SHEWING IT TO BELONG TO PHYSICAL OPTICS. 151 



summit of the bow, and I have this memorandum : ' but the purple 

 of the principal bow was evidently mingled with the red of the second, 

 and I believed the purple of the second also to be mixed with the 

 red, and perhaps the orange also of the third bow. The three bows 

 thus considered were also of decreasing breadths as fringes in diffraction.' 



But an observation by Dr Langwith, quoted by Dr Young, proceeds 

 much more into details than the one I made as above, and the dis- 

 play must have been still more splendid. He says, "You see we 

 had here four orders of colours, and perhaps the beginning of a 

 fifth : for I make no question but that what I call the purple, is a 

 mixture of the purple of each of the upper series with the red of the 

 next below it and the green a mixture of the intermediate colours." 



Again he has this important and philosophical remark : " There are 

 two things which well deserve to be taken notice of, as they may per- 

 haps direct us, in some measure, to the solution of this curious pheno- 

 menon. The first is, that the breadth of the first series so far exceeded 

 that of any of the rest, that as near as I can judge, it was equal to 

 them all taken together. The second is that I have never observed 

 these inner orders of colours in the lower parts of the rainbow, though 

 they have often been incomparably more vivid than the upper parts, 

 under which the colours have appeared. I have taken notice of tiiis 

 so very often, that I can hardly look upon it to be accidental ; and 

 if it should prove true in general, it will bring the disquisition into 

 a narrow compass; for it will shew that this effect depends upon some 

 property whicii the drops retain, whilst they are in the upper part of 

 the air, but lose as they come lower, and are more mixed with one 

 another." 



The first question, as to the decreasing breadths, is answered by 

 Dr Young in the previous quotation, and is an effect familiar to those 

 who liave studied Physical Optics. The second also receives a com- 

 plete solution from considering the expression we have obtained, and 

 the state of rain in falling from a cloud. For though tlie drops v.ere 

 of small size on leaving the cloud, and such as to produce the super- 

 numerary bows, yet as they fall down, having different velocities from 



