60.

CORNELL UNIVERSITY,

DEPARTMENT OF CHEMISTRY.

Ever debbed of notice by new new to system

PROFESSORS :

G. C. CALDWELL,
GENERAL AND AGRICULTURAL CHEMISTRY.

W. R. ORNDORFF,
ORGANIC CHEMISTRY.

L. M. DENNIS,
ANALYTICAL CHEMISTRY.

J. E. TREVOR,
PHYSICAL CHEMISTRY.

but debbed in

Ithaca, N. Y., November 1-1895.

Professor J.W.Gibbs,

My dear Sir: - I am indebted to you for your letter. After
a few days further reflection on the matter I shall want to write you
again about it,- at the risk of making a nuisance of myself. But in the
meantime I beg to suggest the following, which may then go into the wa-
ste basket.

In a change let us add reversibly a definite amount of
work, a definite amount of heat and besides this a definite new mass
from without. Now the addition of work increases the energy by the
amount of the work; the addition of heat increases the
energy by the amount of the heat; and the addition of new mass increa-
ses the energy by the store of heat and work imparted to that mass to
bring it to the state from which it can be added reversibly, plus the
heat and work absorbed in the reversible addition of it. The variation
of the energy of the original system must appear therefore somehow as
the sum of these six terms, when the matter is viewed in this way.

Or we may say, writing $ε_I$ for the energy of the system in
its original state and $ε_II$ for that after heat, work and new mass from
outside have been added, that

$ε_II - ε_I =$ the energy of the new mass when in position to be added rev'y
+ the total heat added and
+ the total work added, in the change made.

Now the first term of the second member is not $\left(\frac{\partial \epsilon}{\partial m}_I\right)_{H.V.}$
the second term is not $T_d \frac{\partial q}{\partial T}$ and
the third term is not -pdv, when $\eta$ and $v$ represent the en-
tropy and volume of the initial state (I). Of course I do not understand
that you maintain them to be.

The trouble may lie in this:- You say at the outset (p. 103):

The change in the energy is the combined amount
of work and heat received by the system in pass-
ing from the initial state to the final one.

This is not true unless the initial state is understood to include the
new mass which is to be added to it. When such is the case, $\eta$ must re-
present the combined entropies of the original system and the new mas-
ses (taken in any state you please), and $v$ the combined volumes of both.
But then

$dS = Tdq - pdw$
and the terms $\mu dm$ fall out.

Yours very truly,

THE JOURNAL OF PHYSICAL CHEMISTRY

PUBLISHED AT CORNELL UNIVERSITY

EDITORS

WILDER D. BANCROFT
JOSEPH E. TREVOR

ITHACA, NEW YORK, U.S.A. Dec. 11, 1997

Dear Professor Gibbs

A short time ago we received from Duhem, for publication in
our Journal, a paper giving an elaborate general demonstration of the
phase rule. In it he said--

"Il nous a semblé que les démonstrations données jusqu'ici des lois des phases laissaient à désirer en un point; elles admettant, au moins implicitement, que les composants indépendants de chacune des phases en lesquelles se partage un système sont les mêmes que les composants indépendants du système entier."

I wrote to him, hereupon, pointing out that in your original paper
you had treated the subject in a wholly general way, and outlining your
demonstration in some detail. He answers that--

"Votre réclamation de priorité en faveur de J. W. Gibbs est absolument fondée. ... Je vous remerci ... de m'avoir évité, a l'égard de J. W. Gibbs, que j'admire si profondément, une involontaire injustice ... ."

His paper, however, is to appear in our January and February
issues (it is too long for a single number), when it will contain the
remark that--

"M. J. W. Gibbs, cependant, a montré (p. 153), en quelques
lignes, par quelle voie on pouvait établir la loi des phases
de telle sort que la demonstration fut d'une entière généralité.
Nous avons cru devoir détailler, avec tout la précision possible,
la demonstration qu'il avait indiquée."

Now, this is not quite fair, as you see; with the best of intentions

63a.

EDITORS

ITHACA, NEW YORK, U. S. A.

Duhem does not seem fully to comprehend the situation. I have done all I can consistent with the fact that we do not wish to refuse a paper from him; this is written, therefore, that you may understand our position in the matter.

Yours faithfully

Professor J. Willard Gibbs
Yale University

New Haven, Connecticut