Page:Elementary Text-book of Physics (Anthony, 1897).djvu/309

§ 360] distance $$R' - R$$ between the two spherical surfaces. Let $$A$$ and $$A'$$ represent the area of the surfaces of the two spheres of radius $$R$$ and $$R'.$$ Then we have $$R^2 = \frac{A}{4\pi}$$ and $$R^2 = \frac{A'}{4\pi}\cdot$$ The capacity of the spherical condenser may then be written $$\frac{\sqrt{AA'}}{4\pi d}\cdot$$ If $$R'$$ and $$R$$ increase indefinitely, in such a manner that $$R' - R$$ always equals $$d,$$ in the limit the surfaces become plane and $$A$$ becomes equal to $$A'.$$ The capacity therefore equals $$\frac{A}{4\pi d}\cdot$$ Since the charge is uniformly distributed, the capacity of any portion of the surface cut out of the sphere is proportional to the area $$S$$ of that surface, or  This value is obtained on the assumption that the distribution over the whole disk is uniform, and the irregular distribution at the edges of the disk is neglected. It is therefore only an approximation to the true capacity of such a condenser.

The so-called Leyden jar is the most usual form of condenser in practical use. It is a glass jar coated with tin-foil within and without, up to a short distance from the opening. Through the stopper of the jar is passed a metallic rod furnished with a knob on the outside and in conducting contact with the inner coating of the jar. To charge the jar, the outer coating is put in conducting contact with the ground, and the knob brought in contact with some source of electrification. It is discharged when the two coatings are brought in conducting contact. When the wall of the jar is very thin in comparison with the diameter and with the height of the tin-foil coating, the capacity of the jar may be inferred from the preceding propositions. It is approximately proportional directly to the coated surface, to the specific inductive capacity of the glass, and inversely to the thickness of the wall.

260. Systems of Conductors.—If the capacities and potentials of two or more conductors be known, the potential of the system