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THE

LONDON, EDINBURGH, AND DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

CONDUCTED BY

SIR DAVID BREWSTER, K.H. LL.D. F.R.S.L. & E. &c.
RICHARD TAYLOR, F.L.S. G.S. Astr. S. Nat. H. Mosc. &c.
SIR ROBERT KANE, M.D., F.R.S., M.R.I.A.

WILLIAM FRANCIS, PH.D. F.L.S. F.R.A.S. F.C.S.
JOHN TYNDALL, PH.D. F.R.S. &c.

"Nec aranearum sane textus ideo melior quia ex se fila gignunt, nec noster
vilior quia ex alienis libamus ut apes." JUST. LIPS. Polit. lib. i. cap. 1. Not.

VOL. XII.-FOURTH SERIES.

JULY-DECEMBER, 1856.

GLASGOW

MICAL

LONDON.

TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET,
Printers and Publishers to the University of London:

BOLD BY LONGMAN, BROWN, GREEN, LONGMANS, AND ROBERTS; SIMPKIN,
MARSHALL AND CO.; WHITTAKER AND CO.; AND PIPER AND CO.,
LONDON :-BY ADAM AND CHARLES BLACK, AND THOMAS
CLARK, EDINBURGH; SMITH AND SON, GLASGOW ;

HODGES AND SMITH, DUBLIN; AND
PUTNAM, NEW YORK.

"Meditationis est perscrutari occulta; contemplationis est admirari perspicua. . . . . Admiratio generat quæstionem, quæstio investigationem, investigatio inventionem."-Hugo de S. Victore.

-"Cur spirent venti, cur terra dehiscat,

Cur mare turgescat, pelago cur tantus amaror,
Cur caput obscura Phoebus ferrugine condat,
Quid toties diros cogat flagrare cometas ;
Quid pariat nubes, veniant cur fulmina cœlo,
Quo micet igne Iris, superos quis conciat orbes
Tam vario motu."

J. B. Pinelli ad Mazonium.

CONTENTS OF VOL. XII.

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THE

LONDON, EDINBURGH AND DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

[FOURTH SERIES.]

JULY 1856.

I. On the Demonstration of Fresnel's Formulas for Reflected and Refracted Light; and their Applications. By the Rev. BADEN POWELL, M.A., F.R.S. &c., Savilian Professor of Geometry in the University of Oxford*.

1.

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QUESTION between two fundamentally different views of the theory of polarization, which has been long agitated among inquirers into the undulatory theory, viz. as to the direction of the plane of vibrations in relation to that of polarization, has of late excited more peculiar interest, partly from the announcement, a few years ago, of a remarkable crucial experiment by Professor Stokes, and partly from several subsequent investigations, especially the recent elaborate discussion of the general bearing of the experimental evidence by M. Haidinger.

The revival of this question recalls the attention of the student to the very unsatisfactory condition in which the elementary demonstration of those parts of the theory on which it depends has long been left, and from which recent speculations have done little to deliver it.

2. The well-known and remarkable formulas originally given by Fresnel to express the amplitudes of the vibrations, and thence the intensities, of reflected and refracted rays of polarized light (for singly-refracting media), which are found to represent so beautifully all the observed changes, in fact including the whole doctrine of plane polarization, and thus invaluable as inductive laws, yet long remained confessedly defective as to their systematic deduction from theory.

3. Fresnel, indeed, with that marvellous sagacity for which he was so conspicuous, satisfied himself of their truth by reason* Communicated by the Author.

Phil. Mag. S. 4. Vol. 12. No. 76. July 1856.

B

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