202 Mr. E. B. Rosa on the Specific 



can be due to a common cause or property of the liquid when 

 their variations are so discordant in sign as well as in magni- 

 tude. This may be better seen perhaps by putting the expres- 

 sion for the force into mathematical form, and noting the 

 consequences of the assumption that the force depends in some 

 way upon the quantity of current. 



Let us then assume that the large force of attraction ob- 

 served in the cases of water and alcohol is the resultant of 

 two effects, due respectively to the induction (which is propor- 

 tional to the true specific inductive capacity) and the conduc- 

 tion or quantity of current passing ; and that the second effect 

 is large in proportion to the first. We may then write, 



F = AKV 2 + ac, (1) 



where F = the resultant force on the movable plate of the con- 

 denser, 

 V = the difference of potential between the plates, 

 K = the true specific inductive capacity, 

 A = a constant depending on the geometry of the con- 

 denser, 

 c=the current, 



<x = an undetermined coefficient. 

 We may write equation (1) as follows : — 



F=AKV 2 + /3V, or^=AK + |. 



F 



Now experiment shows (see Tables II., III., IV.) that — 



is constant for a given liquid, and hence {3 is either zero or 

 proportional to V. Suppose it is not zero. Then 



F = AKV 2 + AV 2 3 (2) 



or F=AKV 2 + a/ (3) 



Thus the second term, if it is not zero, is proportional to the 

 square of the current ; a x being an undetermined coefficient. 

 Now we have for the case of a homogeneous medium 

 between the plates of a condenser the following equations : — 



c-f-iMf> <*> 



where C x is the capacity of the condenser whose medium has 

 a specific inductive capacity K ; and ^ is the conductivity 



