Mathematical and Physical Papers, Volume 1University Press, 1880 - Hydrodynamics |
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Page 30
... referred to the old axes , which are themselves 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 ...
... referred to the old axes , which are themselves 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 ...
Page 31
... referred to polar co - ordinates r , e , in a plane perpendicular to the axis , r being measured from the axis . Let a be the radius . of the inner surface , b that of the outer , f ( 0 ) the normal velocity of any point of the inner ...
... referred to polar co - ordinates r , e , in a plane perpendicular to the axis , r being measured from the axis . Let a be the radius . of the inner surface , b that of the outer , f ( 0 ) the normal velocity of any point of the inner ...
Page 36
... referred to axes fixed in space , which after differentiation we might suppose to coincide with others fixed in the body . But the additional terms so introduced de- pending on the square of the velocity , which by hypothesis is ...
... referred to axes fixed in space , which after differentiation we might suppose to coincide with others fixed in the body . But the additional terms so introduced de- pending on the square of the velocity , which by hypothesis is ...
Page 50
... referred to axes fixed in space . Let Ox , Oy , be rectangular axes passing through the centre of any section of the cylinder , the angle which the direction of motion of the axis makes with Ox , ' the inclination of any radius vector ...
... referred to axes fixed in space . Let Ox , Oy , be rectangular axes passing through the centre of any section of the cylinder , the angle which the direction of motion of the axis makes with Ox , ' the inclination of any radius vector ...
Page 57
... solid ( Art . 8 ) . I have however retained it , in order to render the solution of the problem in the present article independent of the proposition referred to . аф do dr = аф rde A γ = - ON SOME CASES OF FLUID MOTION . 57.
... solid ( Art . 8 ) . I have however retained it , in order to render the solution of the problem in the present article independent of the proposition referred to . аф do dr = аф rde A γ = - ON SOME CASES OF FLUID MOTION . 57.
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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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