WiaP REPORT—1885. 
decomposed equivalent comes half from each half of the cell—the anode 
half and the cathode half; whereas, by supposing H,O to conduct the 
whole current, CuSO, is decomposed by secondary action only in the 
neighbourhood of the cathode, and the amount of salt in the anode 
portion of the solution remains unchanged. The proper apportioning 
of conduction, therefore, explains migration just as well as the direct 
Hittorfian hypothesis. 
Moreover, we shall find that this mode of regarding the subject is 
capable of explaining the formation of free acid or other secondary pro- 
ducts exactly where experiment shows them to be formed. Ifit be found to 
account for their appearance in precisely right amount, it may be held to be 
proved; let us therefore examine more closely the full effect of supposing 
the current to be shared between the two ingredients of a doubly com- 
pound liquid in any assigned proportion. 
Theory of Double Electrolysis : or the decomposition of a mixture of 
two substances. 
We must begin by excluding the possibility of double decomposition or 
interchange of radicles, because if such occur there are really not two 
substances mixed, but four. No stress is to be laid on the word ‘ mix- 
ture,’ as distinct from combination; and I shall consider a solution of 
‘copper sulphate as a mixture of CuSO, and H,O, dilute acid as a mix- 
ture of acid and water, without troubling about the perfectly certain fact 
that all these cases (and probably most other cases) of mixture are really 
cases of—it may be very feeble—chemical combination. But commonly 
called ‘mixed’ solutions, such as the heading might at first sight sug- 
gest—like, say, KI+ NaCl, or even KI4+KCl—are excluded, not only by 
double decomposition, but by the presence of water, which is distinctly a 
third substance. 
Limiting ourselves strictly then to two substances, e.g., a salt and 
water, there are still several possible cases : 
(1) The liberated ions may belong wholly to one of the two compounds. 
(2) The liberated ions may belong one to each of the two compounds. 
(3) They may each belong to both. 
At first sight the first case is a mere simple decomposition, like that 
of a fused salt, but not necessarily so; it all depends upon whether the 
substance is primarily decomposed or not—i.e. on whether it conducts 
the whole current or not. If the other substance, whose ions are not libe- 
rated, either wholly or partially conducts the current, it is a true case of 
double electrolysis. 
To simplify the problem we will use unalterable electrodes—e.g. pla- 
tinum ; and we will suppose that the liberated ions do not dissolve, or 
cat any rate have not dissolved, in the liquid, else the mixture will not 
remain merely dual but will become more complex. 
We have next to make some hypothesis concerning the relative speeds 
of opposite corresponding ions—i.e., of the anion and cation of one and 
the same substance. For the sake of simplicity I will first make the 
simplest assumption, in favour of which several considerations may be 
urged, though none of them are conclusive—viz. that opposite correspond- 
ang ions travel at equal opposite rates. We shall find this sufficient to 
