Mathematical and Physical Papers, Volume 1University Press, 1880 - Hydrodynamics |
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Page 3
... portion of the paper , since in the two classes of steady motion to which the paper relates , namely those of motion in two dimen . sions , and of motion symmetrical about an axis , the three analogous equations are reduced to one , and ...
... portion of the paper , since in the two classes of steady motion to which the paper relates , namely those of motion in two dimen . sions , and of motion symmetrical about an axis , the three analogous equations are reduced to one , and ...
Page 27
... portion of each surface , separately . Such a portion may be either finite or infinitesimal . In fact , in some of the cases of motion that will be presently given , where is expressed by a double integral with a function under the ...
... portion of each surface , separately . Such a portion may be either finite or infinitesimal . In fact , in some of the cases of motion that will be presently given , where is expressed by a double integral with a function under the ...
Page 35
... portion of this fluid contains solid bodies bounded by cylindrical surfaces perpendicular to these planes . The whole being at first at rest , suppose that the surfaces of these solids are moved in any manner , the motion being in two ...
... portion of this fluid contains solid bodies bounded by cylindrical surfaces perpendicular to these planes . The whole being at first at rest , suppose that the surfaces of these solids are moved in any manner , the motion being in two ...
Page 40
... portion of an infinitely extended fluid be disturbed by the motion of solid bodies , or otherwise , if all the fluid beyond a certain distance from the part disturbed were at first at rest , the velocity at a great distance will ...
... portion of an infinitely extended fluid be disturbed by the motion of solid bodies , or otherwise , if all the fluid beyond a certain distance from the part disturbed were at first at rest , the velocity at a great distance will ...
Page 51
... portion of the fluid , whose radius is r , and whose centre is near the solid , so that dS refers to the surface of this portion . Let us now suppose r to become infinite : then the second side of ( a ) will vanish , provided p , remain ...
... portion of the fluid , whose radius is r , and whose centre is near the solid , so that dS refers to the surface of this portion . Let us now suppose r to become infinite : then the second side of ( a ) will vanish , provided p , remain ...
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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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