236 Laws of Metallic Reflexion, and Mode of 



the last two observations, which, however, were really the first ; 

 for the observations were made in the inverse order of the inci- 

 dences, and their accuracy may have improved as they went on. 

 However that may be, the differences are quite within the 

 limits of the errors of observation ; and they are actually less 

 than those which Fresnel found to exist between calculation 

 and experiment in the much simpler case of reflexion at the 

 surface of a transparent ordinary medium, when he proceeded 

 to verify the formula which he had discovered for computing 

 the effect of such reflexion.* 



It may seem extraordinary that these experiments should 

 have been in my possession for nearly six years before I became 

 aware of their close agreement with my formulae ; but the fact 

 is, that I did not regard them with much interest, because, 

 from the circumstances in which they were made, I did not ex- 

 pect more than a general accordance with theory. And even 

 now I am in no haste to infer the absolute exactitude of the 

 formulae, though they are found to represent the phenomena 

 so well. It was far more allowable to infer that the formula of 

 Fresnel was exact in the case just mentioned, though it appeared 

 to represent the phenomena less perfectly. For, to say nothing 

 of the small number of our experiments, the present is a much 

 more complicated case, and the phenomena depend on two con- 

 stants instead of one, so that the formulae might be slightly 

 altered, and yet perhaps continue to agree very well with rough 

 experiments. Where there is only one constant this is not so 

 probable. Again, there is one of the quantities in the preceding 

 formulae which may be greatly altered without producing more 

 than a slight effect on the values of 8 and /3. This quantity is 

 the ratio of sin i to sin i', which, according to the value in for- 

 mula (c), is a number so large as to make the angle / always 

 small, so that its cosine never differs much from unity; and 

 therefore if the above ratio were taken equal to any other large 

 number, the value of p in formula (D) would remain nearly the 



* See the Table which he has given in the Annales de Chimie, torn, xviii. 

 p. 314. 



