266 • Transactions of the Society. 



Professor Abbe's references to the former — no single point in 

 common, unless the aerial image of a diffraction grating — concerning 

 which I will add an observation in the next paragraph — be such a 

 point. Altmann's paper is based upon Helmholtz's paper of 1874, 

 concerning which I read a paper before the Society in March 1903 

 (Journal, p. 381), but when I wrote my paper on the Abbe theory 

 I had not read and had not even heard of the paper written by 

 Helmholtz. It was therefore actually impossible for me to traverse 

 the same ground as Professor Altmann, and, in fact, as I say, the 

 only point wliich I gather to be common to the two is the 

 experiment with an aerial image of a diffraction grating. The 

 substantial difference between the two papers will sufficiently 

 appear from Mr. Conrady's account of the Altmann paper. He 

 says (p. 645), " Altmann's theory thus tries to account for the 

 image under all conditions on Helmholtz's basis," and (p. 646) 

 " For the Abbe theorv Altmann has little but smiles and sneers." 

 With the first of these points I have already dealt. My paper on 

 the Abbe theory was entirely innocent of any relation to the 

 Helmlioltz basis, for the simple reason given above, that when it 

 was written I knew nothing about the Helmholtz basis. With 

 regard to the second feature of Altmann's paper, I hope that it is 

 not necessary for me to protest that in discussing the Abbe theory 

 I have had no recourse either to smiles or to sneers. 



Now to deal very briefly with the aerial image point. It 

 will be remembered that in the experiments described by 

 Dr. Zimmermann, in proof of the Abbe theory, a prominent place 

 was given to the intercostals, which appear when a diffraction 

 ^grating is viewed thi^ough certain diaphragms placed in the back 

 focal plane of the objective. In comparison with this experiment 

 I showed another in which side by side with the Abbe 

 diffractionsplattc on the stage of the Microscope was an aerial 

 image of a grating, the image having the same dimensions as the 

 real grating by its side. These two objects, viewed through the 

 same diaphragm, presented precisely the same appearance, the 

 image being obviously incapable of yielding a diffraction spectrum. 



EXPLANATION OF PLATE XII. 



Eig. 1 shows the apparatus arranged in the manner prescribed by Professor Abbe 

 for making his experiment. It also illustrates the formation upon this 

 system of the spectrum of the grating in the principal back focal plane of 

 the objective. 



Eig. 2 shows the same apparatus re-arranged for the purpose of the experiments 

 described in the paper, in which the image of the slit is formed between the 

 condenser and the grating, so that the distance of the source of light from 

 the grating can be varied at will. It illustrates the formation of the spectrum 

 in a plane conjugate to the position of the image of the slit. 



Eig. 3 is a Gauss diagram illustrating the law of the formation of the spectrum, 

 by which its position, type, and dimensions are determined. 



