Schaw. — On Rainboivs. 453 



sensation of white light. The laws of the refraction of the differ- 

 ent-coloured rays as they pass from one transparent medium 

 into another of different density are known, and the angles at 

 which the extreme visible rays, violet and red, are emitted in 

 the cases of the primary and the secondary bow are noted in 

 PI. L., fig. 5, from which it will be observed that in the case of 

 the primary bow the less refrangible red rays will reach the 

 eye from raindrops on the outside of the band of light, the 

 violet rays from raindrops on the inside ; while in the case of 

 the secondary bow, owing to the second reflection the reverse 

 will be the case, and the outer part of the band of light is 

 violet, the inner edge red. 



Two other facts connected with the ordinary rainbow must 

 be noted before we pass to the special cases which are to be 

 discussed : First, that owing to the apparent size of the sun a 

 rainbow is formed by the light coming from each point in the 

 sun's disc : this results in the formation of a number of rain- 

 bows superimposed upon one another, and producing the 

 blending of the colours in the spectrum of the rainbow which 

 we always observe. From this also follows a degree of un- 

 certainty in the exact measurement of the angles subtended 

 at the eye by the circles forming the edges of the bows, and 

 of the bands of colour in them. Different observers have 

 obtained slightly varying results. The angles I have quoted 

 can therefore only be taken as near approximations. Second, 

 that, though there is a principal maximum of emergent 

 parallel rays produced, as before stated, both by a single and 

 by a double reflection inside the drop, there are also secondary 

 fainter maxima which produce the spurious rainbows some- 

 times seen inside the primary and outside the secondary bow, 

 and described in Mr. Harding's paper. 



We may now pass on to the case of a rainbow produced by 

 the reflected light of the sun. 



An observer in a boat on a. calm sheet of water may see on 

 a rain-cloud in front of him not only a primary and a secondary 

 rainbow having the same centre as usual, but also a third bow 

 having its centre at a higher elevation than that of the others. 

 He will ascertain the source of this third rainbow by turning 

 round to face the sun, when he will notice that by reflection 

 a virtual image of the sun is seen at the same depression 

 below the horizon as the elevation of the sun itself above the 

 horizon. It is the light from this reflection which produces 

 the third rainbow, the centre of which is in the line inclining 

 upwards from the reflected sun through the observer's eye. If 

 the sun be close to the horizon the sun and its reflection will 

 be so close together that the centres of the primary rainbow 

 and of that formed by the reflection of the sun will nearly coin- 

 cide, and the third bow may be difficult to distinguish, or it 



