movement of the pulley was very much reduced. A string, passing over the circumference of the pulley, was wrapped round r, so that, as the weight descended, the pulley moved round, and the string of the pulley caused rto rotate very rapidly. Now, the motion of the axis r was conducted within the covered box B, where there was attached to r a system of paddles, of which a sketch is given in figure; and therefore, as r moved, these paddles moved also. There were, altogether, eight sets of these paddles revolving between four stationary vanes. If, therefore, the box were full of liquid, the paddles and the vanes together would churn it about, for these stationary vanes would prevent the liquid being carried along by the paddles in the direction of rotation. Now, in this experiment, the weight was made to descend through a certain fixed distance, which was accurately measured. As it descended, the paddles were set in motion, and the energy of the descending weight was thus made to churn, and hence to heat some water contained in the box B. When the weight had descended a certain distance, by undoing a small peg p, it could be wound up again without moving the paddles in B, and thus the heating effect of several falls of the weight could be accumulated until this became so great as to be capable of being accurately measured by a thermometer. It ought to be mentioned that great care was taken in these experiments, not only to reduce the friction of the axles of the pulley as much as possible, but also to estimate and correct for this friction as accurately as possible; in fact, every precaution was taken to make the experiment successful. 61. Other experiments were made by Joule, in some of which a disc was made to rotate against another disc of cast-iron pressed against it, the whole arrangement being immersed in a cast-iron vessel filled with mercury. From all these experiments, Dr. Joule concluded that the quantity of heat produced by friction, if we can preserve and accurately measure it, will always be found proportional to the quantity of work expended. He expressed this proportion by stating the number of units of work in kilogrammetres necessary to raise by 1° C. the temperature of one kilogramme of water. This was 424, as determined by his last and most complete experiments; and hence we may conclude that if a kilogramme of water be allowed to fall through 424 metres, and if its motion be then suddenly stopped, sufficient heat will be generated to raise the temperature of the water through 1o C., and so on, in the same proportion. 62. Now, if we take the kilogrammetre as our unit of work, and the heat necessary to raise a kilogramme of water 1° C. as our unit of heat, this proportion may be expressed by saying that one heat unit is equal to 424 units of work. This number is frequently spoken of as the mechanical equivalent of heat; and in scientific treatises it is denoted by J., the initial of Dr. Joule's name. 63. We have now stated the exact relationship that subsists between mechanical energy and heat, and before proceeding further with proofs of the great law of conservation, we shall endeavour to make our readers acquainted with other varieties of energy, on the ground that it is necessary to penetrate the various disguises that our magician assumes before we can pretend to explain the principles that actuate him in his transformations. CHAPTER IIL THE FORCES AND ENERGIES OF NATURE: 64. In the last chapter we introduced our readers to two varieties of energy, one of them visible, and the other invisible or molecular; and it will now be our duty to search through the whole field of physical science for other varieties. Here it is well to bear in mind that all energy consists of two kinds, that of position and that of actual motion, and also that this distinction holds for invisible molecular energy just as truly as it does for that which is visible. Now, energy of position implies a body in a position of advantage with respect to some force, and hence we may with propriety begin our search by investigating the various forces of nature. Gravitation. 65. The most general, and perhaps the most important. of these forces is gravitation, and the law of action of this force may be enunciated as follows:-Every particle of the universe attracts every other particle with a force depending jointly upon the mass of the attracting and of the attracted particle, and varying inversely as the square of distance between the two. A little explanation will make this plain. Suppose a particle or system of particles of which the mass is unity to be placed at a distance equal to unity from another particle or system of particles of which the mass is also unity—the two will attract each other. Let us agree to consider the mutual attraction between them equal to unity also. Suppose, now, that we have on the one side two such systems with a mass represented by 2, and on the other side the same system as before, with a mass represented by unity, the distance, meanwhile, remaining unaltered. It is clear the double system will now attract the single system with a twofold force. Let us next suppose the mass of both systems to be doubled, the distance always remaining the same. It is clear that we shall now have a fourfold force, each unit of the one system attracting each unit of the other. In like manner, if the mass of the one system is 2, and that of the other 3, the force will be 6. We may, for instance, call the components of the one system A, A, and those of the other A, A, A, and we shall have A pulled towards 5 1 2 1 A, A, and A, with a threefold force, and A pulled 2 towards A, A, and A, with a threefold force, making 3 4 altogether a force equal to 6. |