decrease of with the temperature should be so clearly brought out by observations performed on different liquids, at different tempera tures. (2.) On the Heat developed by the Compression of Air. Carnot demonstrates the following proposition : Equal volumes of all elastic fluids, when compressed to equal smaller volumes, disengage equal quantities of heat. This very remarkable proposition, given as a theorem by Carnot, was enunciated as a probable experimental law by Dulong; and it therefore affords a very powerful confirmation of Carnot's fundamental principle. Mr Joule of Manchester has made some important experiments on this subject. The view which he takes of a thermal "equivalent" for motive power is at variance with Carnot's theory, but his experimental results agree with its indications in a very satisfactory manner. In endeavouring to effect a comparison, I found that the following propositions are a consequence of Carnot's Theory. 1. In compressing a gas of which the temperature is kept invariable, the amount of work spent is exactly proportional to the quantity of heat developed. 2. The amount of work necessary to produce a unit of heat in this manner is the same, whatever be the gas operated on, but depends upon the temperature, being determined by the expression μ (1+ Et) (3.) On the Specific Heats of Gases. Carnot proves, as a theorem, that the excess of the specific heat* under a constant pressure above the specific heat at a constant volume is the same for all gases at the same temperature and pressure. This result agrees well with the experimental results obtained by Dulong. Carnot's theory affords the following determinate expression for the difference alluded to in the enunciation: E2 p μ (1+ Et)2 i.e. The "capacity for heat" of a unit of volume. (4.) Comparison of the Relative Advantages of the Steam-Engine and Air-Engine. In the steam-engine, with the expansive principle pushed to the utmost, as Carnot points out, the effective range of temperature, or the fall utilised, is from the temperature of the boiler to that of the condenser. The superior limit of temperature is restricted by the circumstance, that the pressure of saturated steam is enormously great for high temperatures; so that in practice, the temperature in the boiler is not in any ordinary engines so high as 150° per cent., but is in general very much below this limit. Carnot points out, that in this respect, the air-engine has a vast advantage over the steamengine; as there is no limit to the temperature in the hot part, except such as the preservation of the materials requires; and, therefore, in it an enormously greater portion of the whole fall, from the temperature of the coals to that of the atmosphere, may be made use of. In other respects, we have no reason a priori for giving a preference to one kind of engine above the other. We cannot, however, feel confident that any air-engine has yet been constructed, which is capable of economising the fall actually used, as well as is done by steam-engines, with their comparatively limited range of temperature, or even that the duty for fuel consumed has in any actual air-engine exceeded or even come up to the duty performed by the best steam-engines. (5.) On the Economy of Actual Steam-Engines. The following table affords a synoptic view of the performances and theoretical duties, in various actual cases. * When heat is transmitted from a body at 140°,† through an engine, to a body at 30°, the work due to each unit of heat is 439 foot-pounds. This is the theoretical duty" referred to in the last column in the table. * I am indebted to the kindness of Professor Gordon, of Glasgow, for the experimental data. † Pressure 3 atmospheres; 37 lb. on the square inch of the safety-valve. TABLE A. Various Engines in which the Boiler is at 140°, and the Condenser at 30°. 5. Note regarding an Experiment suggested by Professor Robison. By Professor J. D. Forbes. In his memoir of Dr Chalmers, lately read to this Society, Mr Ramsay has referred to an experiment which Dr Chalmers was anxious to have performed on the tide-wave in the Bay of Fundy. The object was to determine the earth's density by the attraction of the tide-wave on a plummet or spirit-level, on the same principle as Maskelyne's experiment on Schiehallion, but with the superior advantages arising from the perfect homogeneity of the attracting mass, and from the circumstance that all the observations might be made at a single station. The experiment might, in short, appear to unite the advantages both of Maskelyne's and Cavendish's methods of determining the earth's density. The suggestion was Dr Robison's, and Dr Chalmers had it from him. It is contained in the Elements of Mechanical Philosophy, Edit. 1804, page 339, and is given in the following words:" Perhaps a very sensible effect might be observed at Annapolis-Royal in Nova Scotia, from the vast addition of matter brought on the coast twice every day by the tides. The water rises there above 100 feet at spring tide. If a leaden pipe a few hundred feet long were laid on the level beach, at right angles with the coast, and a glass pipe set upright at each end, and the whole filled with water, the water will rise at the outer end, and sink at the end next the land as the tide rises. Such an alternate change of level would give the most satisfactory evidence. Perhaps the effect might be sensible on a very long plummet, or even a nice spirit-level." * It is needless to observe that the methods proposed by Dr Robison are not the best which might be suggested; but that, in consequence of the extreme simplicity of the observation, considered as a purely astronomical one, a deviation of the direction of gravity of only a very few seconds could be ascertained within small limits of error.* I thought it worth while to make the calculation approximately for an assumed height of the tide-wave. Had the result been at all encouraging I should have taken pains to ascertain, on good authority, the exact rise of the tide, and the circumstances of the locality whence the rise is greatest. I have calculated the horizontal attraction of a semicylinder of water 100 feet thick, and of about two, four, and eight miles radius upon a point at the extremity of the axis of such a semicylinder; because these conditions can easily be reduced to calculation, and because The micrometric observation of a plumb-line, as in a zenith sector, would be sufficient; or, as Professor Smyth has suggested to me, the view of the wires of a transit instrument, with a collimating eye-piece, as reflected in a mercury trough,—an observation, the accuracy of which may, he states, be brought within 2 of a second. VOL. II. Y they represent very approximately the circumstances of an attracted point placed at high water-mark on a vertical sea-wall facing a basin or estuary. The radius of the attracting mass of water being represented (more accurately) by 10,000, 20,000, and 40,000 feet, I find the influence of a tide-wave 100 feet thick upon a plumb-line to produce a deviation of only 0-"44 (forty-four hundredths of a second), 0-"50, and 0-53; the effect increasing extremely slowly with the radius, as might be expected. If the tide rose only fifty feet, the first effect would be reduced to 0:"246. Even the greatest of these calculated deviations affords no ground for hoping that the method of Robison could be applied with any success to determine the earth's density. It is rather singular that this ingenious suggestion is not once alluded to, so far as I am aware, by any writer on the figure and density of the earth; yet surely it was as worthy of notice as Dr Hutton's proposal to measure the attraction of an Egyptian pyramid.-(Phil. Trans. 1821.) The following Donations to the Library were announced :— American Journal of Science and Arts. Conducted by Professors 8vo.-By the Editor. Passages in the History of Geology. By Andrew C. Ramsay, F.G.S. 8vo. (2 copies.)-By the Author. On the Nature of Limbs. By Richard Owen, F.R.S. 8vo.--By the Author. Proceedings of the Philosophical Society of Glasgow. Vol. II. The Philosophy of Trade; or Outlines of a Theory of Profits and 1 |