Mr. J. H. Pratt on the Supernumerary Bows in the Rainbow, 81 



8. I will first find the intensities of these emergent rays, and 

 compare them. 



A cylindrical pencil of parallel rays falling on the drop of 

 rain will emerge through an element of the surface of the drop, 

 of dimensions different to those of the element through which it 

 passed on entering ; and the pencil will emerge, in the general 

 case, not parallel, but diverging, both in the plane of the paper 

 and at right angles to that plane. It will be necessary to cal- 

 culate this in order to find the intensity of the emerging light. 



9. And first, I will calculate the divergence at right angles to 

 the paper. 



Fig. 3. 



Let SflficE (fig. 3) be the course of a ray through the drop. 

 Draw Sc parallel to the incident rays through the centre of the 

 drop. Let the figure revolve round Sc through a very small 

 angle, so that the above ray may assume the position of a new 

 ray SV6VE'. Thus ««' is the breadth of the incident pencil 

 measured at right angles to the paper, =w suppose. Then the 



angle through which the plane revolves = —. — r ; and 

 ° ° ^ rsm^' 



, w • //I . .A sin (^H-<^) 



rsm<j> ^ ^' suKf) 



This is the width of the pencil when it is emerging. The rays 

 cE, c'E' make, each of them in its own plane, an angle with 



