Low Frequency and their Resonance. 423 



sional force is evidently an accumulative effect of the im- 

 pressed force, and can easily be made so large as to break the 

 suspension. This is a complete analogy to the breaking down 

 of condensers due to a great rise in potential produced by 

 resonance described further below. 



The analogy can be carried further by considering the mo- 

 tion of a torsional pendulum A which is acted upon by a 

 periodically varying force F, not directly, but through another 

 torsional pendulum B to which A is suitably connected. The 

 study of the motion of this system under different conditions 

 as regards resonance between A, B and F gives a complete 

 mechanical picture of the electrical flow in an electrical system 

 consisting of a primary and a secondary circuit, each circuit 

 having localized self-induction and capacity, when a periodi- 

 cally varying e. m. f. acts upon the primary circuit. An ana- 

 lytical discussion of the motion of this mechanical system 

 would lead far beyond the limits of this paper. It seems suffi- 

 cient to point out, that the analysis is almost identical with 

 the following mathematical discussion of the electrical flow in 

 resonant circuits and that it is possible to imitate in a mechan- 

 ical model most of the electrical effects discussed below, by 

 properly constructed torsional pendulums connected to each 

 other in a suitable manner. 



II. On the Natural Period of an Electrical Circuit Possessing 

 Localized Capacity and Self-induction. 



The circuit consists of a coil, whose coefficient of self-induc- 

 tion is L henry s, connected in series to a condenser of capacity 

 C farads. Let the ohmic resistance be R ohms. An elec- 

 trical impulse having started the electrical flow it is required 

 to describe the flow. Let Q be the positive charge of the con- 

 denser in coulombs, at any moment, then the differential equa- 

 tion of the flow is obtained by writing down a symbolical ex- 

 pression of the generalized form of Ohm's law (disregarding 

 losses due to magnetic and dielectric hysteresis) 



L f+ R 1^=» ••• <"> 



Comparing these equations to (1) and (2) we see that certain 

 well known conditions being fulfilled the familiar integral first 

 discussed by Sir W. Thomson, can be written down as follows : 



