His researches in hydrodynamics were highly useful for marine engineering, while the reflecting and repeating circles, as improved by him, were of great service in nautical astronomy.
At a later period he was one of the leading contributors to the Encyclopaedia Britannica (seventh and eighth editions), the articles on Electricity, Hydrodynamics, Magnetism, Microscope, Optics, Stereoscope, Voltaic Electricity, &c., being from his pen.
Thus rational mechanics, based on the Newtonian Laws, viewed as mathematics is independent of its supposed application, and hydrodynamics remains a coherent and respected science though it is extremely improbable that any perfect fluid exists in the physical world.
One of the most successful labourers in the science of hydrodynamics at this period was Pierre Louis Georges Dubuat (1734-1809).
Two methods are employed in hydrodynamics, called the Eulerian and Lagrangian, although both are due originally to Leonhard Euler.
Now the kinetics of a medium in which the parts can have finite relative motions will lead to equations which are not linear - as, for example, those of hydrodynamics - and the phenomena will be far more complexly involved.
It is true that the theory of vortex rings in hydrodynamics is of a simpler type; but electric currents cannot be likened to permanent vortex rings, because their circuits can be broken and the element of cyclic steadiness on which the simplicity depends is thereby destroyed.
By his mode of regarding a liquid as a material system characterized by the unshackled mobility of its minutest parts, the separation between the mechanics of matter in different forms of aggregation finally disappeared, and the fundamental equation of forces was for the first time extended to hydrostatics and hydrodynamics.'
The branch of hydrodynamics which discusses wave motion in a liquid or gas is given now in the articles Sound and Wave; while the influence of viscosity is considered under Hydraulics.
Lamb, C. Chree, Lord Rayleigh); and to hydrodynamics (Lord Kelvin, Sir G.
Now it is shown in hydrodynamics that she velocity of propagation of waves in deep water is that acquired by a heavy body falling through half the radius of the circle whose circumference is the wave-length, or _ f_X _ ga 27rT 'I ' v2- 2r 2r pn This velocity is a minimum when X=2.7r gp' and the minimum value is v= 4 - p g For waves whose length from crest to crest is greater than X, the principal force concerned in the motion is that of gravitation.
Basset's Hydrodynamics, i.