Some of this energy which travels along the highest level surfaces will converge on the acid, and there be, at any rate ultimately, converted into heat. Some of it will move along those surfaces which crowd in between the acid and copper and there converge to supply the energy taken up by the escaping hydrogen. The rest spreads out to converge at last at different parts of the circuit, and there to be transformed into heat according to Joule's law.
It may be noticed that if the level surfaces be drawn with equal differences of potential, equal amounts of energy travel out per second between successive pairs of surfaces. For the amount transformed in the circuit in a length having a given difference of potential V between its ends will be current, and therefore the amount transformed between each pair of surfaces drawn with the same potential difference will be the same. But since the current and the field are steady, the energy transformed will be equal to the energy moving out from the cell between the same surfaces—the energy never crossing level surfaces. This admits of a very easy direct proof, but the above seems quite sufficient.
This result has a consequence which, though already well known, is worth mentioning here. Let be the difference of potential between the zinc and acid, that between the acid and copper. If be the current, is the total energy travelling out per second from the zinc surface. Of this is absorbed at the copper surface, the rest, viz., , being transformed in the circuit. The fraction, therefore, of the whole energy sent out which is transformed in the circuit is, a result analogous to the expression for the amount of heat which can be transformed into work in a reversible heat-engine.
One or two interesting illustrations of this movement of energy may be mentioned here in connection with the voltaic circuit.
Suppose that we are sending a current through a submarine cable by a battery with, say, the zinc to earth, and suppose that the sheath is everywhere at zero potential. Then the wire will everywhere be at higher potential than the sheath, and the level surfaces will pass from the battery through the insulating material to the points where they cut the wire. The energy then which maintains the current, and which works the needle at the further end, travels through the insulating material, the core serving as a means to allow the energy to get in motion.
Again, when the only effect in a circuit is the generation of heat, we have energy moving in upon the wire, there undergoing some sort of transformation, and then moving out again as heat or light. If Maxwell's theory of light be true, it moves out again still as electric and magnetic energy, but with a definite velocity and intermittent in type. We have in the electric light, for instance, the curious result that energy moves in upon the arc or filament from the surrounding medium, there to be converted into a form which is sent out again, and which, though still the same in kind, is now able to affect our senses.
