Mathematical and Physical Papers, المجلد 1University Press, 1880 |
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الصفحة x
... directions Supplement to a Memoir on some cases of Fluid Motion On the Theory of Oscillatory Waves On the Resistance of a Fluid to two Oscillating Spheres On the Critical Values of the Sums of Periodic Series 157 158 161 176 178 179 ...
... directions Supplement to a Memoir on some cases of Fluid Motion On the Theory of Oscillatory Waves On the Resistance of a Fluid to two Oscillating Spheres On the Critical Values of the Sums of Periodic Series 157 158 161 176 178 179 ...
الصفحة 8
... direction normal to the surface , which gives аф dx wy ) dy - ( 2 аф dy wx ) dx = 0 ...... ... ( a ) , at any point of the boundary . If ƒ ( x , y ) = 0 be the equation of the boundary , we must substitute - df / dxdf / dy for dy / dx ...
... direction normal to the surface , which gives аф dx wy ) dy - ( 2 аф dy wx ) dx = 0 ...... ... ( a ) , at any point of the boundary . If ƒ ( x , y ) = 0 be the equation of the boundary , we must substitute - df / dxdf / dy for dy / dx ...
الصفحة 11
... direction of motion , at each point of a section of the entering , and also of the issuing stream , to be such as any case requires , by supposing the fluid sent in and drawn out with the requisite velocity and in the requisite direction ...
... direction of motion , at each point of a section of the entering , and also of the issuing stream , to be such as any case requires , by supposing the fluid sent in and drawn out with the requisite velocity and in the requisite direction ...
الصفحة 17
... directions . The latter of these is a necessary consequence of the former , as has been shewn by Mr Airy * . An exactly simi- lar proof may be employed in Hydrodynamics , by which it may be shewn that , if the mutual action of two ...
... directions . The latter of these is a necessary consequence of the former , as has been shewn by Mr Airy * . An exactly simi- lar proof may be employed in Hydrodynamics , by which it may be shewn that , if the mutual action of two ...
الصفحة 24
... direction of x ; then shall C , v = 0 , w = 0 . For these values render uda + vdy + wdz an exact differential dp , where satisfies ( E ) ; they also satisfy ( a ) ; and , lastly , the value of q obtained by integrating equations ( F ) ...
... direction of x ; then shall C , v = 0 , w = 0 . For these values render uda + vdy + wdz an exact differential dp , where satisfies ( E ) ; they also satisfy ( a ) ; and , lastly , the value of q obtained by integrating equations ( F ) ...
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alter abruptly angle angular velocities approximation arbitrary axes axis become infinite Cambridge Philosophical Society canal centre co-ordinates condition Consequently considered constant convergent series corresponding cosines cylinder denote depth determined direction discontinuous displaced distance divergent series dx dy dx² dy dz dy² elastic equal equations of motion equilibrium ether exact differential expansion expression finite fluid motion formula friction function given h vanishes Hence homogeneous function incompressible fluid increases inertia integral limit luminiferous ether mass molecules moment of inertia observed obtained order of approximation oscillation paper parallel particles perpendicular plane Poisson pressure quantities ratio refracting respect result satisfied shew shewn sines solid sphere suppose surface theorem theory tion U₁ variables velocity of propagation waves whence zero ηπα аф
مقاطع مشهورة
الصفحة 114 - The capability which solids possess of being put into a state of isochronous vibration shews that the pressures called into action by small displacements depend on homogeneous functions of those displacements of one dimension. I shall suppose moreover, according to the general principle of the superposition of small quantities, that the pressures due to different displacements are superimposed, and consequently that the pressures are linear functions of the displacements.
الصفحة 142 - ... in the terrestrial methods of determining the velocity of light, the light comes back along the same path again, so that the velocity of the earth with respect to the ether would alter the time of the double passage by a quantity depending on the square of the ratio of the earth's velocity to that of light, and this is quite too small to be observed.
الصفحة 181 - ... accurate means of comparing theory and experiment in a class of motions in which they have not hitherto been compared, so far as I am aware. When a box of the form of a rectangular parallelepiped, filled with fluid and closed on all sides, is made to perform small oscillations, it appears that the motion of the box will be the same as if the fluid were replaced by a solid having the same mass, centre of gravity, and principal axes as the solidified fluid, but different principal moments of inertia....
الصفحة 126 - there seems no line of demarcation between a solid and a viscous fluid...
الصفحة 281 - U unless the convergency of the series (67) becomes infinitely slow when h vanishes. 'The convergency of the series is here said to become infinitely slow when, if n be the number of terms which must be taken in order to render the sum of the neglected series numerically less than a given quantity e, which may be as small as we please, n increases beyond all limit as h decreases beyond all limit. 'DEMONSTRATION. If the convergency do not become infinitely slow it will be possible to find a number...
الصفحة 182 - It is not absolutely necessary thaty(r") and F (r) should always have the same sign. In forming the equations of motion M. Navier adopts the hypothesis of a symmetrical arrangement of the particles, or at least, which leads to the same result, neglects the irregular part of the mutual action of neighbouring molecules. The equations at which he arrives are those which would be obtained from the common...
الصفحة 165 - Gréent» who has considered the case in which the depth is infinite. The oscillatory waves just considered are those which are propagated uniformly in fluid of which the depth is everywhere the same. When this condition is not satisfied, as for instance when the waves are propagated in a canal whose section is not rectangular, it is desirable to know how the velocity of propagation and the form of the waves are modified by this circumstance. There is one such case in which a solution has been obtained....
الصفحة 158 - Tom. ii. p. 42. III. The discharge of gases through small orifices. IV. Theory of sound. V. Simultaneous oscillations of fluids and solids. VI. Formation of the equations of motion when the pressure is not supposed equal in all directions. I. Although the common equations of hydrodynamics have been so long known, their complexity is so great that little has been done with them except in the case in which the expression usually denoted by udx+vdy+wdz (A.) is the exact differential of a function of...
الصفحة 50 - A similar result may be proved to be true for any solid symmetrical with respect to two planes at right angles to each other, and...
الصفحة 88 - In most cases in which it would be interesting to apply the theory of friction of fluids, the density of the fluid is either constant or may without sensible error be regarded as constant, or else changes slowly with the time. In the first two cases the results would be the same and in the third nearly the same whether T)v were equal to zero or not.