We shall now use these simple cases for illustrating the principle by which capacity and potential are determined. First, it is clear that we can use the jar composed of concentric spheres with its known capacity as our unit jar and by means of this ascertain, in the manner above laid down, the capacity of any given jar _F_. We find, for example, that 37 discharges of this unit jar of the capacity 100, just charges the jar investigated at the same striking distance, that is, at the same potential. Hence, the capacity of the jar investigated is 3700 centimetres. The large battery of the Prague physical laboratory, which consists of sixteen such jars, all of nearly equal size, has a capacity, therefore, of something like 50,000 centimetres, or the capacity of a sphere, a kilometre in diameter, freely suspended in atmospheric space. This remark distinctly shows us the great superiority which Leyden jars possess for the storage of electricity as compared with common conductors. In fact, as Faraday pointed out, jars differ from simple conductors mainly by their great capacity. [Illustration: Fig. 37.] For determining potential, imagine the inner coating of a jar _F_, the outer coating of which communicates with the ground, connected by a long, thin wire with a conductive sphere _K_ placed free in a large atmospheric space, compared with whose dimensions the radius of the sphere vanishes. (Fig. 37.) The jar and the sphere assume at once the same potential. But on the surface of the sphere, if that be sufficiently far removed from all other conductors, a uniform layer of electricity will be found. If the sphere, having the radius _r_, contains the charge _q_, its potential is _V = q/r_. If the upper half of the sphere be severed from the lower half and equilibrated on a balance with one of whose beams it is connected by silk threads, the upper half will be repelled from the lower half with the force _P = q²/8r² = 1/8V²_. This repulsion _P_ may be counter-balanced by additional weights placed on the beam-end, and so ascertained. The potential is then _V = [sqrt](8P)_.[35] That the potential is proportional to the square root of the force is not difficult to see. A doubling or trebling of the potential means that the charge of all the parts is doubled or trebled; hence their combined power of repulsion quadrupled or nonupled. Let us consider a special case. I wish to produce the potential 40 on the sphere. What additional weight must I give to the half sphere in grammes that the force of repulsion shall maintain the balance in exact equilibrium? As a gramme weight is approximately equivalent to 1000 units of force, we have only the following simple example to work out: _40×40 = 8× 1000.x_, where _x_ stands for the number of grammes. In round numbers we get _x_ = 0.2 gramme. I charge the jar. The balance is deflected; I have reached, or rather passed, the potential 40, and you see when I discharge the jar the associated spark.[36]