392 



Prof. G. G. Stokes on the Foci of Lines [June 21, 



We see from (2) that as changes from to 90°, p changes from 

 a" 1 c 2 to c~ l a 2 , of which one is greater than a and the other less than a. 

 Hence for an intermediate value of p—a. For this value we have 

 from (2) 



tan 2 = at e~ + & ) = * /*'*) (4) 



In this case, as in that of a uniaxal crystal cut perpendicular to the 

 axis, there are only two focal distances at which a distinct image is seen. 

 But the two cases are easily distinguished ; for in the present case the 

 ordinary and extraordinary images are both polarized in definite planes ; 

 also at one of the focal distances only one of the systems of cross lines, 

 namely, those parallel to the principal plane, are seen distinctly ; and, 

 further, either extraordinary image becomes confused when the plate is 

 rotated in its own plane. 



For this particular inclination we have, in the case of Iceland spar, 

 according to the indices above quoted for the line D, 6=53° 34'. 



In this mineral the normal to the plane of easy cleavage is inclined to 

 the axis at the angle 44° 37'. Substituting this value in (2) and (3), 

 writing fi~ l , fx' 1 for a, c, we have, for the apparent indices of the 

 extraordinary pencil : — 



For lines For lines 



perpendicular to the parallel to the 

 principal plane. principal plane. 



r C 1-5777 .... 1-4094 



For the fixed line . . . . j D 1-5809 .... 1-4104 



{ E 1-5849 .... 1-4116 



In biaxal crystals the simplest case, and at the same time the most 

 important, is that of a plate cut perpendicular to one of the principal 

 axes, or so-called axes of elasticity. As the calculation for both pencils 

 is precisely the same as for the extraordinary pencil in a plate of a uni- 

 axal crystal cut parallel to the axis, it will be sufficient to give the 

 result. 



Let the principal axes be designated as those of y, z, to which relate 

 the parameters or principal velocities of propagation, a, b, e, and their 

 reciprocals, the principal indices, jjl, li, fi". I will suppose a, b, c, taken 

 in descending, and consequently fi, p' , li" in ascending order of magni- 

 tude *. For the arrangement of the Table, it will be convenient to specify 

 the direction of the line seen in focus, and that of the normal to the plane 

 of polarization of the image observed. "When these directions are dif- 

 ferent, the plane of the plate is defined, being that containing them both. 



* In the previous investigation for Iceland spar a was taken for the ordinary wave- 

 Telocity, in order to conform to the notation in Airy's tract, so that c was greater 

 than a. 



