to the Wave Theory of Light. 39 



For a medium of the common kind, or a singly refracting 

 medium, we may use the letters S and s. Thus the incident ray 

 S'OS, or any ray emerging parallel to OS from the second sur- 

 face of the crystal, may be marked by the letter S ; while the 

 ray Os produced by common reflection, or any ray emerging pa- 

 rallel to Os from the first surface, may be denoted by the letter s. 

 39. The course of a ray through the crystal may now be 

 easily expressed. A ray SMps, for example, is a ray (S) inci- 

 dent on the crystal, undergoing minus refraction (M) at the 

 first surface, plus reflection (p) at the second, and emerging (s) 

 from the first surface in a direction parallel to Os. Of this ray 

 the part within the crystal is Mp. A ray SPS is a ray plus re- 

 fracted, and then emerging in a direction parallel to that of 

 incidence. A ray SPpMS is a ray plus refracted at the first 

 surface, then plus reflected at the second surface, then minus 

 reflected at the first surface, and finally emerging from the second 

 surface in a direction parallel to that of incidence. Its path 

 within the crystal is PpM. 



These examples indicate the general method of expressing 

 the path of a ray. 



Suppose light to be moving in the same direction and with 

 the same velocity along two proximate parallel rays, so that it 

 is at the point A in one ray when it is at the point B in the 

 other ; and through the points A and B conceive two planes 

 perpendicular to the common direction of the rays. These planes 

 are either coincident, or maintain a constant distance. In the 

 first case, the rays are said to be in complete accordance. In the 

 second case, the constant distance between the planes is called 

 the interval between the portions of light composing the rays, or 

 the interval between the waves that move along the rays. 



We proceed to find the lengths of these intervals in the case 

 of rays emerging parallel to each other, at either side of the 

 crystal that we have been hitherto considering. 



41. Let the tangent planes at P, M, p, m, intersect the plane 

 of the figure (Fig. 15) in the right lines PP y , MM, , pp^ mm,, 

 which of course are tangents to the section of the surface of re- 



