July 18, 1902.] 



SCIENCE. 



85 



oretieal considerations of analogous exam- 

 ples to go by, but no direct experimental 

 data. Lord Rayleigh has considered the 

 problem. It has been noticed that in the 

 progress of a group of waves in water, the 

 individual waves appear to advance 

 through the group and die away at the 

 anterior limit. Stokes has explained this 

 by regarding the group as formed by the 

 superposition of two infinite trains of waves 

 of equal amplitudes and of nearly equal 

 wave-lengths advancing in the same dii-ec- 

 tion. The mathematical formulation of 

 this phenomenon as thus explained gives a 

 I'esultant periodic motion with a periodic 

 amplitude varying from zero to the sum 

 of the two elements. The velocity of this 

 maximum, which is called the group-velocity 

 U is related to the wave-velocity V by the 

 variation with respect to the wave-length ;.. 

 If the wave-velocity V is definitely Imo'wn 

 as a function of the wave-length, then the 

 group-velocity can be ascertained. On the 

 other hand, we cannot determine the wave- 

 velocity V from a complete knowledge of 

 the function Z7. It is necessary that we 

 Tmow the relation of V to the wave-length, 

 liayleigh finds that U={l—n)V if the 

 wave-velocity V varies as the 7!th power of 

 the wave-length ;.. Thus for deep-water 

 waves «=l/2, U^3/2r. In the case of 

 aerial waves U and V are nearly the same. 

 In this instance the ear detects the periodic 

 variation of the resultant amplitude as 

 "beats which are propagated out with the 

 velocity of the component waves. The re- 

 sultant of two such systems of light waves 

 may be illustrated by the interference of 

 the two sodium lines in Newton's rings 

 and the periodic variation in the luminos- 

 ity of the rings when a great number are 

 examined together. This of course is the 

 fluctuation which occurs in the resultant 

 radiations propagated into space but not 

 •capable of being seen by the eye. 



The argument from the kinematical 

 point of view for the relation of the two 

 velocities is not entirely beyond criticism 

 as this requires a gradual variation in the 

 amplitude according to the cosine law. 

 As the group sent out by either of these 

 two methods must deviate considerably 

 from this law, it would be necessary to 

 include a niunber of harmonics in Fourier's 

 series to give the proper configuration to the 

 group. In order that we may then use 

 the kinematical argument we must assume 

 these harmonics are rapidly frittered 

 down and that they never return. This 

 may have some significance in the toothed- 

 wheel method, where some observers have 

 noted a coloration of the i-eturn image. 

 Further analysis of the kinematical prob- 

 lem is necessary before we can feel sure of 

 its application to the physical counterpart. 

 The argument which Lord Rayleigh has 

 advanced, based on the consideration 

 of the energy propagated, assumes absorp- 

 tion due to a frictional term proportional 

 to the velocity. Now while absorption in 

 ponderable media is explained on the as- 

 sumption of imbedded particles in the ether 

 of some specific period, it has not yet been 

 proven that this is the only way in which 

 absorption may take place. If there be 

 absorption in the ether itself it is not easy 

 to see just how it does occur. On the as- 

 sumption already made above it would be 

 impossible for the ether to transmit waves 

 of certain frequencies corresponding to 

 its natural period and we should have 

 selective absorption, a condition quite con- 

 trary to the conception of such a medium. 

 On the above assumption, however, the 

 ratio of the energy passing a given point 

 in a unit of time to the energy in the train 

 after this unit of time is the ratio of the 

 group -velocity to the wave- velocity. Thus 

 we see the ratio depends directly on the 

 amount of absorption. It is not quite clear, 



