Hicks was one of the first students of J.C. Maxwell.
He pioneered in vortex dynamics including the theory of vortex rings.
In particular, he gave a derivation of the formula for the speed of a thin
cored vortex ring, over which there was some controversy.
"This result was given without proof by Sir W. Thompson in an appendix to
a translation of Helmholtz' paper, Phil. Mag.(4), xxxiii, 511(1867)...
It was verified by Hicks, Phil. Tnans. A, clxxvi. 756(1985)..."
Hydrodynamics, Lamb(1932) p.241
This error, observed e.g. in J.J. Thomson's
'Teatise on the motion of vortex rings'(1883),
was more serious than it may seem, because it spoiled
a Hamiltonian structure underlying the 3D Euler equations.
Fluid dynamics has a long history and it is a highly difficult subject
mathematically. One should not be surprised at paucity and sporadic nature
of exactly worked out solutions.
For example, A.B. Basset's 'A treatise on hydrodynamics with numerous
examples' (1888) collects some important cases. Its cover on Dover's
reprint version (1961) says
"Of particular value to the advanced student is the great amount of
documentation it contains. The results and methods of hundreds of papers
by such men as J.J. Thompson, A.E.H. Love, Hicks, Greenhill, G.H.Darwin,
Besant, Lamb, Kirchhoff and other turn-of-the-century investigators who
created modern hydrodynamics are presented here in a convenient and logical
order. The original papers in which these results first appeared are
practically (if not actually) impossible to find elsewhere. "
But even this is now out of print...
"His main line of work was mathematical, however. In 1880, there was no
complete text-book on hydrodynamics - Lamb's treatise had not yet matured -
and a very full report by Hicks to the British Association on the progress
in this subject (British Association Reports, 1881-2) greatly
stimulated work in the science, and is of lasting value."
"William Mitchinson Hicks 1850-1934"
by S.R. Milner
"Obituary Notices of the Royal Society of London"
No.4, pp.392-393 December 1935
His complete list of publications may be found here. If you are interested in getting
one of the papers, please let me know.
Some of his books in the public domain
"Elementary dynamics of particles and solids" W.M. Hicks
"A treatise on the analysis of spectra, based on an essay to which
the Adams prize was awarded in 1921" W.M. Hicks
To get their PDFs, go to http://www.archive.org/details/texts and search "William Mitchinson Hicks" in Texts.