ABSTRACT
The schema of proportionality has been examined in several forms, both in connection with the equilibrium schema (Chaps. 11 and 12) and independently of it (Chap. 13). We now have to examine one more case in order to define the relationship between the proportionality schema and the schema of multiplicative compensation. Here we are not speaking of compensation in the most general sense of the term, in which it is synonymous with reversibility. Rather, we are referring to compensation between heterogeneous factors x and y, such that an increase in the value of one gives the same result as an increase or decrease in the value of the other. We have already come across compensations of this type: in the flexibility problem (Chap. 3); in the balance problem, where distances and weights compensate each other; in the problem of traction on an inclined plane, where inclination and weights are involved; and finally, in the case of shadow projection, where diameters and distances compensate each other. Still, we thought it worth while to analyze a new example, one in which two possibilities are open to the subject. He can construct metrical proportions (which he could not in the flexibility problem), and he can isolate the factors that determine equilibrium in terms of the “all other things being equal” method (which he could not do in the traction problem). Our aim is to discover whether, psychologically, proportions carry with them the idea of compensation or whether it is the other way around.
