JAMIN ON METALLIC REFLEXION. 83 



of the reflected light, it also shows that two rays of the same phase 

 before incidence, polarized in azimuths of 0° and of 90°, after 

 undergoing the action of the metal, have a difference of phase 

 (S) variable with the incidence, and expressed by the formula 



tan S = tan 2 w sin u; (9.) 



(w) is found by the equation of condition 



U cos i 



tan CO = — ■ ,, . -. 



It is by means of this formula that the numbers calculated in 

 the preceding tables have been obtained ; and the almost perfect 

 identity of the theoretical and experimental results can leave no 

 doubt as to the accuracy of the formulae of the skilful geometer. 

 In order to show still more clearly that the agreement is as com- 

 plete as possible, we shall observe that in the table relating to 



silver, wherever the fractions (—1 have equal values, the cor- 

 responding incidences of restored polarization differ among each 

 other by very small quantities, often insignificant, and always 

 less than thirty minutes. These differences afford us, so to 

 speak, a measure of the errors liable to be committed in the de- 

 termination of the angles ; and if I add that the numbers in the 

 table are the result of three series of experiments, performed by 

 varying each time the azimuth of the incident ray, the conviction 

 will follow that this limit to error is rarely attained : on the other 

 hand, an error of thirty minutes in the determination of the 

 angle produces one of only yi^ in the difference of phase ; so 

 that we may conclude that y^^ is the probable limit of error in 

 determining the difference of phase. 



Now, if in the foregoing tables the column of differences be 

 examined, it will be found that in more than fifty observations 

 there are only three which give a difference of 0*08, eleven amount 

 to 0*01, and amongst the rest many are identical, even to the 

 thousandth part : the difference between calculation and obser- 

 vation is therefore limited to the errors recognised as possible in 

 experiment. 



At the time when I made these experiments I was not aware 

 of the formulae of M. Cauchy ; and in presenting my results to 

 the Academy of Sciences, I had sought to represent them by an 

 empirical formula, which, although differing essentially from that 

 , of M. Cauchy, gives the numerical results sensibly the same. As 

 it is very simple, and may be employed usefully in an approxi- 

 mative calculation, I shall give it here. 



Put tan ?', = n and sin i = n sin >■ ; 



G 2 



