Mathematical and Physical Papers, Volume 1University Press, 1880 - Hydrodynamics |
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Page 17
... 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 adjacent elements of a fluid in motion is normal to their common surface ...
... 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 adjacent elements of a fluid in motion is normal to their common surface ...
Page 22
... , are denoted by small letters . The latter class serve to determine the forms of the arbitrary functions contained in the integrals of the former . ( ) being an arbitrary function of t , which 22 ON SOME CASES OF FLUID MOTION .
... , are denoted by small letters . The latter class serve to determine the forms of the arbitrary functions contained in the integrals of the former . ( ) being an arbitrary function of t , which 22 ON SOME CASES OF FLUID MOTION .
Page 24
... former and not the latter is the true solution of the problem . The fact that the analytical conditions of a problem in fluid motion , as far as those conditions depend on the velocities , may be satisfied by values of those velocities ...
... former and not the latter is the true solution of the problem . The fact that the analytical conditions of a problem in fluid motion , as far as those conditions depend on the velocities , may be satisfied by values of those velocities ...
Page 33
... former set of series do not alter abruptly , it follows that cannot alter abruptly . The same may be proved in a similar manner of the differential coefficients of 4. The other infinite series expressing the value of which occur in this ...
... former set of series do not alter abruptly , it follows that cannot alter abruptly . The same may be proved in a similar manner of the differential coefficients of 4. The other infinite series expressing the value of which occur in this ...
Page 36
... former . The motion of translation of the axis of the cylinder will differ from a recti- linear motion by quantities depending on 2 : the motion of rotation about its axis will be of the order , but will have no effect on the fluid ...
... former . The motion of translation of the axis of the cylinder will differ from a recti- linear motion by quantities depending on 2 : the motion of rotation about its axis will be of the order , but will have no effect on the fluid ...
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Common terms and phrases
according angle apply approximation arbitrary axes axis become infinite Cambridge Philosophical Society canal centre co-ordinates condition Consequently considered constant convergent series corresponding cosines cylinder Demy Octavo denote depth determined direction discontinuous divergent series dx dy elastic equal equation essentially convergent ether exact differential expansion expression finite force formula friction function given h vanishes Hence homogeneous function horizontal increases inertia integral length limit molecules moment of inertia observed obtained Octavo order of approximation oscillation oscillatory waves paper parallel parallelepiped particles perpendicular plane Poisson positive pressure quantities ratio rectangular refracting respect result satisfied shew shewn sines solid solitary wave sphere St John's College suppose surface tangential theorem theory tion variables velocity of propagation wave motion whence zero ηπα аф
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