92 Mr. Moon 07i Fresnel's TJieory of Diffraction. 



3 1 



why should we neglect the cases where a (^ (5) = — ^^ ~^ ^"^ 



Other intermediate quantities? 



Such a method of appi'oximation is wholly untenable, and 

 the only way in which I can account for its having been for a 

 moment admitted, is that Fresnel, having proved (vide Her- 

 schel, arts. 628, 629) that the motion of a vibrating molecule 

 is governed entirely by that portion of the front of the wave 

 from which the secondary waves emanate, immediately conti- 

 guous to the perpendicular drawn from the molecule upon the 

 front, conceived himself to be warranted in coming to this 

 conclusion. But it is one thing to prove that the disturbance 

 is due to the part of the wave about the perpendicular, and 

 another to show that that part of the wave only is effective, 

 the intensity of the secondary waves from which, when they 

 arrive at the molecule, differ insensibly from 1, which cannot 

 be done (as I have shown) without falsifying the formulae. 

 It may be said that this objection, whatever be its weight as 

 bearing on the actually calculated results, is not fatal to the 

 principle of the explanation ; whether it is so or not I shall 

 not at present inquire. 1 make the remark principally in order 

 that the reader may estimate the degree of care with which 

 this investigation has been conducted. 



I next would observe that the formula 



X = / dscos2'!r (jyi — )j 



where /= b + —■. j- + Z i , 



is true only when N is very near to M ; and yet by taking oo 

 as the superior limit of s in the integration, it is assumed to 

 hold for all points of the circumference AMN, as well of that 

 part which is cut off by the body AG as of any other. 

 What is meant by making oo the superior limit? A more 

 preposterous absurdity was never propounded. 



Draw P F touching A M N in F; then if the expression for 

 X were true for all the elements of the arc A M F, we should 

 find the disturbance at P by taking for the limits of s, 

 s= —AM and s=MF respectively. But that expression only 

 holds when 5 is small, it being agreed that the effect of all 

 other parts of the front may be neglected ; hence we can only 

 assume for the superior limit of s a quantity s', respecting 

 which all we can say is that it is small compared with a. To 

 talk of giving ^ a definite value is an absurdity. If it be asked, 

 How are we to find the values of the integrals, since the inde- 



