1. January 1862. Mittheilungen der Naturforschenden Gesellschaft in Zürich, vol. vii January, 48–48. Translated from thehaving been communicated to the Society on the 27th
2. Poggendorff's. Annalen, vol. xc 513–513.
3. Philosophical Magazine, S. 4. vol. ix 523–523. In my previous memoirs I have separated from one another theinternaland theexternalwork performed by the heat during the change of condition of the body. If the former be denoted bydI, and the latter bydW, the above equation becomesdQ+dH+AdI+AdW=0. (a) Since, however, the increase in the quantity of heat actually contained in a body, and the heat consumed by internal work during an alteration of condition, are magnitudes of which we commonly do not know the individual values, but only the sum of those values, and which resemble each other in being fully determined as soon as we know the initial and final conditions of the body, without our requiring to know how it has passed from the one to the other, I have thought it advisable to introduce a function which shall represent the sum of these two magnitudes, and which I have denoted by U. AccordinglydU=dH+AdI, (b) and hence the foregoing equation becomesdQ+dU+AdW=0; (c) and if we suppose the last equation integrated for any finite alteration of condition, we have Q+U+AW=0. (d) These are the equations which I have used in my memoirs published in 1850 and in 1854, partly in the particular form which they assume for the permanent gases, and partly in the general form in which they are here given, with no other difference than that I there took the positive and negative quantities of heat in the opposite sense to what I have done here, in order to attain greater correspondence with the equation (I.) given in § 1. The function U which I introduced is capable of manifold application in the theory of heat, and, since its introduction, has been the subject of very interesting mathematical developments by W. Thomson and by Kirchhoff (seeand Poggendorff'sAnnalen,vol. ciii. p. 177). Thomson has called it “the mechanical energy of a body in a given state,” and Kirchhoff “Wirkungsfunction.” Although I consider my original definition of it (see Pogg.Ann.vol. lxxix. p. 385, and vol. xciii. p. 484), as representing thesum of the heat added to the quantity already present and of that expended in internal work,starting from any given initial state, as perfectly exact, I can still have no objection to make against an abbreviated mode of expression
4. Philosophical Magazine, S. 4. vol. v 106–106. Edinburgh New Philosophical Journal, vol. ii. p. 120; Manual of the Steam-engine