Dr. G. J. Stoney on Microscopic Vision, 439 



being more than a second in width. By this process the 

 whole hemisphere may be mapped out into these patches 

 placed in vertical series, each series with a corresponding 

 series on the opposite side of the polar axis, and the whole 

 ending up in one patch or in one pair of patches at the pole. 

 From the middle of each patch draw a radius of the sphere, 

 omitted from the diagram to avoid confusion, but easily con- 

 ceived. These are the axial rays of the secondary beams W, 

 which we are at liberty to substitute for the elementary sheafs 

 of beams that really exist. 



In this as in all similar problems it is convenient to begin 

 by resolving each beam of light into two plane-polarized 

 beams, one polarized in and the other perpendicular to the 

 meridional plane in which its axial ray lies. We may then 

 confine our attention first to the light polarized in one of 

 these ways. Let us then call the secondary beams which are 

 polarized in one of these ways a, b, &c, and the corresponding 

 beams opposite to them and polarized in the same way, a', V, 

 &c, as in the figure. 



h\ general, beam a and beam a will not be alike. How^ 

 ever, beam a' may by the proposition in § 23, p. 435, be sub- 

 divided into a\ and a' 2 , of which a\ shall be exactly similar 

 to a. Accordingly a and a\ produce a definite ruling of 

 equal and equidistant lines extending over the whole standard 

 image ; and a' 2 has still to be disposed of. Resolve b into 

 two beams of which b x is similar to a' 2 , and b 2 is the other 

 component. Then a' 2 and b x produce another ruling, and b. 2 

 has next to be disposed of. To do this, resolve b' into b\ and 

 b' 2 , of which b\ is similar to b 2 . Then b 2 and b\ produce a 

 ruling and b' 2 is what remains over. By continuing this 

 process the whole of the vertical columns over a and a' 

 may be disposed of : and in a similar way the other columns 

 can be treated. All the rulings extend over the whole 

 of the standard image, and between them use up the whole 

 of the light polarized one way, except that residium which 

 is left over in the last patch at the pole. This residium can 

 be made as small as we please by diminishing the size of 

 our elementary cones ; and of whatever amount it is, it 

 only represents the limiting case of a ruling produced by 

 two beams advancing at a vanishing angle to one another, 

 ■and of which accordingly the spacing is infinite. 



A similar treatment applies to the light polarized the other 

 •way, which also produces its body of rulings; so that finally 

 the ivhole of the light emitted by the objective field, however 

 varied its contents, can be laid down on the standard image in 

 the form of a number of luminous rulings of uniform parallel 

 lines, each of them of that optically most simple character 



2 12 



