452 Transactions. — Miscellaneous. 



to one another, in the two directions e E, e E ; and these direc- 

 tions were inclined at opposite angles of 41° to the sun's rays, 

 or of 82° to one another. 



This result is true for all sections of the sphere or drop of 

 water passing through its centre and in the direction of the 

 sun's rays ; from which it follows that, viewing the drop in 

 front (PI. L., fig. 3), the rays entering on the circle s, s, s, s, will 

 be emitted on the circle e, e, e, e, and will issue back at the 

 constant angle of 41° with the original direction of the sun's 

 rays, forming a cone or shell of concentrated parallel rays 

 spreading out from the drop of water which forms the apex of 

 the cone, the angle at the apex being 82°, or twice 41°. We 

 can now see how Tyndall's cone, turned the other way, with 

 its apex at the eye and its base on the rain-sheet, coincides 

 exactly with a particular set of strong pencils of parallel rays 

 proceeding from the raindrops which are momentarily situated 

 at the base of this cone : the divergent rays from these par- 

 ticular raindrops converge exactly in the observer's eye, as 

 they start from the precise spots and are directed at the 

 precise angle to reach the eye. All the rest of the rays, 

 whether strong pencils of parallel rays or weaker scattered 

 rays, merely assist in the general illumination or are lost. 



Another eye, however, in another position, will see another 

 rainbow formed in the same way by the divergent pencils of 

 brilliant parallel rays from other raindrops which happen to 

 be in the right position to send their rays so as to converge on 

 that other eye. 



The special brilliance of the rainbow as compared to the 

 illumination of the rest of the rain-cloud is due to this maxi- 

 mum of parallel emitted rays, which, in accordance with the 

 laws of refraction and reflection of light, emerge in a cone of 

 brilliant rays from each raindrop that the sun shines on ; the 

 circular or ^wasi-circular form of the brilliant band follows 

 because the angle at which the light emerges is constant in 

 all directions from the impinging parallel rays of the sun. 



The secondary or outer bow often observed is produced in 

 a similar manner, except that the rays which produce it have 

 been twice reflected in the raindrop, as shown in PI. L., figs. 4 

 and 4<x. This double reflection diminishes the force of the 

 light, for each reflection is only partial, a portion of the im- 

 pinging rays passing out, and consequently the secondary bow 

 is always fainter than the primary bow ; but the secondary 

 cones of light act in the same way as the primary, the angle 

 of divergence on each side of the sun's rays being in this case 

 52°, or the angle at the vertex of the cone 104°. Hence, this 

 bow must be about 11° outside the primary bow. 



The colours of the rainbow are due to the varying refrangi- 

 bility of the coloured rays, which, when combined, give us the 



