the exchange ratio will vary with the extent to which the common quality is present in each of the goods. We can have no quantitative ratios between unlike things. And yet, we must have terms for our ratios. The situation here is not unlike the situation that arises when we compare two weights. We have no unit of weight in the abstract. Weight never appears as an isolated quality, but always along with other qualities, as extension, color, and the like. And when we compare weights, we really compare two heavy objects, and make our weight ratio between the object to be weighed and the physical standard of weight. Nor does value ever appear as an isolated quality. And we have no unit of abstract value which we can apply abstractly in a measurement. Instead, we choose some valuable object, as 23.22 grains of gold, and make our ratio between the given quantity of gold and the object whose value we wish to measure. But we must not forget that this is merely a symbol, a convenient mode of expression, and that the fact expressed is something different--that the real terms of our ratios are so many units of abstract weight, or of abstract value, as the case may be. Otherwise conceived, the ratio itself is meaningless: it has no terms. We have four to one up in the air, not four units of something to one unit of something. The abstract ratio is a thing for pure mathematics, and not a thing for economics. An economic ratio must have "economic quantities" as terms.[29] The difficulty with the doctrine we are maintaining arises from the difficulty of isolating and defining this quality of value. It is not a quality "inherent" in the good (whatever "inherent" may mean). It does not arise from the simple relation between our senses and the object, or even from an intellectual elaboration thereof. It rather grows out of the relation between our emotional-volitional life and the object, and the definition of this relation, and the determination of the quality, have been so difficult, that some writers, as Professor Davenport,[30] have explicitly given it up as a hopeless task, and have determined to content themselves with the surface facts of relativity. But there is no logical resting place in those surface facts. Relativity implies _things_ related, ratios must have quantitative _terms_, additions require _homogeneous_ quantities to make up a sum.