V. Mathematical Considerations on the Prohlem of the Rainbow, shewing 

 it to belong to Physical Optics. By R. Potter, Esq. of Queens- 

 College. 



[Read Dec. 14, 1835.] 



Having lately, in the course of my academical studies, had occa- 

 sion to read more carefully the theory of the Rainbow, I was con- 

 vinced of the inadequacy of the popular mode in which it is treated 

 in elementary books (this is Sir Isaac Newton's explanation, see 

 his Optics, p. 147). The reason which is given, why the various 

 prismatic colours are seen, each, so brilliantly in the rainbow, is that 

 the intensity of any colour fades away so rapidly from its maximum, 

 that it does not prevent, in any great degree, the other colours being 

 seen as such. 



This is clearly an arbitrary assumption, which will not bear ex- 

 amination, for within the primary bow, the grayish light is of very 

 considerable intensity when the display is a fine one, and in a like 

 proportion in fainter displays. So that we should naturally expect the 

 brilliant colours yellow and green (even laying aside the red and orange) 

 to have still an intensity at the places of the indigo and violet, suffi- 

 cient to drown the effect of colour in those weak sliades. 



We find that this is the fact in certain cases, as in Fog bows 

 and similar appearances, when the size of the aqueous spheres is very 

 small, but in other cases the violet especially is very bright. The 

 popular theory, however, offers no reason why the sixe of the spherical 

 drops should influence in any degree the colours of the bows, and it 



