9*2 Professor Airy on the 



tion is greatest; and are inversely as T, or are least when the thickness 

 of the plate is greatest. They are directly as X, and consequently are 

 greater for red rays than for blue. Hence after a little time the bright 

 rings of one colour correspond with the dark of another. This gives the 

 peculiar coloured character to the rings: it also prevents any of them 

 from being totally black: whereas the evanescence of light in the cross 

 is independent of X, and the cross is totally black. 



2 d . Let the plates be parallel or opposite : or a = 0. The expression 

 for the intensity becomes 



4-51+ cos* 2 20 + cos — ^ 9 . sin"" 20} . 

 2 X 



If = 0, or = 90°, or = 180°, or = 270' 1 , this becomes r: thus there is a 

 bright cross instead of a dark one. For other values of the light is 



Q 27T 



greatest if — = 0, or = 2ir, &c, and least if — 6 =*r, or = 3^ &c. : 



in the former case it = c", in the latter c" cos" 2<p. These indications 

 point out exactly the form of fig. 2. In fact it is easily seen from the. 

 expressions that the intensities in corresponding parts of fig. 1. and 

 fig. 2. are precisely complemental. 



3 rd . In the general case, if sin 20 = (that is if = 0, or = 90", or 

 = 180°, or = 270°) the expression becomes 



(y q} 



— \\ +C0S 2.O + .COS 20} = — {1 +C0S 2a}. 



This indicates a faint cross, which is bright when a is small, and dark 



when a is nearly = 90". And if sin 2 . a + = 0, another cross of equal 

 intensity is found, inclined to the former at an angle a. Generally if 



be between and 90 — a, the intensity is greatest when —0=0, 



A 

 2?r 



= 2 ir, &c, and least when — 9 = tt, = 3tt, &c. : but if be between 



X 



90° — a and 90°, the intensity is greatest when ^- = tt, =3w, &c, and 



X 



