C. S. Hastings — Double Refraction in Iceland Spar. 71 



observed extraordinary deviations by the refracting angles PQ 

 and PR. First, we have the well known law, 



r 1 V cos 2 ^ sin'S 



where fi and ju s are the reciprocals of the principal wave ve- 

 locities as before, and // e is the reciprocal of the velocity of the 

 extraordinary wave whose normal makes an angle # with the 

 crystalline axis. This enables us to compute // e , knowing #. 

 Second, we have the series of relations given by Professor 

 Stokes (British Association Report, 1862), 

 , _ sin</9 _ sin;/' 

 £— sincp 1 ~ sin^' 

 q> -\-tt —A-\-a 

 cp'-\-f=za 



cp' — ib' a <p—H> A.-X-a 



tg^=tg r t g ^yi.oot-^-, 



where <p </> are the angles of incidence and emergence respec- 

 tively, and <p' <p' the angles which the wave normal makes with 

 the faces of the prism within it. These relations enable us to 

 derive a value for [x' e from the observations, perfectly independ- 

 ently of any assumption as to the law of double refraction if 

 we know either <p or <p. They afford a much readier test than 

 that of calculating the deviations for an assumed law. 



We do not, it is true, know the values of <p for the extra- 

 ordinary refractions by PQ and PR, but as the prism was 

 always set for minimum deviation it is easy to find these 

 values, either by taking advantage of the fact that Huyghens's 

 law is already known to be nearly true, whence the angle of 

 incidence for minimum deviation can be calculated, or, more 

 simply, from the relation 



sin*?? sin?/.' 



%\ncp'' smib n 



and the two purely geometrical equations which follow this 

 equation above. 



It is found by trial that for PQ, the light being incident on 

 Q the value of <p which satisfies the condition is 50° 25', and 

 for PP and incidence on P, the value of <p is 50° 21'. A 

 small change in these angles does not alter the difference 

 between the observed and calculated values of // e , which 

 affords the test of the law. 



The substitution of these values in the equation of Stokes 

 gives — 



M'e 

 PQ l-606114dc;'J.-6 



PR 1 -606103^1-6 



