CHAP V., 1.] 



OPTICS. YOUNG. 



101 



the pheno- 

 menon of 

 the rain- 

 bow as a 

 test of 

 Theory. 



a general equality of size. For the effects of inter- 



Iference 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 T ^ of an 

 inch in diameter. 



(466.) I have merely indicated the nature of an argu- 

 ihcacy of men ^ o f ex treme interest and beauty. It would be diffi- 

 cu ^ to cite (except perhaps in the science of physical 

 astronomy) a more complete specimen of gradual in- 

 ductive research. Here is a phenomenon the rain- 

 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. It is 

 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 1 and Professor Stokes 2 

 (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. 



Exterior Fringes of Shacf.ows. I have men- 

 ^ one ^ on ly generally Young's application of his 

 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 screen. 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 



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 

 case 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 I 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- ful1 . ex P la ' 

 puting, on strict geometrical principles, the sum total them^ue 

 of the disturbance produced at any point of a screen to FresneJ. 

 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 or minima. 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 diffracted light at its centre precisely 

 as bright as if the disk were removed ! How, after 



1 Camb. Trans., vol. vi. (1838.) 2 Ibid., vol. is. (1850.) 3 Ibid., vol. vii. (1842.) 



