Mathematical and Physical Papers, Volume 1University Press, 1880 - Hydrodynamics |
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Page 12
... passing through the axis . Before considering this case , it may be well to prove a prin- ciple which will a little simplify our equations . The general equations of motion are , - v du dy 1 dp du du = X И W . ( 11 ) , ρ dx dx dz 1 dp ...
... passing through the axis . Before considering this case , it may be well to prove a prin- ciple which will a little simplify our equations . The general equations of motion are , - v du dy 1 dp du du = X И W . ( 11 ) , ρ dx dx dz 1 dp ...
Page 24
... passes through the value 27. The condition ( d ) then alone shews that the 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 ...
... passes through the value 27. The condition ( d ) then alone shews that the 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 ...
Page 38
... passing through the centre , w the angle which a plane passing through these two lines makes with a fixed plane through the latter , the value of corresponding to any radius vector comprised between a and b can be expanded in a ...
... passing through the centre , w the angle which a plane passing through these two lines makes with a fixed plane through the latter , the value of corresponding to any radius vector comprised between a and b can be expanded in a ...
Page 40
... passing through the origin . The motion will therefore be the same as that round a ball pendulum in an incompressible fluid , the centre of the ball being in the origin ; a case of motion which will be considered im- mediately . In ...
... passing through the origin . The motion will therefore be the same as that round a ball pendulum in an incompressible fluid , the centre of the ball being in the origin ; a case of motion which will be considered im- mediately . In ...
Page 43
... passing through the axis of rotation , since the alteration of pressure in that plane is insensible , the air would not have a tendency alternately to rush in and out at the slit . 10. Effect of a distant rigid plane on the motion of a ...
... passing through the axis of rotation , since the alteration of pressure in that plane is insensible , the air would not have a tendency alternately to rush in and out at the slit . 10. Effect of a distant rigid plane on the motion of a ...
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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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