191 1.] AGGREGATES OF ELECTRONS. 357 



be very great compared with the natural frequency of the spring. 

 In that case the shakiness of the support will have very little effect 

 on the spring. If however the frequency of the tremors happens to 

 be equal or nearly equal to the natural frequency of the spring the 

 latter is set into very violent agitation, for the reason that the 

 natural swings of the spring are continually being helped by the 

 oscillations of the support. 



A precisely analogous eft'ect takes place when the period of the 

 light is close to the natural period of the electrons. In fact it can 

 be shown that, if there is nothing analogous to a frictional force to 

 damp down the vibrations of the electrons, they will execute oscilla- 

 tions of infinite amplitude when there is exact coincidence between 

 the periods. Since the displacement of the electrons in unit electric 

 field is the important factor in determining the refractive index we 

 should expect its value to change very considerably in this region. 

 As a matter of fact, in the extreme case where there is no damping, 

 the value of ^- falls rapidly from a small positive quantity on the 

 short wave-length side of the position of coincidence to the value 

 — oc at exact coincidence (A = Ao). As the period of exact coinci- 

 dence is passed ix- changes suddenly to -f- x and on the long wave- 

 length side falls rapidly to a rather larger positive value than the 

 one that it had at a great distance from the natural period on the 

 short wave-length side. 



Several very important deductions can be drawn from the results 

 which have just been described. In the first place we notice that 

 provided we always keep to the same side of the natural period, no 

 matter which side we choose, then the refractive index jj. always 

 diminishes as the wave-length A increases. Hence, since the devia- 

 tion of light by a prism is greater when the refractive index is 

 greater it will be smaller the greater the wave-length. The blue 

 light will therefore be deviated more than the red light in the spec- 

 trum. This is the well known kind of dispersion which is exhibited 

 by prisms of glass and similar colorless transparent substances. 



When part of the spectrum lies on one side of the natural period 

 and part on the other there is a sudden increase in the value of the 

 refractive index when the natural period is crossed. The spec- 

 trum will then consist of two groups of colors, that on the long 



