Page:Scientific Papers of Josiah Willard Gibbs - Volume 2.djvu/279

The constructive power thus exhibited, this ability to bring order out of confusion, this breadth of view which could apprehend one truth without losing sight of another, this nice discrimination to separate truth from error,—these are qualities which place the possessor in the first rank of scientific men.

In the development of the various consequences of the fundamental propositions of thermodynamics, as applied to all kinds of physical phenomena, Clausius was rivalled, perhaps surpassed, in activity and versatility by Sir William Thomson. His attention, indeed, seems to have been less directed toward the development of the subject in extension, than toward the nature of the molecular phenomena of which the laws of thermodynamics are the sensible expression. He seems to have very early felt the conviction, that behind the second law of thermodynamics, which relates to the heat absorbed or given out by a body, and therefore capable of direct measurement, there was another law of similar form but relating to the quantities of heat (Le., molecular vis viva) absorbed in the performance of work, external or internal.

This may be made more definite, if we express the second law in a mathematical form, as may be done by saying that in any reversible cyclic process which a body may undergo

$\int {\frac {dQ}{t}}=0,$

where $dQ$ is an elementary portion of the heat imparted to the body, and $t$ the absolute temperature of the body, or the portion of it which receives the heat. Or, without limitation to cyclic processes, we may say that for any reversible infinitesimal change,

$dQ=t\,dS,$

where $S$ denotes a certain function of the state of the body, called by Clausius the entropy. The element of heat may evidently be divided into two parts, of which one represents the increase of molecular vis viva in the body, and the other the work done against forces, either external or internal. If we call these parts $dH$ and $dQ_{w},$ we have

$dQ=dH+dQ_{w}.$

Now the proposition of which Clausius felt so strong a conviction was that for reversible cyclic processes

$\int {\frac {dQ_{w}}{dt}}=0,$

and that for any reversible infinitesimal change

$dQ_{w}=t\,dZ,$

where $Z$ is another function of the state of the body, which he