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XLIII. An Abstract of the essential Principles of M. Cauchy's 

 View of the Undulatory Theory^ leading to an Explanation 

 of the Dispersion of Light ,- with Remarks. By the Rev. 

 Baden Powell, M,A,^ F,R.S., Savilian Professor of Geo^ 

 met7y, Oxford, 



[Continued from p. 193, and concluded.] 



Tl| AVING thus obtained the expression which establishes 

 -■--■• a general relation between the length of a wave and the 

 velocity of its propagation, or the time of its transmission, or, 

 again, (which is the same thing,) the time of the vibration of a 

 molecule, we might proceed at once to certain more particular 

 inferences ; but it may be useful, perhaps, here to premise a 

 remark or two on the general nature of the inquiry respecting 

 the theory of dispersion. 



The unequal refrangibility of the primary and component 

 parts of which ordinary light is constituted, is a general fact, 

 of which, as yet, no plausible explanation has been proposed, 

 and which has presented great difficulties to any theory. 

 These difficulties have, indeed, been triumphantly held forth 

 by the opponents of the undulatory theory as absolutely fatal 

 to its claims ; but the truth is they are by no means ^peculiar 

 to this theory. The hypothesis of emission has not been at all 

 more successful in affording any satisfactory explanation. 



Let us, however, look at the nature of the difficulty as it 

 occurs upon the ordinary hypothesis of undulations. The 

 front of a wave incident obliquely on the surface of a transpa- 

 rent medium, and arriving successively, e, g. at any two points 

 of the surface, at each originates a new spherical wave within 

 the medium. If the refractive power be greater, these are 

 propagated with diminished velocity. The second of these 

 new waves within the medium has propagated itself a little 

 way before the first has gone through the same space as the 

 original wave in the same time. Hence the plane touching 

 their contemporaneous surfaces will be inclined to the surface 

 of the medium at a less angle than the front of the original 

 wave; and (it is easily seen) precisely so much so, as that the 

 ratio of the sines is that of the velocities, or is equal to the 

 index of refraction. 



The refraction, then, depends solely on the diminished velo- 

 city of propagation of the waves, and ought to be exactly the 

 same for waves of all lengths, unless there could be shown any 

 connexion between the length of a wave and the velocity of its 

 propagation. 



" It is particularly to be remarked," observes Prof. Airy, 



