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nydus/A History of MathematicsPublic

This text examines the transition from the Middle Ages to the Modern era, highlighting how the fall of Constantinople and the invention of the printing press catalyzed a revival of classical learning. It traces the shift toward scientific inquiry through the rise of pure mathematics and astronomy, detailing the intellectual struggle against established scholastic and ecclesiastical authority.

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Table of Contents

Applied Mathematics

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

surface." The subject was extended afterwards so as to embrace the mathematical theory of cyclones, tornadoes, water-spouts, etc. In 1885 appeared his Recent Advances in Meteorology. In the opinion of a leading European meteorologist (Julius Hann of Vienna), Ferrel has "contributed more

to the advance of the physics of the atmosphere than any other living physicist or meteorologist."

Ferrel teaches that the air flows in great spirals toward the poles, both in the upper strata of the atmosphere and on the earth's surface beyond the 30th degree of latitude; while the return current blows at nearly right angles to the above spirals, in the middle strata as well as on the earth's surface, in a zone comprised between the parallels 30° N. and 30° S. The idea of three superposed currents blowing spirals was first advanced by James Thomson, but was published in very

meagre abstract.

Ferrel's views have given a strong impulse to theoretical research in America, Austria, and Germany. Several objections raised against his argument have been abandoned, or have been answered by W. M. Davis of Harvard. The mathematical

analysis of F. Waldo of Washington, and of others,

has further confirmed the accuracy of the theory. The transport of Krakatoa dust and observations made on clouds point toward the existence of an upper east current on the equator, and Pernter has mathematically deduced from Ferrel's theory

the existence of such a current.

Another theory of the general circulation of the atmosphere was propounded by Werner Siemens of Berlin, in which an

attempt is made to apply thermodynamics to aërial currents.

Important new points of view have been introduced recently by Helmholtz, who concludes that when two air currents blow

one above the other in different directions, a system of air waves must arise in the same way as waves are formed on the

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