SUPPLEMENTARY REPORT ON METEOROLOGY. 127 
bow, it is well understood that a limit of deviation, due to two 
refractions and one reflexion of the sun’s light within the drop 
is adefinite and impassible one. The illumination of the bow is 
produced by the accumulation of rays near the limit of maximum 
deviation ; an incidence a little greater or a little less than that 
due to the limit will equally give a smaller deviation ; and as in 
a shower there are assumed to be drops which shall send rays 
to the eye in any given direction consistent with the relative 
position of the observer and the sun, rays more or less approach- 
ing to parallelism (therefore more or less densely luminous) will 
reach the eye from drops placed so as to furnish rays at less 
angles than that of extreme deviation. Confining our attention 
to a single colour (the red, for instance, which is the outermost 
in the primary rainbow), we should expect to find a red bow, 
quite sharply terminated exteriorly, but shading off gradually, 
though pretty rapidly, towards the interior. When we recollect, 
too, that this reflexion within the angle of maximum deviation is 
derived from rays which have fallen at a smaller as well as at a 
greater angle of incidence than the critical one, and which 
therefore emerge rigorously parallel, we are surprised at first 
sight that the insulation of the colours in the successive arcs 
should be as great as it appears to be. 
268. The doctrines of physical optics, as laid down by Dr. 
Young, enable us to explain this satisfactorily ; for the very re- 
duplication of the reflected light just alluded to (which a very 
little reflection will show to be derived from opposite halves of 
the drop, separated by the position of critical internal reflexion 
for producing the maximum deviation) reminds us of the funda- 
mental fact of interference, that annihilation as well as increase 
of light may attend the union of rays proceeding in a common 
direction, derived from a common source, but which have tra- 
versed paths of different lengths. Whilst, then, near the critical 
angle of reflexion the luminiferous waves necessarily reach the 
eye in the same, or nearly the same phase, the rays derived from 
a greater and a less incidence have (though they ultimately 
coincide in direction) described paths whose difference will 
soon amount to half an undulation, when their effects will be 
mutually destructive. Thus by the principle of interference the 
bow of any colour has its interior boundary far more sharpl 
defined than if such a cause (which is manifestly modified by 
the size of the drop) had not existed*. 
* See Young’s original paper, Phil. Trans. 1804, where he estimates the pos- 
sible breadth of the diffused zone of light, which otherwise would have shaded 
off from the rainbow, at 25°. 
