PHYSICAL OPTICS. J25 



ihadow, and the afymptotes nearly with the diagonal line. 

 Such, therefore, muft be the diredlion of the fringes ; and 

 this conclufion agrees perfe<5lly with the obfervation. But it 

 muft be remarked, that the parts near the outlines of the (ha- 

 dow, are fo much (leaded off, as to render the chara6ler of the 

 curve fomewhat lefs decidedly marked where it approaches to 

 its axis. Thefe fringes have a flight refemblance to the hy- 

 perbolic fringes obferved by Newton ; but theUnalogy is only 

 diftant. 



III. APPLICATION TO THE SUPERNUMERARY RAINBOWS. 



. The repetitions of colours fometimes obferved within the Applicatjon of 

 common rainbow, and defcribed in the Philofophical Tranfac-*Jj^ ?^^""e of 

 tions, by Dr. Langwith and Mr Daval, admit alfo a very eafy of light to Xt^ 

 and complete explanation from the fame principles. Dr. Pern- fupernumerary 

 berton has attempted to point out an analogy between thefe co-Lanewith° d 

 lours and thofe of thin plates; but the irregular refledlion Daval. 

 from the pofterior furface of the drop, to which alone he attri- 

 butes the appearance, rouft be far too weak to produce any 

 yifible effe6ls. In order to underftand the phenomenon, we have 

 only to attendto the two portions of light which are exhibited 

 in the common diagrams explanatory of the rainbow, regularly 

 refleded from the pofterior furface of the drop, and croffing 

 each other in various directions, till, at the angle of the great- 

 ^ft deviation, they coincide with each other, fo as to produce, 

 by the greater intenfity of this redoubled light, the common 

 rainbow of 41 degrees. Other parts of thefe two portions 

 will quit the drop in dire6lions parallel to each other; and thefe 

 would exhibit a continued diffufion of fainter ligiit, for 25** 

 within the bright termination which forms the rainbow, but 

 for the general law of interference, which, as in other fimilar 

 cafes^ divides the light into concentric rings; the magnitude 

 of thefe rings depending on tiiat of the drop, according to the 

 (Jifference of time occupied in the paflTage of the two portions, 

 which thus proceed in parallel directions to the fpe6tator\s eye, 

 qfter having been differently refracted and reflefted within the 

 4rop. This difference varies at firft, nearly as the fquare of 

 the angular diftance from the primitive rainbow: and, if the 

 Ijrft additional r-ed be at the diftance of 2^^ from the red of the 

 TAinboNy, fo as to interfere a little with the primitive violet, 

 the fourth aclditiqnal red will be at a diftance of nearly 2*^ 



more , 



