observed; but it cannot by any process of its own de termine those ratios, for quantitative conclusions imply quantitative premises, and these are wanting. There is then no future for this kind of study, and it is only waste of intellectual power to pursue it. But the importance of mathematics as an educational introduction to all the higher orders of research is not affected by this conclusion. The study of the physical medium, or environment, in which economic phenomena take place, and by which they are affected, requires mathematics as an instrument; and nothing can ever dispense with the didactic efficacy of that science, as supplying the primordial type of rational investigation, giving the lively sentiment of decisive proof, and disinclining the mind to illusory conceptions and sophistical combinations. And a knowledge of at least the fundamental principles of mathematics is necessary to econo mists to keep them right in their statements of doctrine, and prevent their enunciating propositions which have no definite meaning. Even distinguished writers some times betray a serious deficiency in this respect ; thus they assert that one quantity " varies inversely as " another, when what is meant is that the sum (not the product) of the two is constant ; and they treat as capable of numerical estimation the amount of an aggregate of elements which, differing in kind, cannot be reduced to a common standard. As an example of the latter error, it may be mentioned that " quantity of labour," so often spoken of by Ricardo, and in fact made the basis of his system, includes such various species of exertion as will not admit of summa tion or comparison. Italy. The first Italian translation of the Wealth of Nations appeared in 1780. The most distinguished Italian economist of the period here dealt Avith was, however, no disciple of Smith. This was Melchiorre Gioja, author, besides statistical and other writings, of a voluminous work entitled Nuovo Prospetto delle Scienze Economiche (6 vols., 1815-17; the work was never completed), intended to be an encyclopaedia of all that had been taught by theorists, enacted by Governments, or effected by popula tions in the field of public and private economy. It is a learned and able treatise, but so overladen with quotations and tables as to repel rather than attract readers. Gioja admired the practical economic system of England, and enlarges on the advantages of territorial properties, manu factures, and mercantile enterprises on the large as opposed to the small scale. He defends a restrictive policy, and insists on the necessity of the action of the state as a guiding, supervising, and regulating power in the indus trial world. But he is in full sympathy with the sentiment of his age against ecclesiastical domination and other medi aeval survivals. We can but very briefly notice Romagnosi (d. 1835), who, by his contributions to periodical literature, and by his personal teaching, greatly influenced the course of economic thought in Italy ; Antonio Scialoja (Principii d Economia Sociale, 1840; and Carestia e Governo, 1853), an able advocate of free trade (d. 1877); Luigi Cibrario, well known as the author of Economia Politica del medio evo (1839 ; 5th ed. 1861; French trans, by Barneaud, 1859), which is in fact a view of the whole social system of that period; Girolamo Boccardo (b. 1829; Trattato Teorico-pratico di Economia politica, 1853); the brilliant controversialist Francesco Ferrara, professor j at Turin from 1849 to 1858 (in whose school most of the present Italian teachers of the science were, directly or indirectly, educated), a partisan of the laissez faire doc trine in its most extreme form, and an advocate of the peculiar opinions of Carey and Bastiat on the subject of rent ; and, lastly, the Neapolitan minister Ludovico Bian- chini (Principii della Scienza del Ben Vivere Sociale, 1845 and 1855), who is remarkable as having followed in some 387 degree an historical direction, and asserted the principle of relativity, and who also dwelt on the relations of economics with morals, by a due attention to which the Italian economists have, indeed, in general been honourably distinguished. Spain. The Wealth of Nations was translated into Jovel- Spanish by Ortiz in 1794. It may perhaps have influenced Caspar de Jovellanos, who in 1795 presented to the council of Castile and printed in the same year his celebrated Informe de la Sociedad Economica de Madrid en expediente de Ley Agraria, which was a powerful plea for reform, especially in taxation and the laws affecting agriculture, including those relating to the systems of entail and mort main. An English version of this memoir is given in the translation (1809) of Laborde s Spain, vol. iv. Germany. Roscher observes that Smith did not at first produce much impression in Germany. 1 He does not appear to have been known to Frederick the Great ; he certainly exercised no influence on him. Nor did Joseph II. take notice of his work. And of the minor German princes, Karl Friedrich of Baden, as a physiocrat, would not be accessible to his doctrines. It was otherwise in the generation whose principal activity belongs to the first decade of the 19th century. The Prussian statesmen who were grouped round Stein had been formed as economists by Smith, as had also Gentz, intellectually the most important man of the Metternich regime in Austria. The first German expositors of Smith who did more than merely reproduce his opinions were Christian Jacob Kraus (1753-1807), Georg Sartorius (1766-1828), and August Ferdinand Liider (1760- 1819). They contributed independent views from different stand points, the first from that of the effect of Smith s doctrine on practical government, the second from that of its bearing on history, the third from that of its relation to statistics. Some what latter came Gottlieb Hufeland (1760-1817), Johann Friedrich Eusebius Lotz (1771-1838), and Ludwig Heinrich von Jakob (1759-1827), who, whilst essentially of the school of Smith, apply themselves to a revision of the fundamental conceptions of the science. These authors did not exert anything like the wide influence of Say, partly on account of the less attractive form of their writings, but chiefly because Germany had not then, like France, a European audience. Julius von Soden (1754-1831) is largely founded on Smith, whom, however, he criticizes with undue severity, especially in regard to his form and arrangement ; the Wealth of Nations he describes as a series of precious fragments, and censures Smith for the absence of a co7nprehensive view of his whole subject, and also as one-sidedly English in his tendencies. The highest form of the Smithian doctrine in Germany is represented by four distinguished names : Karl Heinrich Rau (1792-1870), Friedrich Nebenius (1784-1857), Friedrich Benedict Wilhelm Hermann (1795-1868), and Johann Heinrich von Thiinen (1783-1850). Rau s characteristic is "erudite thoroughness." His Lehrbucli Rau. (1826-32) is an encyclopedia of all that up to his time had appeared in Germany under the several heads of Volkswirtliscliaftslclire, VolkswirthscliaftspolitiJc, and Finanzivisscnschaft. His book is rich in statistical observations, and is particularly instructive on the economic effects of different geographical conditions. It is well adapted for the teaching of public servants whose duties are con nected with economics, and it has in fact been the source from which the German official world down to the present time has derived its knowledge of the science. In his earlier period Rau had insisted on the necessity of a reform of economic doctrine (Ansichten der Volksivirthschaft, 1821), and had tended towards relativity and the historical method ; but he afterwards conceived the mistaken notion that that method "only looked into the past without studying the means of improving the present," and became himself purely practical in the narrower sense of that word. He has the merit of having given a separate treatment of Unternchmer- geivinn, or wages of management. The Prussian minister Xebe- Nebenius. nius, who was largely instrumental in the foundation of the Zoll- verein, was author of a highly esteemed monograph on public credit (1820). The Staatsivirthschaftliclic Untersuchungen (1832; 1 The first German version of the Wea Uh of Nations was that by Johann Friedrich Schiller, published 1776-78. The second, which is the first good one, was by Christian Garve (1794, and again 1799 and
1810). A recent one by C. W. Asher (1861) is highly commended.