380 Dr. M.C. White, Diffraction in Microscopic Vision. 
If M, fig. 3, represents a transyerse section of a cylinder (as 
% section of woody fibre or other small tube) seen in the micro- 
Scope, spurious rings m,, m,, m,, will under favorable circum- 
stances be seen outside the cylinder, and also internal spurious 
2. 3. 
rings as shown in the figure. I have frequently counted a8 
many as five such spurious rings produced by diffraction sur 
rounding a transverse section of human hair. Internal spurious 
rings may be seen in transverse sections of woody fibre. 
Formula (1.) also shows, by substituting successively }, 2, 8 
and 4 in place of m, that the distances of the successive fringes 
from the opake body ‘will be relatively as the square roots of 
the odd numbers 1, 8, 5, 7, and soon; showing that the distances 
between the remoter fringes are less than between the lower 
orders. Thus if the distance of the first fringe is reckoned 4S 
unity the distance of the third fringe will be but a little mor 
than two. ‘The higher orders of fringes, in addition to being 
indistinct, will be so close together that they will not be a oo 
Thus these diffraction fringes bear a close resemblance to -\¢ 
ton’s rings. M and 
We see by the position of the spurious lines between * 
M, fig. 2, that if the real lines are very near together the - oa 
lines may seriously interfere with the resolvability of suc ay wh 
of lines as are found on Nobert’s test. From formula @) és 
see that the value of y, or the distance of the first dark bane n of 
the object, represented by PC, fig. 1, is an increasing parse cut 
x, or of the depth to which the lines we are considering Ms 
into the glass. In this analysis we shall ont Be the hat the 
illumination is at a little distance below hy object, and t 
thickness, AP, of the object is very small. 
_ Let us take m=1, ne inch, and suppose C ig af 
arge in comparison with 2, we may then neglect #* 1» 
_ tion (2.), whieh thus becomes, gy =méz. 
