8 Dr. Young’s Experiments and Calculations 
paths described by the two portions of light are equal to a con- 
stant 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 con- 
clusion 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 some- 
what less decidedly marked where it approaches to its axis. 
These fringes have a slight resemblance to the hyperbolic fringes 
observed by Newton ; but the analogy is only distant. 
III. APPLICATION TO THE SUPERNUMERARY RAINBOWS. 
The repetitions of colours sometimes observed within the 
common rainbow, and described in the Philosophical Transac- 
tions, by Dr. Lang with and Mr. Daval, admit also a very easy 
and complete explanation from the same principles. Dr. Pem- 
berton has attempted 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 explanatory of the rainbow, regularly reflected 
from the posterior surface of the drop, and crossing each other 
in various directions, till, at the angle of the greatest deviation, 
they coincide with each other, so as to produce, by the greater 
intensity of this redoubled light, the common rainbow of 41 
degrees. Other parts of these two portions will quit the drop 
