354 Transactions of tJie Society. 



image,' nor do I bold that the microscopical image of an object con- 

 sists of two superimposed images of different origin or different mode 

 of production."* 



The matter, however, is not left in the clearness of this very 

 definite statement ; for the disclaimer is accompanied by an explanation 

 in which the reader is told that with coarse objects the whole result 

 is the same as if the image did not depend at all upon diffracted light, 

 whereas the representation of the fine details is apparently dependent 

 upon the successful collection of the light which they disperse by 

 diffraction. The explanation is too long for textual quotation, since 

 it is with the disclaimer only that I am now concerned, and those who 

 desire to know what was passing in Professor Abbe's mind when he 

 wrote it should consult the text in the place that I have named. I 

 am unable to elucidate it ; for, reading the disclaimer and the explana- 

 tion together. I am wholly at a loss to understand either the one or 

 the other. The editor of Carpenter's book apparently considers that 

 the disclaimer makes no difference to the theory, for on p. 62 he 

 writes : — 



" It has been demonstrated (by Abbe's researches) that micro- 

 scopic vision is ' sm generis.' There is and can be no comparison 

 between microscopic and macroscopic vision. The images of minute 

 objects are not delineated microscopically by means of the ordinary 

 laws of refraction ; they are not dioptrical results, but depend entirely 

 on the laws of diffraction" 



This is the original Abbe theory with which you have long been 

 familiar, and to which the criticisms will be directed that I have this 

 evening to submit for your consideration. I should introduce the 

 personal element, which I am above all things desirous of shunning, 

 were I to attempt any more curious inquiry into the measure of 

 Professor Abbe's past responsibility for the Abbe theory or of his 

 present adhesion to it. 



If you place a diffraction grating upon the stage of a Microscope, 

 illuminate it with a beam of parallel light obtained from a luminous 

 line, so arranged that its axis lies in a plane passing through the axis 

 of the instrument and parallel to the direction in which the diffraction 

 grating is ruled, you will, upon removing the ocular and looking 

 down the tube of the instrument, see in the principal focal plane of 

 the objective a central image of the source of light flanked by spectra 

 right and left, the spectra being likewise images of the source of light, 

 true representations corresponding in shape and dimensions with the 

 principal image with monochromatic light, and more or less impure 

 spectra in the case of mixed light, the degree of impurity being 

 determined by the extent to which the monochromatic images of 

 differing colours overlap. Of the rays which meet and by interference 



* The 8th edition of Carpenter's book has appeared while this paper has been 

 passing through the press; it follows the 7th in all that relates to the present 

 subject, and the references above given to the 7th edition apply equally to the latest. 



