3. A space is bounded by an ideal fixed surface S drawn in a homogeneous incompressible fluid satisfying the conditions for the continued existence of a velocity potential o under conservative forces. Prove that the rate per unit time at which energy flows across S into the space bounded by S is 20 09 as, where p is the density and on an element of the mormal to 8S drawn into the space considered. 4. Prove that if the velocity potential at any instant be 2 xyz, the velocity at any point (x+5, y+ n, z+() relative to the fluid at the point (x, y. z) where E, n, 5 are small, is normal to the quadratic xn + y$5+ zen = contant, with centre at (x, y, z). 5. Deduce from the principle that the kinetic energy set up is a minimum that, if a mass of incompressible liquid be given at rest, completely filling a closed vessel of any shape and if any motion of the liquid be produced suddenly by giving arbitrarily prescribed normal velocities at all points of its bounding surface subject to the condition of constant volume, the motion produced is irrotational