A Course of Modern Analysis: An Introduction to the General Theory of Infinite Series and of Analytic Functions, With an Account of the Principal Transcendental Functions

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A Course of Modern Analysis: An Introduction to the General Theory of Infinite Series and of Analytic Functions, with an Account of the Principal Transcendental Functions

Edmund Taylor Whittaker

Franklin Classics Trade Press

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1907 Excerpt: ...in a medium of index /, its height / being at right angles to the plane of the diagram. Let the instrument form an image / of 0, in a medium of index /»', by a thin sagittal pencil whose plane is at right angles to the plane of the diagram, and whose chief ray OPQI makes an angle O with the axis initially, and O' finally. Let a denote the angle between the extreme rays of the pencil initially, and let a be the final value of this angle: and suppose that df is the angle between the meridian planes which pass through the extreme rays of the pencil, so a = sin O. df, a = sin O', df. Clausius' equation (§ 7) gives at once fwl = fi'o'/', or /sinfl. l = p'smO'. /', so the linear magnification of a small object, when the image is formed by rays which pass through this zone on the refracting swrfaces, is This result is true for all optical instruments, independently of whether they are affected with spherical aberration or not. Suppose now that the instrument is corrected for spherical aberration, so that the images of 0 formed by different zones are situated at the same point of the axis. In order that the images of a small object at 0 may be in all respects identical, they must be of the same size; and therefore the equation wsintf H smO where m is the linear magnification for the image formed by the paraxial rays, must be satisfied by every ray which issues from the axial point 0. This equation is called the sine-condition. As might be expected, the sine-condition also ensures that the images formed by meridian pencils have the same magnification, whatever be the zones through which the pencils pass. For again applying Clausius' equation (§7) /i. COS i/. la = p' COS. l'a, we have in this case (the object and image being taken in the plane of the d...

The theory of optical instruments

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A History of the Theories of Aether and Electricity: From the Age of Descartes to the Close of the Nineteenth Century (Classic Reprint)

Excerpt from A History of the Theories of Aether and Electricity: From the Age of Descartes to the Close of the Nineteenth Century Th observation of the heavens, which has been pursued continually from the earliest ages, revealed to the ancients the regularity of the planetary motions, and gave rise to the conception of the universal order. Modern research, building on this foundation, has shown how intimate is the connexion between the different celestial bodies. They are formed of the same kind of matter; they are similar in origin and history; and across the vast spaces which divide them they hold perpetual intercourse. Until the seventeenth century the only influence which was known to be capable of passing from star to star was that of light. Newton added to this the force of gravity; and it is now recognized that the power of communicating across vacuous regions is possessed also by the electric and magnetic attractions. It is thus erroneous to regard the heavenly bodies as isolated in vacant space; around and between them is an incessant conveyance and transformation of energy. To the vehicle of this activity the name aether has been given. The aether is the solitary tenant of the universe, save for that infinitesimal fraction of space which is occupied by ordinary matter. Hence arises a problem which has long engaged attention, and is not yet completely solved: What relation subsist between the medium which fills the interstellar void and the condensations of matter that are scattered throughout it? About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

Science & Math

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Excerpt from A History of the Theories of Aether and Electricity: From the Age of Descartes to the Close of the Nineteenth CenturyNewton shows that rays Obtained by double refraction have sides his Objections to the undulatory theory.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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Books by Edmund Taylor Whittaker

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A Course of Modern Analysis: An Introduction to the General Theory of Infinite Series and of Analytic Functions, with an Account of the Principal Transcendental Functions

The theory of optical instruments

A History of the Theories of Aether and Electricity: From the Age of Descartes to the Close of the Nineteenth Century (Classic Reprint)

A History of the Theories of Aether and Electricity: From the Age of Descartes to the Close of the Nineteenth Century (Classic Reprint)