22 Sir D. Brewster on a new Species of Coloured Fringes. 



to that in Fig. 3, I observed them to be crossed with another 

 system of minute fringes parallel to one another, and to the 

 line joining the centres x and x. The object-glass which ex- 

 hibited this curious effect is not now within my reach, so that 

 I am unable to give any further account of this new system. 



In order to determine the surfaces of the double object- 

 glass, AD, Fig. 5, which are essential to the production of the 

 rings, I covered the convex surface A 1 B with oil of nearly 

 the same refractive power as glass, and the rings wholly dis- 

 appeared. Having removed the oil, I filled with the same 

 fluid the space or hollow meniscus between the lenses, when 

 the rings again disappeared. The lenses being again cleaned, 

 I removed CD, and could no longer observe any fringes. 

 Hence, it follows, that the action of the two surfaces of the 

 convex lens, and the inner surface of the concave one, are 

 necessary to the production of the fringes. 



From these facts it will appear that the coloured rings arise 

 from the interference of two pencils of light, one of which has 

 suffered three reflections within the convex lens AB, and has 

 passed yo^^r times through its thickness, with another pencil 

 which has suffered /too reflections within the convex lens, and 

 one reflection from the inner surface of the concave lens, and 

 has passed four times through the thickness of the convex lens, 

 and twice through the thickness of the meniscus of air. 



When the light is incident perpendicularly on the centre of 

 the lens, the interval of retardation, or the difference between 

 the lengths of the paths of the two rays, is equal to twice the 

 greatest thickness of the meniscus of air. Hence, if this thick- 

 ness is very small, the tints con-esponding to it will be dis- 

 tinctly observed; but if the thickness is considerable, as it 

 often is, the tints will belong to such high orders, that they 

 will only be seen when a small flame of homogeneous light is 

 used. 



As the incident ray advances from the centre towards the 

 circumference, the meniscus of air diminishes in thickness, 

 and also the interval of retardation, so that the orders of the 

 rings descend, as in Fig. 1. But there is a particular point 

 between the rings m and n, whei'e the interval of retardation 

 is nothing, or where the lengths of the paths of the two inter- 

 fering pencils are equal, so that we have a •white I'ing at that 

 place. Beyond this, the interval of retardation becomes per- 

 ceptible, and another system of rings commences, rising to 

 their highest order at the very circumference of the object- 

 glass. 



When the eye and the flame are in the axis of the object- 

 glass, the isochromalic lines are circles ; but at oblicjue inci- 



