SHEWING IT TO BELONG TO PHYSICAL OPTICS. 143 



consequently assist the distinctness of the colours. The magnitudes of 

 the drops of rain, required for producing such of these rainbows as 

 are usually observed, is between the 50'^ and 100'" of an inch; they 

 (i. e. the supernumerary hows) become gradually narrower as they are 

 more remote from the common rainbows, nearly in tlie same propor- 

 tions as the external fringes of a shadow, or the rings seen in a con- 

 cave plate." 



At page 643. Vol. ii. in a reprint of a paper of his in the Phil. 

 Trans, for 1803, he goes further into particulars, and says, "In order 

 to understand the phenomenon, we have only to attend to tiie two por- 

 tions of light whicli are exhibited in the common diagrams explanatoiy 

 of the rainbow, regularly reflected from tlie posterior surface of the drop, 

 and crossing each other in various directions, till, at the angle of greatest 

 deviation, they coincide witli each other, so as to produce, by tlie greater 

 intensity of this redoubled light, the common rainbow of 41 deo-rees. 

 Other parts of these two portions will quit the drop in directions parallel 

 to each other ; and these would exhibit a continued diffusion of fainter 

 light for 25" within the bright termination which forms the rainbow, 

 but for the general law of interference, which, as in other similar cases' 

 divides the light into concentric rings; the magnitude of these rings 

 depending on that of the drop, according to the difference of time oc- 

 cupied in the passage of the two portions, which thus proceed in parallel 

 directions to the spectator's eye, after having been differently refracted 

 and reflected within the drop. Tliis difference varies at first, nearly as 

 the square of the angular distance from the primitive rainbow: and 

 if tlie first additional red be at the distance of 2" from tlie red of the 

 rainbow, so as to interfere a little with- the primitive violet the fourth 

 additional red will be at the distance of nearly 2" more, and the in- 

 termediate colours will occupy a space nearly equal to' the original 

 rainbow. In order to produce tliis effect the drops must be about ^ of 

 an inch or .013 in diameter : it would be sufficient if they were be- 



tween 7^ and J3." &c. 



Dr Young does not explain the method by which he found the 

 diameters of the rain-drops sliould be ^ of an inch. 



