[Note 1 (p. 401)] "Wages in the aggregate depend on a ratio between capital and population."- Fawcett, Pol. Econ., B. II. c. 4.

[Note 2 (p. 401)] In his last work, Some Leading Principles of Political Economy, published 1874.

[Note 3 (p. 402)] It might have seemed unnecessary to state this; but Cairnes (Some Leading Principles, p. 186) really implies that Mill seriously propounded, as an important economic doctrine the great truth that a fraction cannot be increased without either enlarging the numerator or diminishing the denominator; and other writers have attributed to him the same absurdity.

[Note 4 (p. 402)] In order not to complicate the discusdon in the present article, I have followed the usual course of considering exclusively the wages of productive labourers. I must, however, observe that it is rather misleading to say, as Mill does, that such wages form "nearly the whole of the wages-fund of a country," since the number of unproductive labourers neglected amounts to a good deal over a million.

[Note 5 (p. 403)] His proof may easily be compressed into two or three lines of algebraic reasoning, thus: Let a be the total capital determined by saving, b the supply of labourers, and x the average rate of wages; then if the proportion of capital not wages-fund to labour, or (a-bx)/b be determined by the character of the national industries, x and therefore bx are also known. Put (a-bx)/b=c and we get x=a/b-c and bx=a-bc.

[Note 6 (p. 404)] I may observe that it is not even true that this possibility of increase in the wages-fund of a partirular trade depends entirely on the action of trades unions in limiting the number of labourers in the respective trades. No doubt Mill held that this was the case; but it is now universally admitted that he, in common with other members of the earlier Ricardian school, greatly exaggerated the equalising effect which unrestricted competition tends to exercise upon wages, and that even in old countries where competition is freest, the movement of labour - whether from employment to employment, or from district to district - is far too slow and imperfect to produce this equalising effect with any certainty or within any definite limits of time, even if trades unions did not exist.

[Note 7 (p. 406)] In the last edition of his Manual, Professor Fawcett has even removed the qualification of "temporariness" in some cases. He considers that in some cases, "when the equalising effect of competition is neutralized through an indefinitely long period… there can be no doubt that labourers can by combining secure a permanent advance in wages." And he does not say, or seem to hold that this advance must be at the expense of other labourers wages. But if this be so, the proposition that Professor Fawcett still maintains, that "wages depend upon the ratio between capital and population," seems to have lost its chief significance; since, whatever else it may mean, it has not the meaning usually attributed to it, that "wages depend on saving and not on bargaining."

[Note 8 (p. 406)] It is not necessary to assume (as Cairnes seems to think) a "complete and all-embracing organization of trade unions," but only a movement throughout industry so general as to leave no important field for the employment of capital outside the trades afrected by it.

[Note 9 (p. 407)] Work and Wages.

[Note 10 (p. 407)] Pol. Econ., B. II. c. xv.

[Note 11 (p. 409)] Such, Professor Walker says, was the practice in New England till 1854 or 1855, in the West and South of the United States till much later.- The Wages Question, c. viii.

[Note 12 (p. 410)] In the ingenious paradox of Cairnes, noticed on p. 5, this margin of accumulated products has been overlooked. But, apart from this, the state of things contemplated in the paradox is more arbitrarily assumed, and more unlikely to occur, than Cairnes seems to think; for such an increase in the amount of labour and instruments as he supposes involves a corresponding increase in the production of wealth, and, therefore, in the stock from which savings are made; hence, to assume that no fresh savings have been made from it, is to assume what is, at least, highly improbable.

[Note 13 (p. 410)] The Wages Question, c. x.

[Note 14 (p. 412)] It should be observed that this limit may be a sliding one, as it is possible that any given fall in wages may be exactly balanced by the decrease in produce resulting from efficiency.

[Note 15 (p. 413)] Strictly speaking, if the check operates slowly, we ought to allow for the difference to any actual labourers between the value of present and that of future wages.