[156] PROFESSOR STOKES, ON THE 



It readily follows from this expression that a system of rings is formed similar to the 

 transmitted rings of the system to which Newton's name is especially attached. The rings in 

 the present case, however, especially when viewed in air, are far more brilliant, and in this 

 respect more resemble the reflected system. If e x be the radius of the first bright ring, for 

 which R = X, the length of a wave of light, 



A A*X 



«i - V -j- . c ; 



and for the bright ring of the order n, e' = y/n , e x . The formula (14) has already been dis- 

 cussed by Sir John Herschel, and compared with Newton's measures, with which it manifests 

 a very close agreement. 



With white light, only a moderate number of rings can be seen, on account of the varia- 

 tion of the scale of the system depending on a variation in the refrangibility of the component 

 parts of which white light is made up. When the rings were formed in air, and the source 

 of light was the flame of an oil-lamp with a small wick, I have counted seven or eight sur- 

 rounding the central bright spot. But when the system is viewed through a prism, or when 

 the flame of a spirit-lamp is used, an immense number of rings may be seen. 



7. Next, suppose the luminous point out of the axis. Referring to the formula (5), 

 we see that the retardation is not now equal to zero at the axis, but throughout a circle whose 

 radius e is equal to e. Hence the achromatic line* of the system, which was formerly 

 reduced to a point, is now a circle having its centre in the axis, and passing through the 

 luminous point and its image, which are situated at the opposite extremities of a diameter. 

 The fringes of the first order will be a pair of circles having their centre in the axis, and 

 lying, one outside, and the other inside the central fringe : the fringes of the second order will 

 be another pair of circles lying, one outside the larger, and the other inside the smaller fringe 

 of the first order, and so on. It is to be remarked, however, that only a finite number of fringes 

 are formed inside the central white fringe. If the value of R when e = be denoted by 

 — M X, » will be a numerical quantity, a function of X, which determines the number of 

 fringes and the fraction of a fringe, belonging to the light of which the wave-length is X, 

 which are formed inside the central white fringe. The value of n may be got from equation 

 (5) on putting e = 0, which gives 



te 2 

 niXc 2 



If white light be used, and if n exceed 8 or thereabouts for rays of mean refrangibility, all 

 the fringes which the overlapping of the different colours allows to be visible are formed inside 

 as well as outside the central white fringe ; and if the luminous point be moved still further 

 from the axis, a portion of the field of view around the axis will appear free from rings. If 

 the radius of the central white fringe, or, which is the same, the distance of the luminous 



* I use this term to denote the locus of the points for which the retardation is equal to zero, which forms a curve on either 

 side of which the colours are arranged in descending order. 



