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A HISTORY OF MATHEMATICS.

oped 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 correlations that exist among the varied motions of the atmosphere was obtained by William Ferrel (1817–1891). He was born in Fulton County, Pa., and brought up on a farm. Though in unfavourable surroundings, a burning thirst for knowledge spurred the boy to the mastery of one branch after another. He attended Marshall College, Pa., and graduated in 1844 from Bethany College. While teaching school he became interested in meteorology and in the subject of tides. In 1856 he wrote an article on "the winds and currents of the ocean." The following year he became connected with the Nautical Almanac. A mathematical paper followed in 1858 on "the motion of fluids and solids relative to the earth's