152 Messrs. Young, Grerrard, and Jevons on Electrical 



E. Wave Motion. 



Electrical disturbances are produced by wave-motion 

 similar to those due to tidal motion. If a series of regular 

 undulations passes over a body of water, each water particle, 

 according to the trochoidal theory, moves with uniform 

 motion in a circular path whose diameter, for a particle at 

 the surface, is equal to the height h of the wave from trough 

 to crest. Hence water filaments parallel to the wave-crests 

 will revolve in cylindrical paths passing to and fro across 

 the lines of the earth's field. The effective strength ¥ l of 

 the earth's field will in this case vary from the total field F 

 ( = 0*4:7) for waves propagated in a northerly or southerly 

 direction to V ( = 0*43) for waves propagated in an easterly 

 or westerly direction. The effect of the oscillations will be 

 to produce oscillating E.M.F/s in the water in a direction 

 at right angles to the direction of propagation. 



If W is the velocity of propagation and I the wave-length, 



If t is the period of oscillation and v the speed of a water 

 particle taken near the surface, 



v = 7rh/t. 



But t = l/W= \/2irl/g, 



whence v = h *s/iryl2l; 



or if k is the ratio Z//i, 



v= \/7rgh/2k. 



Hence if e is the amplitude of the E.M.F. induced in a 

 water filament of length s, 



<? = F,s \/7rgh/2k. 



According to the observations of Sir Wm. White * an 

 average value for k is 20. Thus for a wave whose height 

 has the very moderate value of 10 ft. ( = 305 cm.), y = 153 

 cm./sec. or about 3 knots; that is, the induced E.M.F. when 

 at a maximum will be comparable with that due to a 3 knot 

 tide. In the case taken, 



e = 6 to 6*5 millivolts per 100 yds. 



As in the case of the tidal disturbances, e is the upper limit 

 both of the amplitude e 1 of the E.M.F. acting between two 

 stationary electrodes and of the amplitude e 2 of the E.M.F. 

 acting between two electrodes whose connecting leads are 

 oscillating with the water. 



* 'Manual of Naval Architecture.' 



