452 Mr. L. N. G. Filon on certain Diffraction Fringes 



be outside the other. These two points must be carefully 

 borne in mind in adjusting the instruments. 



When this,, however, is done, we see that Michelson's 

 assertions are confirmed, and that when we increase the 

 aperture of the telescope in this way, the results obtained are 

 of the same character as when the "slits are placed directly in 

 front of the object-glass. 



5. Let us now proceed to consider an extended source, 

 which we shall suppose for simplicity to be of uniform 

 intensity. 



The intensity at a point (p, q) on the screen will be of the 

 form 



2irk(q + v) . 27rh(p + u) ^ 2 



the integral being taken all over the geometrical image of 

 the extended source. 



We have now three cases to consider. 



(a) When the angular dimensions of the source are large 

 compared with \/h. 



(5) When the angular dimensions of the source are small 

 compared with \/h. 



(c) When the angular dimensions of the source are 

 neither large nor small compared with X/h. 



Let us begin with case (a). Then, if we consider a point 

 inside the geometrical image, the two limits for u will be very 

 large, except where the vertical through the point cuts the 

 image ; the quantity 



2irli(p + u\ 

 n a 



2irh{p + u) 



being insensible for all points outside a thin strip (shaded in 

 the figure) having for its central line the line through p } q 

 perpendicular to the slits. 



We may therefore, in integrating with regard to w, replace 

 the limits by + oo , and then integrate with regard to v along 

 the chord of the image perpendicular to the slits. 



