086 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
This expression for I r shows that when v is largo, a considerable 
number of the terms in the Fourier expansion are important, so that 
the discontinuous character of the luminous grating or row of points is 
fairly well represented in the image ; but as v diminishes, the higher 
terms drop out in succession until v is equal to 2 7 r, in which case I 2 is 
zero, and only I 0 and I, remain. When v drops below 7 r, T t also dis- 
appears. The field is then uniformly illuminated, and shows no trace 
of the original structure. This is the case of fig. 106, and curve iii. 
shows that when an infinite series shows no structure, a pair of luminous 
points or lines of the same closeness are still in some degree separated. 
Fig. 106. 
The case of a grating or row of points perforated in an opaque 
screen and illuminated by plane waves of light incident perpendicularly 
is next considered. In this case amplitudes and not intensities have to 
be superposed. If A be the resultant amplitude, 
sin u sin (w + 0) , sin ( u — v) 
( ' ~ u u - {- 0 u — v ^ 
which, by calculation, becomes equal to 
7T , 
V \ 
, _ 2 7TU . ~ 4 TTll 
1+2 cos f- 2 ccs [- 
V V 
the series being continued so long as 2 irr •< v. 
I 
