171 



upwards, all waviness disappears ; the waves are displaced 

 by chequers or lattice work. 



Again, if the shadows all fall on one side a series of cres- 

 centic shadows in miniature simulate straight lines, and 

 intersecting lines of shadows exhibit squares or hexagons 

 according to the special arrangement. Figs. 4, 5. 



By no conceivable torture of the rays can rhomboid al or 

 triangular shadows really be produced by rows of spherical 

 beads, yet such are often seen Avith high powers, as the 

 l-12th or l-16th, falsely corrected. 



If beads be arranged angularly, like a pile of shot, hexagonal 

 lines appear, supplemented by a double set, at right angles 

 to each other (Fig. 3). There are seven beads in contact, a 

 central bead surrounded by six. A double line of indistinct 

 shadow forms a hexagonal fringe, filling up, as it were, the 

 interstices, Avhilst the extreme tenuity of the focal region pre- 

 sents merely a sectional view ; but, with low power, a repe- 

 tition of these shadoAvy lines or spaces exhibits continuous 

 lines. Figs. 4, 5. 



Another interesting illustration of difficult definition is 

 found in parallel rows of minute beads, placed on opposite 

 sides of a thin membrane (Fig. 14). Unless the aberration 

 be finely corrected, the images of the upper and loAver set 

 obliterate each other ; but if they cross at varying angles, 

 blank spaces are exhibited, variegated with markings more or 

 less distinct ; better definition shows striae and cross lines 

 resembling the rounds of a ladder. Figs. 6, 7, 8. 



The first approach to a fine and brilliant definition is 

 heralded by a red flashing of the striae, resembling somewhat 

 threads of amber shown upon a sea-green ground. Gradually 

 the real structure can be brought into view by judicious 

 illumination ; and under direct 'sunlight alternate rows of 

 pale ruby-coloured spheroids flash, in beautiful contrast with 

 the emerald rows behind and partly hidden by those in 

 front. 



With a third or C eye-piece, beading is not in general 

 visible so as to be defined as beading unless the diameter 

 exceeds for any object-glass the 5000th part of its focal 

 lei gth, or the observer possesses extraordinary acuteness of 

 vis, on. The magnifying power (ordinarily in excess of fine 

 definition) is found for a given objective by dividing 100 by 

 the focal length. Thus the highest powers at all practically 

 useful are, for most of them — 



