Page:The Harvard Classics Vol. 51; Lectures.djvu/331

varies; but the product will seldom vary in exact proportion as any single factor is varied. Adding one-tenth to the quantity of moisture in the soil will seldom, and only accidentally, result in the increase of exactly one-tenth to the crop. The same may be said with respect to fertilizer, or to any single element of fertility, with respect to the labor of cultivation, or with respect to any other single factor which enters into the determination of the size of a crop. Moreover, all this can be repeated with respect to any productive plant, say a factory, and of the factors of production which have to be combined in it.

The work of assembling the factors of production in any productive establishment, whether it be a shop, farm, factory, or transportation system, calls for a degree of knowledge and care comparable with that of the chemist in the assembling of chemical elements, though, as stated before, the chemist must follow definite formulae with mathematical precision, because of the law of definite proportions.

This law of variable proportions is difficult to state concisely, but the following formulae may serve to give a fairly accurate notion as to its meaning and import. Let us assume that three factors, x, y, and z, are necessary to get a certain desirable product, which we will call p.

If 10 x with 20 y with 30 z will produce 100 p,
then 11 x with 20 y with 30 z will produce	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$	(1) more than 110 p; (2) 110 p; (3) less than 110 but more than 100 p; (4) 100 p; (5) less than 100 p.

If it should be found by experiment that the addition of one unit of x resulted in (1) more than 110 p, or (2) 110 p, that would indicate that the proportion of x to the other factors y and z was too low. Since an additional unit of x will result in such a large increase in the product, it is evident that more of x will be strongly desired, as compared with more of y and z, for if there is too little of x in the combination there must be too much of y and z. If, however, it were found that the addition of one unit of x resulted in (4) 100 p—that is, no increase at all—or (5) in less than 100 p—that is, less