The  Diffraction  Theory  of  Microscopic  Vision.  155 
Fig.  1. 
y    amfslltitde. 
A 
H-k Jb" 
y^.-CL--  --) 
at  rtghi  angles  to  t^c 
lines. 
In  the  case  under  consideration 
a 
2' 
a 
f(x)  =  A  from  x=0  to  x\ 
=  0  from  x  =  ~  to  x  =  ^  +  b, 
=  A  from  x  —  ~  +  b  to  x  =  a  -f  b 
and      c  =  a-\-b. 
Hence 
.     1    Acos— — ,da?  +  0-M  „     Acos — 7rtV 
a  +  b\_J0  a  +  f>  J  .,  +  »  a~r''      J 
2      fa  .         m7r#  7         2 A   .    mirx 
—y      Acos  dx  =  —  sm  — -  . 
tf-W>Jo  «  +  6  ?/i7r       fl  +  6 
It  follows  that 
b»  = 
and 
2A« 
2  A  .     it  a 
A   .    2ira 
~,  i  ?     ?>i—  —  sm  -,  / >     ^2=  5     sin— -y  ,  &c.       .     (1) 
a  +  b7  77         a  +  o  2tt        a  +  b 
„,    ,        Acs        2A   .      nra  irx        2A  .     2ira  2irx 
J(x)  =  — -=  +  -     sm  —  7 .  cos     -j ■  +  fc,  -sm     -  . .  cos——    + 
a  +  6       7T        a  +  6         «.  +  £      27r       a  +  />         a  +  o 
2A  .    mira  mirx   ,  .  .,x 
-f         sm      ■   .  .  cos  -—.-+...     (J) 
