530 SUMMARY OF CURRENT RESEARCHES RELATING TO 



focused on a distant object) by moving the index bar which carries the 

 vernier and index mirror. The difference between the readings of the 

 arc in the two cases gives B at once, from which C can be computed as 

 above. 



It may be of interest to note that the above method of finding C is 

 also capable of giving the N.A. up to about 0*5. If the objective be 

 placed in the draw-tube as an eye-piece (of course, with its front lens 



" n 



outwards), then the X.A. = sin -, being obtained as above. Also 



Li 



the N.A. = C -^ V 250000 + C^. 



Diffraction Bands.* — In this paper J. W. Gordon attempts to 

 exhibit the theory of diffraction patterns in a comprehensive form, and 

 by means of an elementary mode of treatment. He aims at putting 

 the theory of diffraction upon the same text- book level as the theories 

 of refraction and reflection. The mode by which the author introduces 

 this simplification into the subject consists essentially in substituting as 

 the surface of resolution the envelope which forms the boundary of an 

 aplanatic pencil in place of the wave-front which occupies its aperture. 

 By this alteration in the mode of analysis a great simplification in the 

 processes of the analysis is effected, the analogies between different 

 forms of aperture which have little resemblance to one another become 

 apparent, and the elementary form of exposition is rendered possible. 

 The author develops the general doctrine in seventeen propositions, of 

 which the following are specimens : — 



(I) The diffraction pattern produced by an aplanatic pencil of poly- 

 gonal cross-section, when that pattern is formed and observed in an 

 apertural plane remote from the focus, is a series of Fresnel bands 

 bordering the edge of the aperture of the pencil in that plane. 



(5) Whatever the shape which the diffraction pattern in a focal plane 

 may assume, that shape is always bilaterally symmetrical. 



(II) The ray velocity of diffracted light is equal to the ray velocity 

 of aplanatic light in the region beyond the boundary of the aplanatic 

 pencil. 



(16) The diffraction pattern visible within the aperture of an aplan- 

 atic pencil near the focal point is produced by visual projection upon 

 the plane examined of the diffraction pattern formed by optical projec- 

 tion in the focal plane. 



(6) Miscellaneous. 



Note on Pleurosigma angulatum.f — E. M. Nelson gives reasons 

 for thinking that the upper and lower membranes of P. angulatum do 

 not " eye-spot " each other, i.e. the apertures in the lower membrane 

 are not directly below those in the upper membrane. Observation with 

 a Leitz apochromat, y^ in. of 1*40 N.A., reveals that the apertures in 



* Proc. Optical Convention, ii. (1912) pp. 173-204 (17 figs.). 

 t Joum. Quekett Micr. Club, xii (1913) pp. 99-100 (4 figs.). 



