Vol. IX] WOODWORTH— OPTICS OF THE MICROSCOPE Igl 



tion. For instance Figure ^7 on p. 64 of Southall's "Geo- 

 metrical Optics" illustrates the loci of the meridianal and 

 sagittal planes as a pair of lines intersecting, at two points, 

 a line passing through the central point of the ray bundle at 

 the surface of refraction. A plane surface is only the special 

 case of a spherical surface with an infinite radius. According 

 to Law I all possible foci lie on the normal from the object 

 point S which is represented by the line AS. The two eds-e 

 rays on the sagittal plane JS' & J_ S' being equidistant from 

 the normal should meet on this plane precisely as drawn ac- 

 cording to Law II, but this point should be slightly further 

 from the object point than the intersection of the median line 

 BS' with the normal, according to Law III. According to 

 the same law the edge rays of the meridianal plane would 

 intersect this normal or focus line as shown but at unequal 

 distances. These two rays should also intersect the median 

 or chief ray at different points and intersect each other at a 

 third point. The most cursory examination of a figure show- 

 ing the nature of a locus of a point produced by a refracting 

 surface will convince one that on a meridianal plane rays on 

 the same side of the normal invariably intersect each other at 

 some distance before they come to their respective foci in the 

 case of positive aberrations or beyond in the case of negative 

 aberrations as seen in this case. These intersections are not 

 foci but only individual crossings of rays. Foci result from 

 the simultaneous convergence of many rays. In the case of 

 a single refracting surface a focus is the convergence of all 

 the rays intersecting the lens on a zone equidistant from the 

 normal from the object point. Perhaps the failure to make 

 the distinction between individual ray crossings and ray con- 

 centrations is accountable for the prevalent misconceptions. 

 No one makes this mistake in reference to the foci from axial 

 objects, and if an oblique focus were conceived of as the 

 lateral half of an axial focus one would retain the true under- 

 standing of the nature of the focus. 



Such a figure as this is thus seen to be inaccurate in all its 

 details and to give a completely erroneous picture of the nature 

 of oblique refraction. Apparently from a knowledge that this 

 view of the nature of oblique refraction does not accord to 

 experimental observations it is usual to contend that this 



