188 Proceedings of the Royal Irish Academy. 



a proper position, whilst at the same time the sun shines upon it, we 

 shall observe a brilliant arc of rainbow lying apparently within the 

 drop, and accompanied by many supernumerary rings. The colours of 

 these rings are alternately green and purple, and they are all concen- 

 tric with the principal bow. If we now alter the position of the drop a 

 little towards the sun, these colours will disappear, and the secondary 

 bow, encircled with brilliant supernumerary rings on its outside, will 

 come into view. By changing the position of the drop with respect 

 to the eye, at the same time retaining it at the proper elongation 

 from the sun, we get a view successively of every portion of the arcs 

 produced by the drop, and can perceive that the form of each bow is 

 nearly that of a circle, convex to the sun. The curvature of the caustic 

 for the secondary bow is much greater than that of the primary, 

 so that within the limits of the visible arcs it is seen to intersect the 

 primary at two points equally distant from the centre of the drop, its 

 supernumerary rings converging towards it as they approach those 

 points. 



In order to show that the large drops do not produce the inter- 

 ference rings, we may contrive to make a hair take up a comparatively 

 large drop of water, or we may bring some of the small drops together 

 so as to form larger ones, l^ow, upon examining those whose dia- 

 meters are greater than about -^ of an inch, we can perceive that they 

 form beautiful bows, both primary and secondary, but in each case 

 without any trace of supernumerary rings. In these drops, also, it is 

 seen that there is " a continued diffusion of fainter light within the 

 bright termination which forms the rainbow'," and the colours of the 

 latter are more brilliant and homogeneous than those formed in the 

 small drops, especially the red, which is strikingly distinct at the edge. 

 The limit of size beyond which interference does not take place may 

 be determined by subjecting one of the large drops to a gentle evapo- 

 ration. For this purpose the heat of the sun, in summer, will be suf- 

 ficient. As soon as the diameter of the drop is decreased below the 

 assigned quantity the supernumerary rings will be formed, being at 

 first very narrow, though in great numbers, and they will continue to 

 be produced at all smaller sizes. Upon examining various dimensions 

 of the drop, we observe that the nearer its diameter approaches the 

 limit referred to the more numerous are the rings, but the smaller 

 sizes cause the colours to be broader. Also, as the size of the drop de- 

 creases, the colours produced are somewhat blended, the red of the 

 principal bows appearing partly orange or yellowish even at the edge, 

 and the supernumerary colours becoming yellowish and dark purple. 

 "When the drop is still further diminished, the primitive bows are 

 exactly similar to the others, consisting of two colours only, and, be- 

 fore it finally vanishes, only bright and dark bands are produced. 



The foregoing experiments may be made with other fluids, and it 

 appears that the limiting diameter of the drop diminishes as the refrac- 

 tive power increases : thus it is less in oil of turpentine, linseed oil, &c., 

 than in water. The rings are particularly brilliant and numerous in. 



