19. Proceeding as in § 16 for the determination of the C.P. of an area, the same argument will show that an inclining couple due to the movement of a weight P through a distance c will cause the ship to heel through an angle [theta] about an axis FF´ through F, which is conjugate to the direction of the movement of P with respect to an ellipse, not the momental ellipse of the water-line area A, but a confocal to it, of squared semi-axes a² - hV/A, b² - hV/A, (1) h denoting the vertical height BG between C.G. and centre of buoyancy. The varying direction of the inclining couple Pc may be realized by swinging the weight P from a crane on the ship, in a circle of radius c. But if the weight P was lowered on the ship from a crane on shore, the vessel would sink bodily a distance P/wA if P was deposited over F; but deposited anywhere else, say over Q on the water-line area, the ship would turn about a line the antipolar of Q with respect to the confocal ellipse, parallel to FF´, at a distance FK from F FK = (k² - hV/A)/FQ sin QFF´ (2) through an angle [theta] or a slope of one in m, given by 1 P P V sin [theta] = --- = ----- = --- · -------- FQ sin QFF´, (3) m wA·FK W Ak² - hV where k denotes the radius of gyration about FF´ of the water-line area. Burning the coal on a voyage has the reverse effect on a steamer. HYDRODYNAMICS 20. In considering the motion of a fluid we shall suppose it non-viscous, so that whatever the state of motion the stress across any section is normal, and the principle of the normality and thence of the equality of fluid pressure can be employed, as in hydrostatics. The practical problems of fluid motion, which are amenable to mathematical analysis when viscosity is taken into account, are excluded from treatment here, as constituting a separate branch called "hydraulics" (q.v.). Two methods are employed in hydrodynamics, called the Eulerian and Lagrangian, although both are due originally to Leonhard Euler. In the Eulerian method the attention is fixed on a particular point of space, and the change is observed there of pressure, density and velocity, which takes place during the motion; but in the Lagrangian method we follow up a particle of fluid and observe how it changes. The first may be called the statistical method, and the second the historical, according to J. C. Maxwell. The Lagrangian method being employed rarely, we shall confine ourselves to the Eulerian treatment. _The Eulerian Form of the Equations of Motion._ 21. The first equation to be established is the _equation of continuity_, which expresses the fact that the increase of matter within a fixed surface is due to the flow of fluid across the surface into its interior.