Abstract
PARIS. Academy of Sciences, September 5.—M. Hervé Mangon in the chair.—Photochronography applied to the dynamic problem of the flight of birds, by M. Marey. Having in a previous note shown that the kinematics of flight may be completely illustrated by photochronography, the author here proves that the same process contains all the elements necessary for solving the dynamic problem of flight; that is to say, for measuring the muscular forces and the work performed by the bird. Here is applied the mechanical principle that, if the mass of a body and the movements animating it be known, it is possible to deduce the value of the forces by which those movements are produced. On the photochronograph are measured all the displacements of the mass of the bird on the wing, together with the velocities of these movements. On the other hand the weight, that is, one of the forces to which the mass is submitted, is also known, while the resistance of the air, another of these forces, may be determined experimentally. Consequently the unknown quantity to be eliminated will be the muscular force of the bird with its momentum of action, and the value of its two components, one acting vertically against the weight, the other horizontally against the inert resistance of the mass and of the air. In these experiments the displacements of the bird are successively measured according to these two vertical and horizontal elements.—Measurement of luminous sensations in function of the quantities of light, by M. Ph. Breton. Since the invention of Bouguer's photometer it is known that if a dull white surface be disposed in contiguous zones receiving equi-different quantities of light, the perceptible contrasts between such zones are very far from being equal. To explain this phenomenon it has been suggested that the eye perceives the relation between two contiguous lighted surfaces. But the law (attributed to Fechner and Weber) based on this assumption—to the effect that, if several contiguous luminous surfaces are in geometrical progression, the sensations of the contrasts are equal—is shown to be incorrect by the experiment here described.—Observations of Brooks's new comet, made at the Observatory of Algiers with the 0.50-metre telescope, by MM. Trépied, Rambaud, and Sy.—Observations of the same comet made at the Observatory of Lyons with the 6-inch Brunner equatorial, by M. Le Cadet. The positions of this comet for August 29 and 30 and September I are also given from measurements taken by M. Gruey at the Observatory of Besançon. Its brightness is that of a star of the tenth magnitude.—Differential formulas for the variation of the elements of an orbit, by M. R. Radau. To correct a provisional system of elements it is often preferable to have recourse to the equations supplied by the ephemerides, rather than repeat the direct calculation of the elements. But the method is somewhat laborious, as the equations generally include six unknown quantities. The author, however, here shows that it is possible to give them a form in which the number of unknown quantities will be diminished without causing any complication in the calculation of the coefficients.—Note on M. Bertrand's problem, by M. Désiré André. A direct solution is given of this problem, followed by some remarks by M. Bertrand himself, pointing out its application to the question of chances in games of hazard as treated by Huygens. Moivre, Laplace, Lagrange, and Ampère. He offers a fresh solution of the problem: if a player stake the nth part of his fortune and continue the game indefinitely, what is the probability of his being ruined within a given number of rounds?
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Societies and Academies . Nature 36, 480 (1887). https://doi.org/10.1038/036480a0
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DOI: https://doi.org/10.1038/036480a0