of the Primart/ and Secondary Rainbows, 1 1 



surie its breadth." And again, " The least distance between 

 this iris and the exterior iris was about 8 degrees and 30 mi- 

 nutes." We see that the fundamental measures are for the 

 extreme red of the primary bow, which has its utmost radius 

 42° 4}', and the least distance between this and the correspond- 

 ing part of the secondary bow = 8° 30'. Now, Sir Isaac 

 Newton has taken ^ for the refractive index of this extreme 

 visible red, which brings, as he says, the computations to agree 

 nearly with the observations ; but from Frauenhofer's correct 

 tables of refractive indices we find that it coincides very nearly 

 with the letter D, or the middle of the orange. After all, — 

 with this calculation for orange and measurement for extreme 

 red, there is a discrepancy of no less than 14', for with re- 

 fractive index = |, we have radius (if the sun were a point) 

 = 42° 2', and adding sun's semidiameter =16' we have 

 42° 18', diiFering 14' from the extreme measurement; the 

 measured radius being less than the calculated one. 



Before we can proceed with the correct calculation we must 

 fix on some refractive index as corresponding to the extreme 

 visible red ; and the letter C being about the middle of the 

 red, if we take about the letter B this will not be pushing the 

 case too far, and will probably err in the favour of the old 

 theory rather than otherwise. 



With this refractive index = 1*3309 we find for the radius 

 of the primary bow, if the sun were a point, 42° 23', and add- 

 ing sun's semidiameter, we have radius of extreme visible bow 

 = 42° 39', and the difference between this and the observed 

 quantity 42° 4' is 35', a quantity far beyond the limits of 

 error of observation. 



The distance between the bows, however, shows the dis- 

 crepancy in the strongest point of view, on account of its 

 bearing so large a ratio to the whole distance. The above 

 refractive index gives for the radius of the extreme red of 

 the secondary bow 50° 20', and the difference between this 

 and 42° 23' is 7° 57' ; subtracting from this the sun's semi- 

 diameter for each bow, or 32' for both, we have 7° 25', whilst 

 the observed distance is 8° 30', leaving a discrepancy of no 

 less than 1° 5' in this small angle, which cannot possibly be 

 attributed to faults in the measures. 



To test Mr. Airy's conclusions that the light at the position 

 of the primary bow, according to the old theory, should be 

 about one half of that at the brightest part if the sun were a 

 point, and therefore distinctly bright in the real rainbow, we 

 will allow a greater latitude in favour of the theory, and take 

 the letter C refractive index = 1*33171 as belonging to the 

 extreme Visible red ; this gives the radius of the primary bow 

 42° 32', whilst the observed extreme bow has only a radius 



