Huyghens's Principle in Physical Optics. 245 



the line B C which is perpendicular to the plane of the aper- 

 ture, and let C B = h. 



Let p P q be any element of the aperture, whose breadth 

 = 8r, and distance Cp or Cq from C = r, therefore its di- 

 stance from B = V r* + ti* and its area = Q r 8 r. 



Then, by the principle under discussion, we have the dis- 

 placement of the particle at B caused by this element, pro- 

 portional to 



area of element f 2 TT , 



~~A- p p sin 1 -* (vt BP) 

 distance 13 P L X v 



a0rSr . f ZTT , 



sin - - i^t- </r*+ I 



L X \ 



where a is some number. 



Integrating for the whole vibration we have 



sn 





= COS (ri--v/^ + A 8 )+C between the limits 



2 7T l_ X 



r = 



7T 



sin 



which gives the intensity of the light at B 



a* 



V 



^9 02 ^2 



The intensity becomes a maximum and = , or equal 



77" 



to 4) a 2 X 2 when = 2 TT. 



2 n + K 



If V r a + A 8 - V r* + A- = 



where w is any integer. This equation may be satisfied by 

 an indefinite number of values of r l and r 2 . 



When T-J and r 2 are very great, and h small, we have 



= ?* 2 /-, nearly. 



