EXPJ.ANATION 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 



of the image represented in the figure corresponds to 360° of w^ or is = — r-^* 



If we express the area of each of the curves by summing the ordinates and dividing 

 the sura by thirty-six, we find the following values : 



o 



R = 0, 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. 



First. Suppose the value of — r- to be small, at least m comparison with the di- 

 stance between those points of the image of the spectrum in which R has changed 

 by 360°. 



1 . Let — T— 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 ditfused 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 y^^j . cos2 \w — -^j^ the whole light coming from that luminous point 



is/ (^^^j . cos2 yv — g-), the limits of the integral being 4: oc. Now this definite 



integral is independent of R. For 



2 ^^ _ _ j = _ _ y cos R -f cos R . cos2 w -f- sin R . cos tt? . sin w, 



COS' 



