Philosophical Transactions of the Royal Society of London, Volume 175,Deel 1W. Bowyer and J. Nichols for Lockyer Davis, printer to the Royal Society, 1884 |
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Pagina 3
... functions of y . If we write in k'2 = k2 + ע ( 8 ) , ( 9 ) , we have as the most general solutions of ( 8 ) V1 = Ae - ky + Bethy 42 = Ce¬ky + De + k'y ( 10 ) , ( 11 ) . With respect to the value of k ' , we see from ( 9 ) that it is ...
... functions of y . If we write in k'2 = k2 + ע ( 8 ) , ( 9 ) , we have as the most general solutions of ( 8 ) V1 = Ae - ky + Bethy 42 = Ce¬ky + De + k'y ( 10 ) , ( 11 ) . With respect to the value of k ' , we see from ( 9 ) that it is ...
Pagina 6
... functions of 2nt . It is with the first only that we are here concerned . The mean value of the velocity parallel to x is thus u2 sin 2kx e 4n -By k cosh ky cos By + √2.ß sinh ky sin ( By— ‡ π ) —ke¬®v } . On account of the factor e ...
... functions of 2nt . It is with the first only that we are here concerned . The mean value of the velocity parallel to x is thus u2 sin 2kx e 4n -By k cosh ky cos By + √2.ß sinh ky sin ( By— ‡ π ) —ke¬®v } . On account of the factor e ...
Pagina 7
... function with arbitrary coefficients satisfying v = 0 . In the calculation of the first part we may identify v with da / dy * , on account of the smallness of k relatively to B. In this way our equation becomes d * p d ( By ) 4 nku 2 ...
... function with arbitrary coefficients satisfying v = 0 . In the calculation of the first part we may identify v with da / dy * , on account of the smallness of k relatively to B. In this way our equation becomes d * p d ( By ) 4 nku 2 ...
Pagina 12
... function , satisfying v = 0 , so that to the second order of approximation the fluid in contact with the plate may have no relative motion . The complementary function is whence y = ( A + By ) e - 2ky sin 2kx , = { B - 2k ( A + By ) 12 ...
... function , satisfying v = 0 , so that to the second order of approximation the fluid in contact with the plate may have no relative motion . The complementary function is whence y = ( A + By ) e - 2ky sin 2kx , = { B - 2k ( A + By ) 12 ...
Pagina 15
... functions of t , all the periodic quantities are proportional to eint , and write q for a2 + inv + inv , ( 62 ) ... function ' , satisfying v2p ' = 0 , as the motion corre- sponding thereto may be regarded as covered by y . whence ...
... functions of t , all the periodic quantities are proportional to eint , and write q for a2 + inv + inv , ( 62 ) ... function ' , satisfying v2p ' = 0 , as the motion corre- sponding thereto may be regarded as covered by y . whence ...
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