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 

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

 stance from B = V r 2 + fr and its area = 6 r h 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 ir . , „ ™ 1 



— TV- «-o- sin < — — (vt — BF) y 



distance Br L \ v ' J 



where a is some number. 



Integrating for the whole vibration we have 



*y.-rf=F sin "(t 1 ><-'^>} 



J *![ ( r * _- 4/ r 2 + /* 2 )~l + c between the limits 



aOX 2tt 



-— — cos 



2tt 



r = r 2 J 



ad\ 

 sin 



IT 



in { ~- ( • r/ + A« - V r, 2 4 **) j" • 



|!-ZL (,t-iV r7+F^| A/r?+F)| , 



sin 



which gives the intensity of the light at B 

 a*6 2 \ 2 



sin 3 |-^- ( • r 2 2 -f-/z 2 - • r^+^J J 



a 2 6 2 X 2 

 The intensity becomes a maximum and = r z — , or equal 



to 4? a 2 \ 2 when 6 = 2 7r. 



If 4/ ^ + ^ _ */ r * + tf = 



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

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



When r x and r 2 are very great, and h small, we have 



h 2 (\ 1 \ f Q 2 « + 1 



= r 2 — rj nearly. 



