Illustrations of Certain Optical Phenomena. 241 



with the statements contained in Lord Kelvin's paper * " On 

 the Rate of a Clock or Chronometer as influenced by the 

 Mode of Suspension," some of which are quoted in recent 

 editions of Tait and Steele's ' Dynamics.' 



Lord Kelvin selects the second mode as the practical mode 

 for a pendulum supported on a yielding stand, presumably 

 because the amplitude of the pendulum in the first mode is 

 comparable with that of the point of support and therefore 

 inappreciable. He also selects it as the practical mode for an 

 ordinary spring"" clock suspended like a compound pendulum 

 from a fixed axis; presumably because the escapement would 

 not work with such an enormous departure from correct time 

 as the first mode would involve. 



On the other hand, Lord Rayleigh, in a paragraph which 

 is often quoted in discussions on anomalous dispersion, ignores 

 the second mode and adopts the first. The justification seems 

 to be that his argument relates to the behaviour of the upper 

 pendulum, and that in the second mode the excursions of the 

 upper pendulum are infinitesimal. 



In the first mode, the ratio of the amplitude of the upper 

 to that of the lower pendulum is l/k= (a— b)/a, which may 

 be small, but not negligible, and the ratio of the changed 

 to the natural (frequency) 2 for the upper is 1 +sb/(b — a). 

 The upper pendulum is therefore quickened if Z> — a is positive, 

 that is, if the lower pendulum is naturally the slower, and is 

 retarded if the lower pendulum is naturally the quicker. 

 Lord Rayleigh suggested many years ago that the paradoxical 

 appearances presented in "anomalous dispersion " are due to 

 an action analogous to this. In anomalous dispersion there is 

 always excessively strong selective absorption, evidenced by 

 a black band in the spectrum produced by a prism of the 

 anomalous substance ; and the colours which are not thus 

 blotted out are displaced from their usual order. A general 

 statement of the facts, which has been deduced from the 

 comparison of a number of anomalous spectra, is that, in 

 passing through the colours of the ordinary spectrum from 

 red to violet, the refractive index is increased where the 

 absorption increases rapidly, and diminished where absorption 

 diminishes rapidly. In the case of iodine vapour, red is thus 

 rendered more refrangible than blue and violet. 



According to Lord Rayleigh, we are to regard the vibrating 

 aether as analogous to the heavy upper pendulum, and the 

 vibrating molecules of the substance to the light lower pen- 

 dulum. The colour which is absorbed is the colour which 

 has the same frequency as the molecules of the substance, 

 * Glasgow, Trans. Inst. Engin. x. 1867. pp. 139-150. 



