## The Quarterly Journal of Pure and Applied Mathematics, Volume 1J.W. Parker, 1857 - Mathematics |

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### Common terms and phrases

algebraical angle ARTHUR CAYLEY axis becomes body caustic CAYLEY centre circle coefficients coincident points condition conic conic section coordinates corresponding curve cusps degree denote determined dF dF differential double tangents dx dy elastic elements ellipsoid equal equation expression factor finite finite differences fluid force forme cubique formula function Geometrical Geometrical Theorem given gives Hence hodographs infinite integer integral J. J. SYLVESTER lignes Malfatti's Problem method na² ouales parallelepiped pass perpendicular plane point of contact points of intersection polar quantities refracted relation respect result roots sides solution substituting suppose surface theorem tion touch triangle Trinity College u₂ vanish variables whence zero ΦΩ

### Popular passages

Page 80 - PRIZE," be awarded every two years to the author of the best Essay on some subject of Pure Mathematics, Astronomy, or other branch of Natural Philosophy. 2. That the...

Page 33 - THE rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides.* Let ABCD be any quadrilateral inscribed in a circle, and join AC, BD ; the.

Page 81 - ... to enclose another, folded up, having the candidate's name and college written within. The papers containing' the names of those candidates who may not succeed will be destroyed unopened. Any candidate is at liberty to send in his exercise printed or lithographed.

Page 57 - A BODY which is either emitting heat, or altering its .£\. dimensions against resisting forces, is doing work upon matter external to it. The mechanical effect of this work in one case is the excitation of thermal motions, and in the other the overcoming of resistances. The body must itself be altering in its circumstances, so as to contain a less store of work within it by an amount precisely equal to the aggregate value of the mechanical effects produced; and conversely, the aggregate value of...

Page 80 - The problem may be treated on the supposition that the system of rings is exactly or very approximately concentric with Saturn, and symmetrically disposed about the plane of his equator, and different hypotheses may be made respecting the physical constitution of the rings. It may be supposed, (1.) that they are rigid; (2.) that they are fluid, or in part aeriform; (3.) that they consist of masses of matter not mutually coherent. The question will be considered to be answered by ascertaining, on...

Page 73 - From thermodynamic theory* it is concluded that cold is produced whenever a solid is strained by opposing, and heat when it is strained by yielding to, any elastic force of its own, the strength of which would diminish if the temperature were raised ; but that, on the contrary, heat is produced when a solid is strained against, and cold when it is strained by yielding to, any elastic force of its own, the strength of which would increase if the temperature were raised.

Page 74 - If a wire already twisted be suddenly twisted further, always, however, within its limits of elasticity, cold will be produced ; and if it be allowed suddenly to untwist, heat will be evolved from itself (besides heat generated externally by any work allowed to be wasted, which it does in untwisting). It is assumed that the torsional rigidity of the wire is diminished by an elevation of temperature, as the writer of this article...

Page 374 - If two circular hodographs, having a common chord, which passes through, or tends towards, a common centre of force, be cut...

Page 81 - ... name and college written within. The papers containing the names of those candidates who may not succeed will be destroyed unopened. Any candidate is at liberty to send in his exercise either written (but not in his own hand), or printed, or lithographed.

Page 70 - ... arrangement of actual pieces of matter may be made, constituting a homogeneous whole when considered on a large scale (being, in fact, as homogeneous as writers adopting the atomic theory in any form consider a natural crystal to be), which shall have an arbitrarily prescribed value for each one of these twenty-one coefficients. No one can legitimately deny for all natural crystals, known and unknown, any property of elasticity, or any other mechanical or physical property, which a solid composed...