RELATIVE TO PHVSICAL OPTICS. 



643 



two classes of phenomena to the same cause. 

 It is very easily shown, with respect to the 

 colours of thin plates, that each kind of light 

 disappears and re^ippears, where the differ- 

 ence of the routes of two of its portions are 

 in arithmetical progression ; and we have 

 seen, that the same law may be in general 

 inferred from the phenomena of diffracted 

 light, even independently of the analogy. 



The distribution of the colours is also so 

 similar in both cases, as to point immedi- 

 ately to a similarity in the causes. In the 

 thirteenth observation of the second part of 

 the first book, Newton relates, that the in- 

 terval of the glasses where the rings appeared 

 in red light, was to tlie interval where they 

 appeared in violet light, as 14 to 9 ; and, in the 

 eleventh observation of the third book, that 

 the distances between the fringes, under the 

 same circumstances, were the 22d and 27th 

 of an inch. Hence, deducting the breadth of 

 the hair, and taking the squares, in order to 

 find the relation of the difference of the 

 routes, we have the proportion of 14 to 9|, 

 which scarcely differs from the proportion 

 observed in the colours of the thin plate. 



We may readily determine, from this ge- 

 neral principle, tlie form of the crested 

 fringes of Grimaldi, already described; for 

 it will appear that, under the circumstances of 

 the experiment related, the points in which 

 the differences of the lengths of the paths 

 described by the two portions of light are 

 equal to a constant quantity, and in which, 

 therefore, the same kinds of light ought to 

 appear or disappear, are always found in 

 equilateral hyperbolas, of which the axes 

 coincide with the outlines of the shadow, and 

 the asymptotes nearly with the diagonal line. 

 Such, therefore, must be the direction of the 



fringes ; and this conclusion agrees perfectly 

 with the observation. But it must be re- 

 marked, that the parts near the outlines of the 

 shadow are so much shaded off, as to render 

 the character of the curve somewhat less de- 

 cidedly marked where it approaches to its 

 axis. These fringes have a slight resemblance 

 to the hyperbolic fringes observed by New- 

 ton ; but the analogy is only distant. 



HI. APPHCATION TO THE SUPERNUME- 

 RARY RAINBOWS. 



The repetitions of colours, sometimes ob- 

 served within the common rainbow, and de- 

 scribed in the Pliilosophical Transactions, by 

 Dr. Langvvith and Mr. Daval, admit also a 

 very easy and complete explanation from the 

 same principles. Dr. Pemberton has at- 

 tempted to point out an analogy between 

 these colours and those of thin plates; but 

 the irregular reflection from the posterior 

 surface of the drop, to which alone he attri- 

 butes the appearance, must be far too weak 

 to produce any visible effects. In order to 

 understand, the phenomenon, we have only 

 to attend to the two portions of light which 

 are exhibited in the common diagrams ex- 

 planatory of the rainbow, regularly reflected 

 from the posterior surface of the drop, and 

 crossingeach other in various duections, till, at 

 the angle of the greatest deviation, they.coin- 

 cide with each other, so as to produce, by the 

 greater intensity of this redoubled light, the 

 common rainbow of 41 degrees. Otherparts of 

 these two portions will quit the drop in direc- 

 tions parallel to each other ; and these would 

 exhibit a continued diffusion of fainter light, 

 for .23° within the bright termination which 

 forms the rainbow, but for the general law 

 of interference, which, as in other similar 



