Suppose we have the compound _m a_, if we present _b_, it will unite with _m_ and displace _a_, because the attraction between _m_ and _a_ is only x, while that between _m_ & _b_ is x+1: _c_ will displace _b_; _d_ will displace _c_, and so on, for the same reason. On this account Bergman considered affinity as an _elective attraction_, and in his opinion the intensity may always be estimated by decomposition. That substance which displaces another from a third, has a greater affinity than the body which is displaced. If _b_ displace _a_ from the compound _a m_, then _b_ has a greater affinity for _m_ than _a_ has. The object of Berthollet in his Chemical Statics, was to combat this opinion of Bergman, which had been embraced without examination by chemists in general. If affinity be an attraction, Berthollet considered it as evident that it never could occasion decomposition. Suppose _a_ to have an affinity for _m_, and _b_ to have an affinity for the same substances. Let the affinity between _b_ and _m_ be greater than that between _a m_. Let _b_ be mixed with a solution of the compound _a m_, then in that case _b_ would unite with _a m_, and form the triple compound _a m b_. Both _a_ and _b_ would at once unite with _m_. No reason can be assigned why _a_ should separate from _m_, and _b_ take its place. Berthollet admitted that in fact such decompositions often happened; but he accounted for them from other causes, and not from the superior affinity of one body over another. Suppose we have a solution of _sulphate of soda_ in water. This salt is a compound of _sulphuric acid_ and _soda_; two substances between which a strong affinity subsists, and which therefore always unites whenever they come in contact. Suppose we have dissolved in another portion of water, a quantity of barytes, just sufficient to saturate the sulphuric acid in the sulphate of soda. If we mix these two solutions together. The barytes will combine with the sulphuric acid and the compound (_sulphate of barytes_) will fall to the bottom, leaving a pure solution of soda in the water. In this case the barytes has seized all the sulphuric acid, and displaced the soda. The reason of this, according to Berthollet, is not that barytes has a stronger affinity for sulphuric acid than soda has; but because sulphate of barytes is insoluble in water. It therefore falls down, and of course the sulphuric acid is withdrawn from the soda. But if we add to a solution of sulphate of soda as much potash as will saturate all the sulphuric acid, no such decomposition will take place; at least, we have no evidence that it does. Both the alkalies, in this case, will unite to the acid and form a triple compound, consisting of potash, sulphuric acid, and soda. Let us now concentrate the solution by evaporation, and crystals of sulphate of potash will fall down. The reason is, that sulphate of potash is not nearly so soluble in water as sulphate of soda.