THE RAINBOW. 415 



a circumference drawn, with as a centre and with V as 

 radius, being opposite the sun and having the same angular 

 distance from OE, viz., 40, will 

 send violet colored rays to the eye 

 at E, and the violet colored part of a 

 the bow will be a circular arch. s'~ 

 For the same reason, the red of the s 

 bow is a circular arch lying without 



the violet and at an angular dis- 



tance of two degrees therefrom; 



the other colors will form circular 



arches lying between these two. FIG. 320. 



If the sun be at the horizon, EO 



will be horizontal and the arches will be semicircles. If 



the sun be above the horizon, will be depressed below 



the horizon and less than semicircles will be seen. If the 



observer be on a mountain-top or up in a balloon, he may 



see more than a semicircle. 



645. The Secondary Bow. Sometimes two col- 

 ored arches are seen, one within the other. The inner 

 which we have just considered is called the primary bow ; 

 the outer, the secondary bow. 



(a.) In explaining the primary bow we traced a ray of light fall- 

 ing upon the top of the raindrop ; to explain the secondary bow we 

 trace a ray falling upon its lower part. Such a ray, as 8m, will be 

 refracted at m, reflected at n and n', and again refracted at m', 

 coming to the eye at E. If the ray which thus comes to the eye at 

 E be a red ray, the violet will follow m' V, and thus, passing below 

 the eye because of its greater refrangibility, be lost to sight. The 

 drop that sends a violet ray to the eye at E must be placed abov$ 

 instead of below the drop that sends the red ray. (Fig. 321 ) 



(5.) In the secondary bow, the red arch will be on the inside, with 

 an angular distance from the axis EO of about 51, while the violet 

 will be on the outside at an angular distance of about 54. In the 



