186 Proceedings of the Royal Irish Academy. 



XXXII. — Ox THE SuPEENTJilEEAJRT ElJfGS OF THE EaDOOW. Bj 

 PhTT.TP BuRTOis'. 



[Eead November 11, 1878.] 



The explanation of the rainbo-vr, Tvliich was given by Sir Isaac 

 iN'ewton in his " Optics," did not comprise any account of the 

 coloured rings frequently to be seen within the violet of the primary 

 bow, and, more rarely, outside that of the secondary ; nor is it pro- 

 bable that these phenomena had been noticed when he wrote. The 

 theory thus remained defective until 1803, when Dr. Toung showed 

 that the supernumerary colours were caused by the interference of two 

 portions of light, which, though incident upon the drops of rain at dif- 

 ferent angles, were emitted parallel, and reached the eye, after having 

 traversed unequal spaces. According to this principle, the places of 

 the additional rings, with respect to the primitive rainbows, must vary 

 with the size of the di'ops by which they are formed ; but a different 

 method of estimating the effects of interference, devised by Sir Gr. 

 Aiiy in 1838, seems to be generally adopted at the present day. In the 

 account of the latter system, which is given in a recent publication,^ it 

 is stated universally that the calculation shows ' ' there is a succession 

 of feebler and feebler concentric cii'cles of maximum brightness — in- 

 side the principal maximum in the primary bow, and outside it in 

 the secondaiy " ; and no reference being made to the effect of different 

 dimensions of the di'ops, the results obtained would seem to be indepen- 

 dent of such variation, from which it may be inferred that the pheno- 

 mena are always similar, and that all the di'ops are equally effective 

 to produce them. As many appearances of these bows have come 

 under my notice, I can perceive that the conclusions now referred to 

 are not warranted by obseiwation ; I am, therefore, induced to put 

 forward this Paper, in which I shall endeavoiu' to show that the posi- 

 tions and breadth of the interference bows do actually vary within 

 certain limits, though not perhaps to the extent which Dr. Young's 

 theory would seem to requii'e ; also, that the phenomena in question 

 can only be produced by drops, which do not exceed a certain size. 



The most usual appearance presented by the additional bows 

 agrees very well with the description given in 1722 by Dr. Langwith, 

 who seems to have been one of the first to observe them. " The colours 

 of the primary bow," he says, " were as usual, only the purple very 

 much inclining to red, and well defined : under this was an arch of 

 green, then alternately two arches of reddish purple, and two of green, 

 and under all a faint appearance of another arch of purple. . 

 "We had here four orders of colours, and perhaps the beginning 

 of a filth : and the breadth of the first series so far exceeded that 



^ Chambers' " Encyclopsedia." 



