EPOCH OF YOUNG AND FRESXEL. 97 



In this Memoir of Fresnel's, he takes very nearly the same course 

 as Young had done ; considering the interference of the direct lk>-ht 



O ' O O 



with that reflected at the edge, as the cause of the external fringes ; 

 and he observes, that in this reflection it is necessary to suppose half 

 an undulation lost : but a few years later, he considered the propaga- 

 tion of undulations in a more true and general manner, and obtained 

 the solution of this difficulty of the half-undulation. His more com- 

 plete Memoir on Diffraction was delivered to the Institute of France, 

 July 29, 1818 ; and had the prize awarded it in 1819 : 6 but by the 

 delays which at that period occurred in the publication of the Pari- 

 sian Academical Transactions, it was not published 6 till 1820, when 

 the theory was no longer generally doubtful or unknown in the scien- 

 tific world. In this Memoir, Fresnel observes, that we must consider 

 the effect of every portion of a wave of light upon a distant point, 

 and must, on this principle, find the illumination produced by air. 

 number of such waves together. Hence, in general, the process of 

 integration is requisite ; and though the integrals which here offer 

 themselves are of a new and difficult kind, he succeeded in making 

 the calculation for the cases in which he experimented. His Table 

 of the Correspondences of Theory and Observation? is very remarka- 

 ble for the closeness of the agreement ; the errors being generally 

 less than one hundredth of the whole, in the distances of the black 

 bands. He justly adds, "A more striking agreement could not be 

 expected between experiment and theory. If we compare the small- 

 ness of the differences with the extent of the breadths measured ; 

 and if we remark the great variations which a and b (the distance of 

 the object from the luminous point and from the screen) have received 

 in the different observations, we shall find it difficult not to regard the 



O 



integral which has led us to these results as the faithful expression of 

 the law of the phenomena." 



A mathematical theory, applied, with this success, to a variety of 

 cases of very different kinds, could not now fail to take strong hold 

 of the attention of mathematicians ; and accordingly, from this time, 



O * * 



the uudulatory doctrine of diffraction has been generally assented to, 

 and the mathematical difficulties which it involves, have been duly 

 studied and struggled with. 



Among the remarkable applications of the undulatory doctrine to 

 diffraction, we may notice those of Joseph Fraunhofer, a mathemati- 



5 Ann. Ckim. May, 1S19. c Mim. Inst. for 1821-2. 7 Jfim. List. p. 420-424 

 VOL. II. 7. 



