...commonly called the velocitypotential. Thus a knowledge of the function F, for all values of x, z, t, completely defines the displacement and the velocity...an application of fundamental hydrokinetics gives where g denotes gravity ; IT the uniform atmospheric pressure on the free surface ; and p the pressure...

...determination of F we have, in virtue of the incompressibility of the fluid, S+S- ..................... ass, In virtue of this equation, the well-known primary...an application of fundamental hydrokinetics gives where g denotes gravity ; II the uniform atmospheric pressure on the free surface ; and p the pressure...

...determination of F we have, in virtue of the incompressibility of the fluid, 0 ..................... 033). In virtue of this equation, the well-known primary...an application of fundamental hydrokinetics gives where g denotes gravity ; II the uniform atmospheric pressure on the free surface ; and p the pressure...

...for brevity when convenient, is a function which may be called the displacementpotential ; and P(x, z, t) is what is commonly called the velocitypotential....is zero at every point infinitely distant from it tlie value of F is determinate throughout the fluid. The motion beinjj infinitesimal, and the density...

...commonly called the velocity-potential. Thus a knowledge of the function F, for all values of .r, ., t, completely defines the displacement and the velocity...an application of fundamental hydrokinetics gives where <j denotes gravity: II the uniform atmospheric pressure on the free surface ; and p the pressure...

...And towards the determination of F we have, in virtue of the incompressibility of the fluid, (133). In virtue of this equation, the well-known primary theory of Gauss and Given shows that, if F is given for every point of the free surface of the water, and is zero at every...