120 



SUMMARY OF CURRENT RESEARCHES RELATING TO 



viz. that in the case of minute objects which are less than a fow wave- 

 lengths in diameter the laws of geometrical optics no longer apply, that 

 is, the structures are no longer imaged according to the laws which 

 govern the delineation of objects observed with the naked eye, but that 

 the delineation is dependent upon the rays which are diffracted by the 

 object. The matter is, however, obviously of more importance to histo- 

 logists than to the observers of diatoms. In the case of histological 

 structures the conditions are, of course, much more complicated than with 

 diatoms, but the principles remain the same, and if they are not taken 

 into account very false deductions may be made. A notable instance of 

 this was the case on which we commented in 1881,* where Mr. J. B. 

 Haycroft f put forward an explanation of the appearances presented by 

 muscle-fibre which, while an eminently simple one, was unfortunately 

 entirely founded on the supposition that the fibres acted in the same 

 manner as cylindrical threads of larger size. 



Prof. S. Exner, who has recently investigated the question of muscle- 

 fibre, has published an article on the subject, in the course of which he 

 deals fully with the operation of diffraction on such structures. This 

 article from the point of view we are now considering is a very interest- 

 ing one, and we have translated his remarks without abridgment. 



In order that the subject may be fully understood, we have prefaced 

 the translation by notes on (1) the appearances presented by air-bubbles 

 and oil-globules, by solid and hollow fibres, and by depressions and 

 elevations where the objects are larger than a few multiples of a wave- 

 length, and (2) the appearances presented by Pleurosigma angulatum 

 under different optical conditions. 



(1) Appearances presented by Air-bubbles and Oil-globules, by solid 

 and hollow Fibres, and by Depressions and Elevations of relatively large 

 size.% — The accompanying figs. 24 and 25 supplement those given at 



Air-bubbles under the Microscope. Focus, a below the centre (at the focal plane), 

 b to the centre, c the same with oblique light stopped off. 



p. 743 of Vol. II. (1882), a in fig. 24 representing an aix--bubble when 

 the Microscope is focused below its centre (x being the image of a 

 window bar), b when focused to the centre, and c the same with oblique 



* See this Journal, 1881, p. 964. 



t Proc. Roy. Soc. Lond., xxxi. (1881) pp. 360-79 (1 pi.). 



X Cf. Dippel, L., ' Das Mikroskop und seine Anwendung,' 1867, pp. 313-4 (4 figs.), 

 pp. 355-60 (9 figs.), and 2nd ed. 1882, pp. 822-4 (4 figs.), pp. 852-6 (6 figs.). 



