Application of Ohm's Law to Problems of Electrostatics. 331 



the sphere multiplied by the inductive resistance that separates 

 that sphere from surrounding objects, or T = QI, where T = 

 tension to the earth as datum, Q= quantity of electricity on the 

 sphere, and I = inductive resistance separating the sphere from 

 surrounding conductors connected to earth. This expression 

 gives a perfectly definite meaning to the term tension, which 

 has often before been used in a vague sense. And since I is 



proportional to - and T , we have 



T= -Q= — for the tension of one sphere, 



and T'= -, Q= ~ for the other sphere. 



And since the density is proportional to the quantity divided 

 by the surface over which it is distributed, or D= ^, we have 



D= -g for the density on one sphere, 



and D'= -^ for the density on the other. 



The attached Table gives a few of the calculated values of Q 

 (the quantity), D andD' (the densities), and T and T' (the ten- 

 sions) for a few values of r and r 1 , — the quantity, density, and 

 tension, when one sphere of unit radius is attached to one 

 pole and the other pole is connected to surrounding conductors 

 (or to earth), being taken as unity of quantity, density, and ten- 

 sion respectively. 









II. 



Q. 



D. 



D'. 



T+, 



T'-. 



No. 



r. 



r'. 



! + !■ 



1 



Q 



Q 



Q 



Q 









r r' 



R 



r 2 ' 



r' 2 ' 



r 



r' 



1. 



1 



1 



2 



0-5 



0-5 



0-5 



0-5 



0-5 



2. 



1 



2 



1-5 



0-66 



0-66 



0-165 



0-66 



0-33 



3. 



1 



3 



1-33 



0-75 



0-75 



0-083 



0-75 



0-25 



4. 



2 



2 



1 



1 



0-25 



0-25 



0-5 



05 



5. 



2 



3 



0-83 



1-2 



0-3 



0-133 



0-6 



0-4 



6. 



3 



3 



0-66 



1-5 



0-166 



0-166 



0-5 



0-5 



7. 



1 



100 



101 



0-99 



0-99 



0-000099 



0-99 



0-0099 



The method of considering problems of electrostatics by means 

 of inductive circuits, I submit, explains many of the phenomena of 

 electrical experiments hitherto unexplained, or at least very imper- 

 fectly explained . Thus, if an electrical machine has its rubber insu- 

 lated, it is well known that but little accumulation takes place on 



