286 Professor Airy on a remarkable 



The intensities of the reflected streams are found to be : 

 For the light polarized in the plane of reflexion, 



(where A' and B are quantities analogous to A and B, and 

 where it is probable that A is always positive and B not very 

 great). 



For the light polarized perpendicular to the plane of reflexion, 



The intensity of the compound light which comes to the eye is 

 the sum of these. The value of T corresponding to the middle 

 of a bright or dark ring is determined by making the sum a 

 maximum or minimum with respect to the variation of T. This 



gives, 



2tt / _ , B+B\ 



tan — f 2 T cos < + — = — 1 



_ A' cos" a . cos (i -i') — A sin 2 a . cos (< + i) ir ig _g>^ 

 A' cos" a . cos (i — /) + A sin" a . cos (( + «') X 



If tan- (B — B") is positive, and cos(i-i') negative; upon in- 



creasing a from to 90° the value of tan ~ \2 T cos «' + — - — J 



increases to infinity and then becomes negative and decreases : 



tnat j s J!L U T cos i + — 5 — ) increases : and therefore the diameter 



of the ring increases. Upon increasing « from 90° to 180° the op- 

 posite change takes place. This represents exactly the fact of 



