128 REPORT—1840. 
269. Thus, but for interference, we should have had but a 
feeble andimpure rainbow. But further, the same considerations 
explain the supernumerary arcs: for it is evident, from what 
has now been stated, that after destruction of light by opposi- 
tion of phases has been produced, an equal additional retarda- 
tion of the one ray upon the other will produce concurrence of 
phase, and double light ; hence, as in all similar cases, a series of 
luminous bands rapidly diminishing in breadth and in intensity 
will be formed with more or less vividness, depending upon 
the brilliancy of the reflexion and the separation of the bands 
(which again depends on the size of the drop). The distance 
between the true and spurious bow gives the data (upon prin- 
ciples which will be very readily conceived *) upon which the 
diameter of the drops of rain may be calculated, which Dr. 
Young finds to be between jth and 4th of an inch. By similar 
principles it is found that the supernumeraries of the secondary 
bow will be exterior to it and somewhat broader. 
270. The darkness of the space between the primary and 
secondary bows is equally a consequence.of the common theory 
and the corrected one t. It is dark compared to the spaces 
containing the diffused lights (what Dr. Young calls the double 
lights, or duplicatures) corresponding to the respective bows. 
This darkness was described by Descartes§. The light of the 
primary and secondary bows]|, and also of the supernumeraries 
so far as observed, is polarized in the place of reflexion. 
271. Mr. Airy has recently investigated fully the intensity of 
the light in the neighbourhood of a caustic formed by reflexion 
* Viz. for the observed deviation of the red ray in the spurious bow, find the 
angles of incidence and reflexion within the drop for the two rays which com- 
bine to produce it, and find the difference of the paths of the rays which corre- 
spond to this in terms of the radius of the drop. Reduce the difference of 
paths in water to that in air, and equating it to the length of a wave of red light, 
find the radius of the drop. Dr. Young hasindicated this process in his obscure 
but ableand comprehensive article Chromatics, in the Encyclopedia Britannica, 
with which Mr. Potter, who has recently written in support of Dr. Young’s 
views (Camb. Trans. vi. 141), appears not to have been acquainted. 
¢ Philosophical Transactions, 1804, and Chromatics. 
{ It is, however, very imperfectly or inaccurately explained in most popular 
treatises. Mr. Ainger has given a very detailed account of it in the Journal 
of the Royal Institution (Feb. 1831), in which he has added nothing material to 
what was shown by Dr. Young ; nor has he adverted to the cause of the super- 
numerary bows. 
§ Brandes, art. Regenbogen, in Gehler, p. 1324. Kamtz, Meteorologie, iii. 
p- 158. It is very singular that neither of these authors seems to be aware of 
the true theory of the rainbow, or of Dr. Young’s writings on the subject. 
|| First observed by Biot. See Annales de Chimie, xxxix. 430. 
q Arago, Annales de Chimie, ibid. 
