170 Mr Larmor, On a mechanical representation of a [May 4, 



[The different types of vibration that may theoretically exist 

 would therefore appear to be as follows. A reciprocating flow 

 may be set up between the plates, along the connecting wires ; if 

 the capacities are at all considerable its period will be compara- 

 tively slow, being calculable from capacity of condenser and self- 

 induction of wire alone, because there will be involved very little 

 disturbance in the dielectric except the static value of the dis- 

 placement at each instant, and there will be no sensible amount of 

 radiation. An oscillation of the dielectric to and fro between the 

 two plates may be set up, corresponding to a very small period, 

 the wave-length being twice the distance between the plates in the 

 case in the diagram, when the earth connexion is good ; this will not 

 be sensibly affected by the presence or nature of the connecting 

 wire, and it will involve rapid decay by radiation, but it will 

 probably be very difficult to excite to any sensible amount. And 

 there may be superficial dielectric waves running along the con- 

 necting wire, of period about the same as the preceding when the 

 wire is straight. 



For the linear type of vibrator consisting of two equal cylinders 

 with a spark gap between them, and no capacities at the ends, 

 the wave-length would be the length of the vibrator simply, as 

 from the mode of excitation its two halves would always be in 

 opposite phases.] 



The nature of the approximations involved in this method of 

 representation will be sufficiently put in evidence by the following 

 investigation of the circumstances of the reflexion of a system of 

 waves from a metallic plate. It will be found that for wave- 

 lengths of a centimetre or more the reflexion of all ordinary 

 metallic plates is sensibly perfect, and involves an acceleration of 

 phase of half a wave-length. For smaller wave-lengths, corre- 

 sponding to those of light waves, the circumstances of the reflexion 

 are more complicated. 



We shall proceed on Maxwell's theory, which postulates the non- 

 existence of condensational effects : no other theory can make the 

 velocity of propagation of waves of transverse displacement in- 

 versely proportional to the square root of the specific inductive 

 capacity of the medium 1 . 



The first point is to assume precise definitions of the quantities 

 that enter into the equations. With the usual notation 



dG dF , 



c = fa-dt> a = -" b = -> 



so that, if J denote 



dF dG dH 



dec dy dz ' 



1 See Proc. Roy. Soc. 1891, Vol. xlix. p. 521. 



