Mathematical and Physical Papers, Volume 1University Press, 1880 - Hydrodynamics |
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Page vi
... taken up . Mathe- maticians have been too little in the habit of considering the mechanical difficulty of setting up in type the expressions which they so freely write with the pen ; and where the setting up can be facilitated with only ...
... taken up . Mathe- maticians have been too little in the habit of considering the mechanical difficulty of setting up in type the expressions which they so freely write with the pen ; and where the setting up can be facilitated with only ...
Page x
... taken between infinite limits SECTION IV . - Examples of the application of the formulæ proved in the preceding sections 279 • 286 Supplement to a paper on the Theory of Oscillatory Waves Index 314 327 ERRATA . P. 103 , 1. 14 , for ...
... taken between infinite limits SECTION IV . - Examples of the application of the formulæ proved in the preceding sections 279 • 286 Supplement to a paper on the Theory of Oscillatory Waves Index 314 327 ERRATA . P. 103 , 1. 14 , for ...
Page 8
... taken as the boundary of the fluid . Thus for Ukr3 cos 30 we have for the lines of motion or -wr2 + kr3 cos 30 C ........ -wr2 + k { 4 ( rcos 0 ) 3 – 3r2 . r cos 0 } = C · ( 7 ) , . ( 8 ) , which therefore are cubic curves , recurring ...
... taken as the boundary of the fluid . Thus for Ukr3 cos 30 we have for the lines of motion or -wr2 + kr3 cos 30 C ........ -wr2 + k { 4 ( rcos 0 ) 3 – 3r2 . r cos 0 } = C · ( 7 ) , . ( 8 ) , which therefore are cubic curves , recurring ...
Page 20
... taken an exact differential . It is true that in motion in two dimensions there is one sort of rotatory motion for which that quantity is an exact differential ; but if a close vessel , filled with fluid at first at rest , be made to ...
... taken an exact differential . It is true that in motion in two dimensions there is one sort of rotatory motion for which that quantity is an exact differential ; but if a close vessel , filled with fluid at first at rest , be made to ...
Page 33
... taken posi- По n n tively ; and since by hypothesis ƒ ( 0 ) is finite for all values of from 0 to 2π , it follows that neither C nor D can be numerically greater than a constant quantity which is independent of n . The same will be true ...
... taken posi- По n n tively ; and since by hypothesis ƒ ( 0 ) is finite for all values of from 0 to 2π , it follows that neither C nor D can be numerically greater than a constant quantity which is independent of n . The same will be true ...
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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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