Mr. R. Templeton's Remarks suggesting doubts respecting the Mr. C. Brooke on the Dynamical Theory of Electricity Prof. Sylvester's Note on the Properties of the Test Operators which occur in the Calculus of Invariants, their Derivatives, Analogues, and Laws of Combination; with an incidental application to the development in a Maclaurinian series of any power of the Logarithm of an augmented Variable.... 461 Proceedings of the Royal Society :— On the Influence of the Earth's Rotation on the Deviation of Projectiles from Rifled Cannon, by M. Martin de Brettes.. 478 Mr. J. Gill on the Temperature of the Vapours of Boiling Sa- 481 Page Mr. P. M. Duncan on the Madreporaria of the Infra-lias 544 Mr. H. Woodward on some points in the structure of the 545 On the Tangent Photometer, by Dr. F. Bothe 546 On the Conductivity of Mercury for Heat, by G. Gripon 547 Index 548 PLATES. I. Illustrative of Prof. R. Bunsen's Paper on Flame Reactions, IV. Illustrative of Mr. R. Gill's Paper on an Air-pump without Clearance VI. Illustrative of Mr. R. Templeton's Paper on the Index of Refraction of the Lens. I. On the Determination of the Energy and Entropy of a Body. By Professor R. CLAUSIUS*. IN N the second Number for this year of the Zeitschrift für Mathematik und Physik there is a paper by Bauschinger, chiefly relating to the integral which occurs in the second funda dQ mental theorem of the mechanical theory of heat, where dQ denotes an element of the quantity of heat which a body takes up in the course of any reversible change of condition, and T the absolute temperature of the body at the moment of absorbing this element of heat. Bauschinger developes an expression which represents the value of the integral for finite changes of condition under certain simplifying circumstances, and which, for the case where the final condition is the same as the initial condition, and the body accordingly goes through a circular process, becomes equal to nothing. In consequence of this last circumstance, Bauschinger supposes that the equation he has developed expresses a general principle, which includes, as a special case, my principle of the equivalence of transformations in circular processes. I cannot say that I agree with this view of the import of his developments. In the equation which I established for reversible circular processes, there is * Translated from the Zeitschrift für Mathematik und Physik, vol. xi. part 1, p. 31. Phil. Mag. S 4. Vol. 32. No. 213. July 1866. B Page Mr. P. M. Duncan on the Madreporaria of the Infra-lias 544 Mr. H. Woodward on some points in the structure of the 545 On the Tangent Photometer, by Dr. F. Bothe 546 On the Conductivity of Mercury for Heat, by G. Gripon 547 Index. 548 PLATES. I. Illustrative of Prof. R. Bunsen's Paper on Flame Reactions. II. III. Illustrative of Prof. R. Bunsen's Paper on the Phenomena observed in the Absorption-spectrum of Didymium, IV. Illustrative of Mr. R. Gill's Paper on an Air-pump without Clearance V. Illustrative of Mr. R. Walker's Paper on Ancient Shell Mounds at St. Andrews. VI. Illustrative of Mr. R. Templeton's Paper on the Index of Refraction of the Lens. I. On the Determination of the Energy and Entropy of a Body. By Professor R. CLAUSIUS*. N the second Number for this year of the Zeitschrift für Mathematik und Physik there is a paper by Bauschinger, chiefly relating to the integral, which occurs in the second fundamental theorem of the mechanical theory of heat, where dQ denotes an element of the quantity of heat which a body takes up in the course of any reversible change of condition, and T the absolute temperature of the body at the moment of absorbing this element of heat. Bauschinger developes an expression which represents the value of the integral for finite changes of condition under certain simplifying circumstances, and which, for the case where the final condition is the same as the initial condition, and the body accordingly goes through a circular process, becomes equal to nothing. In consequence of this last circumstance, Bauschinger supposes that the equation he has developed expresses a general principle, which includes, as a special case, my principle of the equivalence of transformations in circular processes. I cannot say that I agree with this view of the import of his developments. In the equation which I established for reversible circular processes, there is * Translated from the Zeitschrift für Mathematik und Physik, vol. xi. part 1, p. 31. Phil. Mag. S 4. Vol. 32. No. 213. July 1866. B |