436 LIMITS OF OPTICAL CAPACITY OF THE MICROSCOPE. 



the movement in the point I will be given by an expression in the 

 form 



A sin. J — [ac'\-a'b — af] + Const > 



"Where X is the wave length in empty space, A the speed of 

 progressing movement, t the time. The sum of these quantities 

 taken for every point c of the aperture (in which the factor a can 

 be considered as approximatively independent of c) will finally 

 determine the movement at h. 



If now we suppose the rays passing from {a) and {h) to the point 

 (c) of the relatively narrowest aperture to be prolonged in the 

 direction which they have at the point {c) until they intersect each 

 other in the points (o) and (/3), these last points will be the images 

 of the points («) and (J), formed in the medium of {c). Since, then, 

 from what has been said above, the optical lengths {aa) and (5/3) 

 being lengths measured between conjugate foci, are constant, we 

 may put 



{ac)={aa)—{ca) 



{cb)=m-[iic) 



The direction of movement of the ray must be conceived as 

 always advancing from the first to the second letters; and 

 therefore, 



{ca) be put = — {ac) as also {Pc)=^ — (/7/3) 



Then the expression for the eflPect of each separate ray on the point 

 {h) becomes 



A sin. \ -^ l(ac)—{l3c) f- {aa) + (/35)] + Const \ 



The only terms amongst the signs bracketed under the sine that 

 vary with the point c are {ac) — (/3c). These optical lengths, 

 however, lie wholly in the medium of {c), and are, therefore, 



