**Hydrodynamical** methods received increased attention and the investigation of the movements of the ocean by means of physico-mathematical devices developed as a result of the older work of Bjerknes, continued chiefly by Helland-Hansen and Sandstrom.

The empirical data on which the **hydrodynamical** investigations are based are: (I) observed velocities and directions of oceanic currents and drifts; (2) salinity; (3) density; (4) temperature of the sea water in situ; (5) oceanic soundings.

Although modern mercurial pumps have assumed a multiplicity of forms, their actions can be reduced to two principles, one statical, the other **hydrodynamical** - at the same time instruments have been devised utilizing both these principles.

The **hydrodynamical** equations with moving axes, taking into account the mutual gravitation of the liquid, become dp +4 p Ax+ du - vR {-wQ?

In the general motion again of the liquid filling a case, when a = b, 52 3 may be replaced by zero, and the equations, **hydrodynamical** and dynamical, reduce to d =- 2+ 2 J, = 2 x22111, d = 2 2`2 (+/'15-Om) (1 yy y n`t dt a +c dt a +c dt a +c) dc2, a2-1-c2 d122 a2 c2 dt ="2) +a2= G2y 71' dt = 121 1 - a 2 -c 2SJ, (19) of which three integrals are e +777 r z y 2= L -?2J2, (20) (a2 + c2) 2 2 121+14 =M+ 2c2(a2-c2)1 ' (21) 121+522hN = + x24 2,2 and then (dt / 2 = (a2 + c 2) 2(° v 2 - 12171) 2 4C4 2 2 - (+ c2)2?(E+77) (?

But the **hydrodynamical** discovery of Helmholtz that a vortex in a perfect liquid possesses certain permanent characteristics has been applied by Sir W.

Since the phase of vibration depends upon the time elapsed, it is always the same at the same point in space, and thus the motion is steady in the **hydrodynamical** sense, and the boundary of the jet is a fixed surface.