Page:Electricity (1912) Kapp.djvu/79

Rh sphere was in a large room or in the open. Comparing now the two cases, namely, the sphere in the open and the sphere closely surrounded by a metallic envelope, it will be seen that to get the same charge on the spheres is not equally easy. The sphere hanging free requires the application of a much larger e.m.f. than the sphere within an envelope, or, to put it another way, the sphere with an envelope will, under the application of the same e.m.f., acquire a much greater charge than the sphere hanging free in space. The capacity of the sphere for taking a charge has been increased. This reasoning leads us to the conception of capacity as a property of the configuration of metallic bodies. We define capacity as the ratio of charge divided by e.m.f. Using the symbol $$C$$ for capacity, the definition mathematically expressed is

Since we found previously that $$Q = eR$$, it follows that the capacity of a sphere in the open is given by the length of its radius expressed in cm. For the sphere with its envelope the capacity is