330 SCIENTIFIC AMUSEMENTS. 



and secondly, when it occurs twice. Fig. 175 represents the first 

 case : a ray of sunlight Sa meets the outside of a spherical drop 

 of water at a, and is partly reflected and scattered ; whilst part 

 enters the drop, being refracted along db. At b internal re- 

 flection takes place along be ; and at c part of the light emerges, 

 being again refracted along cO to the eye of an observer at 0, in 

 such a fashion that the red part of the prismatic spectrum formed 

 in consequence of refraction meets his eye. Another ray of light, 

 Sd, meets a second drop of water situated slightly lower down, 

 and is similarly refracted and reflected along the course Bde/0 

 in such fashion that the violet ray of the spectrum now formed 

 is seen by the observer at 0. Hence the observer perceives the 

 red colour of the primary bow outside and the violet inside, the 

 other colours being intermediate in due order. 



Fig. 176 represents the second case. Here the ray Ba is first 

 refracted along ab, then twice successively internally reflected along 

 be and cd, and finally emerges at d, and is refracted to the eye of 

 the observer at 0, the ray reaching his eye being now the violet 

 one; whilst a drop situated at a lower level acts similarly, the 

 ray Be being refracted and reflected along the course BefghO, so 

 that the red ray of the spectrum now meets his eye. In this case, 

 consequently, the violet is outside and the red inside, i.e., the 



colours come in the 

 reverse order in the 

 secondary bow rela- 

 tively to that in which 

 they occur in the pri- 

 mary bow. Moreover, 

 on account of the mode 

 of formation of the two 

 bows and the values of 

 the index of refraction 

 between water and air 

 Fig. 176. Secondary Rainbow. for the various coloured 



rays, it results that whilst in the case of the primary bow 

 the angle between the lines Ba and Oe is about 42, and that 

 between Bd and Of 40J, the corresponding angles for the 

 secondary bow between Sa and Od and Be and Oh are respectively 

 about 54 and 51, or considerably greater ; so that the secondary 

 bow lies above the primary one. 



All drops situated on the surface of a cone, the apex of which 

 is the observer's eye and the axis of which is parallel to the sun's 

 rays, will act alike upon the light falling upon them, and produce 

 the same effect on the observer's eye ; so that when the angle 



