70 Cambridge Philosophical Society .— 



This fraction decreases as the deviation 0—0, increases; it is 

 therefore less for the violet rays than the red, for the indigo than 

 for the yellow; and this serves to explain in a general way the dingy 

 yellow stripe in the plane of polarization, and the bright violet stripe 

 in the plane at right angles. 



The author has also considered the effect in a plane making an 

 angle (p with the plane of greatest polarization, and arrives at the 

 following result : that, provided we attribute to the distribution of 

 the optic nerve such a variation of sensibility as, taken in conjunc- 

 tion with the action of the iris^ shall produce a field of view uni- 

 formly bright from the centre outwards when common daylight is 

 viewed (a condition which the author believes is common to all eyes 

 with his own), we shall have for the brightness at any point of the 

 field of view the following expression, 



M .(1— ey — cos 20), 



where M is the central brightness, e the degree of polarization (being 

 for common daylight, and 1 for completely polarized light), and 

 y= -07309 for rays of mean refrangibility. 



The last expression gives us without difficulty the form of the 

 curves of equal brightness. 



Assuming this constant brightness to be c M, and putting 



x=0cos0, 

 y=0sin0, 

 we find for the equation sought 



ey 



The curves are therefore equilateral hyperbolas having the lines in 

 octants for their common asymptotes, which confound themselves 

 with the curves themselves when c=0, the case of mean brightness. 



The yellow fasciculi have their vertices in the plane of polariza- 

 tion, and the violet fasciculi have their vertices in the plane at right 

 angles. 



It will be seen that for a given value of d, the brightness, for rays 

 of all degrees of refrangibility, that is for all values of y, is least in 

 the plane of greatest polarization and greatest in the plane at right 

 angles — contrary to the idea of Moigno, who, for insufficient rea- 

 sons, imagined that the maximum occurred in the plane of polariza- 

 tion and the minimum in the plane at right angles. 



The yellow tint in the position of minimum intensity, and the vio- 

 let tint in the position of maximum intensity, is nevertheless per- 

 fectly accounted for by the consideration that y is greater for the 

 violet and indigo rays than for the red and yellow. 



The paper further contains some observations respecting a subjec- 

 tive centre of the eye, distinct from the usual objective centre, which 

 may be read with interest, as they remove some difficulties con- 

 nected with the theory of vision, which had often occurred to the 

 author, and may have occurred to others. 



