SUPPLEMENTARY REPORT ON METEOROLOGY. 129 
and refraction as in the rainbow*. Computing the intensities 
rigorously on the principles of the undulatory Theory of Light, 
he arrives by laborious numerical computations at the following 
results :— 
1. The boundary of the caustic is not a mathematical line ; 
but the light shades off with extreme rapidity. 
2. The radius of the primary bow does not coincide with the 
geometrical caustic deduced by the common theory. It lies 
within it at a distance depending on the size of the drops, and 
on the consequent separation of the interference fringes. 
3. To find the radius of the geometrical bow from observation, 
“Add to the radius of the brightest observed bow 11 of the 
distance between it and the first supernumerary bow.” __ 
4. Between the primary and the first supernumerary there is 
a space absolutely dark. 
272. As several of these results differ quantitatively from 
those deducible by the simpler methods of Dr. Young, it is of 
importance to verify them experimentally. For the reasons 
already stated (264.), it is difficult to obtain satisfactory compa- 
rative measures from the natural rainbow. Much more deli- 
cate observations are obtained by an ingenious experiment de- 
vised by M. Babinet, of allowing a minute stream of water to 
flow through an opening #,th of an inch, or less, in diameter, 
and observing the deviation of rays proceeding from a small 
luminous body}. In this way Professor Miller, of Cambridge, 
has confirmed Mr. Airy’s result as to the deviation of the prin- 
cipal bow from the geometrical place of the caustict. 
273. The existence and positions of the supernumerary bows 
and their dependence on the diameter of the refracting cylinder 
of fluid (and likewise on its index of refraction), have been shown 
by M. Babinet himself, who has observed no less than sixteen 
interior, and nine exterior supernumeraries, by means of a 
streamlet of water of the diameter above-mentioned §. 
274. With acomparatively large (;4;ths of an inch) cylinder of 
glass he obtained the usual theoretical dimensions of a bow for 
the appropriate index of refraction. The supernumeraries were 
excluded by the size of the cylinders; but he obtained bows 
caused not only by one and two internal reflexions, but three 
and four, up to seven. These, the ternary, quaternary, &c. 
rainbows have been long theoretically known, though rarely, if 
ever, observed in nature. The ternary rainbow ought to occur 
* Camb. Trans. vi. 379. The abstract in the Phil. Mag., Third Series, vol. 
Xli. p. 452, is inaccurate. + Comptes Rendus, iv. 647. 
¢ Phil. Mag., Third Series, vol. xiii. p- 10. This experiment was shown to 
me by Professor Challis. § Comptes Rendus, ut sup. 
VOL. 1x. 1840. K 
