Munro, Prof. J. E. Sliding Scales in the Coal and Iron Industries, 1885-89 The Local Taxation of Chief Rents O'Brien, Murrough A Description of Registration and Transfer of Stat. Soc. Ireland Rochester N. C. Manch. Geol. Soc. Journal X. 468 1890 Belfast N. H. Phil. Soc. Manch. Geol. Soc. Manch. Geol. Soc. Birm. Phil. Soc. Manch. Stat. Soc. Belfast N. H. Phil. Soc. Manch. Stat. Soc. Roch. Naturalist I. 473 Stat. Soc. Ireland Journal For 1890-91 X. 113 1891 1890 1891 119 1890 1 1891 448 1890 Section F ECONOMIC SCIENCE AND STATISTICS (continued). Bannister, M. C. Brown, M. W. Cotterell, A. P. I. On the Reconstruction of Viaducts on the On Irrigation and Water Storage in the Western States of America Comparative Experiments upon a Capell and Farren, G. Frew, A. The Reclamation of Waste Lands in the Clyde Estuary Work Liv'pool E. Soc. Trans. N. Eng. Inst. Manch. Geol. Soc Belfast N. H. Phil. Soc. Bristol Nat. Soc. Chesterf. Mid. Count. Inst. Belfast N. H. Phil. Soc.. Some Considerations of Asia Minor and its Glasgow Phil. Soc. Roman Camp at Springfield Antiquarian Discoveries at Kirkcudbright Anniversary Address-Field Sports and their Bearing on the National Character The Duggleby Howe' Tumulus at Cauldside The Grave at Conchistown The Fjort: the Manners and Customs of the The Gold Antiquities of Ireland Trans. II. 294 1891 Antiquities in Edinburgh Journal 220 207 1890 I. of Man N. H. A. Soc. Yn Lioar Manni I. 174 1891 263 Recent Discovery of a Bone Cave at Deep Dale, Liv'pool Geol. Soc.. near Buxton Abbreviated Title of Kermode, P. M. C. The Burial Mound known as Lezayre, Isle of Man Cronk Aust, The Antiquities of the Parish of Bride Notes on a Staffordshire Witch Brooch Note on Punctured Pottery found at Fryerning Essex F. C. Folk Lore in Tynron. Budbury Rings Danbury Camp, Essex Hæsten's Camps at Shoeburyness and Benfleet, An Ancient Custom observed at Cossey, Norfolk Ramsey Stone Implements 1891 Report and Trans. Proc. . Trans. 99 Report of a Committee, consisting of Messrs. J. LARMOR and G. H. BRYAN, on the present state of our knowledge of Thermodynamics, specially with regard to the Second Law. [Ordered by the General Committee to be printed among the Reports.] PART I.-RESEARCHES RELATING TO THE CONNECTION OF THE SECOND LAW WITH DYNAMICAL PRINCIPLES. DRAWN UP BY G. H. BRYAN. Introduction. 1. The present report treats exclusively of the attempts that have been made to deduce the Second Law of Thermodynamics from purely mechanical principles. Before considering the several methods in detail it may be well to summarise the meaning of the various terms which enter into the mathematical expressions of the laws of thermodynamics, with a view of showing more fully what conditions must be kept in view in establishing the dynamical analogues. This has been done more or less fully by several authors of papers on the subject, but more especially by von Helmholtz in his paper on the Statics of Monocyclic Systems.' The substance of this paper will be dealt with more fully later on in the present Report, but we will now mention the principal points touched on in the introduction. 2. Meaning of the Second Law.-Let a quantity dQ of work in the form of heat be communicated to a body whose absolute temperature is 0. Let E be the internal energy of the body, dW the work done against external forces by the change in the configuration of the body which takes place during the addition of dQ. It is not assumed that the external forces are conservative. Then the First and Second Laws are expressed by the equations where dS is a perfect differential of a quantity S, called the entropy, whose value depends only on the state of the body at the instant considered. The essential principle involved in the Second Law does not lie solely in the fact that dQ has an integrating divisor 0. In fact, if we assume that the state of a body is completely defined by two variables a and y, it must always be possible to put dQ in the form dQ=Mdx+Ndy, where M, N are functions of x and y only. And it is always possible to find an integrating factor for an expression of this form. Moreover, if one integrating factor can be found for dQ, an infinite number of such factors can be found. For in equation (2) let s be any arbitrary function of S; then we may write the equation in the form ds dQ=0ds. ds 1 Crelle, Journal, vol. xcviii. |