THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



MARCH 1890. 



XXIV. The Form of Newton's Rings. By A. W. Flux, 



B.A., Fellow of St. Johns College, Cambridge* . 



THE following essay deals with the formation of the equa- 

 tions of Newton's Kings, when the inclination of the 

 surfaces concerned in their formation is taken into account, 

 not merely with regard to its effects in producing a gradually 

 varying thickness of the intervening medium, but also in 

 deflecting the rays so that, though parallel at incidence, they 

 are no longer so on emergence. 



Owing chiefly to the finite size of the sources of light avail- 

 able, in spite of the use of the best collimating instruments, 

 the incident light is not a single plane wave, but consists of 

 an infinite series of such waves having their fronts inclined at 

 small angles. Each incident wave will produce a series of 

 colour-effects at any point in the field of view, but these are 

 in general masked by the effects due to other waves ; only in 

 the neighbourhood of a certain surface does there exist distinct 

 coloration. The main result of the calculations of this paper 

 is the determination of the surface on which the colour-effects 

 are most clearly defined. This has been effected both for 

 reflected and for transmitted light. 



The conclusions arrived at are the following : — 

 (1) The rings lie on a certain ruled surface of the third 

 order, which cuts the planes through the central spot parallel 



* Communicated by the Author. 

 Phil. Mag. S. 5. Vol. 29. No. 178. March 1890. S 



