244 Laws of Metallic Reflexion, and Mode of 



&, 0", and taking their sum for 29 ; also by measuring the 

 angles 7', 7", and taking their sum for the same quantity. 

 Now each of these methods gives a true value of 0, because by 

 the preceding formulae we have 20 = &' + 0" = 7' + 7" ; and 

 this accounts for the agreement, shown by the tables of M. de 

 Senarmont, between the values* of 29 obtained by these different 

 methods. But the values of /3 were deduced from the angles 

 7', 7 // , by simply making their difference equal to 2/3 ; and we 

 see by the second of formulae (N) that, when the plate is not of 

 the proper thickness, this value of 2/3 is erroneous by the whole 

 amount of the angle 0' - 0", the difference between /3' and j3 

 being supposed so small that it may be neglected. As M. de 

 Senarmont proceeded on the common assumption that when the 

 thickness of the plate has been adjusted to that part of the 

 spectrum to which the observations are intended to refer, it 

 may afterwards, through the whole series of experiments, be re- 

 garded as exact, he necessarily conceived 0' and 0" to be the 

 same angle ; and it was on the principle of taking an average 

 between two measures of the same quantity that he made the 

 supposition 20 = ff + 0", which happened to be correct. When 

 therefore he found & and 0" to be different, he of course looked 

 upon the difference as merely an error of observation, which it 

 would be superfluous to tabulate. Not having the values of 

 this difference, therefore, we have not the means of immediately 

 correcting the values of 2/3. But as observations were made 

 for several azimuths at each angle of incidence, we may use the 

 values of to determine those of /3 ; for when at any inci- 

 dence (except that of maximum polarization, where = for all 

 azimuths) the values of are known for two given values of a, 

 we can deduce the corresponding values of /3, without any other 

 theory than that of the composition of vibrations. The values 



* Or rather the values of 180 + 20 ; because the angle , the double of which 

 appears in the tables of M. de Senarmont, is equal to 90 + 6. The angles which 

 he calls 71 and yz are equal to 90" + y" and 9Q + y respectively. It therefore 

 comes to the same thing, whether the one set of angles or the other is supposed to 

 be measured. The letter has the same signification in both notations. 



