NO ea A ee the 
Dr. M. C. White, Diffraction in Microscopic Vision. 379 
The known relation B?=C?—A® gives, acre: 
B?=C?2—C C—(2m—1)= =C(2m=1) 5. 
The equation of the hyperbola referred to its centre and to its 
axes is therefore, 
2 d A A 
h 
or Cy? —(2m—1) st C2; omitting the terms which contain 
h : 
4 and neglecting (2m—1); as too small to be considered when 
added to the quantity C. If we desire to refer the curve to the 
int A, as its origin we have only to replace x in the formula 
y <+C when the equation becomes, 
(c - (2m—1)=) y2= (2m— 1) 5(2?-+-202) or, 
(1.) y= |(en - 1) (2-+-2Cz)—+C | 
. a i 
considering as before (2m—1)> very small as compared with C. 
If we consider only the first fringe m=1 and the equation be- 
comes, 
(2) y= pepe 
Considering these equations it is evident that the value of y, 
or the distance of a dark band produced by diffraction from the 
teal line which produces it, will be directly prone to the 
att the square root of 4. Now as the length of a wave of 
Violet light is least and a wave of red is greatest, and the waves 
of other colors are of intermediate lengths, it is evident that the 
k band produced by diffraction will consist of all the colors 
of the spectrum, the violet being nearest and the red most dis- 
tant from the true shadow or image of the object. The dotted 
lines SV and AV, fig. 1, show the paths of the rays that produce 
a violet band, and MV shows the trajectory of the curve of violet . 
light on the other. side of the opake object. Mm,, Mm,, and 
a show the trajectories of the first, second and third orders 
the microscope from above, the other parts of the figure show 
the a, the spurious lines or series of colored fringes of 
the first, second and third orders, lapentg by diffraction. These 
dark bands or fringes can easil : 
dering a line deeply ruled of glass with a diamond. 
