246 Mr. R. Potter on the Application of 



If now 6 be not large and r 2 —r l be only a small odd num- 

 ber of multiples of—, the aperture will be nearly a parallelo- 



a? 2 X 2 

 gram, and the maximum intensity = s — . But if in the 



original expression we make r x = 0, the aperture becomes the 

 whole sector, and the maximum intensity, by giving r 2 the 



a <Z 00. ^2 



proper value, is - z — . This shows that at however great a 



distance from C such a quadrilateral aperture be situated, 

 and however near to C the point B may be, the intensity 

 ought to be the same as for the sector. 



The result of the principle is therefore that light ought to 

 bend into the shadows of bodies to an indefinite extent, as 

 sound is known to pass through all apertures, and bend round 

 all obstacles. 



It proves that the result Mr. Airy (Tract, page 270.) has 

 obtained by an approximate method is not to be depended 

 upon, and that the objection to the undulatory theory which 

 was believed to have been removed remains in full force. 



If it be said that these expressions involving X 2 as a multi- 

 plier, must represent light of very feeble intensity, and there- 

 fore insensible, or nearly so, we shall see that we have the 

 same small quantity in the expression for a large circular 

 aperture. 



If we make 6 = 2 ir 9 r 2 very large, and r x = 0, we have 

 a large circular aperture, and the intensity 



= 4 a 2 X 2 sin 2 {-£ ( s/Ti + W-h) J, 



= 4 a 2 X 2 when ^Tf±fc-h = 2U £ * x ? 



and however great or small k may be, compared with r 2 , we 

 see that there will be a succession of maxima and minima 

 values for different values of h. This is at variance with the 

 admitted properties of light, which it is allowed passes 

 through large apertures without any change or diminution, 

 or when diverging from a luminous point follows the law of 

 the inverse square of the distance, except near the boundaries 

 of the shadow. 



If we compare the maximum intensity from an annulus, 

 however narrow it may be, and however large the radii, with 

 that from a large circular aperture, we see that they are the 

 same ; and the multiplier X 2 would either show that only a very 

 small quantity of light could pass directly through any large 



