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The Foot-Pound and Kilogrammetre.

The same amount of Work-power was needed to raise the huge pile of the pyramids in olden times, by whatever means it may have been supplied, as would be required at the present day; though, by unskiful mechanical contrivances, much more Energy may have been spent in those days in motions not conducing to the direct elevation of the masses.

Thus, then, if we have a definite quantity of matter which we can depend on being able always to measure, and if we have a definite standard, or unit, of length or distance which we can also be sure of ascertaining at any time, we are certain that the force, or Energy, or Work-power required to raise this mass vertically from the earth through this distance is unchangeable at the same spot on the globe, and may, therefore, be chosen as a standard of reference.

"The Foot-Pound, or British Unit of Work."

176. The quantity of matter that we call a pound (in London), and the space that we call a foot, are measures now so well known, and so often recorded over the world, that nothing short of the destruction of our race would prevent them from being at any time recovered as standards of measurement.

The unit of Work is accordingly defined as the Energy required to raise one pound of matter of any sort vertically through the space of one foot at London, and this is known as the FOOT-POUND or unit of Work in this country.

"The Kilogrammetre, or French Unit of Work."

177. The French have different units of measure which they call the metre, and the kilogramme; the former is about a twelfth part longer than the English yard; or, more exactly, the metre is 39'37 inches, that is, 12 metres go to make nearly 13 English yards; and the kilogramme is a little over two pounds avoirdupois ; or, more exactly, 15,432 35 English grains. In France, then, the unit of work is defined as the Energy required to raise a kilogramme through the space of a metre, and this is called the Kilogrammetre. It is about 7 (or 7.233) times greater than the foot-pound, and may sometimes be more convenient in stating large amounts of Energy.

"The practical measure of Work."

178. Work, as we have defined it, must depend on two things for its measurement: (1.) on the weight raised; and, (2.) on the height

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to which it is raised. If we have got to raise five books, each weighing a pound, through five feet, it will obviously require the same amount of Energy to raise the whole at once to this height, as to raise the books singly a foot at a time: that is, the work done in this case is equal to twenty-five foot-pounds. Hence the simple

rule

The whole weight raised in pounds, multiplied by the whole vertical height in feet, gives the amount of Work done against the resistance of gravity in foot-pounds. Or, on the French scale, The whole weight in kilogrammes, multiplied by the whole vertical distance in metres, gives the Work measure in kilogrammetres.

A steam-crane raising a hundred-weight of goods from the hold of a ship up to the deck or the quay, say a distance of twenty feet, does 20 times 112, or 2240 foot-pounds of Work, the same amount as if it raised a ton through the space of one foot.

"Connection between Work-power and Velocity of a moving body."

179. A railway train going with double velocity possesses double quantity of motion, momentum, or shock-giving power; but its Energy or power of overcoming resistance is more than doubled. It will go on not twice but four times as far as when its velocity is only half what it is.

A rifle ball shot vertically up with a velocity of 120 feet a second will reach not three times but nine times as far as with a velocity of forty feet a second.

A steamer going along at ten knots an hour will, after the steam is turned off, and the motion is left to the friction of the water to subdue, go on for twenty-five times the space that it would go if it had a speed of only two knots.

A cannon ball sent out with a velocity of 100 feet a second, will penetrate not twice but four times as far into an earthwork or sandbank as with a velocity of 50 feet a second; or it will pierce through four planks of wood in the first case, and one plank in the second.

Thus penetrating power, Work-power, power of overcoming resistance, or Energy, increases at the square of the rate at which the velocity increases.

And the reason is obvious when we consider that the Energy acquired in falling through any space under the influence of gravity is necessarily identical with the Energy subtracted from a moving

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Illustrations of Energy.

body by the same force of gravity during the same space. The one case is merely the obverse of the other. Now, we have seen that in order to double the velocity acquired by a stone falling through ten feet, we must let it fall through forty feet; in order to triple the velocity we must let it fall through ninety feet; in other words, that the spaces passed over under the accelerating force of gravity increase at the square of the rate that the velocity increases. Consequently, the energy or power of passing over space against gravity or any uniform resistance, is proportioned to the square of the velocity possessed by the moving mass.

180. Of course, if the force of resistance be more intense than that of gravity, shorter time and space will be required for it to produce the same amount of work or change of energy.

The work-power generated in a heavy hammer-head by the force of gravity drawing it through a space of a few feet, is equivalent to that of the force of friction against the small mass of a nail acting only through perhaps half an inch.

Pile-driving illustrates the same fact.

181. The following instances are explained by the fact, that the Energy or power of overcoming resistance increases at a greater rate than the bare velocity :

A door standing open would yield readily to the gentle push of a finger, yet is not moved by a cannon-ball shot swiftly through it, because the force of cohesion between the molecules of wood is not strong enough to produce, within the limit of fracture, energy sufficient to overcome that of the flying ball. The cohesion of the circle cut out in the door by the ball might resist more than a hundred pounds laid quietly upon it; but, supposing the bullet to fly 1200 feet in a second, and the cohesion to be destroyed onetenth of an inch, it would require to be strong enough to destroy in the 144,000th part of a second the moving force of the heavy mass, a task to which it is wholly unequal.

So a leaden bullet, pressed slowly against a pane of glass, breaks it irregularly, where the strength happens to be least, but shot at it from a pistol, makes a clean, round hole. It has been anusingly explained, that the particles struck and carried away have not had time to warn their neighbours of what was happening.

Thus, too, a cannon-ball, having very great velocity, passes clean through a ship's side; while one with less speed splinters and breaks the wood to a considerable distance around. A near shot

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93

thus often injures a ship less than a more distant or a weaker

one.

A sheet of paper bent to stand edgeways on a table, may not be driven down by a pistol-ball fired through it.

This explains, with respect to gun-shot wounds, why a person often remains ignorant for a time of his misfortune, and why a rapid bullet kills only the part which it touches, while a spent ball may bruise and injure widely around. In many cases of injury, popularly attributed to the wind of a ball, the ball has really touched the part. A circular plate of soft iron, rotated with extreme rapidity will cut through a stone, or even the hardest steel file, almost as a knife cuts through a carrot. In cases where a soft powder spread on the rim of a wheel suffices to polish a hard body, it acts partly like this plate, by the motion or velocity given to the wearing particles.

Fine sand or emery projected from a tube by steam with a very high velocity, will pierce a hole in stone or metal, or even glass; and this fact has been recently turned to useful account in the arts of stone cutting and engraving.

That penetrating or work-power depends on velocity more than on mere momentum, is shown by the comparatively insignificant effect of the recoil of a cannon or rifle, though in momentum it is equal to that of the ball.

Paradoxical, then, though it may appear at first sight, it is an important truth that of two bodies moving with equal momenta, the one which has the higher velocity and the less mass will have the greater Energy. The result of a large number of experiments has shown that the penetrating power of a rifle ball is much increased by reducing the weight of the ball and increasing its velocity.

"Different Forms of Energy."

182. It is in many cases very advantageous to regard the different so-called forces of nature, some of which we have already considered, as but so many forms of Energy, or sources of Work-power. By denominating them Energy rather than force, we imply that they may all be referred to some common standard of comparison, and thus make one step towards that assimilation of the various agencies around us, which is the crowning glory of modern science. These forms of Energy, then, may be thus enumerated :

(1.) Gravitation, or Molar Attraction, one of the most apparent,

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The Different Forms of Energy named.

and one of the most important forms of Energy, because it is allpervading. That bodies falling under the attraction of the earth have a power of combating resistance, scarcely needs illustration.

Mills driven by falling water, clocks and other machines driven by falling weights, pile-engines, tilt-hammers, &c., all make use of this form of Energy.

(2.) Cohesion, or Molecular Attraction, the form of Energy exhibi ted in springs and elastic substances-such as india-rubber. The bow, the boy's catapult, the mainspring of a watch, exemplify the work-power of this nature. The apparently passive exhibition of power to resist separation of the particles of a body is really this form of Energy, and a most valuable one it is; rigidity entering as an essential element or factor into all pieces of machinery.

(3.) Chemical Attraction, or Atomic Energy, a widespread agency in the world about us, most familiarly exhibited in the collapse or falling together of oxygen and carbon atoms, which constitutes the all-powerful action of burning.

(4.) Heat is a most potent form of Energy. It is from our coalfields, through their heat-producing power, that we obtain nearly all the mechanical power of the present day.

(5.) Magnetism, as shown by the action of the earth on the mariner's compass; by a piece of steel which has been treated in a certain way; and by the electric or galvanic current when it is made to pass in a spiral wire, as will be afterwards explained.

(6.) Electricity. By rubbing a stick of sealing wax or a rod of glass with a silk cloth, we produce in the stick or rod a curious power of lifting small bodies from a short distance, against the force of gravity. So in the galvanic battery, to be afterwards explained, we have a more obedient and docile form of this same electric Energy, by means of which, at the beck of a person's finger in London, a little arm may be pulled to one side or the other at Edinburgh, just as surely as if the person pulled a frictionless string.

(7.) Light is a still more impalpable and immeasurable form of Energy. That it is a motion or vibration of an ethereal fluid filling all space, is now very generally believed. Though the Work it if capable of doing, and the effects it produces on sensible matter, have as yet utterly baffled calculation, there can be no question but they are equally real with those of the other forms mentioned above.

(8.) Vitality, or Animal Energy, is the most mysterious and elusive form of all.