\ 
126 REPORT—1840. 
sy we obtain 
Pie che ArsEoP sd! Li, os Ee gga 
For the second . . . . 50°59), 
264. The comparison of these theoretical angles with obser- 
vation is not so easy as might appear, depending (1) on the 
doubt which ray of the red space we are to consider as the last 
visible one in the rainbow, and (2) on the gradual shading off 
depending on the sun’s apparent diameter. There is reason to 
think that the measures of the rainbow require revision ; but 
we would rather place the fate of the theory upon other grounds. 
265. The first fact which Newton’s theory did not embrace, 
was the existence of supernumerary or spurious bows ; within 
the Inner, or Primary Rainbow, and without the Outer, or 
Secondary one. These were very accurately described by 
Langwith in 1722 +,—three internal rings of green and purple 
(with traces of a fourth) associated with the primary rainbow. 
The much rarer phenomenonof the supernumerary exterior bows 
of the secondary rainbow has been noticed by Dicquemare { 
and Brewster§. The supernumeraries have the same order of 
colours as the bows to which they belong, 7. e. those within the 
Primary have the Red exteriorly, those without the Secondary 
the Red interiorly. 
266. Pemberton || explained these spurious bows by the 
colours of thin plates ; and at a much later period Venturi J 
attempted to account for them by the deviation of the figure of 
falling drops from sphericity. Such fallacious endeavours 
show how cautiously we should receive explanations of such 
phenomena on the grounds of general plausibility. The true 
explanation had already been given by Dr. Young, who in pur- 
suing his fertile discovery of interference, pointed out its appli- 
cation to the rainbow ina manner so clear**, that it is surprising 
how for thirty years, this, one of its happiest adaptations to 
phenomena, has been so generally overlooked. 
267. In the ordinary geometrical theory of the primary rain- 
Adopting with Newton * the index m = 
* Optics, book i. part ii. prop. 9. 
+ Philosophical Transactions, 1723, quoted by Dr. Young. Dr. Young 
cites Mariotte as the first who mentions supernumerary bows (Chromatics, 
Encye. Britt.), but without a reference. 
t Quoted by Young, Lectures, vol. ii. p. 316. 
§ Edinburgh Journal of Science, vol. x. p. 163. 
|| Philosophical Transactions, 1723, quoted by Dr. Young. 
{| Commentari sopra la Storia et le Teorie dell Ottica. Bologna, 1814. 
Quoted by Dove and Kamtz (Meteor. iii. 165). 
** Phil. Trans. 1804. Read Nov. 24, 1803. Lectures, vol. i. 470; ii. 316. 
