552 Lord Rayleigh : Further 
replace the ordinary eyepiece o£ the telescope by a cylin- 
drical lens or by a combination o£ spherical and cylindrical 
lenses. This arrangement can be employed in the present 
instance, bnt the result is not satisfactory. A complete 
focussing, leading to a point-to-point correspondence between 
image and object, may however be attained by suitably 
sloping the object-lens of the telescope. In this way excellent 
observations upon interference-rings are possible under a 
magnifying power which otherwise would be inadmissible, as 
entailing too great a loss of light. The subject will be more 
fully treated in a special paper. 
Adjustment for Parallelism. 
If the surfaces are flat, and well-adjusted, Haidinger's 
rings depend entirely upon obliquity. A slight departure 
from parallelism shows itself by an expansion or contraction 
of the rings as the eye is moved about so as to bring different 
parts of the surfaces into play. In making this observation 
the eye must be adjusted to infinity, if necessary with the aid 
of spectacle-glasses, and it may be held close to the plates ; 
but a telescope is not needed or even desirable. If the 
departure from parallelism be considerable, no rings at all 
are visible ; but there is an intermediate state of things where 
circular arcs may be seen by an eye drawn back somewhat 
and focussed upon the plates. 
The character of these bands is intermediate between those 
of Newton's and Haidinger's rings, the retardation depending 
both upon the varying direction in which the light passes the 
plates and reaches the eye and also upon the varying local 
thickness. If we take as origin of rectangular coordinates 
in the plane of the plates, the place corresponding to normal 
passage of the light, the retardation due to obliquity is as 
— (x 2 -\-y 2 ). The retardation due to local thickness is repre- 
sented by a linear function of x and y, so that the variable 
part of it may be considered to be proportional to x. Hence 
the equation of the bands is 
ocx — x 2 —y 2 = constant, 
cc being positive if x is considered positive in the direction of 
increasing thickness. Accordingly the bands are in the form 
of concentric circles and the coordinates of the centre are 
x=\a, # = 0. 
When curved arcs are seen by an eye looking at the plates 
perpendicularly, the greatest thickness lies upon the concave 
