Nature and their Mutual Dependence* 1 7 



Roche and Berard, 



O) 



ft)/ ~ 0-266V 



from which results that the mechanical energy equivalent to the 

 energy of heat in a unit quantity of heat is 



&>, = 1204*3 pounds (33) 



This expression for the specific heat of water shows that when 

 the quantity of heat which is able to heat 1 pound of water 1 

 degree Celsius (the so-called unit of heat) is used in the most 

 profitable manner for producing mechanical energy, then 1204*3 

 units of work may be produced from it, as a unit of work is 

 equated to 1 foot-pound; and conversely, when an energy 

 = 1204*3 units of work is imparted to the material particles of 

 a body, then the internal energy among the particles, when ap- 

 pearing as energy of heat, will be increased by exactly one unit 

 of heat. 



When this result is compared with what I formerly derived from 

 my experiments upon the heat produced by friction of solid 

 bodies, by which I found an average of 1 unit of heat equal to 

 1185*4 units of work*, then we perceive that this average differs 

 a little from that represented in (33) — however, not more than 

 might be expected from the few experiments which I have hitherto 

 had opportunity to undertake f. 



In the preceding we have examined the quantity of energy 

 produced in a fluid undergoing compression ; let us now proceed 

 to determine the general expression for the magnitude of the 

 energy contained in a fluid at a given temperature, pressure, 

 and density. 



If the material points of which the fluid consist are (as above) 

 denoted by w?, m!, m", &c, their coordinates by x, y 3 z ; x [ \ y 1 , z' ; 

 x", y" } z" } &c, and the accelerating forces, by which these 

 points are moved, by X, Y, Z; X', Y', Z'; X", Y", Z", &c, and 

 if we suppose that the fluid by degrees yields some part of its 

 energy, under the form of mechanical energy, for the production 

 of a certain work, then, in conformity to the formulae (9) and 

 (10), the whole quantity of energy which the fluid has lost, after 

 the lapse of time t, may be expressed by 



q = 2m§{Xdx; + Ydy + Zdz)-w + C, . . (34) 

 as S mxfJLdsc + Ydy + Zdz) denotes the sum of all terms analo- 

 gous to m§ (Xdx + Ydy + Zdz) answering to all the material 



* See Vidensb. Selsk. SJcr. 5 Rcekhe, naturv. og math. p. \46. 

 t Experiments upon this subject have lately been made by Mr. J. P. Joule, 

 Pogg. Ann. vol. lxxiii. p. 479. 



Phil. Mag. S. 4. Vol. 42. No. 277. July 1871. C 



