28 Prof. Airy on the Phenomena of Newton's Rings, as formed 

 the expression assuming the form p sin X — (vt — x)— >- 



where increases from to it. This may be popularly ex- 

 plained in the following manner. The common Newton's 

 rings, formed between two lenses, are produced by the inter- 

 ference of the light reflected from the lower surface of the 

 upper lens with that reflected from the upper surface of the 

 lower lens. Now if the upper lens be raised a little, or the 

 lower depressed a little, the rings contract. As the only im- 

 mediate effect of depressing the lower lens is to cause the light 

 reflected from it to describe a longer path, or to have its phases 

 retarded, it appears that a contraction of the rings may be 

 considered as the effect of a retardation in the phase of the 

 light reflected from the lower surface. The contraction of the 

 rings then in passing the polarizing angle of the diamond re- 

 quires us to admit that the phase of the reflected light (the in- 

 cident light being polarized perpendicular to the plane of the 

 reflexion) is, on increasing the angle of incidence by a few 

 degrees, retarded nearly 180°. 



The retardation, however, is not quite 180°. For if it were, 

 the character of the rings would be exactly changed, so that 

 the proportion of the size of the central black. spot to that of 

 the first white ring would be the same as that of the central 

 white spot (before the change) to the first black ring. But as 

 the central black spot formed by rays polarized perpendicular 

 to the plane of reflexion is distinctly larger than that formed 

 by rays polarized in the plane of reflexion, it seems that the 

 black ring has not contracted completely, or that the alteration 

 of phase is not quite 180°. This reasoning it must be con- 

 fessed is not certain, as the same thing would be explained by 

 supposing a small alteration of phase in the light polarized in 

 the plane of reflexion. I may mention here, that in the New- 

 ton's rings formed between two lenses of the same kind of 

 glass, the central black spot in those formed by light polar- 

 ized perpendicular to the plane of reflexion is larger than in 

 those formed by the light polarized in the plane of reflexion. 



If, while the white-centred rings are under examination, 

 the tourmaline and doubly-refracting prism are turned round, 

 the rings become faint, but do not disappear, and are changed 

 into black-centred rings by the contraction of the rings. 

 This is exactly similar to what takes place when a lens is 

 placed on a metallic surface, and it proves that (as in the 

 former paper), while the angle of incidence is a few degrees 

 less than the maximum polarizing angle of the diamond, the 

 phase of light polarized perpendicular to the plane of re- 

 flexion is more retarded than the phase of light polarized in 

 that plane. 



