160 Mr. T. H. Havclock on 



Thus from (14:) \vc have 



J^=i. "a^TB^* ' • • • ^^^ 



and from equations (10) we find 



^-^J^h^^ (16) 



We may regard this force as the pressure at of the 

 vibrations in the string to tlie left of the origin, though on 

 the above analysis it is in reality an integrated bodily force 

 on the string to the right of the origin. 



§ 3. There is a limiting case to which we may approach 

 by supposing a to increase indefinitely ; the limits to which 

 the different quantities approximate are 



S = 0; S' = 0; A+B = O = 0; and F = E . . (17) 



This would be the case of perfect reflexion at a fixed point 

 0, and we see that the pressure would then be equal to the 

 mean density of the energy ; but this is only an ideal liuiit 

 which cannot actually be reached. 



Electric Waves. 



§ 4. To proceed now to electrical radiation, we use the 

 circuital relations in the form 



— {u^ V, zy) = Curl (a, /3, j) 



c 



-i|^(a,Ay) = Our](X,Y,Z) 



(18) 



where (a, /3, y) is the magnetic force in electromagnetic units, 

 (X, Y, Z) is the electric force measured electrostatically, and 

 c is the velocity of propagation of effects in the free aether. 

 In general the total current is given by 



{u,v,w) = ^^^a,Y,Z-), . . . (19) 

 where 



6=7i'{i-iky, (20) 



n being the refractive index and k the coefficient of absorp- 

 tion. 



Consider plane-polarized waves propagated along Oc^, so 

 that we have 



