Gary Novak Background Second Proof math explained complete math Consise Math Joule's constant potential energy Contradictions

On the Existence of an Equivalent Relation between By James P. Joule, Esq. Gentlemen, The apparatus exhibited before the association consisted of a brass paddlewheel working horizontally in a can of water. Motion could be communicated to this paddle by means of weights, pulleys, &c., exactly in the manner described in a previous paper**. The paddle moved with great resistance in the can of water, so that the weights (each of four pounds) descended at the slow rate of about one foot per second. The height of the pulleys from the ground was twelve yards, and consequently, when the weights had descended through that distance, they had to be would up again in order to renew the motion of the paddle. After this operation had been repeated sixteen times, the increase of the temperature of the water was ascertained by means of a very sensible and accurate thermometer. A series of nine experiments was performed in the above manner, and nine experiments were made in order to eliminate the cooling or heating effects of the atmosphere. After reducing the result to the capacity for heat of a pound of water, it appeared that for each degree of heat evolved by the friction of the water a mechanical power equal to that which can raise a weight of 890 lb. to the height of one foot had to be expended. The equivalents I have already obtained are:—1st, 823 lb., derived from magnetoelectrical experiments; 2nd, 795 lb., deduced from the cold produced by the rarefaction of air; and 3rd, 774 lb. from experiments (hitherto unpublished) on the motion of water through narrow tubes. This last class of experiments being similar to that with the paddlewheel, we may take the mean 774 and 890, or 832 lb., as the equivalent derived from the friction of water. In such delicate experiments, where one hardly ever collects more than half a degree of heat, greater accordance of the results with one another than that above exhibited could hardly have been expected. I may therefore conclude that the existence of an equivalent relation between heat and the ordinary forms of mechanical power is proved; and assume 817 lb., the mean of the results of three distinct classes of experiments, as the equivalent, until more accurate experiments shall have been made. Any of your readers who are so fortunate as to reside amid the romantic scenery of Wales or Scotland could, I doubt not, confirm my experiments by trying the temperature of the water at the top and at the bottom of a cascade. If my views be correct, a fall of 817 feet will of course generate one degree of heat, and the temperature of the river of Niagara will be raised about one fifth of a degree by its fall of 160 feet. Admitting the correctness of the equivalent I have named, it is obvious that the vis viva of the particles of a pound of water at (say) 51° plus the vis viva which would be acquired by a weight of 817 lb. after falling through the perpendicular height of one foot. Assuming that the expansion of elastic fluids on the removal of pressure is owing to the centrifugal force of revolving atmospheres of electricity, we can easily estimate the absolute quantity of heat in matter. For in an elastic fluid the pressure will be proportional to the square of the velocity of the revolving atmospheres, and the vis viva of the atmospheres will also be proportional to the square of the velocity; consequently the pressure will be proportional to the vis viva. Now the ratio of the pressures of elastic fluids at the temperatures 32° and 33° is 480 : 481; consequently the zero of temperature must be 480° below the freezingpoint of water. We see then what an enormous quantity of vis viva exists in matter. A single pound of water at 60° must possess 480° + 28° = 508° of heat; in other words, it must possess a vis viva equal to that acquired by a weight of 415036 lb. after falling through a perpendicular height of one foot. The velocity with which the atmospheres of electricity must revolve in order to present this enormous amount of vis viva must of course be prodigious, and equal probably to the velocity of light in planetary space, or to that of an electric discharge as determined by the experiments of Wheatstone. *The experiments were made at Oak Field, Whalley Range. **Phil. Mag. ser. 3. vol. xxiii. p. 436. The paddlewheel used by Rennie in his experiments on the friction of water (Phil. Trans. 1831, plate xi. fig.1) was somewhat similar to mine. I employed, however, a greater number of "floats," and also a corresponding number of stationary floats, in order to prevent the rotatory motion of the water in the can. I remain, Gentlemen, Oak Field, near Manchester, Reference: Energy: Historical Development of the Concept. R. Bruce Lindsay. 1975. p345. This paper had to be retyped, because the ink on the original was almost unreadable.
