making Experiments upon Elliptic Polarization. 245 



of j3 so deduced must indeed be expected to be very inaccurate, 

 partly because of errors in the observed values of 0, partly be- 

 cause 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 0'-0". For example, putting and j3 for the 

 values of 9 and ]3 when a = 45, M. de Senarmont gives, at the 

 incidence of 60 upon steel, 20 = 64 15' (taking the mean of 

 his two determinations), and for the azimuths 55, 30, 25, he 

 gives 20 equal to 88 5', 37 2', and 29 36' respectively. Com- 

 bining these values of 29 in succession with that of 20 , we get 

 for 2j3 the series of values 32 38', 33 28', 34 30'; the dif- 

 ferences between which are to be attributed to the causes above 

 stated. The mean value of 2j3 thus found is 33 32' ; while 

 its value, as given by M. de Senarmont, is only 28 41'. The 

 difference 4 51' is the value of 0' - 0", which, divided by the 

 tangent of 2|3 , gives 7 19' for the mean value of t, the error of 

 the mica plate corresponding to that part of the spectrum which 

 was observed at the incidence of 60. 



At incidences nearer the angle of maximum polarization 

 the errors are probably much greater. Beyond that angle 

 they again diminish, and in some cases they almost vanish. 

 Thus, at the incidence of 85 upon steel, with the value of 20 

 and the value of 20 corresponding to a = 20, we get, by com 

 putation, a value of 2j3 , which differs only by a few minutes 

 from that given by M. de Senarmont. Nearly the same thing 

 happens at the same incidence when we take a = 25. In these 

 cases, therefore, the results belong to that particular ray for 

 which the thickness of the plate was exact. 



The observations of M. de Senarmont on speculum metal 

 were not carried beyond the incidence of 60. He states that 

 he was unable to observe at higher incidences, on account of the 

 uncertainty arising from the dispersion of the metal ; but though 

 this cause operated in some degree, his embarrassment must 

 have been really occasioned by the increasing magnitude of the 

 difference 0' - 0", as he ^approached the angle of maximum po- 



