As an author Karl Marx was enviably fortunate. No one will affirm that his work can be classed among the books which are easy to read or easy to understand. Most other books would have found their way to popularity hopelessly barred if they had laboured under an even lighter ballast of hard dialectic and wearisome mathematical deduction. But Marx, in spite of all this, has become the apostle of wide circles of readers, including many who are not as a rule given to the reading of difficult books. Moreover, the force and clearness of his reasoning were not such as to compel assent. On the contrary, men who are classed among the most earnest and most valued thinkers of our science, like Karl Knies, had contended from the first, by arguments that it was impossible to ignore, that the Marxian teaching was charged from top to bottom with every kind of contradiction both of logic and of fact. It could easily have happened, therefore, that Marx's work might have found no favour with any part of the public–not with the general public because it could not understand his difficult dialectic, and not with the specialists because they understood it and its weaknesses only too well. As a matter of fact. however, it has happened otherwise.
Nor has the fact that Marx's work remained a torso during the lifetime of its author been prejudicial to its influence. We are usually, and rightly, apt to mistrust such isolated first volumes of new systems. General principles can be very prettily put forward in the "General Sections" of a book, but whether they really possess the convincing power ascribed to them by their author, can only be ascertained when in the construction of the system they are brought face to face with all the facts in detail. And in the history of science it has not seldom happened that a promising and imposing first volume has never been followed by a second, just because, under the author's own more searching scrutiny, the new principles had not been able to stand the test of concrete facts. But the work of Karl Marx has not suffered in this way. The great mass of his followers, on the strength of his first volume, had unbounded faith in the yet unwritten volumes.
This faith was, moreover, in one case put to an unusually severe test. Marx had taught in his first volume  that the whole value of commodities was based on the labour embodied in them, and that by virtue of this "law of value" they must exchange in proportion to the quantity of labour which they contain; that, further, the profit or surplus value falling to the capitalist was the fruit of extortion practised on the worker; that, nevertheless, the amount of surplus value was not in proportion to the whole amount of the capital employed by the capitalist, but only to the amount of the "variable" part–that is, to that part of capital paid in wages–while the "constant capital," the capital employed in the purchase of the means of production, added no surplus value. In daily life, however, the profit of capital is in proportion to the total capital invested; and, largely on this account, the commodities do not as a fact exchange in proportion to the amount of work incorporated in them. Here, therefore, there was a contradiction between System and fact which hardly seemed to admit of a satisfactory explanation. Nor did the obvious contradiction escape Marx himself. He says with reference to it, "This law" (the law, namely, that surplus value is in proportion only to the variable part of the capital), "clearly contradicts all prima facie experience."  But at the same time he declares the contradiction to be only a seeming one, the solution of which requires many missing links, and will be postponed to later volumes of his work.  Expert criticism thought it might venture to prophesy with certainty that Marx would never redeem this promise, because, as it sought elaborately to prove, the contradiction was insoluble. Its reasoning, however, made no impression at all on the mass of Marx's followers. His simple promise outweighed all logical refutations.
The suspense grew more trying when it was seen that in the second volume of Marx's work, which appeared after the master's death, no attempt had been made towards the announced solution (which, according to the plan of the whole work, was reserved for the third volume), nor even was the slightest intimation given of the direction in which Marx proposed to seek for the solution. But the preface of the editor, Friedrich Engels, not only contained the reiterated positive assertion that the solution was given in the manuscript left by Marx, but contained also an open challenge, directed chiefly to the followers of Rodbertus, that, in the interval before the appearance of the third volume, they should from their own resources attempt to solve the problem " how, not only without contradicting the law of value but even by virtue of it, an equal average rate of profit can and must be created."
I consider it one of the most striking tributes which could have been paid to Marx as a thinker that this challenge was taken up by so many persons, and in circles so much wider than the one to which it was chiefly directed. Not only followers of Rodbertus, but men from Marx's own camp, and even economists who did not give their adherence to either of these heads of the socialist school, but who would probably have been called by Marx "vulgar economists," vied with each other in the attempt to penetrate into the probable nexus of Marx's lines of thought, which were still shrouded in mystery. There grew up between 1885, the year when the second volume of Marx's Capital appeared, and 1894 when the third volume came out, a regular prize essay competition on the "average rate of profit," and its relation to the "law of value."  According to the view of Friedrich Engels–now, like Marx, no longer living–as stated in his criticism of these prize essays in the preface to the third volume, no one succeeded in carrying off the prize.
Now at last, however, with the long-delayed appearance of the conclusion of Marx's system, the subject has reached a stage when a definite decision is possible. For of the mere promise one could think as much red. Promises on the one side and arguments on the other were, in a sense, incommensurable. Even successful refutations of attempted solutions by others, though these attempts were held by their authors to have been conceived and carried out in the spirit of the Marxian theory, did not need to be acknowledged by the adherents of Marx, for they could always appeal from the faulty likeness to the promised original. But now at last this latter has come to light, and has procured for the thirty years' struggle a firm, narrow, and clearly defined battle-ground within which both parties can take their stand in order and fight the matter out, instead of on the one side contenting themselves with the hope of future revelations, or on the other passing, Proteus-like, from one shifting, unauthentic interpretation to another.
Has Marx himself solved his own problem? Has his completed system remained true to itself and to facts, Or not? To inquire into this question is the task of the following pages.
 English translation by Moore and Aveling, 1886; 2nd edition, 1888. (Sonnenschein.)
 Das Kapital, i., 1st edition, p. 285; 2nd edition, p.312.
 Das Kapital, i., 1st edition, pp. 285, 286, and 508 foot; 2nd edition, pp. 312 and 542 foot.
 From an enumeration of Loria's, I draw up the following list (L'opera postuma di Carlo Marx; Nuevo Antologia, vol. i., February, 1895, p. 18), which contains some essays not known to me; Lexis, Jabrducher fur Nationalokonomie, 1885, new series, vol. xi. pp. 452-65; Schmidt, Die Durchschmittsprofitrate auf Grund des Marxschen Wertgesetzes, Stuttgart, 1889; a discussion of the latter work by myself in the Tubinger Zeitscbrift f. d. ges. Staatsw., 1890, p. 590 seq.; by Loria in the Jahrbucher fur Nationalokonomie, new series, vol. xx. (1890) pp. 272. seq.; Stiebling, Das Wertgesetz und die Profitrate, New York, 1890; Wolf, Das Ratsel der Durchschnittsprofitrate bei Marx, Jahrb. f. Nationalok., third series, vol. ii. (1891), pp. 3521 seq; Schmidt again, Neue Zeit, 1892-3, Nos. 4 and 5; Lande, in the same, Nos. 19 and 20; Fireman, Kritik der Marxschen Werttheorie, Jahrb. f. Nationalok., third series, vol. iii. (1892) pp. 793 seq.; finally Lafargue, Soldi, Coletti, and Graziadei in the Critica Sociale from July to November, 1894.