[A] I have not stated the length of wire used, because I find by experiment, as would be expected in theory, that it is indifferent.  The same quantity of electricity which, passed in a given time, can heat an inch of platina wire of a certain diameter red-hot, can also heat a hundred, a thousand, or any length of the same wire to the same degree, provided the cooling circumstances are the same for every part in all cases.  This I have proved by the volta-electrometer.  I found that whether half an inch or eight inches were retained at one constant temperature of dull redness, equal quantities of water were decomposed in equal times.  When the half-inch was used, only the centre portion of wire was ignited.  A fine wire may even be used as a rough but ready regulator of a voltaic current; for if it be made part of the circuit, and the larger wires communicating with it be shifted nearer to or further apart, so as to keep the portion of wire in the circuit sensibly at the same temperature, the current passing through it will be nearly uniform.

  [B] Literary Gazette, 1833, March 1 and 8.  Philosophical Magazine,
  1833, p. 201.  L’Institut, 1833, p.261.

854.  On the other hand, the relation between the conduction of the electricity and the decomposition of the water is so close, that one cannot take place without the other.  If the water is altered only in that small degree which consists in its having the solid instead of the fluid state, the conduction is stopped, and the decomposition is stopped with it.  Whether the conduction be considered as depending upon the decomposition, or not (443. 703.), still the relation of the two functions is equally intimate and inseparable.

855.  Considering this close and twofold relation, namely, that without decomposition transmission of electricity does not occur; and, that for a given definite quantity of electricity passed, an equally definite and constant quantity of water or other matter is decomposed; considering also that the agent, which is electricity, is simply employed in overcoming electrical powers in the body subjected to its action; it seems a probable, and almost a natural consequence, that the quantity which passes is the equivalent of, and therefore equal to, that of the particles separated; i.e. that if the electrical power which holds the elements of a grain of water in combination, or which makes a grain of oxygen and hydrogen in the right proportions unite into water when they are made to combine, could be thrown into the condition of a current, it would exactly equal the current required for the separation of that grain of water into its elements again.

856.  This view of the subject gives an almost overwhelming idea of the extraordinary quantity or degree of electric power which naturally belongs to the particles of matter; but it is not inconsistent in the slightest degree with the facts which can be brought to bear on this point.  To illustrate this I must say a few words on the voltaic pile[A].