A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 2
... draw three straight lines PA , PB , PC mutually at right angles , and let a plane whose direction - cosines relatively to these lines are l , m , n , passing infinitely close to P , meet them in A , B , C. across the Let * P , P1 , P2 ...
... draw three straight lines PA , PB , PC mutually at right angles , and let a plane whose direction - cosines relatively to these lines are l , m , n , passing infinitely close to P , meet them in A , B , C. across the Let * P , P1 , P2 ...
Page 8
... draw a surface parallel and infinitely close to F = 0 , and suppose it to move with the particles of which it is composed , the stratum of fluid which is included between this and F = 0 , and which in virtue of the continuity of the ...
... draw a surface parallel and infinitely close to F = 0 , and suppose it to move with the particles of which it is composed , the stratum of fluid which is included between this and F = 0 , and which in virtue of the continuity of the ...
Page 10
... drawn through P parallel to the axes of co - ordinates . Then if PA , PB , PC = a , ß , y respectively , we have dF F ÷ & c . , dx ' where F denotes the value of the function Fat P ( x , y , z ) . The rate of flow of matter into the ...
... drawn through P parallel to the axes of co - ordinates . Then if PA , PB , PC = a , ß , y respectively , we have dF F ÷ & c . , dx ' where F denotes the value of the function Fat P ( x , y , z ) . The rate of flow of matter into the ...
Page 16
... drawn from the particle ( a , b , c ) to the particles ( a + da , b , c ) , ( a , b + db , c ) , ( a , b , c + dc ) , respectively , is d ( x , y , z ) d ( a , b , c ) da db de , d ( x 。, yo , zo ) ( 28 ) , Po d ( a , b , c ) so that ...
... drawn from the particle ( a , b , c ) to the particles ( a + da , b , c ) , ( a , b + db , c ) , ( a , b , c + dc ) , respectively , is d ( x , y , z ) d ( a , b , c ) da db de , d ( x 。, yo , zo ) ( 28 ) , Po d ( a , b , c ) so that ...
Page 21
... drawn from point to point , so that its direction is everywhere that of the motion of the fluid . The differential ... draw a linear element ds in the direction ( l , m , n ) , the velocity resolved in this direction is lu + mv + nw , or ...
... drawn from point to point , so that its direction is everywhere that of the motion of the fluid . The differential ... draw a linear element ds in the direction ( l , m , n ) , the velocity resolved in this direction is lu + mv + nw , or ...
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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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