sound approximate theory was given by J. Boussinesq in 1871,
who obtained an equation for their form, and a value for the velocity in agreement with experiment. Other methods of approximation were given by Rayleigh and J. McCowan. In
connection with deep-water waves, Osborne Reynolds gave in
1877 the dynamical explanation for the fact that a group of such waves advances with only half the rapidity of the individual waves.
The solution of the problem of the general motion of an ellipsoid in a fluid is due to the successive labours of Green
(1833), Clebsch (1856), and Bjerknes (1873). The free
motion of a solid in a liquid has been investigated by W. Thomson,
Kirchhoff, and Horace Lamb. By these labours, the
motion of a single solid in a fluid has come to be pretty well understood, but the case of two solids in a fluid is not developed
so fully. The problem has been attacked by W. M. Hicks.
The determination of the period of oscillation of a rotating liquid spheroid has important bearings on the question of the origin of the moon. G. H. Darwin's investigations thereon,
viewed in the light of Riemann's and Poincaré's researches,
seem to disprove Laplace's hypothesis that the moon separated
from the earth as a ring, because the angular velocity was too great for stability; Darwin finds no instability.
The explanation of the contracted vein has been a point of
much controversy, but has been put in a much better light by the application of the principle of momentum, originated by Froude and Rayleigh. Rayleigh considered also the reflection
of waves, not at the surface of separation of two uniform media, where the transition is abrupt, but at the confines of two media between which the transition is gradual.
The first serious study of the circulation of winds on the
earth's surface was instituted at the beginning of the second quarter of this century by H. W. Dové, William C. Redfield, and
James P. Espy, followed by researches of W. Reid, Piddington,
and Elias Loomis. But the deepest insight into the wonderful