As the Professor possesses several higher objectives, by Mr. Spencer, he has had executed by Mr. Grunow, at the same time with the Binocular, only an object-glass of 1 inch focus with which alone we have had an opportunity of trying the perform ance. This object-glass has a large angle and is corrected exquisitely for chromatic and spherical aberration. That difficult point in microscopy, a view into deep cavities, is perfectly attained. The eye of a fine needle by incident light, exhibited the walls of a cavity deeper than broad; an opened anther cell preserved in fluid and happening to lie edgewise, exhibited by transmitted light its walls with clear vision to the bottom of the depth; the fibres of the fringed end of a silk ribbon floated in space in different planes of superposition with an enlargement of distance in the perpendicular direction strikingly correspondent to their horizontal separation. No doubling or thickening of lines, mistiness, fog or uncertainty accompanied the views, but vision was brilliant. and clear, while thus looking into space instead of being as it were confined by an optical wall of limitation, to a single plane. Neither while thus looking far into space by magnifying distance in proportion to surface, was any thing lost in power of minute discrimination of lines and edges; these were sharply and clearly defined in short true shape and form were perceived in their actual proportions instead of being flattened, and an entire whole seen, as Schacht expresses it, "in optical sections;" and were exhibited simultaneously with minuteness of detail on surfaces. Thus may we congratulate ourselves that binocular vision, so long a desideratum in microscopical science, is at length attained; constituting, as it does, the first important step since the solution of the great problem of the achromatising of the microscope, and the power of enormously enlarging the aperture of the objective. New Haven, March, 1854. ART. IX.-Mechanical Action of Heat; by W. J. MACQUORN RANKINE. Gentlemen-I beg leave to address to you the following remarks on a formula referred to in the very able and interesting paper of Professor Frederick A. P. Barnard on "Heated Air considered as a Motive Power," published in the American Journal of Science for March. The formula in question represents the maximum efficiency of a perfect Thermo-dynamic Engine: that is to say, the greatest fractional portion of the total heat consumed which such an engine converts into motive power; and, in Prof. Barnard's notation, it is as follows: Let H represent the mechanical equivalent of total heat expended; W, the motive power developed; T', the absolute temperature at which heat is received by the elastic substance which works the engine; T,, the absolute temperature at which heat is given out; Then the efficiency of the engine is W = H T" (A.) This formula is ascribed by Professor Barnard to Professor William Thomson of Glasgow. The formula originally proposed by Professor Thomson is, however somewhat different in form from the above, being the following: where is the base of Napier's logarithms; J, "Joule's Equivalent" = 1390 foot-pounds per centigrade degree in liquid water; and ", "Carnôt's Function;" being an unknown function of temperature only, which has to be determined by experiment. This formula was deduced by Professor Thomson from a combination of Carnôt's principle, that the efficiency of a perfect thermodynamic engine is a function solely of the temperatures at which it receives and emits heat, with the law established experimentally by Joule, of the convertibility of the different forms of physical energy. It appeared in a paper on the Dynamical Theory of Heat, read to the Royal Society of Edinburgh in 1851, published in the 20th volume of their Transactions, and reprinted in the London, Edinburgh and Dublin Philosophical Magazine for 1852, Series 4th, volume 4th. During the same session of the Royal Society of Edinburgh, there was read the Fifth Section of my paper on the Mechanical Action of Heat, in which, from the hypothesis that heat consists in certain molecular oscillations or revolutions, I deduced the law, that the efficiency of a perfect thermodynamic engine is expressed by the difference between the absolute temperatures at which it receives and emits heat, divided by the greater of those absolute temperatures diminished by a constant which is the same for all substances; that is to say, W (C.) The constant x, if not absolutely inappreciable, is so small that no material error in practice can arise from neglecting it in comSECOND SERIES, Vol. XVIII, No. 52.-July, 1854. 9 puting the efficiency of engines. This reduces the formula C to identity with A. The section to which I have referred was published in the 20th volume of the Transactions of the Royal Society of Edinburgh, and re-printed in the London, Edinburgh and Dublin Philosophical Magazine for March, 1854. Professor Thomson afterwards pointed out, (in consequence of a suggestion by Mr. Joule) that if Carnôt's Function be supposed to have the following value μ = J the formula B is transformed into A. (D.) It is also obvious, that if Carnôt's Function have the value Although the law expressed by the equation C, being partly founded on hypothetical principles, was at first to a certain extent conjectural, yet it has subsequently being so closely confirmed by the experiments of Messrs. Regnault, Joule, and Thomson, that it may be regarded as almost, if not altogether, demonstrated. It is still, however, uncertain, whether the constant has an appreciable value. The values computed from the experiments range from 0 to 201 Centigrade; absolute temperatures being reckoned from a point 2740-6 Centigrade below melting ice, or 4940-28 below zero on Fahrenheit's scale. The constant represents the position, on the scale of a perfect-gas thermometer, of the point of total privation of heat. If the elasticity of a perfect gas arises wholly from heat, then this point coincides with the absolute zero of a perfect gas thermometer, and x=0. It gives me much gratification to find, that the conclusion to which Mr. Joule, Professor Thomson, and myself have been led by our researches, as to the great economy of fuel to be expected from the Air-Engine when its practical difficulties have been overcome, is confirmed by the opinion of an investigator who has so carefully examined the subject as Professor Barnard. 59 St. Vincent street, Glasgow, 14th April, 1854. ART. X.-On the Resistance experienced by Bodies falling through the Atmosphere; by ELIAS LOOMIS, Professor of Mathematics and Natural Philosophy in New York University. Ar the Cleveland meeting of the American Association, I presented a paper on the hail storm of July 1st, 1853, and introduced some computations for the purpose of determining the velocity. which hail stones acquire in falling through the atmosphere. These results were based upon the experiments of Hutton respecting the air's resistance to bodies in motion, as determined by a whirling machine. Since the case of a body revolving about a fixed axis is different from that of a body descending freely through the atmosphere under the action of gravity, I have endeavored to test these results by experiments upon the direct fall of bodies. For this purpose I have performed various experiments upon the velocity acquired by falling drops of water; also by small spheres made of cork; and have experimented with lumps of ice varying from the size of a pigeon's egg up to masses weighing more than two pounds. These results coincided tolerably well with those obtained by computation from Hutton's data, but I refrain from publishing them at present in the hope of being able to repeat them with greater care and with the advantage of a greater elevation. In the mean time I have sought for experiments of a similar kind made by other individuals. The experiments made at the request of Newton in St. Paul's Cathedral at London, seemed better suited to my purpose than any others I have found. There were two series of these experiments. In the first series, made in the year 1710, several hollow glass globes of about five inches in diameter were let fall from an elevation of 220 English feet, and the times of descent carefully measured. In the second series of experiments made in the year 1719, several bladders formed into spheres about five inches in diameter, were let fall from a height of 272 feet, and the times of descent carefully observed. For the purpose of deducing from these experiments the coefficient of resistance, I proceeded in the following manner. It is evident that the resistance to a falling body beginning from zero, continually increases with the increasing velocity of the body; and since the impelling force is constantly the same, while the resisting force always increases, it must happen that the latter will at length become equal to the former. When this result takes place, that is, when the resistance is just equal to the weight of the body, there can be no further increase of velocity, and the body must thenceforth descend with a uniform motion. I found that in the first series of Newton's experiments, the velocity of descent became sensibly uniform after a fall of 40 feet; and in the second series of experiments after a fall of 10 feet. I carefully computed the time of descent through the space just mentioned, and dividing the remaining distance by the remaining time of descent, obtained the terminal velocity, from which the coefficient of resistance is easily deduced. In these computations I made use of Hutton's formula which are as follows: w the weight of the body expressed in ounces, x = the space fallen through, v = the velocity acquired in falling through the space x, v' the terminal velocity of the body. = The following Table shows the results deduced from the first series of experiments with glass globes. Column first shows the weight of the globes in grains; column second shows their diameters in inches; column third shows the entire time of falling from a height of 220 feet; column fourth shows the velocity acquired in falling through a space of 40 feet; column fifth shows the time of falling 40 feet; column sixth shows the coefficient of resistance deduced from the time of descent; and column seventh shows the same coefficient reduced to a sphere of 5 inches in diameter by assuming the resistance to vary as the square of the diameter. Weights of Diamet'rs of Whole times Velocity in the globes, the globes, of falling. falling 40 ft. Coefficient of resistance. Do, reduced to al sphere of 5 in. Time of fall- |