The Hclmholtz Theory of the Microscope. By J. W. Gordon. 44$ 



the conditions satisfied which Lord Rayleigh lays down as necessary for 

 just perceptible resolution. Incidentally it thus appears that Dr. Dal- 

 linger's famous measurement of the flagellum of Bacterium termo, with 

 a breadth of about one-quarter of a wave-length, would be well within 

 the capabilities of a perfectly corrected lens. Ultimately, if the breadth 

 of the luminous surfaces were indefinitely cut down we should, of course, 

 return to the fringe-curve of fig. 113 from which we started. 



Finally, it appears that the magnitude — to which so much importance 



has for a long period of time been attributed, even by physicists of the 

 highest standing, as setting the ultimate limit of resolving power, is in 

 truth quite innocent of any such propensity, and that its bacl reputation 

 is owing simply to an oversight in the conduct of a calculation. The 

 oversight would have been unimportant if it had led only to a miscon- 

 ception as to the form of the light-intensity curve at the boundary of a 

 bright surface, for the contours of one-half of the antipoint-curve and 

 of the total light curve are in fact very nearly similar. But the im- 

 portance of the oversight lies in this, that it leads to misconception as 

 to the position of the light-intensity curve in relation to the object. The 

 radiant point lies in the case of the antipoint-curve under the highest, 

 point of the curve, and in the other case the outmost radiant point of 

 the surface lies some distance beyond the highest point of the curve. 

 Hence the edge of the luminous surface has been displaced by what 

 amounts in the case of a large surface to £ A, and this has led to the 

 inference that the appearance of a continuous surface would be seen 

 when there was in fact a gap of ^ A bridged over by diffracted light. 



Note III. — Note to Page 410. 



It may be well to add an explanation of the rule deduced on p. 410 

 concerning the absence of diffraction from a focal plane. This does 

 not, of course, imply that an aperture ceases to produce diffraction if 

 light be focussed in its plane, although this seems to have been supposed. 

 Helmholtz himself describes the failure of an experiment, planned 

 apparently on the supposition that the focussing of the source of light 

 within an aperture, would entirely suppress all diffraction whatsoever * 

 from that aperture. But any such impression must be due to a mere 

 oversight. For there passes with the focal light, light that is derived 

 from wave-fronts not yet brought to focus in front of the aperture, and 

 if we make our arrangements so that the eye focusses upon one of these 

 wave-fronts it becomes the effective source of light, and the focal plane 

 in the aperture only a region in which the light from that comparatively 

 feeble source has to make its way through much extraneous light from 

 other sources. Hence, it is always possible to demonstrate the diffraction 

 from any aperture however illuminated. What the rule deduced on p. 410 

 tells us is that diffraction from the aperture in question will be entirely 

 suppressed in all focal planes conjugate to the plane of the aperture. 



* Pogg. Ann., 1874, Jubelband, pp. 577, 578. 



