102 Irving Fisher — Matheraatical investigations 



" practical " man versus the scientist. A sea-captain can sail his 

 vessel and laugh at the college professor in his elaborate explanation 

 of the process. What to him is all this resolution of forces and 

 velocities which takes no account of the varying gusts of wind, the 

 drifting of the keel, the pitching and tossing, the suppositions which 

 makes of the sail an ideal plane and overlook the effect of the wind 

 on the hull ? There is no need to point the moral. Until the 

 economist is reconciled to a refined ideal analysis he cannot profess 

 to be scientific. After an ideal statical analysis the scientist may 

 go further and reintroduce one by one the considerations at first 

 omitted. This is not the object at present in view. But it may 

 be well to merely enumerate the chief of these limitations. 



§ 2. 



In Part I the utility of A was assumed to be a sole function of 

 the 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 a 

 function of all commodities produced and consumed, treating not 

 net production for each article, but the actual amounts separately 

 produced and consumed by the given individual. 



Again we could treat it as a function of the quantities of each 

 commodity produced or consumed by all 2^€rso92s in the market. 

 This becomes important when we consider a man in relation to 

 the members of his family or consider articles of fashion as dia- 

 monds,* also when we account for that (never thoroughl}'- studied) 

 interdependence, the division of labor. 



This limitation has many analogies in physics. The attraction of 

 gravity is a function of the distance from the center of the earth. 

 A more exact anah^sis makes it a function of the revolution of the 

 earth, of the position and mass of the moon (theory of tides) and 

 finally of the position, and mass of every heavenly body. 



Articles are not alwaj^s homogeneous or infinitely divisible. To 

 introduce this limitation is to replace each equation involving mar- 

 ginal utilities by two inequalities and to admit an equilibrium ijide- 

 terrninate between limits. f As an extreme case we may imagine an 

 article 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, Recent Economic Changes, on Diamonds, 

 f Auspitz und Lieben, 117-136 and 467. 



