foot of the ether, must be given by the equation, and for the mass, in pounds, of a cubic mile we have It is quite impossible to fix a definite limit to the ratio which v may bear to V; but it appears improbable that it could be more, for instance, than, for any kind of light following the observed laws. We may conclude that probably a cubic foot of the luminiferous medium in the space traversed by the earth contains not of a pound of matter, and a cubic mile not less than less than 1 1560 × 1017 1 1060 × 106 If the mean velocity of the vibrations of light within a spherical surface concentric with the sun and passing through the earth were equal to the earth's velocity-a very tolerable suppositionsince this is 10170 of the velocity of light, the whole mass of the luminiferous medium within that space would be go of the 30000 earth's mass, since the mechanical value of the light within it, being as much as the sun radiates in about 8 minutes, is about 15000 of the mechanical value of the earth's motion. As the mean velocity of the vibrations might be many times greater than has been supposed in this case, the mass of the medium might be considerably less than this [thirty-thousandth of the earth's mass]; but we may be sure it is not incomparably less, not 100,000 times as small for instance. On the other hand, it is worth remarking that the preceding estimate shows that what we know of the mechanical value of light renders it in no way probable that the masses of luminiferous medium in interplanetary spaces, or all round the sun in volumes of which the linear dimensions are comparable with the dimensions of the planets' orbits, are otherwise than excessively small in comparison with the masses of the planets. But it is also worth observing that the luminiferous medium is enormously denser than the continuation of the terrestrial atmosphere would be in interplanetary space, if rarefied according to Boyle's law always, and if the earth were at rest in a space of constant temperature with an atmosphere of the actual density at its surface*. Thus the mass of air in a cubic foot of distant space several times the earth's radius off, on this hypothesis, would 1 lb. 442 × 10345 be ; while there cannot, according to the preceding esti mate, be in reality less than 1 lb. 156 × 1018 which is 28 × 10326 times as much, of matter in every cubic foot of space traversed by the earth. ART. LXVIII. APERÇU SUR DES RECHERCHES RELATIVES AUX EFFETS DES COURANTS ÉLECTRIQUES DANS DES CONDUCTEURS INÉGALEMENT ÉCHAUFFÉS, ET À D'AUTRES POINTS DE LA THERMO-ÉLECTRICITÉ. [Comptes Rendus, XXXIX. July, 1854.] The substance of this Article is contained in pp. 460–463, of Vol. 1. Art. LI. Newton has calculated (Princ. III., p. 512) that a globe of ordinary density at the earth's surface, of one inch in diameter, if reduced to the density due to the altitude above the surface of one radius of the earth, would occupy a sphere exceeding in radius the orbit of Saturn."—(Herschell's Astronomy, Note on § 559.) It would (on the hypothesis stated in the text) we may now say occupy a sphere exceeding in radius millions of millions of times the distances of any stars of which the parallaxes have been determined. A pound of the medium, in the space traversed by the earth, cannot occupy more than the bulk of a cube 1000 miles in side. The earth itself, in moving through it, cannot displace less than 250 pounds of matter. T. II. ART. LXIX. ON MECHANICAL ANTECEDENTS OF MOTION, HEAT, [From Brit. Ass. Rep., Part II. 1854; Edin. New Phil. Jour. 1. 1855; THIS communication was opened with some general explanations regarding mechanical energy, and the terms which have been introduced to designate the various forms under which it is manifested. Any piece of matter, or any group of bodies, however connected, which either is in motion, or can get into motion without external assistance, has what is called mechanical energy. The energy of motion may be called either "dynamical energy" or "actual energy*." The energy of a material system at rest, in virtue of which it can get into motion, is called "potential energy." The author showed the use of these terms, explained the idea of a store of energy, and conversions and transformations of energy, by various illustrations. A stone at a height, or an elevated reservoir of water, has potential energy. If the stone be let fall, its potential energy is converted into actual energy during its descent, exists entirely as the actual energy of its own motion at the instant before it strikes, and is transformed into heat at the moment of coming to rest on the ground. If the water flow down. by a gradual natural channel, its potential energy is gradually converted into heat by fluid friction, according to an admirable discovery made by Mr Joule of Manchester above twelve years ago, which has led to the greatest reform that physical science has experienced since the days of Newton. From that discovery, it may be concluded with certainty that heat is not matter, but some kind of motion among the particles of matter; a conclusion established, it is true, by Sir Humphrey Davy and Count Rumford at the end of last century, but ignored by even the highest * [A few years later, in advocating a restoration of the original and natural nomenclature,-"mechanics the science of machines,"—"dynamics the science of force," I suggested (instead of statics and dynamics the two divisions of mechanics according to the then usual nomenclature) that statics and kinetics should be adopted to designate the two divisions of dynamics. At the same time I gave, instead of "dynamical energy," or "actual energy," the name "kinetic energy" which is now in general use to designate the energy of motion. W. T., Lensfield Cottage, Cambridge, May 15, 1883.] scientific men during a period of more than forty years. Mr Joule, by a series of well planned and executed experiments, ascertained that a pound of water would have its temperature increased by 1o (Fahrenheit) if it kept all the heat that would be generated by its descent through 772 feet; that is, the "actual" or "dynamical energy of as much heat as raises the temperature of a pound of water 1o is an exact equivalent for the potential energy of a pound of matter 772 feet above the ground. Mr Joule also fully established the relations of equivalence among the energies of chemical affinity, of heat, of combination or combustion, of electrical currents in the galvanic battery, of electrical currents in magnetoelectric machines, of engines worked by galvanism, and of all the varied and interchangeable manifestations of calorific action and mechanical force which accompany them. These researches, with the theory of animal heat and motion in relation to the heat of combustion of the food, and the theory of the phenomena presented by shooting stars, due to the same penetrating investigator, have afforded to the author of the present communication the chief groundwork for his speculations. The heat emitted by animals, and the mechanical effects which they produce, are transformations of the energy of chemical affinity with which the food consumed by them combines with the oxygen they inhale. The heat, sound, and mechanical effects produced by the explosion of gunpowder are, all together, equivalent to the energy of chemical affinity between the different substances of which gunpowder is composed. The potential energy of war is contained in the stores of gunpowder and food brought into the field. The gunpowder carried by artillery and infantry contains all the potential energy ordinarily brought into action by those two arms of the service. The men's food, and the forage for the horses, contain the stores of potential energy drawn upon in a charge of cavalry. Artillerymen, foot soldiers, sailors, steamers with their engines, guns, swords, are only means and appliances by which the potential energy contained in the stores of gunpowder and food is directed to strike the blows by which the desired effects are produced. The heat and mechanical actions of animals are transformations of the potential energy of their food mechanically equivalent to the heat that would be got by burning it. The food of animals is either vegetable, or animal fed on vegetable, or ultimately vegetable after several removes. Now; except mushrooms and other funguses, all of which can grow in the dark, are nourished by organic food like animals, and absorb oxygen and exhale carbonic acid like animals; all known vegetables get the greater part of their substance, certainly all their combustible matter, from the decomposition of carbonic acid and water, absorbed by them from the air and soil. The separation of carbon and of hydrogen from oxygen in these decompositions is an energetic effect, equivalent to the heat of recombination of those elements by combustion or otherwise. The beautiful discovery of Priestley, and the subsequent researches of Sennebier, De Saussure, Sir Humphrey Davy, and others, have made it quite certain that those decompositions of water and carbonic acid only take place naturally in the day time, and that light falling on the green leaves, either from the sun or from an artificial source, is an essential condition, without which they are never effected. There cannot be a doubt but that it is the dynamical energy of the luminiferous vibrations which is here efficient in forcing the particles of carbon and hydrogen away from those of oxygen, towards which they are attracted with such powerful affinities; and that luminiferous motions are reduced to rest, to an extent exactly equivalent to the potential energy thus called into being. Whether or not the coolness of green fields and fresh foliage is to any sensible extent due to this cause, it is quite certain that sun-heat is put out of existence as heat, in the growth of plants in any locality, and that just as much heat, neither more nor less, is emitted from fires in which the whole growth of any period of time is burned. Coal, composed as it is of the relics of ancient vegetation, derived its potential energy from the light of distant ages. Wood fires give us heat and light which has been got from the sun a few years. ago. Our coal fires and gas lamps bring out for our present comfort heat and light of a primeval sun which have lain dormant as potential energy beneath seas and mountains for countless ages. We must look then to the sun as the source from which the mechanical energy of all the motions and heat of living creatures, and all the motion, heat, and light derived from fires and artificial flames is supplied. The natural motions of air and water derive their energy partly, no doubt, from the sun's heat, but partly also from the earth's rotatory motion and the relative motions and mutual forces between the earth, moon, and sun. If we except |