Cuap. V., § 1.] 
@ general equality of size. For the effects of inter- 
ference depend on the precise diameter of the drop ; 
if these be very various the resulting positions of 
maxima and minima will be altogether confused. 
Dr Young pointed out that to accord with the phe- 
nomena the falling drops must be about 75 of an 
inch in diameter. 
(466.) I have merely indicated the nature of an argu- 
peas of ment of extreme interest and beauty. Itwould be diffi- 
ie pheno- 4 3 ‘ * 
menonof cult to cite (except perhaps in the science of physical 
the rain- astronomy) a more complete specimen of gradual in- 
bow asa ductive research. Here is a phenomenon—the rain- 
test of “ys ope ° ag 
Theory.  bow—as familiar as it is beautiful. Even a partial in- 
sight into its cause confers a certain reputation upon 
one individual (De Dominis), its farther explication 
gave Newton one of his most popular triumphs. Itis 
then found that the rainbow is not so simple a fact 
as was supposed, and that Newton’s theory accounts 
for only its broader features, Then, as in the theory 
of gravity, a long period of uncertainty ensues ; but 
observations are continued. A perfect rainbow is 
found to be one of the rarest of natural phenomena, 
instead of the commonest, Not above two or three 
individuals have ever seen, or at least described one, 
Then comes Dr Young, with his theory of interfe- 
rence and diffraction. This theory not only accounts 
for the spurious bows, but for the precise appearance 
of the principal ones, which, but for it, would have 
been different from what Newton supposed, Finally, 
after being canvassed for more than two centuries, 
the theory of Young is carried out into its rigorous 
consequences by Mr Airy! and Professor Stokes? 
(who must first invent a new mathematical method 
for the purpose) and illustrated by the ingenious ex- 
periments of M. Babinet and Professor Miller ;3 until 
at last we begin to believe that we understand this 
matter completely. 
Nnelted Exterior Fringes of Shadows.—I have men- 
fringes of tioned only generally Young’s application of his 
shadows; theory to the coloured fringes observed by Grimaldi 
and Newton to surround the outline of bodies, as 
thrown in shadow by a luminous point upon a dis- 
tant sereen. I have done so because Young’s ex- 
planation was imperfect, not to say incorrect. But as 
it would be inconvenient to discuss the subject here, 
I shall briefly indicate its history and result. Dr 
Young expresses himself more obscurely in his paper 
of 1801 on this point than on any other, indicating 
three possible explanations. In 1803, however, he 
distinctly adopts the opinion that the periodical 
colours in question are due to the interference of 
direct light passing near the opaque edge with a por- 
tion of light very obliquely reflected from that edge ; 
and he enters into calculations to show that such a 
theory represents sufficiently well Newton’s measures, 
But it is unaccountable that Young should have been 
satisfied with the belief that the screens employed 
(467.) 
OPTICS.— YOUNG. 
899 
should in every case have reflected an appreciable 
quantity of light (or indeed any light at all) in the 
required direction, It might be conceivable in the 
ease of a cylindrical wire or a cylindrical hair; but 
how could a film of gold-leaf or a slip of paper re- 
ceiving the light on its broad side furnish such a de- 
gree of oblique illumination? It is wonderful that 
Young’s intuitive sense did not perceive that the por- 
tion of a luminiferous wave passing near an opaque 
edge, is deficient on one side of the interfering wave- 
lets which are necessary to make the boundary of 
the shadow definite, and to extinguish the laterally- 
spreading light. In short, he did not allow to Huy- 
gens’ principle (see art. 455) the full breadth of its 
application—a discovery made some years later by 
Fresnel, who has the credit of first explaining these 
exterior fringes. 
That great philosopher (the worthy rival of Young  (468.) 
in this career of discovery) found the means of com- fl! expla- 
° ‘ : wes nation of 
puting, on strict geometrical principles, the sum total thom due 
of the disturbance produced at any point of a screen to Fresnel. 
by the whole effective portion of a luminiferous wave 
partially stopped by an obstacle of a given form. 
The principle of the calculation is simple enough. 
The origin of the light being distant, the front of the 
wave is considered as flat when it breaks against the 
opaque body. Its front is then divided (in thought) 
into small elementary portions, each of which is con- 
sidered as the source of a disturbance propagated as 
from a new origin. The effect of each wavelet is cal- 
culated in terms of the co-ordinates of its origin, and 
of the point where its effect is to be considered, The 
sum of all these simultaneous effects is collected by 
integration, a process which unfortunately is only 
rigorously possible in a limited number of cases, 
Some of these cases were solved with great ingenuity 
by Fresnel, and compared with observation. The re- 
sult was extremely satisfactory. Yet it is curious to 
observe that Young’s explanation, if it had had a 
sufficient physical basis, leads to nearly similar re- 
sults. In the case of an indefinite opaque body with 
a straight edge, the illumination precisely at the 
boundary of the ‘‘geometrical” shadow is, on Fresnel’s 
theory, one-fourth of what it would have been were 
the bodyremoved. Within this line the light dies away 
gradually, having no maxima orminima. Without it, 
a series of dark and light bands occur, which rapidly 
blend into a uniform illumination. The same theory 
leads to results as to the position of the interior bands 
which are also somewhat different from the simpler 
calculation of Young, and still more conformable to 
experience. Amongst the most singular of these re- 
sults is this (which is perfectly confirmed by obser- 
vation), that the shadow of a small round opaque 
body (as a spot of tin foil) is illuminated by a 
speck of diffraeted light at its centre precisely 
as bright as if the disk were removed! How, after 
1 Camb. Trans., vol. vi. (1838.) -2 Ibid., 
vol, ix, (1850,) 3 Ibid., vol. vii. (1842.) 
