EPOCH OF YOUNG AND FRESNEL. 447 



point, and must, on this principle, find the illumina- 

 tion produced by any number of such waves toge- 

 ther. 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 Corre- 

 spondences of Theory and Observation*, is very 

 remarkable for the closeness of the agreement ; the 

 errours being generally less than one hundredth of 

 the w-hole, 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 smallness 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 integral 

 which has led us to these results as the faithful 

 expression of the law of the phenomena." 



A mathematical theory, applied, with this suc- 

 cess, to a variety of cases of very different kinds, 

 could not now fail to take strong hold of the atten- 

 tion of mathematicians ; and accordingly, from this 

 time, the undulatory doctrine of diffraction has been 

 generally assented to, and the mathematical diffi- 

 culties which it involves, have been duly studied 

 and struggled with. 



6 Mem. Inst. p. 420424. 



