Transactions of the Cambridge Philosophical Society, Volume 5University Press, 1835 - Science |
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a₁ angle application attraction axes axis becomes body c₁ cause coefficient of h consequently considered contain corresponding deduced Definite Integrals denote density determined diameter differential dimensions direction distance effect ellipsoid entire function equal equation equilibrium evidently expanded experiments expression finite fluid force formula given Hence infinite integer law of motion length limits line of pressure mass membrane method multiplied nodes observed obtain optic axes perpendicular plane plate positive preceding produced quantity radius rational and entire rational function reciprocal functions rectangular co-ordinates represent satisfy self-reciprocal shew sphere substituting suppose surface theory tion transient function tube V₁ V₂ vanish variable velocity vibration vis viva voussoirs αλ αξ
Popular passages
Page 151 - ... 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 160 - ... that the condition of the moving body with respect to motion and action, is a cause of any change in the circumstances of its motion ; and from this it follows that these circumstances are determined entirely by the forces extraneous to the body itself. 23. This mode of considering the question shows us in what manner the laws of motion may be said to be proved by their simplicity, which is sometimes urged as a proof. They undoubtedly have this distinction of the greatest possible simplicity,...
Page 102 - 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 141 - ... MECHANICAL EUCLID; containing the Elements of Mechanics and Hydrostatics, demonstrated after the manner of the Elements of Geometry; and including the Propositions fixed upon by the University of Cambridge, as requisite for a Degree.
Page 386 - ... some advantage might thus be obtained, and the attractions in both cases, deduced from one common formula which would only require the auxiliary variable u 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...
Page 159 - The nature of the truth which belongs to the laws of motion will perhaps appear still more clearly, if we state, in the following tabular form, the analysis of each law into the part which is necessary, and the part which is empirical. First Law. Second Law. Third Law. Necessary. Velocity does not change without a cause. The accelerating quantity of a force is measured by the acceleration produced. Reaction is equal and opposite to action. Empirical. The time for which a body has already been in...
Page 302 - ... divide itself into six distinct portions, of which four will revolve about the points S, S', Q, Q' and A, as represented in the figure 16. Now this is what is uniformly observed to take place in the fall of the arch. Gauthey, having occasion to destroy a bridge, caused one of its arches to be isolated from the rest; and, the adhesion of the cement being sufficient to counteract the tendency of the pressure to rupture the piers, he caused them to be cut across. The whole then at once fell, the...
Page 302 - 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 those where the rupture finally took place. This fact presents a remarkable confirmation of the theory expounded in this paper. It is manifest, that according to that theory, with any variation in...
Page 292 - These limits 1 The resistance of surfaces is not exerted exclusively in the direction of the normal, according to an hypothesis, which was probably introduced into the theory of Statics in order to simplify the investigations of those who originated that science, but which there seems no reason for retaining any longer. It is exerted in an infinite number of different directions included within a certain angle to the normal, or rather within the surface of a certain right cone, having the normal...
Page 303 - Q', about which the two upper portions of the arch have a tendency to turn, and about which the material is first observed to yield, has long been known to practical men. The French engineers have named these points the points of rupture of the arch ; and the determination of their position by a tentative method forms an important feature in the theory which they have applied to this important branch of Statics. The theory of the equilibrium of the groin and that of the dome are precisely analogous...