SECONDARY BOW. 331 



between the axis of the cone and a generating line thereof is 

 40 J, a portion of a violet circle will be visible ; concentric with 

 this and outside will lie the other colours, terminating with red, on 

 the periphery of a wider cone where the angle is 42, thus 

 forming the primary bow ; concentric with and outside this again, 

 on the periphery of a still wider cone of 51, will lie another red 

 circle, external to which come the other colours, terminating with 

 violet on the periphery of a cone of 54, thus forming the 

 secondary bow with inverted order of colours. The secondary 

 bow is generally much fainter than the primary one, on account 

 of the greater loss of light through reflection. Under favourable 

 conditions a tertiary bow may be seen, concentric with the others 

 and outside them ; usually, however, the colours are so weakened 

 by repeated reflections, <fec., that the tertiary bow is imperceptible. 



It results from the conical angles above mentioned that if the 

 sun be elevated above the horizon more than 40 to 42, the primary 

 bow will fall wholly below the horizon, as will the secondary bow 

 when the sun is more than 51 to 54 high in the heavens; so that, 

 under these circumstances, no rainbow can be seen excepting when 

 the spectator is so placed that the refracting and reflecting drops are 

 below his level, as when standing on a mountain peak, or when 

 looking downwards into the spray of a cataract. If, however, the 

 sun be less elevated above the horizon, the arches will be corre- 

 spondingly raised, so that when the sun is just setting or rising the 

 summit of the primary bow will be elevated 40 to 42 high, and its 

 " legs " will subtend an angle of 80 to 84 at the observer's point of 

 view; whilst the secondary bow will be elevated 51 to 54, and 

 will subtend at its base an angle of 101 to 108 corresponding 

 variations being introduced according as the sun is at intermediate 

 heights, and according to the position of the observer relatively to 

 the refracting and reflecting droplets. 



Water is by no means the only substance capable of forming 

 " rainbows " ; any transparent fluid' reduced to fine spray by 

 mechanical means or otherwise, and suitably situated in reference 

 to a sufficiently brilliant source of light and to the eye of the ob- 

 server, will produce similar results ; the height and width of the 

 arch seen will necessarily vary with the " index of refraction " of 

 the particular fluid used as compared with air. 



