Huyghens's Principle in Physical Optics, 247 



circular aperture; or otherwise, if it were maintained that the 

 constant a may be very large ; then our former conclusions 

 will be free from any objection that they represent inappre- 

 ciable quantities of light. 



A fact stated by M. Fresnel, which I have confirmed by a 

 severe experimental examination, bears upon the point, of 

 the effect of the limits of apertures. His experiments for the 

 diffraction by a single edge of an opake plate (see the before- 

 mentioned memoir, page 429.) were, in fact, made with an 

 aperture generally of a centimeter in breadth, whilst his lu- 

 minous point and micrometer were in some measures distant 

 about seven metres from each other. Notwithstanding the 

 small breadth of the aperture compared with its distances 

 from the luminous point and micrometer, yet we find him 

 stating that the fringes formed by one edge were not affected 

 by the other edge, and that his measures might be taken as 

 if made with a single edge. The principle under discussion 

 shows, that with the quadrilateral, sectorial or circular forms 

 of apertures, the intensity should depend on the limits, how- 

 ever distant. 



The same results arise when we take plane reflectors in 

 place of apertures, only then the point B must be taken on 

 the same side as that on which the waves are incident. 



To discuss the second case, let A be the luminous origin 

 in the line A C B perpendicular A 

 to the plane of the aperture, 

 through the centre C. Let A C 

 = B C = //, and the other parts 

 as in the former figure. 



We have now for the displace- 

 ment of the particle at B, due to 

 the element p P q, C 



aOrhr 



f27T_ 



(vt 



AP + PB 



- (AP + PB)) j 

 and the whole displacement 



- a6 r r • T27T 1 



~ TJ r VFTP Sln \~x (P *-2 • r* + h*) f 



8 7T ° 0S \ " (vt — 2 a/ r 2 + h?) J + C between the 



limits 



r = rj 



