432 Prof. Powell's Remarks on Mr. Barton's Paper 

 Values of s. Brightness. 



(|g) (-0994.) 9 + (-0098) 9 



('*) (-0981)- + (-0192) 9 



(^}) ('0933) 2 + (-0307) 3 



(5.4) (-0788)^(-0397) 2 



Let us next suppose the aperture wider, such, for example, 

 that, agreeably to the above remarks, we may have for the 

 centre s = + 2* ; and proceeding thence only to J of the 

 breadth beyond the geometrical shadow, we shall have (under 

 the same heads,) 



( + !.') (-9772) 2 + (-6864) 9 



® 



2- 



(-2165)* + (-061 1) ? 



Thus it will be apparent, even without taking the trouble 

 of calculating further, that these results of theory give an ex- 

 act representation of the effects actually observed. The centre 

 is in either case a maximum, or point of relative brightness 

 compared with other parts of the screen. When the aper- 

 ture is extremely narrow the whole intensity is very small, or 

 the image extremely dull, or even almost totally dark, which 

 is precisely the character of the coalescing shadows : when 

 slightly wider, the increase of light is considerable, the centre 

 being the brightest, but the variation towards the sides but 

 small: when of considerable width (within a certain limit), the 

 centre is still a maximum, the increase in the absolute inten- 

 sity great, and the variation from the centre to the edge more 

 rapid. 



The difference in the representation given in Mr. Barton's 

 diagram, from my observations, may possibly be no more than 

 arises from the imperfect nature of the sketch, or of the en- 

 graving; and it may not have been intended to convey the 

 idea of bright fringes continued at the sides, or of the centre as 

 absolutely dark; but however this may be, it is obviously an 

 essential point; and Mr. Barton will, perhaps, in a future com- 

 munication, be able to state it more explicitly. 



Upon the whole I cannot but consider the theory of optics 

 as under obligation to Mr. Barton for having brought forward 

 several objections to the undulatory system ; which are cer- 



