612 Transactions of the Society. 



purposes, at any rate, this usually consists in using the edge of the 

 flame of an oil lamp as the source of light. Now this flame is 

 probably about an inch deep in the direction of the optical axis, 

 and, being almost perfectly transparent, a complete image (of three 

 dimensions) is formed of it by the condenser. It is well known 

 that the magnification (or diminution) in the direction of the 

 optical axis is the square of that at right angles to the optical 

 axis (this follows directly by differentiating the formula for con- 

 jugate foci: j +y = ~/)> an d if we take an average case, say a 

 condenser of £-inch focus used with the lamp 8 inches away, the 

 diminution will be | = -, 9 ; the diminution of the lamp flame in 



the direction of the optical axis will be the square of this or near 

 enough -j-qW ; the image of our flame of an assumed depth of 1 in. 

 will therefore cover y^W m - a l° n g the optical axis. This seems 

 small, but such a condenser would be suitable for high dry powers 

 and objects such as our old friend Plcurosigma anguhttum, with 

 50,000 dots to the inch ; and if we make the further reasonable 

 assumptions that the condenser is opened to give approximately 

 a 60° cone, and that the centre of the lamp flame is focussed in 

 the plane of the structure, we shall have the extreme front and 

 back of the flame focussed 20*00 m - aoove an( l below the structure, 

 and the cones forming their images will be 20W in. diameter 

 where they cut the structure. 



But these small circles have a diameter containing 25 dots in 

 line, or an area containing something like 500 dots, and therefore 

 this great number of dots receives light capable of producing 

 diffraction spectra. 



Of course intermediate points of the lamp flame will be 

 focussed nearer the plane containing the structure, but it will 

 readily be understood that the greater part of the light from the 

 flame is diffused over a considerable number of elements of struc- 

 ture, and that it is probably not far wrong to say that not more 

 than 5 p.c. of the light is or can be focussed nearly enough to 

 satisfy the condition of truly critical light. 



I shall show later on that the remaining 95 p.c. of the light 

 produce diffraction spectra, and through them an image of the 

 object, in much the same way as the parallel light assumed by 

 the theory that we are now driven to depend upon — that of 

 Prof. Abbe. 



One more point in connection with the spurious disc theory 

 should be borne in mind. 



A self-luminous object, such as this theory assumes, would, 

 and should, send out light in all directions like any other source 

 of light ; it would, in consequence, fill uniformly and completely 



