3 oo HERMANN VON HELMHOLTZ 



of each pair of bright lines that can just be recognized as distinct 

 from each other, then this magnitude must be equal to that 

 which in the magnified image of the object is equal in breadth 

 to the outer diffraction fringe of each bright point. A given 

 length in the object is accordingly no longer perceptible as 

 a particular length, if it appear equal to the breadth of the 

 fringe in the magnified image. Since the magnitude depends 

 only on the angle of divergence of the impinging rays, and not 

 upon the construction of the instrument, and the indistinctness 

 of the image produced by diffraction increases with the narrow- 

 ing cone of light, the limit for the differences of magnitude that 

 we are able to distinguish plainly is in general found equal to 

 half the wave-length of the particular light employed. A further 

 increase in optical power beyond that of the best modern 

 instruments does not therefore seem possible. 



Another important work in physical optics was communicated 

 to the Academy by Helmholtz on October 29, 1874, with the 

 title ' On the Theory of Anomalous Dispersion ', which had 

 occupied him for a month on his return from a long tour in 

 Switzerland. On the whole he agrees with the hypothesis put 

 forward in explanation of anomalous dispersion by Sellmeier, 

 which assumes the presence of ponderable molecules embedded 

 in the ether, and capable of sympathetic vibration. This was 

 not, however, adequate for the case in which the specific 

 oscillation-period of the sympathetically vibrating molecules was 

 equal to the period of the luminous oscillations. Since the dis- 

 persion is essentially due to absorption, Helmholtz takes the 

 cause of the absorption to be, on the one hand, the sympathetic 

 vibrations of the ponderable masses, produced by an elastic 

 force acting between the ether and the ponderable atoms; on 

 the other, a frictional resistance, which the vibrating ponderable 

 particles encounter from the ponderable masses which do not 

 vibrate in sympathy with them. This frictional force is pro- 

 portional to the velocity, as in the slow vibrations of a pendulum 

 and of resonating bodies. If only one kind of ponderable atom 

 be present, and if the ether and the ponderable molecules are 

 regarded as two continuous and interpenetrating media (as is 

 permissible when the. distance between the ponderable parts 

 is vanishingly small in comparison with the wave-length), there 

 result from the differential equation of the motion of the ether, 



