The theory of ionization, as studied so far, gives us simple, rational explanations of many of our qualitative reactions—explanations which agree with phenomena taken from separate fields of investigation. But, if our study of the theory ceased at the present stage without further elaboration, we should fail to find in it a satisfactory explanation of a number of other important facts of analysis—notably, why certain reactions, the occurrence of which we might anticipate, ‹do not take place›. For instance, the addition of a soluble carbonate to a barium chloride solution precipitates almost all the barium as barium carbonate (‹exp.›); we have 2 Na^{+} + CO_{3}^{2−} + Ba^{2+} + 2 Cl^{−} → BaCO_{3} ↓ + 2 Na^{+} + 2 Cl^{−}. But the addition of carbonic acid to barium chloride solutions fails to produce the slightest precipitate (‹exp.›), although carbonic acid also gives rise to the carbonate-ion, CO_{3}^{2−}. In the same way silver nitrate readily precipitates silver phosphate from sodium phosphate solutions (‹exp.›), but not from a solution of phosphoric acid (‹exp.›). Hydrogen sulphide precipitates zinc sulphide from a zinc sulphate solution (‹exp.›), Zn^{2+} + SO_{4}^{2−} + 2 H^{+} + S^{2−} → ZnS ↓ + 2 H^{+} + SO_{4}^{2−}; but the addition of hydrochloric acid effectually prevents the precipitation (‹exp.›), although the hydrogen sulphide is still ionized, as is apparent from the precipitation of copper sulphide when copper sulphate is added to the mixture (‹exp.›). In the negative results, we have instances of a very large number of cases which require closer study, and a further development of the theory, if we wish to interpret them satisfactorily. The line of development to be followed is indicated perhaps most sharply by the following experiment. EXP. Some sodium tetraborate (borax) is dissolved in a little water and silver nitrate is added to a small part of the solution. A pure ‹white› precipitate (silver borate) results. Another portion of the borate solution is diluted with a ‹large quantity of water›, and then silver nitrate is added; quite a different result is obtained—a ‹brown› precipitate (silver oxide) is formed. [p091] The change in the quantity of water brought about the difference in result—the ‹quantitative› relations were altered thereby. In order to follow intelligently this and the other actions referred to, the study of reactions in solutions must be taken up from the ‹quantitative side›—the development heretofore has been essentially qualitative in character. On several occasions we have found that all electrolytes do not ionize equally well, and that the intensity of their action, demonstrated, for instance, for potassium and ammonium hydroxides, varies accordingly. We shall now have to study these relations in greater detail.