A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 42
... infinity , then C is the same for all spherical surfaces enclosing the whole of the internal boundaries . For if such a sphere be displaced parallel to x * , without alteration of size , the rate at which C varies in consequence of this ...
... infinity , then C is the same for all spherical surfaces enclosing the whole of the internal boundaries . For if such a sphere be displaced parallel to x * , without alteration of size , the rate at which C varies in consequence of this ...
Page 45
... infinity , but is bounded internally by one or more closed surfaces . We assume , for the * See Reprint , Article XIII . Also Thomson and Tait , Natural Philosophy , Appendix A ( d ) . This method is often attributed by German writers ...
... infinity , but is bounded internally by one or more closed surfaces . We assume , for the * See Reprint , Article XIII . Also Thomson and Tait , Natural Philosophy , Appendix A ( d ) . This method is often attributed by German writers ...
Page 46
... infinity , its value is everywhere determinate . Of more importance in our present subject is the theorem that do dn if the normal velocity be zero at every point of the internal boundary , and if the fluid be at rest at infinity , then ...
... infinity , its value is everywhere determinate . Of more importance in our present subject is the theorem that do dn if the normal velocity be zero at every point of the internal boundary , and if the fluid be at rest at infinity , then ...
Page 47
... infinity tends everywhere to the constant value C. do The same result holds even if the normal velocity be not dn zero over the internal boundary ; for in the theorem of Art . 46 M is divided by r , which is in our case infinite . 52 ...
... infinity tends everywhere to the constant value C. do The same result holds even if the normal velocity be not dn zero over the internal boundary ; for in the theorem of Art . 46 M is divided by r , which is in our case infinite . 52 ...
Page 48
... infinity . Generally , a region such that n irreconcileable paths , and no more , can be drawn between any two points of it , or such that n— - 1 ( simple ) irreconcileable non - evanescible circuits , and 48 [ CHAP . III . IRROTATIONAL ...
... infinity . Generally , a region such that n irreconcileable paths , and no more , can be drawn between any two points of it , or such that n— - 1 ( simple ) irreconcileable non - evanescible circuits , and 48 [ CHAP . III . IRROTATIONAL ...
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Common terms and phrases
angle angular velocity Ave Maria Lane axes axis C. J. CLAY Cambridge University Press centre Christ's College circle circuit CLAY & SONS co-ordinates component constant corresponding Crown 8vo cyclic Demy 8vo denote direction dT dT dx dx dx dy dz dy dy dydz Edited element equation of continuity equations of motion Fellow finite fluid forces formula formulæ given Green's Theorem Hence independent circuits infinitely small infinity integral internal boundary irrotational motion liquid LL.D mass moving Notes obtain origin P. G. TAIT parallel particle perpendicular plane xy portion Professor quantities radius RENDEL HARRIS satisfied shews side simply-connected solid sphere St John's College stream-lines surface theorem theory Thomson Trans Trinity College University of Cambridge University Press Warehouse velocity-potential vortex waves zero аф
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