MICROSCOPIC ILLUMINATION. 75- 



particles which reflect the light to the observer are themselves 

 directly or indirectly lit by the sun, and therefore the source ia 

 in this case also not the source of light, but the virtual sources 

 placed at infinity from which the plane waves illuminating the 

 specimen may be regarded as being derived. In the case where 

 the plane mirror alone is used, the plane-wave illumination 

 commences from the sky ; with the Abbe condenser in addition, it 

 starts as spherical waves from points situated on the lower focal 

 plane of the condenser (for only under this condition can plane- 

 waves leave the upper lens surface of the condenser). 



Now Abbe's emphasis on the use of plane-wave illumination 

 for the microscope was probably made for two reasons : firstly,, 

 when this is the case the spectra formed in the upper focal plane 

 of the objective would have their greatest purity in the spectro- 

 scopic sense (the specimen on the stage being the counterpart of 

 the diffraction grating or prism) ; secondly, it would be possible to 

 confirm by calculation the images seen by the eye, in those cases- 

 where plane waves are incident on the specimen (the treatment 

 for curved- wave fronts being of very much greater mathematical 

 complexity). But this emphasis on the use of plane waves by 

 Abbe does not imply that any practical advantages follow 

 their use. In fact my own experiments serve to show that 

 great divergence from plane-wave illumination is permissible 

 without obvious change in the images presented to the eye. 

 There are probably two reasons that may be advanced for this 

 experimental fact : firstly, as Johnstone Stoney (3) has pointed 

 out, there appears to be physical reality for the mathematical 

 theorem that any train of simultaneous vibrations may be 

 replaced by an equivalent series of plane waves ; secondly, only 

 in quite exceptional cases (ruled gratings and very regular dia- 

 toms such as Pleurosigma angulatum) are the conditions present 

 for the formation of pure diffraction spectra, and therefore the 

 distribution of intensity in the maxima and minima would under 

 ordinary conditions be but little affected by the substitution 

 of an incident beam of light with a curved instead of one 

 with a plane-wave front. This is in agreement with Conrady's. 

 views (4), for he showed that with curved- wave fronts the 

 image must still be formed on the diffraction principle. 



