Pagina:Scientia - Vol. VII.djvu/108

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100 “scientia„


outcome of multitudinous causes which between them govern the wages of shepherds; as the movements of a safety-valve may gauge the outcome of the multitudinous causes that govern the pressure in a boiler1».

I submit that difficulty and logomachy might be avoided by contemplation of a physical analogue, the principle of maximum energy. Suppose in the construction pertaining to Figure 2 that a weight sliding down towards the lowest point of the bowl from the rim, or any intermediate point does so many foot-punds work. The point at which the maximum energy will have been put forth, the position of the minimum potential energy, or equilibrium, is (corresponds to) P. Is it necessary to enquire whether the last step of the path which stops at P is «derivative» or «determinative»?

Incipient Taxes. — An interesting example of the transition from differential to small finite differences — where what is strictly true de minimis is predicated also de parvis — occurs in the remarkable paper of which I have here borrowed the title2. The author, Mr C. F. Bickerdike, argues thai theoretically in normal ciscumstances it is always possible for a country to obtain a net advantage by the imposition of small import or export duties without supposing (as usual when such admissions are made by economists) that the country has a kind of «monopoly» as seller or buyer. The argument is based on the proposition that the loss of consumers’ surplus occasioned by the disturbance of industry is of a negligible order as compared with the gain to the Treasury.

This proposition is a particular case of a wide principle which may thus be worded: «A small change of an economic variable quantity at the margin commonly causes a very small change in the corresponding surplus». The principle is not confined to Economics, being based on the general theory of maxima. Good exemples are afforded by astronomical quantities of which the variation is recorded in the Nautical Almanack. For instance the distance of the sun at noon (along a

  1. Principles Book VI., Chapter I., s. S. (Third Edition, 1895), and context.
  2. Incipient Taxes by C. F. Bickerdike, «Economic Journal», Volume XVI, p. 529; cp. Volume XVII, p. 98.