VeJoc'itij of LuiJit in Gases, Liquids, and Solids. 441 



two unknowns V/C^ (or ^/^), and i\ By (203) we see 

 that 



.;2 



/2 O) 



, = -0,-2; ^ = -^ .... (204). 



This rechices (201) and (202) to 



(^p-ii^f=^'^ = Nm(^-f) . . . (205). 



(206), 



from which we lind 



<r _ mco' _ —K^ 

 ^ mor — (' T- — /c- 

 and XT 9 



A, = ^ + ^(l-f) = -^- + ^-^., . . (207). 



The last members are introduced with the notation 



T=^; fc=2'7rx/- (208); 



CO V c 



where t denotes the period o£ the waves, and k the period o£ 

 an electrion displaced from the centre o£ its atom, and left 

 vibrating inside, while the surrounding ether is all at rest 

 except for the outward travelling waves, by which its energy 

 is carried away at some very small proportionate rate per 

 period ; perhaps not more than 10 ~^. It is clear that the 

 greater the wave-length of the outgoing waves, in comparison 

 with the radius of the sphere of condensation of the vibrating 

 electrion, the smaller is the proportionate loss of energy per 

 period. (Compare wdth the more complex problem, in which 

 there are outgoing waves of two different velocities, worked 

 out in the Addition to Lee. XIY., pp. 190-219. See parti- 

 cularly the examples in pp. 217, 218, 219.) 



§ 242. Look back now to the diagram of Lee. XII., 

 p. 145, representing our complex molecular vibrator of 

 Lee. L, pp. 12, 13, reduced to a single free mass, m ; con- 

 nected by springs wdth the rigid sheath, the lining of an ideal 

 spherical cavity in ether. In respect to that old diagram, let 

 <2? now denote what was denoted on p. 145 by — .^• ; that is 

 to say the displacement of the ether, relatively to m. Thus 

 in the old illustrative ideal mechanism, c.v denotes a resultant 

 force of springs acting on m : in the new suggestion of an 

 electro-ethereal reality ex denotes simply the electric attrac- 

 tion of the atom on its electrion m, when displaced to a 

 distance cc from its centre. In the old mechanism it is the 



