Mathematical Papers of the Late George Green ...Macmillan and Company, 1871 - 336 من الصفحات |
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angle angle of incidence applicable arising axes axis becomes belonging coefficients consequently constant quantity corresponding density determine differential direction distance dv dv dv dw dx dx dx dy dz dx dz dx² dy dx dy dy dz dx electric fluid element ellipsoid entire function equal to zero equilibrium evidently exact differential expression exterior finite formula give given Hence induced integral extending interior luminiferous ether magnetic medium Moreover motion obtain partial differential equation particles perfect conductor perpendicular plane preceding quantity of electricity radius rational and entire rectangular co-ordinates refracted wave represent shell sphere spherical substituted suppose surface of junction term theory tion total potential function tricity V₁ variable velocity vibrations wave's front wire µ² µ³ аф
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الصفحة 15 - OBSERVATIONS. The object of this Essay is to submit to Mathematical Analysis the phenomena of the equilibrium of the Electric and Magnetic Fluids, and to lay down some general principles equally applicable to perfect and imperfect conductors; but, before entering upon the calculus, it may not be amiss to give a general
الصفحة 10 - this proposition is to show, that when two similar conducting bodies communicate by means of a long slender canal, and are charged with electricity, the respective quantities of redundant fluid contained in them, will be proportional to the
الصفحة 14 - upon it; and it is hoped the difficulty of the subject will incline mathematicians to read this work with indulgence, more particularly when they are informed that it was written by a young man, who has been obliged to obtain the little knowledge he possesses, at such intervals and by such means, as other indispensable avocations which offer but few opportunities of mental improvement, afforded.
الصفحة 26 - may be considered as composed of two parts, one due to the sphere itself, the other due to the whole mass exterior to it: but the last part evidently becomes equal to zero when substituted for
الصفحة 74 - of the electric fluid, p, the value of the density near the apex 0, will be determined by the formula Now writing <£ for the angle formed by dx and dw, we have
الصفحة 73 - it results that, when the apex of the cone is directed inwards, the density of the electric fluid at any point p, near to it, is proportional to r
الصفحة 73 - exceeds w, this summit is directed outwards, and when the excess is not very considerable, n will be given as above: but 2/3 still increasing, until it becomes
الصفحة 37 - belonging to a point on the surface of any of these bodies. (5.) From what has been before established (art. 3), it is easy to prove, that when the value of the potential function V is given on any closed surface, there is but one function which can satisfy at the same time the equation
الصفحة 2 - for any assigned portion of the mass will always be the exact differential of some function." This function, it will be seen, is what is now known under the name of Potential Energy, and the above principle is in fact equivalent to stating that the sum of the Kinetic and Potential Energies of the system is constant.
الصفحة 10 - proposition complete, when the two coatings of the glass plate communicate with their respective conducting bodies, by fine metallic wires of any form.