180 



plying them by ; and 6, being the angles of incidence and 



cos d t 

 refraction. 



It follows from thence that, whichever set of formulae we may 

 prefer, we shall have after refraction, in all cases, the following sim- 

 ple relation for two oppositely polarized incident pencils of equal in- 

 tensity ; namely, 



intensity of pencil polarized in the plane of incidence 

 intensity of the pencil polarized at right angles 

 = cos2 (0—0,). 



This fraction decreases as the deviation — 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.(l— ey^cos ty), 



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 cM, and putting 



X = dcOS(j), 



y = 0sin <f>, 

 we find for the equation sought 



x — y* 



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 0, the brightness, for rays 



