410 



Mr. J. C. McConnel. On the 



[Dec. 17 r 



is the influence of the refraction effects. This is discussed at some 

 length in the paper, and is shown to be in all probability negligible. 



The measurements were taken with a spectrometer fitted up as a 

 polariscope, whose great focal length and finely graduated circle were 

 of much service. 



I found it convenient to treat separately the region near the axis, 

 where the abnormal form of the wave surface of quartz is most 

 obvious. I have compared my results with nine different theories,, 

 each of which gives an expression of one of the two following forms. 



D 2 =P 1 2 sin 4 + D o 2. 

 D 2 — Po 2 sin 4 + D 2 cos 4 0. 



Here D is " the number of wave-lengths by which one wave lags 

 behind the other in air, after the light has traversed normally a 

 plate of quartz one millimetre thick, the normal to whose faces makes 

 an angle with the optic axis." D is the value of D when 0=0, 

 and is known from the rotatory power, and P T and P 2 are constants to 

 which the theories assign different values. By inserting the observed 

 values of D and 0, I obtained values of P 2 and P 2 from each ring. 

 The results from one plate about 20 mm. thick were as follows : — 



4° 24' 5° 51^' 6 ° 51 i' 7° 40£' 8° 23J' 9° 38' 11° 41' 



P T 15-054 15-207 15-220 15-260 15-249 15-258 15-269 



P. 3 15-220 15-293 15"290 15-311 15'295 15-292 15-292 



Similar results were obtained from a second plate about 27 mm. 

 thick. 



From these figures I concluded that the second expression was the 

 correct one, and that P 2 =15\30 + -01. There is a considerable dis- 

 crepancy in the case of the first ring, of which two possible ex- 

 planations are given in the paper. 



Cauchy gives P 2 =^_^= 15*351, where a and b are the wave velo- 

 cities perpendicular to the optic axis. 



Lommel gives £±£ ^ =15-178. 



l — b* 2a a*\ 



Kettler „ P 2 = a+la-b = 15 . 486 



2 2b a 2 \. 



Sarrau „ P = a + ba-b = 15306. 



2a a 2 X 



The other five, MacCullagh, Clebscb, Lang, Boussinesq, and Voigt, 



have the first form of expression and give F^^^-- a ~~^ =15\306. 



2a a 2 — X 



