46 Geometrical Propositions applied 



two emergent waves parallel to each other and to the incid( 

 wave, moving along the emergent rays with equal velocities 



and preserving the distance - between their planes, 1 



minus wave being foremost. If 08, the radius of the sphere, 

 taken for unity, PM will be a number generally a very sm 

 fraction and the interval will be the thickness of the crys 

 multiplied by this number. 



50. Suppose the right line PMR, remaining always perpe 

 dicular to the face of the crystal, to describe a cylindrical si 

 face, with the condition that the part PM, intercepted betwe 

 the two sheets of the surface of refraction, shall remain of a cc 

 stant length ; the point R will then describe, on the surface 

 the crystal, a curve whose radii OR are the sines (to the radi 

 08} of the angles of incidence of a cone of rays ; and every r 

 S'O of this cone, when refracted by the crystal, will afford t 1 

 emergent rays, or two waves, having the same given inters 

 between them. Lines drawn from the eye parallel to the sic 

 of this cone are the emergent rays belonging to a ring, wh 

 rings are made to appear, in any of the usual ways, on trai 

 mitting polarized light through the plate of crystal. In nomii 

 conformity to this, we see that the line PM describes a ring 

 constant breadth between the two sheets of the surface of refre 

 tion. The ring described by supposing pm to remain consta 

 corresponds to the interval between two rays p and m reflect 

 at the same point of the second surface of the crystal, and th 

 emerging at the first. The other intercepts Pp, Mm, Pm, Bi 

 are proportional (48) to intervals like those in Newton's rings 

 to the intervals, namely, between the reflected ray Os and t 

 rays 8Pps, SMms, SPms, SMps, emerging at the first surfa 

 after one reflection within the crystal ; or to the intervals betwei 

 rays that are twice reflected in the crystal and the rays tran 

 mitted without reflection. 



51. The general investigation of the figure of a geometric 

 ring does not distinguish between the different intercepts, ai 

 will therefore include all the rings PM, pm, Pp, Mm, Pm, Mj 



