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Written by the renowned British mathematician James Challis, this book explores the relationship between pure and applied mathematics, and discusses how mathematical principles can be used to understand physical phenomena. It is a must-read for anyone interested in the philosophy of mathematics and its practical applications. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1869 edition. Excerpt: ...vibrations in the immediate vicinity of the axes. This argument is referred to in paragraph (2), p. 322, and justifies the limitation there given to the value of r. (16) It being established that the sensation of light ia caused by transverse vibrations, we may hence infer that the undulations of two rays, having a common axis and polarized in rectangular directions, produce independent luminous effects, simply because their transverse accelerative forces act independently. Also since, as is known by experience, the luminous effect of a series of undulations is the same whatever be their phase, it follows that the combined luminous effect of two oppositely polarized series is independent of difference of phase. Thus the theory explains the experimental fact that oppositely polarized rays having a common path do not interfere whatever be the difference of their phases. (17) We have next to consider the effect of resolving a polarized ray into two parts by a new polarization. There are only two conditions which the resolved parts of a polarized ray are required to satisfy in order that when recomposed they may make up the original ray, namely, that the sum of the condensations at corresponding points be equal to the condensation at the corresponding point of the integral ray, and that the velocities at corresponding points be the parts, resolved in directions parallel and perpendicular to the new plane of polarization, of the velocity in the integral ray at the corresponding point. Let that plane make the angle 0 with the axis of x, and let s, arl, cra be the condensations at any corresponding points of the original ray and the resolved rays, and /, /, /, be the factors for the same points, which must be such as to satisfy the differential...
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