Transactions, Volume 5University Press, 1835 - Science |
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a₁ angle applied arbitrary constant attraction axes axis B₁ becomes body c₁ c₂ coefficient of h consequently considered contain corresponding deduced Definite Integrals density determined diameter differential dimensions direction distance effect ellipsoid entire function equal equilibrium evident expanded experiments expression finite fluid force formula given Hence infinite integer law of motion limits line of pressure mass membrane method multiplied nodes observed obtain optic axes P₁ perpendicular plane plate positive preceding produced quantity rational and entire rational function reciprocal functions represent S₁ satisfy the equation self-reciprocal shew sphere substituting suppose surface theory tion transient function tube V₁ vanish variable velocity vibration vis viva voussoirs αλ аф
Popular passages
Page 433 - Having given the radius of an arc of any colour in the secondary rainbow, find the ratio of the sine of incidence to the sine of refraction when rays of that colour pass out of air into water.
Page 400 - An Essay on the application of Mathematical Analysis to the Theories of Electricity and Magnetism...
Page 306 - ... would have, if P were entirely removed. Provided then, that if P were thus removed, the line of resistance would cut the surface, that is, provided the force P be necessary to the equilibrium ; it follows that by diminishing it, we may vary the direction and curvature of the line of resistance until we at length make it touch some point or other in the surface of the mass. And this is the limit ; for if the diminution be carried further, it will cut the surface, and the equilibrium will be destroyed....
Page 159 - ... same. 10. This force or action of bodies upon one another, is that which is meant in the Third Axiom, and we now proceed to consider the application of this axiom in mechanics. Pressures or forces such as I have spoken of, may be employed in producing tension only, and not motion ; in this case, each force prevents the motion which would be produced by the others, and the forces are said to balance each other, or to be in equilibrium. The science which treats of such cases is called Statics,...
Page 110 - The Subject of the Third Book I have also left imperfect, not having tried all the Experiments which I intended when I was about these Matters, nor repeated some of those which I did try, until I had satisfied my self about all their Circumstances. To communicate what I have tried, and leave the rest to others for farther Enquiry, is all my Design in publishing these Papers.
Page 309 - ... pressure and the form of the bounding surface subject to certain conditions not absolutely determining either. For instance, if the form of the intrados of an arch be given, and the direction of the intersecting plane be always perpendicular to it, and if I suppose the line of pressure to intersect this plane always at the same given angle with the perpendicular to it, so that the tendency of the pressure to thrust each from its place may be the same, — I may determine what under these circumstances...
Page 306 - ... to be known ; and varying it, within those limits, let us consider what may be its least and greatest values so as to satisfy the third condition. Let P act at a given point in AC and in a given direction. It is evident that by diminishing it under these circumstances, the line of resistance will be made continually to assume more nearly that direction which it would have, if P were entirely removed. Provided then, that if P were thus removed, the line of resistance would cut the surface, that...
Page 308 - ... circumstances : that line of resistance evidently unites with that of the arch at this point— this line of pressure is therefore completely known, and the conditions of the equilibrium of the piers or other abutments of the arch, and of the arch itself, are determined. I have hitherto considered the form of the solid to be given, together with the positions of the different sections made through it, and I have thence the forms of its lines of resistance and pressure, and their directions through...
Page 312 - ... until they fell. Their fall was always observed to be attended with the same circumstances. Before the arch finally yielded the stone also was observed to chip at the intrados about the points Q and Q', round which the upper portions of it finally revolved. Some experiments made by Professor Robison with chalk models were attended with slightly different results. Having loaded them at the crown until they fell, he observed first, that the points where the material began to yield were not precisely...
Page 396 - ... to become evanescent in the final result. The principal advantage however which arises from the introduction of the new variable u, depends on the property which a certain function V* then possesses of satisfying a partial differential equation, whenever the law of the attraction is inversely as any power n of the distance. For by a proper application of this equation we may avoid all the difficulty usually presented by the integrations, and at the same time find the required attractions when...