OF NEKTON'S OPTICS. 



43 



therefore, O P bears the same proportion 

 to OB, as OA, or TP, bears to OP. 

 Now, since the magnitudes of O P, and 

 OB, are known, we know how many 

 times OB is greater than OP. Then 



P will be the same number of times 

 greater than O A, or T P. Thus, if O B 

 were 182 inches, and O P 8-79ths of an 

 inch, the thickness T P is found by com- 

 mon arithmetic to be about -th 



1774784 



part of an inch. 



Calculating in this manner, Newton 

 found a very singular analogy to subsist 

 between the thicknesses at which the 

 bright and dark rings of each colour 

 were produced. Let the thickness at 

 which the first bright ring of any ho- 

 mogeneous colour is produced, be called 



1 ; the thickness at the next bright ring 

 will be 3 ; the next 5 ; the next 7 ; and 

 so on ; the thicknesses of the successive 

 bright rings being represented by the odd 

 integers. Again, the thickness of the 

 air at the dark ring, which immediately 

 succeeded the first bright ring, was found 

 to be twice its thickness at the first bright 

 ring ; and therefore the central spot being 

 considered as the first dark ring, the 

 second dark ring will be at the thick- 

 ness 2. The third dark ring was found 

 to be at the thickness 4 ; the fourth at 6, 

 and so on : the thicknesses of the air at 

 the several dark rings being represented 

 by the even integers. 



The proportion which we have now 

 explained was found to prevail among 

 the rings, whatever might be the colour 

 of the light projected on the lens ; but 

 the absolute magnitudes of the rings 

 was, as we have stated, different in each 

 kind of light. This will, perhaps, be 

 better understood by example. Suppose 

 an inch divided into 180,000 equal parts, 

 and let one of those parts be the thick- 

 ness at which the first ring of a certain 

 colour, say green, appears, homogeneous 

 green light being projected on the lens. 

 At a thickness equal to two of these 

 parts will be a dark ring. At a thick- 

 ness equal to three of these parts will 

 appear the second bright green ring, and 

 so on alternately. 



The rings of the other colours will 

 succeed each other in a similar manner, 

 with this difference, that the thickness at 

 which the first ring appears will be less 

 for the more refrangible rays, i. e. those 

 of a bluish tint, and greater for the less 

 refrangible rays, which take the yellow 

 or red hues, and that the intervals be- 

 tween the rings will also be less for the 



former rays than for the latter. Hence 

 we may easily perceive how the suc- 

 cession of coloured rins:s is produced 

 when compound solar light is projected 

 on the lens. In this case each compo- 

 nent part of the light forms its own set 

 of rings, and the rings of one colour in- 

 termixing with those^of another, form the 

 several series of coloured rings already 

 described. 



(56.) All that has been observed re- 

 specting the rings produced by the light 

 reflected from the lens will apply, with the 

 requisite modifications, to the rings pro- 

 duced by the light transmitted through 

 it. These latter, however, are much less 

 vivid than the reflected rings. 



Before we proceed further in our ac- 

 count of these phenomena, it may be 

 useful, in impressing them on the me- 

 mory of the reader, to give some ac- 

 count of the manner in which Newton 

 explained them. He considers that every 

 ray of light, in its passage through the 

 surface which separates two media of 

 different densities, is put into a certain 

 transient constitution or state, which, in 

 the progress of the ray, returns at, equal 

 intervals, and disposes the ray at every 

 return to be easily transmitted through 

 the next refracting surface, and between 

 the returns, to be easily reflected by it. 

 Let A B (fig. 45) be a ray of pure 

 homogeneous light falling perpendicu- 

 larly on a refracting surface, S S, Let us 

 suppose that the medium through which 



Fig. 45. 

 A 



7 



9 



3 



4 -- 



6. 



7- 



A B has passed is glass, and that the 

 medium included between the surfaces 

 S S and S' S' is air. Take B 1 in the di- 

 rection of AB, and equal to the thickness 

 of the air between the lenses at which 

 the first ring of the homogeneous light, 

 now supposed to fall on S S, appeared. 

 From 1 take the intervals 2, 3, 4, &c. 

 equal to B 1. The action of the surface, 

 SS, upon the ray, is supposed to 



