Highly Magnified Images. Bg J. W. Gordon. 7 



traction of the lesser from the greater when they have a phase 



9 1 



difference of ^— X. The general expression of which these 



two are particular examples, and by which any two amplitudes A t 

 and A 2 having a phase difference ***' 7r may be compounded is : 



A. 



<f> 



• (1) 



A (1 + 2) = A : 4- cos ^ 2 7r A 2 . 

 or, more generally still, if we assume that both the components A t 



Fig. 3. 



and A 2 are affected with retardation relatively to the phase of the 

 resulting disturbance, we may write these retardations ?~ 2 tt 



/v 



and — 2 2 7r respectively. Then the two amplitudes in question 



A. 



may be compounded thus 



A (1 + 2 ) — < Aj cos ^ 2 7r + A 2 cos ^ 2 7T > . . (2) 



Sir Geo. Airy's table contains the constants A 1; A 2 , etc., required 

 in this equation, and clearly its calculated value would be largely 



