Cambridge Mathematical Journal, Volumen3;Volumen7Duncan Farquharson Gregory, Robert Leslie Ellis, William Thomson Baron Kelvin, Norman Macleod Ferrers Macmillan, Barclay and Macmillan, 1848 |
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angle ARTHUR CAYLEY axes axis bisects body centre circle coefficients coincide cone of revolution considered constant corresponding directrix curve cyclic plane deduced denote differential directive planes directrix distances double contact dx dx dx dy dz electricity electrified ellipse ellipsoid enveloping equal equation evanescent expression finite fixed points fluid focal conic foci focus force function geometrical Hence hyperbola hyperboloid infinite integral intersection limit lines of curvature locus modulus motion normal osculating parallel particles passing perpendicular points of contact polar pole conic positive principal plane proper fraction quantity radius ratio real or imaginary respectively result right line secant plane second order shew side solid solid angle sphere spherical surface straight line suppose surface of revolution symbol tangent plane theorem theory umbilicar velocity vertex
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Página 256 - ... of a beam previously to the application of an external force have been strained to the utmost, when, by the application of such force, however small, they are still farther displaced from their positions of relaxation, they must necessarily undergo a permanent alteration in their...
Página 145 - PE as radius ; is equal to the angle between the radii, EP and EC, of the two spheres. Hence, by considering the isosceles triangle ECE', we find that the cosine of the obliquity is equal to \EE' EE' , • .. ,. vr/r or to , and we arrive at the preceding expression LI, 2a for K 12.
Página 214 - Differentiating the first of these equations with respect to y and the second with respect to x, subtracting...
Página 145 - A very small cone is said to be cut obliquely, when the section is inclined at any finite angle to an orthogonal section ; and this angle of inclination is called the obliquity of the section. The area of an orthogonal section of a very small cone is equal to the area of an oblique section in the same position, multiplied by the cosine of the obliquity. Hence the area of an oblique section of a small cone is equal to the quotient obtained by dividing the product of the square of its distance from...
Página 253 - If, after this, all external stress be removed from the bar, it will assume a position of equilibrium, in which the outer particles will be strained in the direction opposite to that in which it was twisted, and the inner ones in the same direction as that of the twisting, the two sets of opposite couples thus produced among the particles of the bar balancing one another.
Página 254 - It is easy to show that the line of separation between the particles strained in the one direction, and those in the other, is a circle whose radius is f of the radius of the bar. The particles in this line are evidently subject to no strain* when no external couple is applied. The bar with its new molecular arrangement may now be subjected, as often as we...
Página 87 - V can be a solution of (A). The analysis given above, especially when interpreted in various cases of abrupt variations in the value of a, and of infinite or evanescent values, through finite spaces, possesses very important applications in the theories of heat, electricity, magnetism, and hydrodynamics, which may form the subject of future communications.
Página 184 - That the business of Logic is with the relations of classes, and with the modes in which the mind contemplates those relations. (2) That antecedently to our recognition of the existence of propositions, there are laws to which the conception of a class is subject, — laws which are dependent upon the constitution of the intellect, and which determine the character and form of the reasoning process.
Página 256 - It appears to me that the defect of elasticity, which he has shown to occur even with very slight strains, exists only when the strain is applied for the first time ; or, in other words, that if a beam has already been...