applied to the Wave Theory of Light. ‘ 257 
through the crystal ; as will appear by conceiving the planes that we have spoken of 
to be perpendicular to these lines. 
If the incident ray S'O were refracted in the ordinary way with an index equal 
o it would take the direction OP; if it were refracted, in like manner, with 
the index , it would take the direction OM; and if the two rays, thus ordinarily 
oy) 
Os 
refracted, were to emerge from the second surface of the crystal in directions parallel 
to OS, it is evident from what has been said, that they would be in complete accord- 
ance, respectively, with the rays SPS and SMS. 
If the surface of refraction should happen to have a node JN, which is a point of in- 
tersection where it admits an infinite number of tangent planes (3), let the direction 
of the incident ray S’ OS be chosen, so that the right line HS perpendicular to the 
face of the crystal, being produced below S, may pass through J, and we shall have 
a cone of refracted rays formed by the perpendiculars let fall from O upon the tangent 
planes at NV; all of which rays, on emerging parallel to OS from the second surface 
of the crystal, will be in complete accordance with one another. For we have just seen 
that if the ray S'OS were supposed to emerge after being refracted in the ordinary 
: ; WY : : 
way with an index equal to 55 , it would be in complete accordance with any ray of 
the cone. 
48. The interval between any two rays emerging at the same side of the crystal is 
the difference of their retardations. In taking the difference, the letters that are 
common to the names of the two rays may be left out. Thus the ray SPmMS is 
behind the ray SPS by the interval oy (Sm + SM)= <M. m. The line ~ Pp is 
the interval between the rays SMS and SMpPS, or between the reflected ray Os 
and the ray SPps ; and so on. 
49. The retardations of the two refracted rays SPS and SMS, emerging without 
vernal reflection, are SP and 5ySM respectively. The difference of these is 
98 Os 
face in directions parallel to the incident ray, the light in the plus emergent ray is 
eal® Or, in 
other words, the incident plane wave, perpendicular to OS, produces two emergent 
waves parallel to each other and to the incident wave, moving along the emergent 
PM, i 
2 8 S between their planes, 
the minus wave being foremost. If OS, the radius of the sphere, be taken for unity, 
PM will be a number,—generally a very small fraction,—and the interval will be the 
thickness of the crystal multiplied by this number. 
50, Suppose the right line PVR, remaining always perpendicular to the face of the 
crystal, to describe a cylindrical surface, with the condition that the part PM, inter- 
Consequently, when the two refracted rays have emerged from the second sur- 
behind the light in the minus emergent ray by an interval equal to 
rays with equal velocities V, and preserving the distance 
