102 Irving Fisher —Mathematical investigations

“practical” man versus the scientist. A sea-captain can sail hisvessel and laugh at the college professor in his elaborate explanationof the process. What to him is all this resolution of forces andvelocities which takes no account of the varying gusts of wind, thedrifting of the keel, the pitching and tossing, the suppositions whichmakes of the sail an ideal plane and overlook the effect of the windon the hull ? There is no need to point the moral. Until theeconomist is reconciled to a refined ideal analysis he cannot professto be scientific. After an ideal statical analysis the scientist maygo further and reintroduce one by one the considerations at firstomitted. This is not the object at present in view. ' But it maybe well to merely enumerate the chief of these limitations.

§ 2 .

In Part I the utility of A was assumed to be a sole function ofthe quantity of A, and in Part II a function of all commodities con-sumed by a given individual. We could go on and treat it as afunction of all commodities produced and consumed, treating notnet production for each article, but the actual amounts separatelyproduced and consumed by the given individual.

Again we could treat it as a function of the quantities of eachcommodity produced or consumed by all persons in the market.This becomes important when we consider a man in relation tothe members of his family or consider articles of fashion as dia-monds,* also when we account for that (never thoroughly studied)interdependence, the division of labor.

This limitation has many analogies in physics. The attraction ofgravity is a function of the distance from the center of the earth.A more exact analysis makes it a function of the revolution of theearth, of the position and mass of the moon (theory of tides) andfinally of the position, and mass of every heavenly body.

Articles are not always homogeneous or infinitely divisible. Tointroduce this limitation is to replace each equation involving mar-ginal utilities by two inequalities and to admit an equilibrium inde-terminate between limits.f As an extreme case we may imagine anarticle of which no one desires more than a single copy as of a book.The utility of (say) Mill’s Pol. Econ. is considerably greater than

* See David Wells, Eeeent Economic Changes, on Diamonds,f Auspitz und Lisbon, 117-136 and 467.