Wave-4rains through Layers of Electrolyte. 541 



obtained. With salt absolutely no effect could be observed, 

 and soda gave only a slight drooping of the curve. This 

 shows at all events that the constants of these substances 

 approximate to normal values, and not to the very high figures 

 found for water and alcohol. 



Note on the Theory. 



It was my original intention to calculate from the curves, 

 not the dielectric constants, but the conductivities of the 

 liquids. At first sight one might claim that this should be 

 possible, but practically the matter is too complex to serve 

 the purpose. On the assumption that the conductivity be 

 very small, so that one may neglect the phase alteration on 

 reflexion and the increase in the reflected fraction, the equa- 

 tion to the curve may be calculated by a procedure recently 

 described by Mr. Barton*. I will only give the principal 

 equations here, and refer to his paper for a more complete 

 sketch of this method and discussion of fundamental pointsf. 

 We may write the equation of the incident wave-train in the 

 form 



y = ae- at+a i x sin (/3t— fax), (1) 



where 



«/«!=£/&=*>!, (2) 



Vi being the velocity of propagation in the ordinary portion 

 of the long leads. Similarly, for the waves in the liquid, 



a/ci2 = i3/fa = v. a (2a) 



For the primary damping y, or time-rate of decrease of the 

 amplitudes of oscillations in the primary, we have 



lira. 

 7=-0-=«t, (3) 



where r is the period. 



Secondary damping, or damping out of the whole wave- 

 train, owing to the leads between which it travels not being- 

 perfect conductors, is legitimately neglected in this part of 

 the theory as it is known to be small. 



We assume the electrolyte to have a certain, though small, 



* Proc. Roy. Soc. liv. p. 85 (1893), vide more particularly p. 90. I am 

 deeply indebted to Mr. Barton for full explanations of his theory prior to 

 publication. 



f The case discussed by him is one of similar interference where there 

 is no absorption in the medium. 



