, or system of con

104

Centre of Gravity found Experimentally.

nected masses, there is a point of this kind about which the weights of all the parts balance or have equilibrium, and it is this point which is called the centre of gravity. Although in any mass, therefore, every atom has its separate gravity, and the weight of the body is really diffused through the whole, still, by supporting this one point either from above or from below, the whole mass is equally supported if the body be a solid or rigid one; by lifting it, the whole is lifted; by stopping it, the whole is brought to rest; and when it rises or falls, the general mass is really rising or falling. Thus for many purposes the weight of a body, however large, may be considered as concentrated in its centre of gravity.

195. In more precise language, the centre of gravity is the point of application of the resultant of the weights of all the elementary particles of which a body consists, which, for masses of ordinary magnitudes, may be regarded as a series of parallel forces.

Thus the centre of gravity is the centre of a series of parallel forces, and may, like the centre of parallel forces, be found from purely abstract or geometrical considerations.

In a mass of regular shape and of uniform substance, as a ball or a cube of metal, this point is evidently the centre of form; but in bodies that are irregular as to form or distribution of density, the calculation of its position is more troublesome, and in some cases impossible. By the following simple experimental method, however, this centre may often readily be found.

196. Since the centre of gravity is the point about which the weights of its various parts balance, it is clear that it must be vertically under, and in the same line with, a cord by which the body is suspended so as to balance.

a

Thus if an irregular piece of plank or of pasteboard, represented by a ebd (fig. 19), be suspended by a cord from any point, as a, and the cord of a plummet, a g, be attached at the same point, the cord of suspension and the cord of the plummet will be in one line, and the centre of gravity of the board must be somewhere in the line of the plummet, which we can mark on the board. If it be then suspended by another point, as d, and the new direction of the plummet line, de, be marked, the point c, where the two lines cross, will indicate the centre of gravity; and the board, when supported by a cord attached there, or on a point placed there, will remain evenly balanced.

go

Fig. 1.