456 Transactions. — Miscellaneous. 



bow that would be seen from the position of the reflected 

 eye, and in drawing its reflection which might be seen by the 

 actual observer. 



It will be evident that the lower and nearer to the reflect- 

 ing surface the eye of the observer, the less will be the distance 

 between the eye and its reflected image, and, consequently, 

 the locus of the invisible rainbow to be seen by reflection will 

 more nearly correspond with that seen by direct vision, and 

 the reflection would seem very like a reflection of the visible 

 rainbow were it not for the polarisation of the rays emitted 

 from the raindrops after reflection and refraction. This 

 polarisation has been found to correspond with the radii of 

 the arch. Thus the light coming from the summit of a semi- 

 circular arch would be polarised at right angles to the light 

 coming from the feet of the arch, and the direction of polarisa- 

 tion would change gradually between these points. The 

 polarised rays from the top of the arch w 7 ould, I think, be 

 more strongly reflected than those from the sides, and I should 

 therefore expect to see the lower part of the inverted reflection 

 more distinctly than that of the sides. 



The question still remains, Has any one ever seen such a 

 reflection ? I can trace no record of such an experience, and 

 I attribute it to the fact that almost always the surface of 

 the water is strongly illuminated by the sun when a rainbow 

 is formed over still water, and that, consequently, the refracted 

 and reflected rays which would form this reflected image are 

 overpowered by the strong illumination of the water-surface. 

 To see distinctly the reflection of a bright object in a mirror, 

 the mirror itself must be in comparative shade. This con- 

 dition might be produced by the shadow of a ridge of land, 

 however, and, although the meteorological conditions at Wel- 

 lington are rarely favourable to the exhibition of a rainbow 

 reflection in calm water, yet, were a shower to fall over the 

 harbour towards sunset without wind, the shadow thrown by 

 the hills on the west of the harbour might enable us to observe 

 the evidently very rare but possible phenomenon of an inverted 

 rainbow seen by reflection on the water. From a yacht be- 

 calmed in mid-harbour, or from Somes Island, the bow, or 

 bows, formed by the sun reflected in the calm w 7 ater might be 

 observed. 



In considering the subject of rainbows geometrically, I 

 was at first led to the conclusion that they must often appear 

 not as arcs of circles but as portions of ellipses. I have not 

 seen any allusion to this in books, nor had I hitherto thought 

 of looking for or expecting any such distortion of the circular 

 arch, but I think there can be no question that wherever the 

 raindrops emitting the pencils of parallel rays which reach 

 our eyes are not equidistant from the eye they cannot lie in 



