Mathematical and Physical Papers, Volume 1University Press, 1880 - Hydrodynamics |
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Page 6
... axes remain in a section parallel to that axis . I shall now consider the general case , where udx + vdy need not be an exact differential . In this case p , u and v , are 6 ON THE STEADY MOTION OF INCOMPRESSIBLE FLUIDS .
... axes remain in a section parallel to that axis . I shall now consider the general case , where udx + vdy need not be an exact differential . In this case p , u and v , are 6 ON THE STEADY MOTION OF INCOMPRESSIBLE FLUIDS .
Page 19
... axes , but having different moments of inertia , these moments being given by infinite series , which converge with great rapidity . I have also in Art . 11 , given some cases of progressive motion , deduced on the supposition that the ...
... axes , but having different moments of inertia , these moments being given by infinite series , which converge with great rapidity . I have also in Art . 11 , given some cases of progressive motion , deduced on the supposition that the ...
Page 20
... axes of x , y , and z , of the whole velocity of any particle . In applying our investigations however to fluids such as they exist in nature , this principle must not be strained too far . When a body is made to revolve continually in ...
... axes of x , y , and z , of the whole velocity of any particle . In applying our investigations however to fluids such as they exist in nature , this principle must not be strained too far . When a body is made to revolve continually in ...
Page 21
... axes , of the acccelerating force acting on the particle whose co - ordinates are x , y , z . The only effect of such forces , in the case of a homogeneous , incompressible fluid , being to add the quantity pf ( Xdx + Ydy + Zdz ) to the ...
... axes , of the acccelerating force acting on the particle whose co - ordinates are x , y , z . The only effect of such forces , in the case of a homogeneous , incompressible fluid , being to add the quantity pf ( Xdx + Ydy + Zdz ) to the ...
Page 27
... axes in succession , the oscillations being very small . Then , in each case , as may be shewn by the same sort of ... axes of co - ordinates be parallel to the axes of the solid ; let x , y , z , be the co - ordinates of the centre of ...
... axes in succession , the oscillations being very small . Then , in each case , as may be shewn by the same sort of ... axes of co - ordinates be parallel to the axes of the solid ; let x , y , z , be the co - ordinates of the centre of ...
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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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