Evidence in support of a Theory nf Light. 283 



the fundamental suppositions on which he proceeds are more 

 comprehensive : they lead to the conception of vibrations slightly 

 different from those of Fresnel, but as nearly the same as in no 

 way to affect the nature of the resulting waves : yet they include 

 the germs, as it were, of other consequences afterwards deduced, 

 among which is contained the relation on which the explanation 

 of unequal refrangibility depends. 



This characteristic property of the primary and component 

 rays, it has been justly remarked, has hitherto presented great 

 difficulties to any theory. These difficulties are by no means 

 peculiar to the undulatory theory : the hypothesis of emission 

 has not been at all more successful in affording any satisfactory 

 explanation The dispersion has been allowed to be almost the 

 only real objection against the former theory, at least as com- 

 monly propounded. On the ordi7iari^ suppositions of the vibra- 

 tions, the equal refrangibility of rays having waves of all lengths 

 is a necessary consequence. 



The degree in which a ray is deviated, depends solely on the 

 diminished velocity of propagation of the waves within the re- 

 fracting medium, in which we suppose the ether to exist in a 

 state of greater condensation. If, then, for waves of different 

 lengths, the velocity be the same for the same medium, it fol- 

 lows that the amount of their refractions will in all be exactly 

 equal. In order to explain why rays having waves of different 

 lengths should undergo different degrees of refraction, that is, 

 be propagated with different velocities within the medium, it 

 would be necessary for theory to assign a mathematical relation 

 between the length of a wave and the velocity of its transmis- 

 sion. This the theory, as ordinarily conceived, fails to do ; at 

 least it may safely be asserted that no mathematician has as yet 

 exhibited any such deduction from it in a precise and definite 

 form. 



By that modification of the first principles which constitute 

 the basis of M. Cauchy's investigations, he is enabled to deduce 

 the general result that a relation subsists between the length 

 of a nave and the velocity of' its transmission, or the time of 

 the vibration of a molecule of ether. Thus, as far as general 

 explanation is concerned, this formidable obstacle is satisfactorily 

 overcome. But the more precise representation of the facts by 



