381 



incidences, because it is within the last thirty degrees of 

 incidence that the phenomena go through their most rapid 

 changes. 



If we now cast our eyes on the above table, making due 

 allowance for the uncertainty arising from the dispersion of 

 the metal, we shall be struck with the agreement between 

 the calculated and observed numbers. The differences are 

 greatest in the last two observations, which however were 

 really the first ; for the observations were made in the in- 

 verse order of the incidences, and their accuracy may have 

 improved as they went on. However that may be, the dif- 

 ferences are quite within the limits of the errors of observa- 

 tion ; 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. — See the Table which he has given in the Amiales 

 de Chimie, tom. xvii. p. 314. 



It may seem extraordinary that these experiments should 

 have been in my possession for nearly six years, before I be- 

 came aware of their close agreement with my formulas ; 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 expect more than a general accordance with theory. 

 And even now, I am in no haste to infer the absolute exac- 

 titude 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 men- 

 tioned, though it appeared to represent the phenomena less 

 perfectly. For, to say nothing of the small number of our ex- 

 periments, the present is a much more complicated case, and 

 the phenomena depend on two constants instead of one, so that 

 the formulae might be slightly altered, and yet pei'haps con- 

 tinue to agree very well with rough experiments. Where 

 there is only one constant this is not so probable. Again, 



