Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/428

386 If the piston is free to move it will move back to $$P_0$$ and be in equilibrium there. This represents the complete discharge of the dielectric.

During the discharge there is a reversed motion of the liquids throughout the whole tube, and this represents that change of electric displacement which we have supposed to take place in a dielectric.

I have supposed every part of the system of tubes filled with incompressible liquids, in order to represent the property of all electric displacement that there is no real accumulation of electricity at any place.

Let us now consider the effect of opening the stopcock $$Q$$ while the piston $$P$$ is at $$P_1.$$

The level of $$A_1$$ and $$D_1$$ will remain unchanged, but that of $$B$$ and $$C$$ will become the same, and will coincide with $$B_0$$ and $$C_0.$$

The opening of the stopcock $$Q$$ corresponds to the existence of a part of the dielectric which has a slight conducting power, but which does not extend through the whole dielectric so as to form an open channel.

The charges on the opposite sides of the dielectric remain insulated, but their difference of potential diminishes.

In fact, the difference of pressure on the two sides of the piston sinks from $$4a$$ to $$2a$$ during the passage of the fluid through $$Q.$$

If we now shut the stopcock $$Q$$ and allow the piston $$P$$ to move freely, it will come to equilibrium at a point $$P_2,$$ and the discharge will be apparently only half of the charge.

The level of the mercury in $$A$$ and $$B$$ will be $$\fraca$$ above its original level, and the level in the tubes $$C$$ and $$D$$ will be $$\fraca$$ below its original level. This is indicated by the levels $$A_2,\, B_2,\, C_2,\, D_2.$$

If the piston is now fixed and the stopcock opened, mercury will flow from $$B$$ to $$C$$ till the level in the two tubes is again at $$B_0$$ and $$C_0.$$ There will then be a difference of pressure $${}=a$$ on the two sides of the piston $$P.$$ If the stopcock is then closed and the piston $$P$$ left free to move, it will again come to equilibrium at a point $$P_3,$$ half way between $$P_2$$ and $$P_0.$$ This corresponds to the residual charge which is observed when a charged dielectric is first discharged and then left to itself. It gradually recovers part of its charge, and if this is again discharged a third charge is formed, the successive charges diminishing in quantity. In the case of the illustrative experiment each charge is half of the preceding, and the