to melt a thickness of two-fifths of a mile of ice per hour over the whole surface of the sun.

361 A. Sources of Solar Heat.-The only causes that appear at all adequate to produce such an enormous effect, are the energy of the celestial motions, and the potential energy of solar gravitation. The motion of the earth in its orbit is at the rate of about 96,500 feet per second. The kinetic energy of a pound of matter moving with this velocity is equivalent to about 104,000 pound-degrees Centigrade, whereas a pound of carbon produces by its combustion only 8080. The inferior planets travel with greater velocity, the square of the velocity being inversely as the distance from the sun's centre; and the energy of motion is proportional to the square of velocity. It follows that a pound of matter revolving in an orbit just outside the sun would have kinetic energy about 220 times greater than if it travelled with the earth. If this motion were arrested by the body plunging into the sun, the heat generated would be about 2800 times greater than that given out by the combustion of a pound of charcoal. We know that small bodies are travelling about in the celestial spaces; for they often become visible to us as meteors, their incandescence being due to the heat generated by their friction against the earth's atmosphere; and there is reason to believe that bodies of this kind compose the immense circumsolar nebula called the zodiacal light, and also, possibly, the solar corona which becomes visible in total eclipses. It is probable that these small bodies, being retarded by the resistance of an ethereal medium, which is too rare to interfere sensibly with the motion of such large bodies as the planets, are gradually sucked into the sun, and thus furnish some contribution towards the maintenance of solar heat. But the perturbations of the inferior planets and comets furnish an approximate indication of the quantity of matter circulating within the orbit of Mercury, and this quantity is found to be such that the heat which it could produce would only be equivalent to a few centuries of solar radiation.

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Helmholtz has suggested that the smallness of the sun's density— only of that of the earth-may be due to the expanded condition consequent on the possession of a very high temperature, and that this high temperature may be kept up by a gradual contraction. Contraction involves approach towards the sun's centre, and therefore the performance of work by solar gravitation. By assuming that the work thus done yields an equivalent of heat, he brings out the result that, if the sun were of uniform density throughout, the

heat developed by a contraction amounting to only one ten-thousandth of the solar diameter, would be as much as is emitted by the sun in 2100 years.

361 B. Sources of Energy available to Man.-Man cannot produce energy; he can only apply to his purposes the stores of energy which he finds ready to his hand. With some unimportant exceptions, these can all be traced to three sources:

I. The solar rays.

II. The energy of the earth's rotation.

III. The energy of the relative motions of the moon, earth, and sun, combined with the potential energy of their mutual gravitation. The fires which drive our steam-engines owe their energy, as we have seen, to the solar rays. The animals which work for us derive their energy from the food which they eat, and thus, indirectly, from the solar rays. Our water-mills are driven by the descent of water, which has fallen as rain from the clouds, to which it was raised in the form of vapour by means of heat derived from the solar rays.

The wind which propels our sailing-vessels, and turns our windmills, is due to the joint action of heat derived from the sun, and the earth's rotation.

The tides, which are sometimes employed for driving mills, are due to sources II. and III. combined.

The work which man obtains, by his own appliances, from the winds and tides, is altogether insignificant when compared with the work done by these agents without his intervention, this work being chiefly spent in friction. It is certain that all the work which they do, involves the loss of so much energy from the original sources; a loss which is astronomically insignificant for such a period as a century, but may produce, and probably has produced, very sensible effects in long ages. In the case of tidal friction, great part of the loss must fall upon the energy of the earth's rotation; but the case is very different with winds. Neglecting the comparatively insignificant effect of aerial tides, due to the gravitation of the moon and sun, wind-friction cannot in the slightest degree affect the rate of the earth's rotation, for it is impossible for any action exerted between parts of a system to alter the angular momentum of the system. (53 F.) The effect of easterly winds in checking the earth's rotation must therefore be exactly balanced by the effect of westerly winds in accelerating it. In applying this principle, it is to be remembered that the couple exerted by the wind is jointly propor

tional to the force of friction resolved in an easterly or westerly direction, and to the distance from the earth's axis.

361c. Dissipation of Energy.-From the principles laid down in the present chapter it appears that, although mechanical work can be entirely spent in producing its equivalent of heat, heat cannot be entirely spent in producing mechanical work. Along with the conversion of heat into mechanical effect, there is always the transference of another and usually much larger quantity of heat from a body at a higher to another at a lower temperature. In conduction and radiation heat passes by a more direct process from a warmer to a colder body, usually without yielding any work at all. In these cases, though there is no loss of energy, there is a running to waste as far as regards convertibility; for a body must be hotter than neighbouring bodies, in order that its heat may be available for yielding work. This process of running down to less available forms has been variously styled diffusion, degradation, and dissipation of energy, and it is not by any means confined to heat. We can assert of energy in general that it often runs down from a higher to a lower grade (that is to a form less available for yielding work), and that, if a quantity of energy is ever raised from a lower to a higher grade, it is only in virtue of the degradation of another quantity, in such sort that there is never a gain, and is generally a loss, of available energy.

This general tendency in nature was first pointed out by Sir W. Thomson. It obviously leads to the conclusion that the earth is gradually approaching a condition in which it will no longer be habitable by man as at present constituted.

CHAPTER XXXIII.

STEAM AND OTHER HEAT ENGINES.

362. Heat-engines.-The name of heat-engine or thermo-dynamic engine is given to all machines which yield work in virtue of heat which is supplied to them. Besides the steam-engine, it includes the air-engine and the gas-engine. We shall first describe one of the best forms of the air-engine.

363. Stirling's Air-engine.—Fig. 315 is a perspective view, and Fig 316 a section of the engine invented by Dr. Robert Stirling. The particular form here represented is that which has been adopted in France by M. Laubereau. It consists of two cylinders of different diameters, which are in communication with each other. The larger cylinder is divided into two compartments by a kind of large piston made of plaster of Paris, which, however, does not touch the sides of the cylinder, and thus leaves an annular space for communication between the two compartments.

The bottom of the large cylinder, which is directly exposed to the action of the furnace, is slightly concave; the top is double, thus affording an intermediate space, through which cold water is kept circulating by means of a pump which is driven by the machine. From this arrangement it follows that, when the mass of plaster is at the bottom of the cylinder, it will intercept the heat of the fire, being a very bad conductor, and thus the air in the cylinder will be cooled by the water in the double top. On the other hand, when the piston is in contact with the refrigerator, the air will be exposed to the action of the fire, and its elastic force will, consequently, be increased.

The smaller cylinder is open above, and contains a piston which drives a crank on the axle of a heavy fly-wheel of cast-iron. The communication between the two cylinders is in the lower part of each.

Suppose now that the large piston is in contact with the refrigerator, while the small piston is in its lowest position. The air is thus exposed to the action of heat, expands, and raises the small piston. If we now suppose the large piston shifted to the bottom of the

cylinder, the air will cool, and its tension will diminish, becoming equal to or even less than that of the atmosphere. The small piston will thus be carried to the bottom of the cylinder by the movement of the fly-wheel, and will again be pushed up by the expanding air, if we suppose the large piston to rise again to the top of its cylinder.