414? The Rev. B. Powell's Remark* on Mr. Barton's Reply, 



can pronounce even the result as observed by Mr. Barton to be 

 at variance with the theory. And without entering into any 

 calculation, it is obvious, on the mere consideration just re- 

 ferred to, (viz. the influence of the portions of light entering 

 at the wider parts of the aperture in the direction of its length,) 

 that the character of that part of the image corresponding to 

 the narrowest part of the aperture will not be simply deter- 

 mined by the case of a rectilinear slit of the same width. Un- 

 fortunately I am not aware that any such investigation has 

 been given, even in the case of inclined rectilinear edges. 



Now with regard to my experiments : I have tried edges of 

 extremely small curvature, and have never been able to find a 

 black isolated central spot with bright fringes continuing at the 

 sides, which is what 1 understand Mr. Barton to have seen. 

 When, on the approach of the edges, the centre became dull 

 or dark, at the same moment all appearance of bright bands 

 at the sides ceased, these bands breaking off into hyperbolic 

 branches. 



On this part of my description Mr. Barton makes the remark 

 (present vol. p. 1 72), that from the hyperbolic form of the curves 

 it follows that a line at right angles to the length of the aper- 

 ture must at some part cut through bright bands, having a cen- 

 tral dark part between them. This, I must observe, really does 

 not follow, because the hyperbolic branches extend but a very 

 little way before they are quite lost and confounded in the 

 shadow on either side; and the dark part in the centre of the 

 figure stretches across, as it were, forming a junction between 

 the shadows from each side. It is altogether very obscure, 

 and ill-defined, and shades off so gradually into the bright 

 central part above and below that it is quite impossible to say 

 where it terminates. But supposing a dark centre to be really 

 established, then I conceive the case to stand briefly thus: — 

 Mr. Barton has brought forward a new experimental case, — 

 and the science of theoretical optics is under great obligations 

 to him for doing so, — a case to which neither the undulatory 

 nor any other theory (except, I suppose, his own,) has as yet 

 been applied. It remains to be seen how they may apply ; 

 and this case will form a further test of the powers of either 

 theory when formulae applying to this case shall have 



BEEN INVESTIGATED. 



In regard to my use of the expression " the coalescing of 

 the shadows," I will only observe, that I did not employ it as 

 a supplementary correction to the formula. It was suggested 

 only in the case to which (as already observed,) the formula 

 does not apply. It is, however, obviously included in the 

 formula of Fresnel when the edges are parallel, as appears 



