488 Mr. J. Barnes on the Analysis of 
be covered with the two systems of concentric rings. At a 
definite separation of the plates let these two sys tems be in 
coincidence, then we have the relation 
A A @ 
— = ———_~ n 
nN A+dr ‘ 
where n is any whole number, or 
nr? 
A—nxr 
Since A is always large relative to nX we may write 
RA”. aN? 
A 2Dcosé 
Thus by observing the first coincidence of the rings (n=1) 
near the centre of the system where @ is so small that we may 
consider cos 0=1, knowing the value of X,and measuring D, 
the value of dX can be determined with a very high degree of 
accuracy. When dd is very small it is not necessary for the 
determination of its value to separate the plates until the 
first coincidence occurs, but only till the separation of the 
rings is clearly visible. When the separation of the two 
systems of rings is, say, one quarter of the distance between 
consecutive rings of the same radiation, the equation becomes 
ane 

an= 
The resolving power of this method depends upon the dis- 
tance between the plates and also upon the angle of incidence 
of the light. The fringes near the centre have thus the 
largest resolving power. It is also advantageous to make 
observations upon the central fringes because their separation 
is the greatest. This can be shown if we consider the length 
of the radii of the rings. With the centre of the system a 
bright ring 
A=2D=myr 
where m is an integer ; for the first bright fringe out from 
the centre the difference of path is 
2D cos 0=(m—1)r 
nels / 2m—1 
i= ye 
hence 
tan 
and the radius R, of the ring is given by the expression 
(=) ff 2m—1 
m—1 
