76 JAMIN ON METALLIC REFLEXION. 



^ ,^ . / sini\ "1 



cot (2 m — e) = cot s cos I 2 arc tan —T— I, , . 



\ e / ^ . . . . (8.) 



92sm2e = U2sin2?^. J 



The constants (6) and (e) are determined as follows: — at the 

 angle of maximum polai-ization, the variables U and (m) have the 

 particular values 



M = 2A, U = sinij tanzj ; 



replace {u) and U by these particular values in formulas (8.), and 

 (e) and (6) are found from them : these quantities being once 

 determined, the formulas (8.) will give the values of (m) and U 

 for each incidence ; equations (7.) give (i^) and (%) ; and (6.), P 

 and P. 



In applying these formulae, it is perceived that ( . j is always 



so small that we may neglect ( tj I in the calculations : we have 



constantly satisfied ourselves with this degree of approximation, 

 after having convinced ourselves that the errors committed were 

 less than those of experiment. 



Whatever care be used in executing the experiments, it ap- 

 pears to me impossible to obtain a more complete agreement 

 between theory and calculation than is exhibited by our tables. 

 The determinations are, in fact, liable to several sources of error, 

 of which some are very serious, and cannot be entirely avoided, 

 and which the least negligence would render enormous : and, 

 moreover, the theoretical formula are calculated by means of two 

 constants, furnished to ' s by experiment, and which are neces- 

 sarily tainted with errors which alter all our results : it is there- 

 fore difficult to aspire after a more perfect experimental verifi- 

 cation than that exhibited by our tables. 



II. Measure of the Difference of Phase. 



We have new to occupy ourselves with the second transfor- 

 mation operated on light by metallic reflexion ; I refer to the 

 displacement of the nodes of vibration. 



I have occupied myself with a particular case of this question, 

 and my experiments presented to the Academy of Sciences on 

 the 13th of August 1846, prove, — 1st, that a ray polarized perpen- 

 dicularly to the plane of incidence is always retarded with regard 

 to a beam polarized in the azimuth of 0^ ; 2nd, that the differ- 



