6 On Experiments relative to the Interferences of Light. 



venience of this kind, and also liaving the advantage of de- 

 monstrating at once ihefad of the retai'dation, — and its mnount, 

 as being precisely proportional to the refraction. 



If in the interfering rays produced either by the two re- 

 flectors or the obtuse prism there be interposed a prism having 

 so small a refracting angle as to give very little colour, the 

 two rays which would go to form any one stripe will evi- 

 dently pass through different thicknesses of the prism ; also by 

 tracing their course through the successive refractions, it will 

 be I'eadily seen, that the ray which passes through the least 

 tliickness of the glass, is the more deviated, and passes through 

 a greater length of route before'it meets the other; thus that 

 its undulations are more retarded, and unless that retardation 

 be exactly compensated by the effect of the greater thickness 

 of glass on the other ray, no stripe could be formed. But in 

 point of fact, the whole set of stripes are seen in the deviated 

 image, unaltered, except by the trifling degree of colour and 

 a slight shifting towards the more refrangible end of the spec- 

 trum, obviously due to the prismatic refraction : — the truth of 

 the law of retardation is therefore manifest. 



(11.) The mathematical investigation of the difTerence of 

 routes and of retardation, showing that the two effects exactly 

 countei'balance each other, is extremely 

 simple. We have only to consider the 

 two interfering rays incident on a prism 

 of small angle a, in directions very 

 nearly perpendicular, and by conse- 

 quence having their paths within the 

 prism still more nearly perpendicular to 

 its first surface ; and at their emergence 

 being distant from each other by an in- 

 terval b measured on that surface, we 

 shall have the difference of their routes 

 within the prism expressed by 

 d =z b sm a. 



If we trace the course of one of the 

 rays through the several angles of re- 

 fraction (which may be expressed by 

 <J) <^, ■$;, cf>;„), we shall very easily perceive, 

 that, owing to the conditions above 

 stated in regard to the position of the 

 rays, we shall have very nearly 



fii = «;'. 



and thence sin (p^, = m sin «. 



From the smallness of the angle at which the rays meet 

 after emergence, we may take the difference of their lengths 



by 



