The Cambridge and Dublin Mathematical Journal, Volume 1Macmillan, 1846 - Mathematics |
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angles angular velocity ARTHUR CAYLEY axis B₁ body centre of gravity coefficients confocal conic constant coordinates corresponding cos² courbes curves deduced denote derivatives determined dielectric differential distance dx dy dx² dy dz electricity ellipse equal equation equimomental axes equimomental surfaces expression factors force formula functions geometrical fractions given Hence hyperbola hyperboloid inertia round integral intersection Lemniscate line of curvature locus mathematical momental ellipsoid moments of inertia multiplied obtained P₁ parallel perpendicular plane positive principal axes quantities quotient respect result rotation scalar second order sin² solid squares suppose symbol tangent theorem theory tion V₁ values vanish variables vector x₁ Y₁ αμ µ³ ΦΩ
Popular passages
Page 76 - An Essay on the application of Mathematical Analysis to the Theories of Electricity and Magnetism...
Page 129 - ... the percussive action is the same as if the whole mass of the body were concentrated at that point, is called the center of percussion. This point is located at the same point as the center of oscillation. CENTER REAMERS. A " center reamer " is a reamer the teeth of which meet in a point.
Page 88 - ... would in their condition and action exactly resemble what I consider to be the condition and action of the particles of the insulating dielectric itself.
Page 88 - If the space round a charged globe were filled with a mixture of an insulating dielectric, as oil of turpentine or air, and small globular conductors, as shot, the latter being at a little distance from each other so as to be insulated, then these...
Page 197 - Article ; for the product of the squares ot the differences of all the roots is made up of the product of the squares of the differences of the roots of...
Page 86 - All the views which Faraday has brought forward, and illustrated or demonstrated by experiment, lead to this method of establishing the mathematical theory, and, as far as the analysis is concerned, it would, in most general propositions, be even more simple, if possible, than that of Coulomb. (Of course the analysis of particular problems would be identical in the two methods.) It is thus that Faraday arrives at a knowledge of some of the most important of the general theorems, which, from their...
Page 83 - By this idea he has been led to some very remarkable views upon induction, or, in fact, upon electrical action in general. As it is impossible that the phenomena observed by Faraday can be incompatible with the results of experiment which constitute Coulomb's theory, it is to be expected that the difference of his ideas from those of Coulomb must arise solely from a different method of stating, and interpreting physically, the same laws : and farther, it may, I think, be shown that either method...
Page 92 - ... but the particles of a solid non-conductor must be considered as assuming a polarized state when under the influence of free electricity, so as to exercise attractions or repulsions on points at a distance, which, with the action due to the charged surfaces, produce the resultant force at any point. It is no doubt possible that such forces at a distance may be discovered to be produced entirely by the action of contiguous particles of some intervening medium, and we have an analogy for this in...
Page 168 - X, /-t, v, without the assistance of the invariable plane, and Jacobi's discovery of the theorem of the Ultimate Multiplier induced me to resume the problem, and at least attempt to bring it so far as to obtain a differential equation of the first order between two variables only, the multiplier of which could be obtained theoretically by Jacobi's discovery. The choice of two new variables to which the equations of the problem led me, enabled me to effect this in a simple manner ; and the differential...
Page 93 - ... point. It is no doubt possible that such, forces at a distance may be discovered to be produced entirely by the action of contiguous particles of some intervening medium, and we have an analogy for this in the case of heat, where certain effects which follow the same laws are undoubtedly propagated from particle to particle. It might also be found that magnetic forces are propagated by means of a second medium, and the force of gravitation by means of a third. We know nothing, however, of the...