390 



ference equal to 2 j3 ; and we see by the second of formulas (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 Q' — d", 

 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 ob- 

 servations are intended to refer, it may afterwards, through 

 the whole series of experiments, be regarded as exact, he 

 necessarily conceived Q' and 0" to be the same angle ; and it 

 was on the principle of taking an average between two mea- 

 sures of the same quantity, that he made the supposition 

 ^B — B' -\- B", which happened to be correct. When there- 

 fore he found B' and B" 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 im- 

 mediately correcting the values of 2j3. But as observations 

 were made for several azimuths at each angle of incidence, 

 we may use the values of B to determine those of j3 ; for when 

 at any incidence (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, with- 

 out any other theory than that of the composition of vibrations. 

 The values of j3 so deduced must indeed be expected to be 

 very inaccurate, partly because of errors in the observed values 

 of 0, partly because the observations in different azimuths do 

 not answer to the same ray of the spectrum ; but they will 

 be accurate enough to show the great amount of the error 

 committed by neglecting the difference B' — B". For ex- 

 ample, putting 00 and j3o for the values of and /3 when 

 a zz. 45°, M. de Senarmont gives, at the incidence of 60° upon 

 steel, 200 =: 64° 15' (taking the mean of his two determina- 

 tions), and for the azimuths 55°, 30°, 25°, he gives 20 equal to 

 88° 5', 37° 2', and ii9° 36' respectively. Combining these 



