Intelligence and Miscellaneous Articles. 487 



lated in the September Number of your Magazine for 1 859. As some 

 passages of this translation do not agree with the original, in order to 

 express my own views correctly I beg your permission to insert the 

 following corrections and explanations : — 



P. 187 of the translation, line 9, instead of 'it was read it would be. 



— 188, line 18 from below, instead of to another occasion read to 



the immediately following paper (in Poggendorff's Annalen). 



— 188, line 4 from below, instead of if this be so read if we do 



this (that is, if we consider the stratum infinitely close to the 

 surface). 

 If Mr. Stokes will compare these corrections, he will find that I 

 never assumed " that the diffracted ray may be regarded as pro- 

 duced by an incident ray agreeing in direction of propagation with 

 an incident ray which would produce the diffracted ray by regular 

 refraction, but in direction of vibration with the actual incident ray." 

 On the contrary, I said that such a ray would represent the incident 

 ray in its effects on the diffracted ray only in the surface of the glass, 

 not in the stratum infinitely close to that surface. The calculus by 

 which I have obtained the formula of p. 189, I have given in the 

 paper which in Poggendorff's Annalen succeeds the article trans- 

 lated in this Periodical ; it rests only on the hypothesis that, at the 

 bounding surface of the two mediums, the motion, and the differen- 

 tial of the motion with respect to the normal on the surface, must 

 be the same for the two mediums in the intervals of the grating, but 

 absolutely zero at the bars of the grating. Now we may regard the 

 motion in the second medium as composed of an infinite multitude 

 of motions propagated in all possible directions, and we may deter- 

 mine, according to the theory of Fourier's double integrals, the ampli- 

 tude of each of these undular motions by the above-named conditions 

 for the surface. In my paper I have given for the sake of simplicity 

 a somewhat abridged calculus, which, as it rests on the same princi- 

 ples, leads necessarily to the same results. Since then, by a quota- 

 tion in the paper of Mr. Stokes " On the Dynamical Theory of Dif- 

 fraction" (Cambridge Transactions, vol. ix.), which the author had 

 the kindness to present me with, I became acquainted with a paper 

 by M. Cauchy (Comptes Rendus de V Acade^mie des Sciences, vol. xv. 

 p. 670), in which the author had already explained the principles of 

 the above-given solution, but without giving any of the analyses*. 

 Nevertheless the result of M. Cauchy's theory (that is, the formula 

 of my paper) is at variance with that of Mr. Stokes's investigation ; 

 only I would not concede that for that reason alone the assumption 

 on which it rests cannot be admitted, though I value very highly 

 the merit of Mr. Stokes's disquisition. 



The theory of Mr. Stokes, as does that of M. Cauchy, rests on the 

 assumption that the screen which contains the diffracting apertures is 

 infinitely thin ; so that the motion at the issue of the apertures, where 

 it occasions secondary waves in the second medium, is the same as 

 at the entrance, or as in the unbroken incident wave. It appears very 



* It was also on this occasion I saw that, when I said that Mr. Stokes 

 had not communicated the details of his experiments, I was in error, 

 into which I was led by an extract of Mr. Stokes's paper, and for which I 

 beg to be excused. 



