10 Mr. Potter on the Radii and Distance 



sures of the radii of the primary and secondary bows and their 

 distance, as given by Sir Isaac Newton, with the resuks ob- 

 tained from the theory, by using Frauenhofer's correct re- 

 fractive indices. This comparison, which is detailed below, 

 completely establishes the discovery that the ordinary rain- 

 bows are not in the places hitherto asssigned to them. 



I had confirmed Sir Isaac Newton's measures in the year 

 ISS^, by measures of the radii of the iris seen frequently in 

 the mornings of autumn, in the dew-drops which float on the 

 scum of stagnant ponds. These measures, although they had 

 no claims to very great accuracy, were yet so nearly in ac- 

 cordance with those of Sir Isaac Newton as to convince me 

 that the wide discrepancies between the theoretical and ob- 

 served radii could not possibly arise from errors of observa- 

 tion ; and this I urged in a discussion at a meeting of the 

 Cambridge Philosophical Society in the spring of 1836. 

 Since then, the Astronomer Royal has deduced expressions 

 on the undulatory theory of light, (see the May number of 

 this journal, p. 452,) which indicate that the brightest parts of 

 the bow ought to have their position different from those cal- 

 culated from previous theories, and in the direction which 

 the observed measures require; but he finds that the light 

 shading away from the maximum of brightness, has at the 

 old position a brightness which is about one half of that at 

 the maximum, and which ought therefore to be distinctly 

 seen : this is the point to be examined in order to test his ex- 

 pressions. 



The general discovery that the bows are not in the posi- 

 tions assigned to them hitherto, has been confirmed by mea- 

 sures taken by Professor Miller in M. Babinet's experiment, 

 in which the phaenomena analogous to those forming the rain- 

 bows are viewed in a small cylindrical stream of water. 



Proceeding to discuss the observations, we find that Sir 

 Isaac Newton's principal measurements were on the extreme 

 radius of the primary bow and on the least distance between 

 the two bows ; for after giving the results of his computations 

 he says, " And such are the dimensions of the bows in the 

 heavens found to be very nearly, when their colours appear 

 strong and perfect. For once, by such means as I then had, 

 I measured the greatest semidiameter of the interior iris, 

 about 4-2 degrees, and the breadth of the red, yellow, and 

 green in that iris 63 or 64 minutes, besides the outmost faint 

 red observed by the brightness of the clouds, for which we may 

 allow 3 or 4 minutes more. The breadth of the blue was about 

 40 minutes more, besides the violet, which was so much ob- 

 scured by the brightness of the clouds that I could not mea- 



