Surface-Fih a in Total 'Reflexion. 17 



The resultant intensity is therefore 

 E 2 + 2E /2 * 2 ) cos 2 yjr + (E' 2 + 2E-V) sin 2 yfr 



+ 2 { (E 2 + E ,2 k 2 ) cos 2 f + E 2 /c 2 sin 2 ty\ i { E ' 2 + E V) sin 2 ^ + E ,2 /c 2 cc s* f \ 



xcos/T-T'-K + ^-Zi-y-tan-^'+tan- 1 



+ tan -1 k tan i/r — tan - ] 



E ' E' 



fc cot \js J* 

 The extinction position of the compensator is therefore 



given by 



T-T'-K + ro-Zi-y-tan- 1 ^ 4-tan- 1 



fcW . *E 



E- +tan F 

 4-tan -1 /c tan i/r — tan -1 ac cot i^ = 0. 



It deviates from the position which we should obtain if the 

 elliptic propagation of light in quartz were disregarded, by 



— tan 



kE' 



E 



tan" 



kE 



„ T 4-tan- 1 k tan i/r — tan -1 a: cot i/r, 



or —2 tan -1 2/c cot 2^, 



E 

 since for the extinction position tan ^=—j. If E = E', as is 



the case with observations on total reflexion, then the deviation 

 is zero; and this cause does not affect the accuracy of the 

 results. 



Observations were made on this deviation. The zero of the 

 compensator was determined for different positions of the 

 crossed nicols, i. e. for different values of -ty. -yj/ and /c were 

 determined from the observations, k was found to be 0'0016 

 as against values ranging from O0019 to O0012 given by 

 Voigt in the above-mentioned article. k was then substi- 

 tuted in the formula, and the theoretical value of the deviation 

 calculated, tc is the ratio of the axes of the ellipse in which 

 the light vibrates. It is very difficult to take readings for 

 values of i/r near 0° or 90° 



*. 



Observed 



Mean 



Theoretical 



*• 



Observed 



Mean 



Theoretical 



Deviation. 



Error. 



Deviation. 



Deviation. 



Error. 



Deviation. 



o 



o 



o 



o 



o 



o 



o 



o 



88 ... 



8-7 



1-7 



5-2 



55 ... 



-0-2 



02 



01 



86 ... 



2-2 



04 



2-6 



40 ... 



-00 



00 



00 



83 ... 



1-2 



0-4 



1-4 



25 ... 



-04 



0-2 



-0-3 



78 ... 



1-0 



0-2 



0-8 



15 ... 



-0-6 



o-o 



-07 



75 ... 



0-9 



0-2 



0-6 



5 ... 



-2-8 



0-2 



-20 



65 ... 



00 



02 



0-3 



2 



-5-4 



0-8 



-5-6 



Phil. Mag. S. 6. Vol. 10. No. 55. July 1905. 



a 



