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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

that Fresnel's formulæ are correct, for these prophecies might have been made by other forms of the wave-theory. The theory was placed on a sounder dynamical basis by the writings of Cauchy, Biot, Green, C. Neumann, Kirchhoff, McCullagh,

Stokes, Saint-Venant, Sarrau, Lorenz, and Sir William Thomson.

In the wave-theory, as taught by Green and others, the luminiferous ether was an incompressible elastic solid, for

the reason that fluids could not propagate transverse vibrations. But, according to Green, such an elastic solid would transmit a longitudinal disturbance with infinite velocity. Stokes remarked, however, that the ether might act like a fluid in case of finite disturbances, and like an elastic solid in case of the infinitesimal disturbances in light propagation.

Fresnel postulated the density of ether to be different in different media, but the elasticity the same, while C. Neumann and McCullagh assume the density uniform and the elasticity different in all substances. On the latter assumption the direction of vibration lies in the plane of polarisation, and not perpendicular to it, as in the theory of Fresnel.

While the above writers endeavoured to explain all optical properties of a medium on the supposition that they arise entirely from difference in rigidity or density of the ether in the medium, there is another school advancing theories in which the mutual action between the molecules of the body and the ether is considered the main cause of refraction and dispersion.100 The chief workers in this field are J. Boussinesq,

W. Sellmeyer, Helmholtz, E. Lommel, E. Ketteler, W. Voigt,

and Sir William Thomson in his lectures delivered at the

Johns Hopkins University in 1884. Neither this nor the first-named school succeeded in explaining all the phenomena. A third school was founded by Maxwell. He proposed the

electro-magnetic theory, which has received extensive development

recently. It will be mentioned again later. According to Maxwell's theory, the direction of vibration does not lie exclusively in the plane of polarisation, nor in a plane perpendicular to it, but something occurs in both planes–-a magnetic vibration in one, and an electric in the other. Fitzgerald and

Trouton in Dublin verified this conclusion of Maxwell by

experiments on electro-magnetic waves.

Of recent mathematical and experimental contributions to optics, mention must be made of H. A. Rowland's theory of

concave gratings, and of A. A. Michelson's work on interference,

and his application of interference methods to astronomical measurements.

In electricity the mathematical theory and the measurements

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