408 



fij = (f — .,; 



i\.^ — ,\ \- X 



wlierc ,1; i-cpreseiifs a small (|iiaiitil_v. 



(', -|-"., ", 



We calculate liow much ' — diHersi from zero. 



11 IS easilv IiiuihI that =^ , =— -. - . au 



2ff if-.v 2fJ' a 2ö^ 



error of llie second order of magnitude. 



In the example 011 11. 402 - is eciiial lo , so liiat the clianere 



111 the distance between the fringes might he still 4 oi- 5 times 



greater without making the error larger than 1 per tiiousand. 



In the above cited paper ') Javmann derives on p. 4ti2 with his 



"11" — "' 



theory for the KKEsNKL-coefticient the formula h . where 11 is 



«„'■' 



the index of I'efraction for \erv long waves and n that for the 

 colour considered. 



For water n/' = 80.0 and n\\„^= 1.78, so that Jacmann finds for 

 the FKESNEL-coeflicient of sodium light 0.488. This value does not 

 agree with the result of onr experiments and these are so accurate, 

 that- we may say with security, that the theory of Jaumann is in 

 conflict with lealiiy. There is still another point of disagreement 

 between experiment and this theory. The latter gives for decreasing 

 wavelength a i/ecri'cK^e' of the FRKSNEi.-coefficient, while the experi- 

 ments (see p. 404) jirove the contrary. 



Resuming we may say, that we have repeated Fresnei/s experiment 

 will) different colonrs and have proved the exactness of the Fresnel 



1 k du 



coefficient! . -- =r f / within the limits of the experimental 



!'' M 'l^- 

 errors. Ii is pcrlia|is interesting to notice that the relative values of f l 

 for different colours lia\e also been confii-med by these experiments, 

 because these relative vivlues are independent of the effective 

 length of the moving watercolnmn and of the exact value of a 

 numerical coefficient that was put equal to 0,84. So the measurements 

 from which the absolute value of the FRESNEL-coefficienl has been 

 derived, might be considei'cd as an experimental determination of the 

 ratio ir,„.,,^ : ii\. The FizEAi-effect would from this point of view form 

 the fixed theoretical base, as it is an effect of the first order, quite 

 based on the ascertained fundamental equations of electrodynamics, 

 -) See the fust pail of this paper. 



