Mathematical and Physical Papers, Volume 1University Press, 1880 - Hydrodynamics |
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Page 35
... expansion or contraction , or if the expansion of some of the solids should make up for the con- traction of the rest , then in general the most important part of the motion at a great distance will consist of a velocity C'cos 0./2 ...
... expansion or contraction , or if the expansion of some of the solids should make up for the con- traction of the rest , then in general the most important part of the motion at a great distance will consist of a velocity C'cos 0./2 ...
Page 39
... expansion may be performed by the usual formula , if not by inspection : then the first condition gives Σ { n Ya " 1- ( n + 1 ) Z , a- ( n + 2 ) } = ΣP ; and equating Laplace's coefficients of the same order , we get nY1an - 1 − ( n + ...
... expansion may be performed by the usual formula , if not by inspection : then the first condition gives Σ { n Ya " 1- ( n + 1 ) Z , a- ( n + 2 ) } = ΣP ; and equating Laplace's coefficients of the same order , we get nY1an - 1 − ( n + ...
Page 49
... expansion which is the same in all directions , but varies in any manner with the time . The value of o corresponding to a motion of translation of the cylinder is - Ca cos 0.r , C being the velo- city of the axis , and being measured ...
... expansion which is the same in all directions , but varies in any manner with the time . The value of o corresponding to a motion of translation of the cylinder is - Ca cos 0.r , C being the velo- city of the axis , and being measured ...
Page 55
... expansion given by equation ( 3 ) will enable us to get a result , and if it will , we need be in no fear that it is wrong ( Art . 2 ) . The same remarks will apply to the question of the possibility of the expansion of in the series of ...
... expansion given by equation ( 3 ) will enable us to get a result , and if it will , we need be in no fear that it is wrong ( Art . 2 ) . The same remarks will apply to the question of the possibility of the expansion of in the series of ...
Page 56
... ( 26 ′ ) , . ( 27 ) . Let P and Q be expanded in series of cosines of and its mul- tiples , so that P = P cos no , Q = Q , cos nė , 00 70 there being no sines in the expansions of P and 56 ON SOME CASES OF FLUID MOTION .
... ( 26 ′ ) , . ( 27 ) . Let P and Q be expanded in series of cosines of and its mul- tiples , so that P = P cos no , Q = Q , cos nė , 00 70 there being no sines in the expansions of P and 56 ON SOME CASES OF FLUID MOTION .
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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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