AN APPARENT NEW POLARITY IN LIGHT. 
227 
1. By retarding the light which falls upon a portion of the pupil of the eye, bands 
are formed in the indistinct image produced by any one kind of homogeneous light. 
2. These bands are not symmetrical with regard to the centre of the indistinct 
image ; and the extent of asymmetry depends on the retardation. 
3. Therefore if light issues from a number of luminous points of such character 
that the value of retardation changes gradually from one to another, the position of 
the bands, as measured from the centre of the indistinct image of each luminous 
point, will gradually change from one to another. 
4. If then these luminous points be spectrally separated in one certain direction, 
the centres of the indistinct images will be separated in a corresponding manner, and 
the bands produced by all these luminous points may be made to coincide, and 
thereby to produce strong bands, in the confused spectrum formed by the aggregate 
of all the indistinct images. 
5. But if the luminous points be spectrally separated in the opposite direction, the 
bands will be removed further from coincidence than before, and all trace of them 
will be lost in the confused spectrum formed by the aggregate. 
6. Whether the retina be too near to the pupil, or too far from it, for distinct vision 
of the luminous points, the spectral separation must be such as to carry the points 
from which issues the most retardable light towards the side on which the retarding 
plate is placed. 
The remainder of this paper contains the mathematical development of this expla- 
nation. 
Let the wave of light, issuing from any luminous point, have, after passing the lens 
of the eye, the form of a spherical surface converging to the centre of the sphere. 
Let the radius of the spherical surface be c, and let the distance of the retina from 
the lens be c + a (this assumption corresponds to the supposition that the luminous 
point is too far off for distinct vision), and let it be required to investigate the inten- 
sity of light on a point of the retina, whose distance, from the point defined by draw- 
ing a line from the luminous origin through the centre of the sphere, is b. Let x be 
measured from the centre of the spherical surface along that line ; and let y be mea- 
sured in the direction parallel to b, x and y being used to define a point on the wave 
surface. Then x 2 y 2 = c 2 . There is no necessity for introducing another co-ordi- 
nate of the wave-surface, as its effect would only be, to introduce a constant multi- 
plier in the result. 
The distance from the point x, y, to the point on the retina is 
V {x + a\ 2 + y — bl 2 } = V {c 2 + 2 ax — 2 by + a 2 + b 2 }. 
Ip" 
If for x we put its value c — (as far as the second power of y), this expression 
becomes */ c + a] 2 + b 2 — 2 b y — y ?/ 2 j- ; and, expanding to the second power of 
2 g 2 
