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algebraical angle arbitrary axes axis becomes Bernoullian numbers calculation Cayley centre century circles coefficients composite numbers conditions of solubility constant contains continued fraction coordinates corresponding cube root curves cylinder deduced denote determine differential equation distance divisors Edouard Lucas equal exceptional correlations expansion expression factors fluid formula function geometrical given gives H. J. S. Smith Hence hyperelliptic function infinity interpolation J. W. L. Glaisher Laplace's Laplace's equation limits line at infinity linear London Mathematical Society Mathematical method million motion multiplied natural numbers obtain paper parabola Paul Mansion places plane positive potential prime Prof Professor proof quantities radius relation respectively result Riemann's surface rotation satisfy sequences solution sphere spherical Spherical Harmonics square suppose tables tangent theorem values vanishes velocity wave surface whence write zero
Page 128 - Coll (communicated by Prof. Crofton, FRS) entitled "The Calculus of Equivalent Statements." A short account of this analytical method has been given in the July and November numbers (1877) of the Educational Times, under the name of Symbolical Language. The chief use at present made of it is to determine the new limits of integration when we change the order of integration or the variables in a multiple integral, and also to determine the limits of integration in questions relating to probability.
Page 128 - IT has often been remarked that, when a group of waves advances into still water, the velocity of the group is less than that of the individual waves of which it is composed ; the waves appear to advance through the group, dying away as they approach its anterior limit.
Page 128 - ... and velocities of propagation are so related in each case that there is no change of position relatively to the boat. The mode of composition will be best understood by drawing on paper two sets of parallel and equidistant lines, subject to the above condition, to represent the crests of the component trains.
Page 93 - B' drives in the contrary sense a graduated dial, the hand and dial rotating independently of each other about a common centre ; the increased reading of the hand on the dial is thus = Xdx...
Page 159 - ... functions are merely particular cases of Laplace's more general functions, but the fact seems to be very little known. Mr. Ferrers in his elementary treatise on Spherical Harmonics, makes no mention of Bessel's functions, and Mr. Todhunter in his work on these functions states expressly that Bessel'a functions are not connected with the main subject of the book.
Page 128 - ... when a group of waves advances into still water, the velocity of the group is less than that of the individual waves of which it is composed ; the waves appear to advance through the group, dying away as they approach its anterior limit. This phenomenon was, I believe, first explained by Stokes, who regarded the group as formed by the superposition of two infinite trains of waves, of equal amplitudes and of nearly equal wave-lengths, advancing in the same direction.
Page 95 - A'. And thus the throw (and therefore n) being variable, the velocity-ratio n\ is also variable. We may imagine the wheel A as carrying upon it a piece L sliding between guides, which piece L carries the pivot B of the link BC, and works by a rack on a toothed wheel a concentric with A, but capable of rotating independently thereof. Then if a rotates along with A, as if forming one piece therewith, it will act as a clamp upon L, keeping the distance of B from the centre of A, that is, the half-throw,...
Page 128 - Sylvester's construction for the mass centre o! a tetrahedral frustum. (3) On vortex-motion. The problem solved by Stokes as a general question of analysis, and subsequently by Helmholtz for the special case of fluid motion may be stated as follows : given the expansion and the rotation at every point of a moving substance, it is required to find the velocity at every point. The solution was exhibited in a very simple form. Zoological Society, November 6.— Mr.
Page 128 - On the triple generation of three-bar curves. // one ofthf threi-bar systems is a crossed rhomboid, the other two are kites. This follows from the known fact that the path of the moving point in both these cases is the inverse of a conic. But it is also intuitively obvious as soon as the figure is drawn, and thus supplies an elementary proof that the pith >•• the inverse of a conic in the case of a kite, which is not otherwise easy to get.