The Helmholtz Theory of the Microscope. By J. W. Gordon. 419 



he estimates at 266 times at most for dry lenses, such as Mohl and 

 Harting appear to have been using. Altogether, this part of the 

 paper, in which our author is seeking for a basis on which to ground 

 his argument concerning the ultimate limit of resolving power, will 

 probably strike the reader as being the least satisfactory part, and 

 the least satisfactory by very much, of the whole paper. 



Ultimately, after discussing various inconclusive experiments 

 and observations, he fixes upon the image of a ruled surface seen 

 through a rectangular opening as being the most available test of 

 the physical limit of resolving power in optical instruments, and 

 then he says : — 



" It can be shown in the case of diffraction from a rectangular 

 opening that the grating will appear as an uniformly illuminated 

 bright surface when the diffraction fringe is equal in breadth to 

 the interval between adjacent rulings. For circular openings the 

 integration involved in the calculation of the light distribution is 

 extremely laborious. If the diameter of a circular opening is 

 equal to the side of a square, the outermost fringes in the spectrum 

 of a bright point formed by the circular opening are of equal 

 breadth with, the inner are of greater breadth than the fringes 

 formed by the ' square opening. If, then, the square opening 

 suffices to obliterate the structure of a grating when the distance 

 from centre to centre of its lines equals the breadth of the diffrac- 

 tion fringes, this must equally befall in the case of the circular 

 opening with its somewhat broader fringes. In what follows, I 

 have therefore adopted as being within the limit of the indis- 

 tinguishable distance in the object, the centre to centre distance of 

 the outer fringes which a circular opening produces. It is not 

 impossible that, by reason of a favourable disposition of the fringes, 

 somewhat smaller objects may occasionally, be half seen, half 

 imagined. But certain and unambiguous discernment of the 

 object qan hardly be brought about in that way. 



Helmholtz here says, " It can be shown," &c, but he nowhere 

 unfolds the argument by which the conclusion so announced can 

 be established. I have already mentioned the Appendix to this 

 paper in which I have ventured to develop the argument leading 

 to a contrary conclusion.* 



* Fellows of the Society may remember that I exhibited some photographs taken 

 with a lens the aperture of which had been covered by a diffraction grating, by way 

 by enforcing the argument here referred to. But in the course of preparing this 

 paper for publication I have seen reason to be dissatisfied with that experiment and 

 iherefore have omitted all reference to it in the revised proof. The matter is dealt 

 with in the Appendix, Note V. As showing what can be done in the way of fine 

 resolution, even with existing appliances, the following instances may be noted. 

 Dr. Dallinger's measurement of the flagellum of Bacterium termo = vfu^Vrnj i Q » 

 J.R.M.S., 1878, vol. i. p. 169. Mr. Nelson's photographs of diatoms which hang 

 in the Society's rooms, and in which among other exquisitely fine details there may 

 be discerned the angles of the hexagons in a Pleicrosigma angulatum where the 

 angular points extend ^g^n^y in. beyond the radius of the inscribed circle. But Dr. 

 Dallinger's result must now be taken subject to Mr. Nelson's criticism in a paper 

 presented to the Society on the 17th of June, 1903. 



