A Treatise on the Mathematical Theory of the Motion of Fluids |
From inside the book
Results 1-5 of 30
Page 3
... particle . The equations obtained on these two plans are conveniently designated , as by German mathematicians , the Eulerian ' and the ' Lagrangian ' forms of the hydrokinetic equations , although both forms are in reality due to Euler ...
... particle . The equations obtained on these two plans are conveniently designated , as by German mathematicians , the Eulerian ' and the ' Lagrangian ' forms of the hydrokinetic equations , although both forms are in reality due to Euler ...
Page 4
... particle . This we shall denote by OF It a at the symbol being used to express a differentiation following the motion of the fluid . At the time t + dt the particle which at the time t was in the position ( x , y , z ) is in the ...
... particle . This we shall denote by OF It a at the symbol being used to express a differentiation following the motion of the fluid . At the time t + dt the particle which at the time t was in the position ( x , y , z ) is in the ...
Page 7
... particle lying in it must be wholly tangential ( or else zero ) , for otherwise we should have a finite flow of liquid across the surface , which contradicts the assumption that the latter is a boundary . The instantaneous rate of ...
... particle lying in it must be wholly tangential ( or else zero ) , for otherwise we should have a finite flow of liquid across the surface , which contradicts the assumption that the latter is a boundary . The instantaneous rate of ...
Page 8
... particles . If then we 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 ...
... particles . If then we 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 ...
Page 12
... particle of fluid , x , y , z its co - ordinates at time t . We here consider x , y , z as functions of the independent variables a , b , c , t ; their values in terms of these quantities give the whole history of every particle of the ...
... particle of fluid , x , y , z its co - ordinates at time t . We here consider x , y , z as functions of the independent variables a , b , c , t ; their values in terms of these quantities give the whole history of every particle of the ...
Other editions - View all
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 constant corresponding Crown 8vo curves const cyclic Demy 8vo denote direction dt dt dx dx dx dy dz dy dy Edited element equation of continuity Fellow finite fluid forces formulæ given Green's Theorem Hence impulse infinitely small infinity integral internal boundary irrotational irrotational motion J. E. SANDYS liquid LL.D mass moving Notes obtain origin P. G. TAIT P₁ parallel particle plane xy portion pressure Professor quantities radius RENDEL HARRIS satisfied shews simply-connected solid sphere St John's College stream-lines surface theorem Thomson Trinity College University of Cambridge University Press Warehouse velocity-potential vertical vortex waves zero аф
Popular passages
Page 7 - Wilson's Illustration of the Method of explaining the New Testament, by the early opinions of Jews and Christians concerning Christ.
Page 4 - Greek and English Testament, in parallel columns on the same page. Edited by J. SCHOLEFIELD, MA late Regius Professor of Greek in the University. New Edition, with the marginal references as arranged and revised by DR SCRIVENER.
Page 15 - Pindar. Olympian and Pythian Odes. With Notes Explanatory and Critical, Introductions and Introductory Essays. Edited by CAM FENNELL, MA, late Fellow of Jesus College. Crown 8vo. cloth. gs. The Isthmian and Nemean Odes by the same Editor. 9*.
Page 20 - A Treatise on the Theory of Determinants and their Applications in Analysis and Geometry. By ROBERT FORSYTH SCOTT, MA, Fellow of St John's College. Demy 8vo.
Page 6 - SCRIPTURES, &c. The Cambridge Paragraph Bible of the Authorized English Version, with the Text revised by a Collation of its Early and other Principal Editions...
Page 32 - Vols. Super Royal 8vo. £6. 6s. Also a limited Edition of the same, consisting of 120 numbered Copies only, large paper Quarto ; the woodcuts and steel engravings mounted on India paper ; price Twenty-five Guineas net each set.
Page 5 - The Missing Fragment of the Latin Translation of the Fourth Book of Ezra, discovered, and edited with an Introduction and Notes, and a facsimile of the MS., by ROBERT L.
Page 8 - The Pointed Prayer Book, being the Book of Common Prayer with the Psalter or Psalms of David, pointed as they are to be sung or said in Churches.
Page 12 - An Analysis of the Exposition of the Creed, written by the Right Rev. Father in God, JOHN PEARSON, DD, late Lord Bishop of Chester. Compiled...