The striking distance between the knobs of a machine increases with the difference of the potential, although not proportionately to that difference. The striking distance increases faster than the potential difference. For a distance between the knobs of one centimetre on this machine the difference of potential is 110. It can easily be increased tenfold. Of the tremendous differences of potential which occur in nature some idea may be obtained from the fact that the striking distances of lightning in thunder-storms is counted by miles. The differences of potential in galvanic batteries are considerably smaller than those of our machine, for it takes fully one hundred elements to give a spark of microscopic striking distance. * * * * * We shall now employ the ideas reached to shed some light upon another important relation between electrical and mechanical phenomena. We shall investigate what is the potential _energy_, or the _store of work_, contained in a charged conductor, for example, in a jar. If we bring a quantity of electricity up to a conductor, or, to speak less pictorially, if we generate by work electrical force in a conductor, this force is able to produce anew the work by which it was generated. How great, now, is the energy or capacity for work of a conductor of known charge _Q_ and known potential _V_? Imagine the given charge _Q_ divided into very small parts _q_, _q₁_, _q₂_ ..., and these little parts successively carried up to the conductor. The first very small quantity _q_ is brought up without any appreciable work and produces by its presence a small potential _V__{'}. To bring up the second quantity, accordingly, we must do the work _q__{'}_V__{'}, and similarly for the quantities which follow the work _q__{''}_V__{''}, _q__{'''}_V__{'''}, and so forth. Now, as the potential rises proportionately to the quantities added until the value _V_ is reached, we have, agreeably to the graphical representation of Fig. 38, for the total work performed, _W = 1/2QV_, which corresponds to the total energy of the charged conductor. Using the equation _Q_ = _CV_, where _C_ stands for capacity, we also have, _W = 1/2CV²_, or _W = Q²/2C_. It will be helpful, perhaps, to elucidate this idea by an analogy from the province of mechanics. If we pump a quantity of liquid, _Q_, gradually into a cylindrical vessel (Fig. 39), the level of the liquid in the vessel will gradually rise. The more we have pumped in, the greater the pressure we must overcome, or the higher the level to which we must lift the liquid. The stored-up work is rendered again available when the heavy liquid _Q_, which reaches up to the level _h_, flows out. This work _W_ corresponds to the fall of the whole liquid weight _Q_, through the distance _h_/2 or through the altitude of its centre of gravity. We have _W = 1/2Qh_. Further, since _Q_ = _Kh_, or since the weight of the liquid and the height _h_ are proportional, we get also