630 Transactions of the Society. 



successive dark and bright lengths ; and hence the succession of 

 sharp images referred to above. In this case the substitution of a 

 white for a monochromatic point of light does not produce much 

 improvement ; the distance between the successive images is 

 different for different colours, and the discontinuity of the suc- 

 cessive images is in consequence diminished with white light, but 

 the images remain comparatively sharp. But when an extended 

 source of light is substituted, we at once get a great number of 

 points P, from each of which the images of the slits radiate, with 

 the result that a sharp image is only obtainable in the plane 1 1 

 where all the elementary images coincide. 



I hope I have now made it clear that the chief advantage of 

 an extended source of light (which corresponds to a wide illu- 

 minating cone) is, that the ghostliness of the simple diffraction 

 image is done away with, and that the latter is replaced by an 

 easily focussed composite image which is more likely to inspire 

 confidence. I will not at this stage of my inquiry enter into the 

 question whether the image is really better, reserving this until 

 I have dealt with structures consisting of crossed lines and of dots. 



It now remains to be shown in how far the conclusions hitherto 

 arrived at are modified when the assumption is dropped — to which 

 all the above reasoning is subject — that the source of light is at a 

 considerable distance from the grating ; we must inquire whether 

 there are any important changes brought about when the source of 

 light (which will generally be a virtual image of the real source) is 

 brought very close to the object, so that the curvature of the waves 

 passing through the object becomes sensible. In discussing the 

 spurious disc theory, I showed that only a small percentage of 

 so-called " critical light " can be considered as accurately focussed 

 on the object, and that the greater part of such light is diffused 

 over a considerable number of structural elements — and it is this 

 latter case which we have to discuss. Mr. Gordon has put for- 

 ward an extraordinary claim, which I shall show to be contrary to 

 the undulatory theory as well as to direct experiment, that with 

 curved wave-fronts the diffraction spectra " will be seen to diminish 

 in breadth and crowd together," that an aperture which will only 

 accommodate a single spectrum produced by plane waves will pass 

 an ever-growing number of spectra when the waves are curved ; or 

 again, in Mr. Gordon's own words, " A narrow angled objective 

 will in this way yield the diffraction-image of an oil-immersion 

 objective ! " 



If we make the experiment with a diffraction grating or a 

 regularly striated diatom, starting of course by focussing the image, 

 and then, having removed the eye-piece, looking down the tube 

 at the back of the objective, we fail absolutely to see the effect 

 described by Mr. Gordon ; we may open or close the iris, we may 

 rack the condenser up or down, in order to vary the curvature 



