530 VHILOSOPHICAL TRANSACTIONS. [aNNO 1 700. 



the sine of the refracted angle will be -v/ ^"^" ^ , from which angles the pri- 

 mary rainbow proceeds. But for the secondary y/^^lilT will be the sine of in- 

 cidence, and ^ -^p^-^ the sine of the refracted angle. For the third, the sine of 



incidence will be V" -T , , and the sine of the refracted anele will be 



4^ ■ ^^ ~ . For the 4th the sine of incidence will be \/—^^—^, and the sine 



lorr — 15 '2i - 2iss 



tec __ I 



of the refracted angle v' ^-^ — —• And so of the rest. 



° 2-iir — 24 



Admitting the ratio of Descartes, you will find by calculation, that the pri- 

 mary rainbow is distant from the point opposite to the sun 41° 30'; the secon- 

 dary 55° 55'; the third 40° 20'; and the fourth 45° 33', from the sun itself. 

 These last I know not whether any one will be able to see, because of the light 

 of the sun growing more and more feeble in every reflexion and refraction. And 

 this may suffice concerning the magnitude of the rainbow in the transparent 

 drops of a fluid, whose refractive power is known. We must now add some- 

 thing concerning the colours with which the rainbows are painted, and their 

 order in each; being varied by the refraction through all possible degrees. 



First it must be known, that all light of the blue kind is refracted something 

 more than any red light ; from which difference arises the breadth of the rain- 

 bows, which is hardly to be determined by observation, because of the uncer- 

 tain limits of the colours in the cloud. But the greater is the ratio of inequality 

 between ca and cd, or the greater the refraction is, so much the greater is the 

 distance of any rainbow from the sun ; and therefore the limits of rainbows that 

 are more remote from the sun always shine with purple colour, and the nearer 

 are intensely ruddy. This may always be seen in the primary iris, which vanishes 

 opposite to the sun, if the sine of incidence be to the sine of the angle of re- 

 fraction, as ca to CE, or as 2 to 1. If that ratio be greater, no primary rain- 

 bow can be seen at all. 



But it is to be observed, that the secondary iris goes off in a point opposite 

 to the sun, whenever the ratio of refraction is as 1 to 0,847487. Thence it 

 returns to the sun itself, and there vanishes, if the said ratio is as 3 to 1, or 

 as CA to ce. But in intermediate ratios, such as obtain in all known fluids ex- 

 cept air, the greater the ratio is, so much the more the iris is distant from the 

 opposite pliice of the sun, or rather from the sun itself, reckoning the arch be- 

 yond the semicircle. And therefore the colours will be found in an inverted 

 order from the primary, in these returns, unless the distance of the iris from 



