EXPLANATION OF AN APPARENT NEW POLARITY IN LIGHT.” 5 
of the curves. The ordinates, therefore, represent the intensity of light on different 
points of that small diffused image on the retina which is formed by the light coming 
from a single point, even when it is seen accurately in focus; the extreme breadth 
2\e 
of the image represented in the figure corresponds to 360° of w, or is = — ^ — 
If we express the area of each of the curves by summing the ordinates and dividing 
the sum by thirty-six, we find the following values : 
R = 6 , area is represented by 7234 
60, area is represented by 7055 
120, area is represented by 6696 
180, area is represented by 6517 
240, area is represented by 6696 
300, area is represented by 7055. 
I shall proceed now to apply these numbers to the explanation of the phenomena in 
question. 
Light is supposed to be incident on the eye from different points of a spectrum, 
formed in any way; the characteristic of the spectrum as concerned in the present 
investigation being, that the order of position of the different colours is the same as 
the order of the successive values of R. 
2\e 
First. Suppose the value of to be small, at least in comparison with the di- 
stance between those points of the image of the spectrum in which R has changed 
by 360°. 
2\ e 
1 . Let — y~ be exceedingly small. Since the same form of curve recurs for every 
change of 360° in R and not oftener, it is evident that the succession of bands (if there 
are any) in the visible image will depend on the changes of 360° in R. Our suppo- 
sition, therefore, amounts to this ; that the extent of the small diffused image is ex- 
ceedingly less than the interval between the bands (if there are any). Here it is 
plain that the formation of the broad bands cannot depend on the inequalities of 
light in the narrow diffused image, but must depend on the quantity of light in the 
whole of each narrow diffused image considered as a total light from one point of 
the spectrum. Now the total light is equal for all points. For, as the intensity of 
light coming from one luminous point and falling on a point of the retina is repre- 
sented by (~~~) • cos 2 (w — 7 y), the whole light coming from that luminous point 
is J* (“~) • cos 2 ( w — 7 ^), the limits of the integral being + cc. Now this definite 
integral is independent of R. For 
cos 2 (w — 7 ^ = -^ — y cos R + cos R . cos 2 w + sin R . cos w . sin w, 
