Mathematical and Physical Papers, Volume 1University Press, 1880 - Hydrodynamics |
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Page 17
... moving as if it were solid . Thus , oil is sufficiently fluid to obey the laws of fluid equilibrium , ( at least to a great extent ) , yet no one would suppose that oil in motion ought to be considered a perfect fluid . It would appear ...
... moving as if it were solid . Thus , oil is sufficiently fluid to obey the laws of fluid equilibrium , ( at least to a great extent ) , yet no one would suppose that oil in motion ought to be considered a perfect fluid . It would appear ...
Page 29
... moving in any manner , any additional motion of translation communicated to the vessel will not affect the relative motion of the fluid . For it is evident that on the supposition that the relative motion is not affected the equation ...
... moving in any manner , any additional motion of translation communicated to the vessel will not affect the relative motion of the fluid . For it is evident that on the supposition that the relative motion is not affected the equation ...
Page 30
... moving in space with velocities U , V , W. But if x ,, y1 , 21 , be the co - ordinates of the same particle referred to parallel axes fixed in space , we have x = x + fUdt , y1 = y + [ Vdt , z1 = 2 + fWdt , whence , supposing the time ...
... moving in space with velocities U , V , W. But if x ,, y1 , 21 , be the co - ordinates of the same particle referred to parallel axes fixed in space , we have x = x + fUdt , y1 = y + [ Vdt , z1 = 2 + fWdt , whence , supposing the time ...
Page 37
... moving force equal to its weight minus that of the fluid displaced , acting downwards through its centre of gravity , and having its mass increased by an unknown mass collected in the axis . Equating the time of oscil- lation so ...
... moving force equal to its weight minus that of the fluid displaced , acting downwards through its centre of gravity , and having its mass increased by an unknown mass collected in the axis . Equating the time of oscil- lation so ...
Page 41
... moving , we shall have f ( 0 ) = C cos 0 , F ( 0 ) = 0 ; .. P = 0 , P = C cos 0 , P = 0 , & c . , P ' = 0 , & c . , 0 and the value of for this instant is accurately - Ca3 a3 - which , when b = ∞ , becomes r + 272 ) cos 0 , Ca3 cos 0 ...
... moving , we shall have f ( 0 ) = C cos 0 , F ( 0 ) = 0 ; .. P = 0 , P = C cos 0 , P = 0 , & c . , P ' = 0 , & c . , 0 and the value of for this instant is accurately - Ca3 a3 - which , when b = ∞ , becomes r + 272 ) cos 0 , Ca3 cos 0 ...
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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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