In his economic history of the Lancashire cotton industry, Chapman referred to the "doctrine of the labour fund, as the 'lump of labour' fallacy might be called." Here, presumably, Chapman was using the term "labour fund" as a synonym for Marshall's "work fund," that is to say the demand for labor is assumed to be perfectly inelastic – the quantity demanded remains constant regardless of the wage rate.
Elsewhere, notably for example, in the 1887 English translation of Marx's Capital, the labour fund is a synonym for the wage fund, which implies a unit elasticity of demand for labor – the percentage decrease in demand for labor equals the percentage increase in the wage, so that aggregate of wages remains constant. The two terms were even used interchangeably in the same text as in the following passage from Frank Fairplay's (pseudonym) A Brief Plea for the Old Faith and the Old Times of "Merrie England", when Men had Leisure for Life and Time to Die:
What then constitutes the labour-fund? Certainly not money, which is merely the medium of exchange—a sign of value. There is not enough coined money and bank paper in all England to pay the wages of England for four months. The fund with which labour is paid, consists only of those articles which labourers consume. In Ireland the wage-fund is potatoes and old clothes. In England, as yet at least, it is composed of a sufficiently scanty portion of meat, bread, potatoes, and somewhat more decent apparel. It is obvious then, that the richer the labour-fund is in these articles, the more there will be to distribute.It is clear from the context, however, that Chapman's meaning was work fund and not wages fund. The point that he is making is that the "fundamental ideas" behind proposals made by the Society for the Promotion of National Regeneration for reducing the hours of work were sound even though their rhetoric was tarnished with fallacious arguments. This is, of course, in agreement with Pigou's explanation that "conclusions are often right when the reasons adduced by their supporters are ridiculously wrong."
In volume 3 of his "continuation" of Work and Wage, published in 1914, Chapman reprised his analysis of the hours of labor that had been published in the Economic Journal five years earlier and that he had hinted at in declaring to be sound the fundamental ideas of the Society for the Promotion of National Regeneration. This theoretical analysis was also consistent with the evidence that Brassey had offered in his 1872 book. "It is equally true," wrote Brassey, after showing that wage rates were no indication of labor costs, "that the hours of work are no criterion of the amount of work performed."
In Chapter 6 of Work and Wages Brassey presented evidence of numerous cases where output increased following a reduction in the hours of work. Chapman's continuation and journal article supplied the theoretical explanation for that result. Twenty years after publication of Chapman's "Hours of Labour" article, Lionel Robbins observed:
The days are gone when it was necessary to combat the naïve assumption that the connection between hours and output is one of direct variation, that it is necessarily true that a lengthening of the working day increases output and a curtailment diminishes it.Would that were the case.
If Brassey's Work and Wages provided the evidentiary impetus for Chapman's theoretical analysis of the hours of labor, W. S. Jevons's Theory of Political Economy moulded one of its marginalist theoretical pillars. Chapter 5 of that book presents his theory of labor, including the analysis of the disutility of work, beyond a definite point. "A few hours' work per day may be considered agreeable rather than otherwise;" Jevons wrote, "but so soon as the overflowing energy of the body is drained off, it becomes irksome to remain at work. As exhaustion approaches, continued effort becomes more and more intolerable." This he illustrated with a diagram that illustrated the diminishing utility to the worker of wages earned and the increasing irksomeness of remaining at work as the duration of work lengthened. Chapman's diagram in his "Hours of Labour" article includes a work curve that is clearly analogous to the diagram Jevons presented in his theory of labor.