Caj^acity of the Microscope. By Prof. HelmhoUz. 37 
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 (a) and (y6), these last points will be the images 
of the points (a) and (h), formed in the medium of (c). Since, then, 
from what has been said above, the optical lengths (a a) and (h 
being lengths measured between conjugate foci, are constant, we 
may put 
(a c) = (a a) — (c a) 
(c6) = (^6) - (/3 c). 
The direction of movement of the ray must be conceived as 
always advancing from the first to the second letters ; and 
therefore 
(c a) be put = — (a c), as also (fic) = — (c 13). 
Then the expression for the effect of each separate ray on the point 
(b) becomes 
A sin. 1^ [(a c) - (0 c) - + (a a) + (fi 6)] + constantj . 
The only terms amongst the signs bracketed under the sine that 
vary with the point c are (a c) — (fic). These optical lengths, 
however, lie wholly in the medium of (c), and are therefore 
straight lines ; consequently, the diffraction effect of the light from 
(a) at the point (b), apart from the factor A, which expresses its 
total intensity, will be the same as that of the light from a for the 
point /3. But the latter can be calculated according to the known 
method valid for rectiHnear rays. 
