1894.] 



Reflection and Refraction of Light. 



29 



observation than the corresponding numbers for Cauchy.'s formulae, 

 even as modified by Quincke to explain his experiments. For in- 

 stance, in the case of Jamin's experiments on realgar-air, chosen at 

 random, the probable errors of a single observation are according 

 to theory, in tan~ z (R_L/R//), 20'"82, according to Cauchy, 22''96, and 

 in the difference of phase pL />//, measured in wave-lengths, accord- 

 ing to the theory, O0054, according to Cauchy, O0071. This superi- 

 ority is due to the influence of the additional constants D and A; 

 but their effect is very slight, that of A especially so ; in some cases 

 A may be put zero without greatly impairing the accuracy of the 

 theoretical formulae. 



The values of B, as determined . from the intensity experiments 

 agree within the limits of error with those deduced from the equation 

 B = (^/^o)B*; in the one case of essence of lavender-air there is a 

 serious discrepancy, for B is 0'000027, while (/t 1 / / u )E 2 is O000065 ; 

 but here the error is due to the smallness of B, ten times less than 

 for any other pair of media ; in fact the minimum value of (RJ./R//) 3 

 is only tan 2 7' or 0'000004, and an error of only a few minutes in the 

 determination of the azimuth would make a great difference in the 

 value of B. In cases of such difference between B and (/t 1 / / , )E 2 , it 

 is best to rely on the value of E, which can be determined with much 

 greater accuracy than B, in some cases with more than five times 

 greater accuracy. 



As regards the interchange of media, there were available three 

 sufficiently accurate sets of experiments by Quincke. The conditions 

 referred to above are satisfied with very good acpuracy in the case of 

 flintglass-air, the values of B being 0'00533 and O'OOSO, and of /tjE, 

 0*iE)', 0-0925, 0-093; for flintglass- water the numbers are, B, 

 0-0120, 0-0100, and ^E, 0'1490, -(^E)', 0-1426; but for crown- 

 glass-air the discrepancy is great, B, 0*00040, O'OOlll, and /^E, 

 0-0237, -(/tiE)', 0-0427. 



Jamin and Cauchy's corresponding relation between the ellipti- 

 cities, E'/E = /ti/^i'j is not so nearly satisfied; the observed values 

 of E'/E are in the three cases, T741, 1'244, and 3'446, instead of 

 1'616, 1-210, and 1'515. More accurate experiments will be necessary 

 to test this point. 



Cauchy's theory leads to a relation between the ellipticities of 



"R 1 "C^ "C^ 



three media taken two and two, -f + = 0, which relation has 



y"i y"2 /"3 



been tested by Quincke and found not at all in accordance with 

 experiment. 



The above theory has the advantage in requiring no such relation. 



The theory discussed above merely requires the existence of a 

 transition film, whether due to actual transition between the ether 

 of the two media or to an adventitious accumulation of dust, 



