124 SUMMARY OF CURRENT RESEARCHES RELATING TO 



reversed. For accuracy in the determination, the object must be in its 

 natural condition, and must not have been disturbed by any changes in 

 density, or by any previous preparation, drying, &c. 



(2) Appearances presented by Pleurositjma angulatum under different 

 optical conditions.— Hugo v. Mohl and Schacht regarded the markings as 

 formed by three intersecting sets of lines ; to Max Schultze and others 

 they seemed to be six-sided depressions ; to some English microscopists 

 they appeared to bo six-sided elevations, while Schiff and Dippel 

 recognized a chess-board pattern. Stein, Pelletan, and Kaiser have 

 recently referred to round protuberances, while Dr. Flogel has proved, 

 by means of transverso sections, that at any rate the upper surface of 

 the valve (with the exception of the central rib and the edge) is to be 

 regarded as flat, but that it is full of cavities between its upper and 

 under surfaces. 



If we look more closely into Pleurosigma angulatum by the light of 

 the diffraction theory, we obtain the following result : — Using purely 

 central illumination, i.e. a very narrow illuminating pencil, if the 

 numerical aperture of the objective is sufficiently large, and is at least 

 • 90 to ■ 95, we have six spectra a k -a 6 (circle A, plate III. fig. 1), which 

 are arranged regularly round the direct image of the source of light, 

 while the°six spectra of the second series a^-a 6 fall outside the aperture 

 even with very large numerical aperture. If the aperture is so small that 

 with purely central illumination no one of the six least deflected pencils 

 is admitted, the valve appears to be without markings, while with a 

 larger aperture of above 1 ' 00 N.A. the three systems of strife I.-III. 

 (plate III. fig. 2) make their appearance at the same time, and according 

 to the excess of the aperture above unity give rise to a fainter or more 

 sharply defined pattern. Each one of these systems of strife can also be 

 made visible with a numerical aperture of ■ 50 when oblique light is used ; 

 in that case two spectra a and a l or a and a 2 (circle B, plate III. fig. 1) 

 always fall within the aperture. They may also be obtained in the same 

 way with objectives of greater numerical aperture when all the other 

 spectra, with the exception of one of those mentioned, are excluded by 

 suitable diaphragms. With an objective of 0-7 to 0*8 N.A. as soon 

 as the light is oblique enough, three pencils are included, the direct and 

 two diffracted pencils (circle C, plate III. fig. 1), and then the two sets 

 of strife I. and II. intersecting at 60° are obtained. 



If the direct pencil is excluded and only two opposite spectra 

 a x a i -a 2 a 5 , a 3 , a 6 , allowed to operate, there appear in succession three 

 new sets of strife IV.-VI. which owing to the exclusion of a are bright 

 upon a dark field ; and the strife are brought nearer to one another in 

 the ratio of 2:1, so that they appear twice as fine as I.-III. though 

 they coincide with the latter in direction. 



The systems of strife vii.-ix. which are at right angles to the 

 ordinary sets I.-III., and of which the lines are closer together in the 

 proportion *J~3 : 1, are obtained in a bright field when with objectives 

 of very large aperture, the spectra of the first series aj-a e are inter- 

 cepted by suitable diaphragms, and the objective receives the direct 

 pencil a together with one of the spectra of the second series such as 

 a a x , aa 2 . . . a a 6 . The striation IX. can be obtained by a a 2 and a a 6 

 when oblique light is allowed to fall upon the central rib. 



The same sets of strife can be produced upon a dark field when, 

 usin" central light and an objective of large numerical aperture, a and 



