170 PROFESSOR K. PEARSON AND MISS A. LKE ON THK VIUKATIONS 



<, and <fc This is really a kinematic resolution convenient for analysis of the wave 

 phenomena. We might have resolved the displacement in other ways, possibly with 

 equal advantage. But it must not be supposed that a purely kinematical resolution 

 into wave components can have no physical significance. It is true that neither <f> t 

 nor <(>., could exist by themselves, but this is practically true of all the wave resolutions 

 the mathematical physicist habitually deals with. He is accustomed to consider in 

 electro-magnetism waves of electric and magnetic force, neither have an independent 

 existence ; of radial and transverse electric displacement, one is impossible without 

 the other. In the theory of the refraction and reflection of waves at the interface 

 of elastic media, and its applications to the undulatory theory of light, we do not 

 hesitate to separate the waves of transverse from longitudinal displacement and to 

 speak of the former as having an independent existence, yet we are really separating 

 kinematically what can only coexist. Lastly, consider, perhaps, the most familiar 

 case, that of the longitudinal vibrations of rods ; here the physicists carry the 

 kinematic resolution so far that they often forget to mention the coexistence of the 

 vibrations perpendicular to the axis of the rod, without which the longitudinal 

 vibrations could not exist at all. The fact is that a purely kinematic resolution is 

 often of first-class physical importance, for one or other of its factors admits of ready 

 physical determination. Thus, in our present case, <f> 2 is the sole component of 

 electric force in the axis of the oscillator, and determined there it is determined for 

 all points of space at the same distance from the centi'e. Again, <f> t + <f>., is the 

 component of electric force in the equatorial plane, and with determinations there, 

 <f>, will l)e known at all points of space. But it was precisely in the direction of the 

 axis and in the equatorial plane that HERTZ made his chief experiments. Thus there 

 seems considerable advantage in reducing the analysis of the electric force to two 

 functions, both independent of the latitudes and varying only with the distance from 

 the oscillator, which can be directly tested in the localities HERTZ found best suited 

 to experimental enquiries. <, and <, are both independent of the latitude, and give 

 wave speeds V, and V 2 having the same values for all points at the same distances 

 from the centre of the oscillator. 



The reader will notice that in taking <)>. t and <f> t sin as our constituents we have 

 resolved the electric force into two components, one along the axis and one transverse 

 to the ray, and these components will not generally be at right angles. Neither will 

 represent the total force in the given direction ; they are transverse and axial com- 

 jionents and not total transverse and total axial electric forces. 



The total force perpendicular to axis = <, sin cos 0; 

 The total axial electric force r . ( . , = <, sin 2 # + <&>; 



The total transverse electric force . = (<, -f <.,) sin ; and 

 The total radial electric force . . = <f>., cos 0. 



It will be obsers'ed that the amplitude of the axial component does not change 



