Chemistry and Physics. 385 



of dispersion of light shows that there will be no bending when 

 the frequency of the vibration is very great. I have here a curve 

 taken from a paper by Helmholtz, which shows the relation 

 between the refractive index and the frequency of vibration for a 

 substance whose molecules have a natural period of vibration, 

 and one only ; the frequency of this vibration is represented by 

 OK in the diagram. The refractive index increases with the 

 frequency of the light until the latter is equal to the frequency 

 of the natural vibration of the substance ; the refractive index 

 then diminishes, becomes less than unity, and finally approaches 

 unity, and is practically equal to it when the frequency of the 

 light greatly exceeds that of the natural vibration of the molecule. 

 Helmholtz's results are obtained on the supposition that a 

 molecule of the refracting substance consists of a pair of oppo- 

 sitely electrified atoms, and that the specific inductive capacity 

 of the medium consists of two parts, one due to the ether, the 

 other to the setting of the molecules along the lines of electric 

 force. 



Starting from this supposition, we can easily see without 

 mathematical analysis that the relation between the refractive 

 index and the frequency must be of the kind indicated by the 

 curve. Let us suppose that an electromotive force of given 

 amplitude acts on this mixture of molecules and ether, and let 

 us start with the frequency of the external electromotive force 

 less than that of the tree vibrations of the molecules : as the 

 period of the force approaches that of the molecules, the effect of 

 the force in pulling the molecules into line will increase; thus the 

 specific inductive capacity, and therefore the refractive index 

 increases with the frequency of the external force ; the effect of 

 the force on the orientation of the molecules will be greatest 

 when the period of the force coincides with that of the molecules. 

 As long as the frequency of the force is less than that of the 

 molecules, the external field tends to make the molecules set go as 

 to increase the specific inductive capacity of the mixture ; as 

 soon, however, as the frequency of the force exceeds that of the 

 molecules, the molecules, if there are no viscous forces, will all 

 topple over and point so as to make the part of the specific induc- 

 tive capacity due to the molecules of opposite sign to that due to 

 the ether. Thus, for frequencies greater than that of the 

 molecules, the specific inductive capacity will be less than unity. 

 When the frequency of the force only slightly exceeds that of the 

 molecules, the effect of the external field on the molecules is very 

 great, so that if there are a considerable number of molecules, 

 the negative part of the specific inductive capacity due to the 

 molecules may be greater than the positive part due to the ether, 

 so that the specific inductive capacity of the mixture of molecules 

 and ether would be negative ; no waves of this period could then 

 travel through the medium, they would be totally reflected from 

 the surface. 



As the frequency of the force gets greater and greater, its 



