On the Existence of an Equivalent Relation between
        Heat and the Ordinary Forms of Mechanical Power.        

By James P. Joule, Esq.
[In a letter to the
Editors of the 'Philosophical Magazine.']

['Philosophical Magazine,' ser 3. vol. xxvii. p. 205.]

Gentlemen,
        The principal part of this letter was brought under the notice of the British Association at its last meeting at Cambridge. I have hitherto hesitated to give it further publication, not because I was in any degree doubtful of the conclusions at which I had arrived, but because I intended to make a slight alteration in the apparatus calculated to give still greater precision to the experiments. Being unable, however, just at present to spare the time necessary to fulfil this design, and being at the same time most anxious to convince. the scientific world of the truth of the positions I have maintained, I hope you will do me the favour of publishing this letter in your excellent Magazine.
        The apparatus exhibited before the association consisted of a brass paddle-wheel 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 magneto-electrical 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 from experiments (hitherto unpublished) on the motion of water through narrow tubes.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 paddle-wheel, 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 freezing-point 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 paddle-wheel 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,
       Yours respectfully,
         James P. Joule.

     Oak Field, near Manchester,
       August 6, 1845.
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