Schaw. — On Bcdnboius. 455 



be reflected to our eyes. The particular raindrops at that 

 part of the falling sheet of raindrops send their effective con- 

 centrated parallel rays direct to our eyes, and produce the 

 brilliant image apparently at that spot, and, although scat- 

 tered rays from that raindrop may reach the water at the 

 right angle to be reflected to our eyes, they will be weak, scat- 

 tered rays, and will not produce any effect beyond that of 

 general illumination of the water. And the same is true of the 

 particular raindrops forming the image in our eyes of any 

 part and all parts of the rainbow we see. But the question 

 arises, Are there not other raindrops at other parts of the 

 rain-sheet the effective parallel rays from which, falling on the 

 surface of the water, and reflected therefrom, will reach our 

 eyes and produce there the brilliant sensation of a rainbow 

 reflected in the water ? 



Professor Tait, in his treatise on light, puts the question 

 and the answer in this way : " Can a rainbow be seen by re- 

 flection in still water?" "To this, of course, the answer is 

 that a spectator sees, by reflection in still water, the rainbow 

 he would have seen had the water been removed, and had his 

 eye been at the position formerly occupied by its image in the 

 water." He adds, "But a reflected rainbow differs from a 

 rainbow seen directly, in the fact that, as the light forming the 

 latter is partially polarised, the intensity of the former is 

 modified differently at different points in the act of reflection." 

 His reply therefore is that a reflected rainbow can be seen, 

 though, as before observed, it will not be a reflection of the 

 particular rainbow perceived by direct vision. And, although 

 his reply is not quite easy to understand, owing to its extreme 

 brevity, it gives the key to the solution of the question. The dia- 

 gram (PL LI., fig. 8) will explain. By the words "its image "he 

 means the image of the observer's eye as it would be reflected 

 in still water vertically beneath it, where it would appear 

 to be as deep below the surface as his eye was above it. The 

 geometrical construction shows that a line from this point at 

 an angle of 41° with the direction of the sun's rays cuts the 

 water-line at a point where a ray, proceeding from a drop in 

 the rain-sheet at an angle of 41° with the direction of the sun's 

 rays, would be reflected to the observer's eye, the angles of in- 

 cidence and reflection at the surface of the water being equal. 

 The ray reflected to the eye would give an image of the highest 

 point of a rainbow which would appear to be at the same 

 distance below the surface of the water at the rain- sheet as 

 the drop which emitted the ray was above it. Knowing that 

 the centre of the circle must be at the point where the parallel 

 sun's ray, passing through the reflected image of the eye, cuts 

 the vertical rain-plane (produced below the surface of the 

 w r ater), we have no difficulty in describing the arc of the rain- 



