Mathematical Papers of the Late George Green ...

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Macmillan and Company, 1871 - 336 من الصفحات

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الصفحة 239 - We are so perfectly ignorant of the mode of action of the elements of the luminiferous ether on each other, that it would seem a safer method to take some general physical principle as the basis of our reasoning, rather than assume certain modes of action...
الصفحة 269 - From the identity of this formula with that for the centre of gravity, it appears that the velocity of the great primary wave of translation of a fluid is that due to gravity acting through a height equal to the depth of the centre of gravity of the transverse section of the channel below the surface of the fluid. 7- The height of a wave may be indefinitely increased by propagation into a channel which becomes narrower in the form of a wedge, the increased height being nearly in the inverse ratio...
الصفحة 240 - of the advantages of this method, of great importance, is that we are " necessarily led by the mere process of the calculation, and with little care "on our part, to all the equations and conditions which are requisite and "sufficient for the complete solution of any problem to which it may be "applied.
الصفحة 310 - ... vibration, it will not be sufficient merely to allow for the loss of weight caused by the fluid medium, but that it will likewise be requisite to conceive the density of the body augmented by a quantity proportional to the density of this fluid.
الصفحة viii - In whatever way the elements of any material system may act upon each other, if all the internal forces exerted be multiplied by the elements of their respective directions, the total sum for any assigned portion of the mass will always be the exact differential of some function.
الصفحة 275 - Moreover, should the radius of the sphere of sensible action of the molecular forces bear any finite ratio to X, the length of a wave of light, as some philosophers have supposed, in order to explain the phenomena of dispersion, instead of an abrupt termination of our two media we should have a continuous though rapid change of state of the ethereal medium in the immediate vicinity of their surface of separation. And I have here endeavoured to...
الصفحة 3 - CAVENDISH, who having confined himself to such simple methods as may readily be understood by any one possessed of an elementary knowledge of geometry and fluxions, has rendered his paper accessible to a great number of readers; and although, from subsequent remarks, he appears dissatisfied with an hypothesis which enabled him to draw some important conclusions, it will readily be perceived, on an attentive perusal of his paper, that a trifling alteration will suffice to render the whole perfectly...
الصفحة 307 - In the case just alluded to, it is required to determine the circumstances of the motion of an indefinitely extended nonelastic fluid, when agitated by a solid ellipsoidal body, moving parallel to itself, according to any given law, always supposing the body's excursions very small, compared with its dimensions. From what will be shown in the sequel, the general solution of this problem may very easily be obtained. But as the principal object of our paper is to determine the alteration produced in...
الصفحة 14 - ... the radius of the spherical conductor to the thickness of the glass in that point. The total quantity of electricity contained in the interior of any number of equal and similar jars, when one of them communicates with the prime conductor and the others are charged by cascade, is precisely equal to that, which one only would receive, if placed in communication with the same conductor, its exterior surface being connected with the common reservoir.
الصفحة 188 - An Essay on the application of Mathematical Analysis to the Theories of Electricity and Magnetism...

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