Knowledge that Transforms

was inserted in the Annual Report. original paper appeared in the Journal of the Statistical Society for 1866; but it was not till the books on logic were completed that he set to in earnest to elaborate in book form his theory of utility and the mathematical approach to economics. He spent some eight or ten months over writing Theory of Political Economy, which was published in 1871. M. Leon Walras of Lausanne, unaware of the earlier publication of this theory, had arrived at much the same views independently, and in 1874 some correspondence between them occurred as to who was first in the field; M. Walras, on seeing the Statistical Journal for 1866 generously acknowledged my father's priority and published the correspondence in the Journal des 1conomistes under the title Th6orie Mathematique de l'ftchange, Question de Priorite, though as my father wrote, As to the question of priority of publications, it is of course, of less importance than that of the truth of the theory itself. In England, the mathematical theory of economics had, up to that time, been either neglected or criticized adversely, many economists not having sufficient mathematical grounding to follow all the arguments in the book; and Jevons regarded Walras's independent writings as satisfactory proof of the validity of his own application of mathematical principles, though they followed a different course of reasoning. Interest in the mathematical approach to political economy was indeed more advanced then on the Continent than in England, and my father corresponded about this time with various economists abroad on points connected with the Theory of Political Economy, and had the pleasure of seeing it translated into Italian in 1876. In 1871, however, his thoughts had turned to logic again, and the two volume book Principles of Science, his biggest work on logic, appeared that year. Here he criticized some of J. S. Mill's views, as he had done in political economy, and incurred again much opposition from the ardent followers of the latter. Money and the Mechanism of Exchange appeared in 1875, and was translated into French, German, and Italian. It is descriptive of the monetary and banking methods of the world, and the laws of circulation, and was written clearly and simply for the untrained reader. In the same year Jevons raised the question of the possible dependence of harvests on the state of the sun as evidenced by sunspots, reading a paper at the British Association Meeting on The Solar Period and the Price of Corn. This was his first mention of the question of sunspots and trade; but, as he then pointed out, he did not assert the truth of the connection and the paper was afterwards withdrawn for further consideration. Three years later the subject was followed up by a paper on The Periodicity of Commercial Crises and its Physical Explanation, This content downloaded from 207.46.13.132 on Wed, 30 Nov 2016 05:04:00 UTC All use subject to http://about.jstor.org/terms

textabstractThis survey may be opened with some apologetic remarks. The first is that to write a complete survey would mean to write a book. This has not been the intention of the editor, nor does it lie within the power of the present writer. Therefore, this survey is, in principle, incomplete, as will be easily seen by the many important authors whose work is not here discussed. The second remark is that a survey like this is, of necessity, one-sided and restricted. It is one-sided by reason of the special view of the writer on what is interesting and what is not; as, for example,this survey shows special interest in quantitative problems. It is restricted as a consequence of the fact that knowledge of nearly every individual about subjects more removed is less than about subjects in his direct neighborhood-both in a concrete and an abstract sense. The third remark relates to the subdivision of the material; it is difficult to represent, in a one-dimensional exposition, as the current text of a paper, a thing of multi-dimensional character.

1. Intrinsic tendencies towards contraction and expansion in an exchange system 261 2. The indebtedness factor in exchange contraction and expansion ....... 265 3. A simplified example of a planned exchange 272 4. The correction of the request-matrix by the principle of partaker's percentages 273 5. Generalized principles of correcting the request-matrix ..... ...... .. 282 6. The limitational condition for the total volume of operations ......... 286 7. A general differential method of adaptation for the minimum factors.. . 293 8. An analytic method of adaptation 302 9. A numerical example showing details of the computation .... ........ 306 10. Estimate of the amount of work involved when the number of variables is very great 320

THE relationship between a given pair of consumers' goods can assume various forms in an individual's scale of preferences. It is usual, however, to allot the pair of goods to one or other of two main classes, the classes of complementary and of competitive goods. A number of criteria or definitions of the distinction between complementary and competitive goods have been suggested, and of these the most precise, from the mathematical standpoint, are the simple criterion first put forward by Edgeworth and Pareto and the more complicated one given in a recent paper by the present author.' The object of these notes is to examine further both these definitions and, in particular, to discover what connection there is between them. The definition of complementary and competitive goods given by Edgeworth and Pareto assumes the existence of a total utility function which gives, for the individual under consideration, the utility of any combination (x, y, z, ) of the set of consumers' goods X, Y, Z, * , appearing in his scale of preferences. Denoting this function by u =4(x, y, z, ... ), the relation between any pair of goods X and Y de-