120 HISTORY OF OPTICS. 



l>y experiment), ami paitly on misconceptions of the theory; and 1 

 believe there arc none of them which would now be insisted on. 



We may mention, also, another difficulty, which it was the 

 habit of the opponents of the theory to urge as a reproach against 

 it, long after it had been satisfactorily explained : I mean the lialf- 

 ,i,:<l nldtlon which Young and Fresnel had found it necessary, in 

 some cases, to assume as gained or lost by one of the rays. Though 

 they and their followers could not analyse the mechanism of reflection 

 with sufficient exactness to trace out all the circumstances, it was not 

 difficult to see, upon Fresnel's principles, that reflection from the inte- 

 rior and exterior surface of glass must be of opposite kinds, which 

 might be expressed by supposing one of these rays to lose half an 

 undulation. And thus there came into view a justification of the step 

 which had originally been taken upon empirical grounds alone. 



10. Dispersion, on the Undulatory Theory. A difficulty of another 

 kind occasioned a more serious and protracted embarrassment to the 

 cultivators of this theory. This w r as the apparent impossibility of 

 accounting, on the theory, for the prismatic dispersion of color. For 

 it had been shown by Newton that the amount of refraction is dif- 

 ferent for every color ; and the amount of refraction depends on the 

 velocity with which light is propagated. Yet the theory suggested no 

 reason why the velocity should be different for different colors : for, by 

 mathematical calculation, vibrations of all degrees of rapidity (in 

 which alone colors differ) are propagated with the same speed. Nor 

 does analogy lead us to expect this variety. There is no such dif- 

 ference between quick and slow waves of air. The sounds of the 

 deepest and the highest bells of a peal arc heard at any distance in 

 the same order. Here, therefore, the theory w r as at fault. 



But this defect was far from being a fatal one. For though the 

 theory did not explain, it did not contradict, dispersion. The suppo- 

 sitions on which the calculations had been conducted, and the analogy 

 of sound, were obviously in no small degree precarious. The velocity 

 of propagation might differ for different rates of undulation, in virtue 

 of many causes which would not affect the general theoretical 

 results. 



Many such hypothetical causes were suggested by various eminent 

 mathematicians, as solutions of this conspicuous difficulty. But with- 

 out dwelling upon these conjectures, it may suffice to notice that 

 hypothesis upon which the attention of mathematicians was soon con- 

 centrated. Tin* was the hyjmtkesis of finite intervals between the 



