TKANJJACTIONS O*' SKCTlOiN 1'. 675 



trouble, were at least as great as in any other position open to him. Now this equa- 

 tion of the Net Advantages in different occupations is— co-ordinatelv and (in a ma- 

 thematical sense) dmHltaneomly with the equation of final utility for different kinds 

 of expenditure— a condition of normal economic equilibrium {h). Yet again, the 

 free play of this tendency is impeded by the existence of ' non-competing groups.' 



I cannot be expected here to enumerate all the conditions of economic equili- 

 brium. For a complete exposition of the complexities, at which I have thouo-ht 

 It necessary to glance, I must refer to the second book of Professor SidgwicTcs 

 ' Political Economy.' It will be evident to his readers ' that what may be called the 

 general economic problem of several trading bodies distributing and exchanging inter 

 se under the influence of self-interest and in a regime of competition is much more 

 hopelessly difficult than the as yet imperfectly solved dynamical problem of several 

 material bodies acting on each other in vacuo. When Gossen, the predecessor of 

 Jevons as exponent of the law of final utility, compares that principle to the 

 law of gravitation, and the character of our science to that of astronomy, he 

 betrays a parental partiality. A truer, though still too flattering, comparison 

 would be afforded by some very immature and imperfect specimens of physics, say 

 the theory of fluid motion applied to the problems of house ventilation. 



There is a certain resemblance between the uniformity of pressure to which the 

 jostling particles of a gas tend and the unitv of price which is apt to result from 

 the play of competition. As the architect is guided by studying the laws according 

 to which air flows, so it will help the builder of economic theory to have mastered 

 the principle of movement towards equilibrium. But even in the material con- 

 structions practice is apt to lag far behind theory, as every reader in the British 

 Museum knows. Much less are we able to predict what currents will flow between 

 the different compartments of the industrial system. We know so imperfectly the 

 coefficient of fluid friction, and the other conditions of the general problem : what 

 compartments may be regarded as completely isolated and hermetically sealed, 

 which partitions are porous and permeable. 



Indeed there has been noticed one mode of competition, which it does not seem 

 easy or helpful to represent by physical analogies— the transference from one occu- 

 pation to another, the equation of net advantages or total utilities in difterent em- 

 ployments ; industrial as distinguished by Oairnes from commercial competition. 

 The latter operation appears to me to admit much better of mathematical expression 

 than the former, which is not so well represented by the equilibrium of a physical 

 system.- Accordingly the equation of net advantages has been judiciously omitted 

 by Jevons in his formulation of the cost of production. And the Helvetian Jevons, 

 as we may call Professor Walras, appears to have altogether made abstraction of 

 the cost of production considered as importing sacrifice and effort. 



' There occurs to me only one point at which the use of mathematical illustrations 

 more complicated than those which I have refeired to in mv first two headings would 

 conduce to the apprehension of Mr. Sidgwick's theorems "l allude to his repeated 

 statement that, not only in International trade, as Mill pointed out, but also in trade 

 in general, there may be several rates of exchange at wliich the supply just takes off 

 the demand. This statement, taken without reservation, goes the length of destroying 

 the prestige which is now attached to competition. Professor Marshall in an" im- 

 portant passage recommends arbitrators and combmations to imitate the method of a 

 celebrated engineer, who, in order to make a breakwater, first ascertained the slope 

 at whu;h a bank of stones would naturally be arranged under the action of tlie waves, 

 and then let down stones so as to form such a slope {Eemiomics of Iiidnsiry, p. 215). 

 Now, if gravitation acted sometimes vertically and sometimes at "an angle of 45° if 

 the forces of competition tended to two distinct positions of equilibrium, the con- 

 struction of the economic breakwater would become arbitrary. It is important, 

 therefore, to show the limits of Professor Sidgwick's theory. See the appentled note j. 

 Commercial competition might be likened to a system of lakes flowing into 

 each other ; industrial competition to a system of vessels so communicating by 

 means of valves, that when the level in one exceeded that of another to a certain 

 extent, then per saltum a considerable portion of the contents of that one (a finite 

 difference as compared with the differentials of the open system) is discharged into 

 the other. s. j / & 



X X 2 



