perties of Solids; (2) The application of Thermo-dynamical principles to Capillarity; (3) The Continuity of the Liquid and Gaseous states of Matter. My best thanks are due to Dr John Hopkinson, F.R.S., both for the suggestion of these three points, and also for the original and very elegant investigation from first principles, contained in the first Appendix, and in the commencement of the second. My thanks are also due to Lord Rayleigh, F.R.S., E. J. Routh, Esq., and Professor James Stuart, for kindly looking through the first proof of the translation, and for various valuable suggestions made in connection with it. WALTER R. BROWNE. 10, VICTORIA CHAMBERS, WESTMINSTER, November, 1879. AUTHOR'S PREFACE. MANY representations having been made to the author from different quarters that the numerous papers "On the Mechanical Theory of Heat," which he had published at different times during a series of years, were inaccessible to many who, from the widespread interest now felt in this theory, were anxious to study them, he undertook some years back to publish a complete collection of his papers relating to the subject. As a fresh edition of this book has now become necessary, he has determined to give it an entirely new form. The Mechanical Theory of Heat, in its present development, forms already an extensive and independent branch of science. But it is not easy to study such a subject from a series of separate papers, which, having been published at different times, are unconnected in their form, although they agree in their contents. Notes and additions, however freely used to explain and supplement the papers, do not wholly overcome the difficulty. The author, therefore, thought it best so to re-model the papers that they might form a connected whole, and enable the work to become a text-book of the science. He felt himself the more bound to do this because his long experience as a lecturer on the Mechanical Theory of Heat at a Polytechnic School and at several Universities had taught him how the subject-matter should be arranged and represented, so as to render the new view and the new method of calculation adopted in this somewhat difficult theory the more readily intelligible. This plan also enabled him to make use of the investigations of other writers, and by that means to give the subject greater completeness and finish. These authorities of course have been in every case duly recognized by name. During the ten years which have elapsed since the first volume of papers appeared, many fresh investigations into the Mechanical Theory of Heat have been published, and as these have also been discussed, the contents of the volume have been considerably increased. Therefore in submitting to the public this, the first part of his new investigation of the Mechanical Theory of Heat, the author feels that, although it owes its origin to the second edition of his former volume, still, as it contains so much that is fresh, he may in many respects venture to call it a new work. BONN, December, 1875. R. CLAUSIUS. TABLE OF CONTENTS. § 1. Definition and Measurement of Mechanical Work § 2. Mathematical Determination of the Work done by variable com- § 3. Integration of the Differential Equations for Work done § 4. Geometrical interpretation of the foregoing results, and obser- 35 Relation between the two Specific Heats, and its application to calculate the Mechanical Equivalent of Heat Various Formulæ relating to the Specific Heats of Gases Numerical Calculation of the Specific Heat at Constant Volume Integration of the Differential Equations which express the First § 1. Description of a special form of Cyclical Process § 2. Result of the Cyclical Process §3. Cyclical Process in the case of a body composed partly of Liquid Proof that the Relation between the Heat carried over, and that § 8. Cyclical Processes of a more complicated character § 9. Cyclical Processes in which taking in of Heat and change of |