242 Dynamical Illustrations of Certain Optical Phenomena. 



Colours which, in the ordinary spectrum, are on the red side 

 of the absorbed colour have lower frequency than the mole- 

 cular vibrations. This is the case of " upper pendulum 

 naturally the slower/' and the resultant vibration will be 

 slower still. Lord Ray lei gh calls this effect an increase in the 

 " virtual inertia " of the upper pendulum. I subjoin Lord 

 Rayleigh's own words (Phil. Mag. xliii. p. 322), which are 

 quoted in full in Lord Kelvin's ' Baltimore Lectures/ and 

 are paraphrased in Preston's ' Light.' Professor Preston 

 identifies the " pendulum " in the quotation with the lower 

 of the two, and the "point subject to horizontal vibration" 

 with the bob of the upper ; and this is also my own under- 

 standing of the passage. 



" The effect of a pendulum, suspended from a point subject 

 to horizontal vibration, is to increase or diminish the virtual 

 inertia of the mass, according as the natural period of the 

 pendulum is shorter or longer than that of its point of sus- 

 pension. This may be expressed by saying that, if the point 

 of support tends to vibrate more rapidly than the pendulum, 

 it is made to go faster still, and vice versa. 



"Below the absorption band, the material vibration is 

 naturally higher, and hence the effect of the associated matter 

 is to increase (abnormally) the virtual inertia of the aether, and 

 therefore the refrangibility. On the other side the effect is 

 the reverse." 



The latter part of the passage is to me somewhat obscure. 

 The analogy seems to point to a change of frequency, but 

 instead of this we have a change in velocity of propagation. 



§ 13. When a — b approaches zero, the foregoing approxi- 

 mation is insufficient, and the following investigation is 

 preferable. 



If the coefficient of k in the quadratic (29) vanishes, we have 



__a — fr 1 



s ~^+b' -77' 



• • (34) 



As s, being the ratio of the masses, cannot be negative, these 

 conditions require a — b to be positive, and 5 will lie between 

 the limits and 1. We shall have 



a*— A cos Hit + B cos (S2 2 t — x) } 

 £= -^-{AcosXV — Bcos(iy 



and if [the initial values of a?, £, and x are zero, we have a=0 



£= -^{AcosXV-Bcos(X2 2 *- a )} ; ^ 



