274 



SENARMONT ON THE OPTICAL CHARACTERS OP 



It follows from this that the interior angle of the optical axes 

 is, in sulphate of potash 66° 54', and in the chromate 49° 32'. 



This double result is, moreover, verified by particular conse- 

 quences. 



The rings may easily be observed in sulphate of potash through 

 the faces of the prisms of 73° 28' and 112° 22'. In the former 

 case the axes form an apparent angle of 45° 56', and in the 

 second an angle of 66° 52'. 



These data suffice for the calculation of the interior angle of 

 the optical axes without the necessity for determining the index 

 of refraction*, and with the above measurements this angle is 

 found to be = 67° 20', almost identical with the first. 



In chromate of potash, likewise, the rings may be observed 

 through the faces of the prisms of 73° 28'. They have, at least 

 apparently, green outside and the orange inside, but it is easy to 

 perceive that the axes have intersected after their emergence, 

 and the angle which they thus include between them was 

 found equal to 4° 7'» From the above data, then, it follows that 

 * Let (PL IV. fig. 5.) 



m be the semi-angle between the normals of the first pair of faces. 



M the same angle for the second pair. 



<f> the interior semi-angle of the optical axes. 



r and R their interior incidence upon the two kinds of faces. 



t and I the corresponding angles of emergence. 



$, e the apparent semi-angles of the optical axes after their emergence. 



I the index of refraction, 



m=zr-\-(f)=i-\-e, M=R4-0=I-j-0, 

 sin (wi— ^=/sin {m—cp), sin (M— 0)=/ sin (M— <^) ; therefore 



fM-\-m ,\ M — m L. ^ J 



tan 



(^-*)=-" 



tan [^+(^-6)] 

 In the present instance, 



m=3S''49', M=53°17', ^=33° 26', 0=22° 53', 



tan (43° 33'-<^)=tan 9° 44' ^^" ^^^ ^\ <^=33° 40'. 

 tan lo 



