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XXXI.—On the Dynamical Theory of Heat. Part V.* On the Quantities of 
Mechanical Energy contained in a Fluid in Different States, as to Temperature 
and Density. By Witu1am Tuomson, M.A., Professor of Natural Philosophy 
in the University of Glasgow. 
(Read December 15, 1851.) 
81. A body which is either emitting heat, or altering its dimensions against 
resisting forces, is doing work upon matter external to it. The mechanical 
effect of this work, in one case, is the excitation of thermal motions, and in the 
other, the overcoming of resistances. The body must itself be altering in its cir- 
cumstances, so as to contain a less store of work within it, by an amount precisely 
equal to the aggregate value of the mechanical effects produced: and conversely, 
the aggregate value of the mechanical effects produced, must depend solely on the 
initial and final states of the body, and is therefore the same, whatever be the 
intermediate states through which the body passes, provided the initial and jinal 
states be the same. 
82. The total mechanical energy of a body might be defined as the mechanical 
value of all the effect it would produce, in heat emitted and in resistances over- 
come, if it were cooled to the utmost, and allowed to contract indefinitely or to 
expand indefinitely according as the forces between its particles are attractive or 
repulsive, when the thermal motions within it are all stopped ; but in our present 
state of ignorance regarding perfect cold, and the nature of molecular forces, we 
cannot determine this “ total mechanical energy” for any portion of matter, nor 
even can we be sure that it is not infinitely great for a finite portion of matter. 
Hence it is convenient to choose a certain state, as standard for the body under 
consideration, and, to use the unqualified term, mechanical energy, with reference 
to this standard state; so that the “ mechanical energy of a body in a given 
state,” will denote the mechanical value of the effects the body would produce in 
passing from the state in which it is given, to the standard state, or the mechanical 
value of the whole agency that would be required to bring the body from the 
standard state to the state in which it is given. 
83. In the present communication, a system of as founded on proposi- 
* A preceding communication (April 21, 1851) published in the Transactions (Vol. xx., Part ii.), 
under the title, “On a Method of Discovering Experimentally the Relation between the Mechanical Work 
spent, and the Heat produced by the Compression of a Gaseous Fluid,” will be referred to as Part 
IV. of a series of Papers on the Dynamical Theory of Heat; and the numbers of its sections will be 
altered accordingly, so that its first section will be referred to as § 61, and its 20th and last, as § 80. 
VOL. XX. PART III. 6M 
