The Quarterly Journal of Pure and Applied Mathematics, Volume 23James Joseph Sylvester, James Whitbread Lee Glaisher J.W. Parker, 1889 - Mathematics |
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A₁ angular velocity axes axis coefficients condition conic conjugate conjugate line constants coordinates corresponding cosec covariant cubic cubic surface denote determine differential equation ellipsoid equivalent escribed circles expressions finite fluid formula four function given Hence integral intersection isobaric Jacobian K₁ motion multiplied obtained orthogonal reciprocant P₁ P₂ pairs parabola Pascal lines points projective reciprocant pure reciprocant quantic radical axis radical centre radius reduced system satisfy the equation self-conjugate shew similitude simultaneous reciprocant solution sphere Substituting surface theorem touch triad undashed letters v₁ vanish weight XXIII Y₁ zero ди
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Page 87 - ... friction between the solid sphere and the fluid. Hence it appears that it is necessary to suppose that the particles move in planes passing through the axis of rotation, while they at the same time move round it. In fact, it is easy to see that from the excess of centrifugal force in the neighbourhood of the equator of the revolving sphere the particles in that part will recede from the sphere, and approach it again in the neighbourhood of the poles, and this circulating motion will be combined...
Page 95 - K 2 = 1 for air, we see how little the result result. is affected by this line magnetization, and how closely the effect of the sphere due to an inducing molecule is represented by a molecule at the image point. doublet to that of a vortex filament, by making use of the Amperean method of replacing the current by a magnetic shell bounded by its circuit, or the vortex filament by a doublet sheet bounded by it. For the case of a vortex filament which lies on a concentric sphere, we are clearly prompted...
Page 1 - Pt, /'„ ...'P, may be any given functions whatever of x, the differential equations so solved by the simple cycle of integrators cannot, except for the case of i = 2, be regarded as the general linear equation of the order i, because, so far as I know, it has not been proved for any value of i greater than 2 that the general equation, which in its usual form is as follows, _ d'u . d?~lu -du *»+*»*+... ft=-«-0 ............ (5).
Page 29 - Ex. 1. A particle under the action of no external forces is projected from an umbilicus of an ellipsoid, prove that the path is one of the geodesies defined by pD=ae.
Page 194 - II. On the circles, which may be described about the eight small circles of a sphere, taken by triads, which are inscribed in the triangles formed by three planes intersecting in the Centre.
Page 5 - ... zweiten Variation der potentiellen Energie des Systems ergiebt, dass dies nur möglich ist für Drähte und ebene oder gekrümmte Platten, die durch blosses Biegen oder Drehen deformirt werden können. Diese Fälle werden dann genauer discutirt und ein Beispiel wird durchgerechnet. St. C. CHREE. Further applications of a new solution of the equations of an isotropic elastic solid, mainly to various cases of rotating bodies. Quart. J.
Page 76 - ... with respect to x, the second with respect to y, the third with respect to z, and add the results.
Page 98 - FORSYTH. Systems of reduced simultaneous ternary forms equivalent to a given ternary form, which involves several sets of variables. Quart. J. xxm. 102-138. Wenn es sich um die Untersuchung und Aufstellung von Invarianten eines Systems von ternären Grundformen handelt, welche mehrere Reihen der Veränderlichen a;,, x.
Page 96 - ... of a filament which lies in a plane perpendicular to the radius vector drawn to the centre of the sphere, the ordinary analytical supposition being made that such action is ascribed to an element as gives the proper physical result when integrated for a complete filament. This leads to the result given by TC Lewis, Quarterly Journal, Vol. xvi. p. 338. The method just employed will also of course give an image for a filament not on a concentric sphere, but it is too complicated to be of any use....
Page 96 - mass of iron with a plane face near the inducing magnet. This assumption would be correct in the electrostatic problem, for which ^ is infinite ; but it is noticeable, and important with regard to the practical behaviour of iron in a magnetic field, that it is not true for the magnetic problem when...