72 Mr. E. H. Barton. Electrical Interference Phenomena 



waves in passing along lengths of the secondary equal respectively to 

 twice SM and twice MD (fig. 1). 



T' is always a little greater than T except in the limiting cases 

 where T = and T = 1. Thns, the experimentally-determined ratio 

 needs a negative correction. This is easily applied by graphical 

 methods. 



N"ow, since / is a function both of T and of the attenuation (or 

 secondary damping) it becomes necessary, in order to utilise Equation 

 (4), to estimate the value of this damping. 



The theory of one method devised for this purpose is as follows : 



Suppose the arrangement of apparatus shown in fig. 1 to be modi- 

 fied thus. Let the 1-mm. diameter copper wires be continued beyond 

 DD' for some distance, and after that let the wires for a further 

 length be of iron of Ol mm. diameter. Also let the bridge shown at 

 DD' be movable and capable of being placed at pleasure anywhere 

 beyond the electrometer. 



And consider, first, the changes in the electrometer throws as the 

 bridge is moved from the electrometer, but still always upon the 

 copper wires. Let the electrometer throws be plotted as ordinates, 

 and the distances of the bridge from the electrometer as abscissae. 

 Then, for positions of the bridge immediately beyond the electro- 

 meter the curve so obtained is conspicuously wavy, and continues 

 sensibly so for a distance equal to half the appreciable length of the 

 wave-train. This is the part corresponding to the curve shown by 

 V. Bjerknes (' Wied. Ann.,' vol. 44, p. 522, 1891), and is due to the 

 interferences between the wave-trains advancing towards and re- 

 flected from the bridge DD'. Beyond this part, whatever the rate 

 of decay of the waves, we have a continuous droop in the curve. The 

 exact form of the curve depends, in part, upon this decay, and the 

 ordinate of the asymptote to the curve may be shown to be a 

 simple function of <r(where e-* x is the law of decay of the amplitude 

 of the waves). 



Let the distance SB (fig. 1) be L, and let y x be the ordinate of the 

 curve at the point whose abscissa is #, the ordinate at the origin being 

 unity. Then we have for the equation of the curve 



- 



2 1 < 



and for that of its asymptote 



The ratio y n is difficult to determine if the copper wires only 

 are used, but with the thin iron wires the electrometer throws 

 rapidly fall off to their minimum value, and thus y v is readily ob- 

 tained as desired. 



