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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.

00The 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.

00Although 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.

00The hydrodynamical equations with moving axes, taking into account the mutual gravitation of the liquid, become dp +4 p Ax+ du - vR {-wQ?

00In 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) (?

00Bryan, in which the analytical equations of motion are deduced of a perforated solid in liquid, from considerations purely hydrodynamical.

00But the hydrodynamical discovery of Helmholtz that a vortex in a perfect liquid possesses certain permanent characteristics has been applied by Sir W.

00Since 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.

00It is impossible within brief limits to convey more than a general idea of the work of a philosopher who published more than three hundred original papers bearing upon nearly every branch of physical science; who one day was working out the mathematics of a vortex theory of matter on hydrodynamical principles or discovering the limitations of the capabilities of the vortex atom, on another was applying the theory of elasticity to tides in the solid earth, or was calculating the size of water molecules, and later was designing an electricity meter, a dynamo or a domestic water-tap. It is only by reference to his published papers that any approximate conception can be formed of his life's work; but the student who had read all these knew comparatively little of Lord Kelvin if he had not talked with him face to face.

00Hydrodynamical 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.

00The 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.

00Although 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.

00The hydrodynamical equations with moving axes, taking into account the mutual gravitation of the liquid, become dp +4 p Ax+ du - vR {-wQ?

00In 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(Ã‚° v 2 - 12171) 2 4C4 2 2 - (+ c2)2?(E+77) (?

00Bryan, in which the analytical equations of motion are deduced of a perforated solid in liquid, from considerations purely hydrodynamical.

00But the hydrodynamical discovery of Helmholtz that a vortex in a perfect liquid possesses certain permanent characteristics has been applied by Sir W.

00Since 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.

00It is impossible within brief limits to convey more than a general idea of the work of a philosopher who published more than three hundred original papers bearing upon nearly every branch of physical science; who one day was working out the mathematics of a vortex theory of matter on hydrodynamical principles or discovering the limitations of the capabilities of the vortex atom, on another was applying the theory of elasticity to tides in the solid earth, or was calculating the size of water molecules, and later was designing an electricity meter, a dynamo or a domestic water-tap. It is only by reference to his published papers that any approximate conception can be formed of his life's work; but the student who had read all these knew comparatively little of Lord Kelvin if he had not talked with him face to face.

00

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