That portion of the working-day which merely produces an equivalent for the value paid by the capitalist for his labour-power, has, up to this point, been treated by us as a constant magnitude, and such in fact it is, under given conditions of production and at a given stage in the economic development of society. The rate of surplus-value and the length of the working-day depended on the magnitude of this prolongation.
Though the necessary labour-time was constant, we saw, on the other hand, that the total working-day was variable. Now suppose we have a working-day whose length, and whose apportionment between necessary labour and surplus-labour, are given.
Let the whole line a c, abc represent, for example, a working-day of 12 hours; the portion of a b 10 hours of necessary labour, and the portion b c 2 hours of surplus-labour. How now can the production of surplus-value be increased, i. Although the length of a c is given, b c appears to be capable of prolongation, if not by extension beyond its end c, which is also the end of the working-day a c, yet, at all events, by pushing back its starting-point b in the direction of a.
Assume that b'b in the line ab'bc is equal to half of b c or to one hour's labour-time. If now, in a c, the working-day of 12 hours, we move the point b to b', b c becomes b' c; the surplus-labour increases by one half, from 2 hours to 3 hours, although the working-day remains as before at 12 hours. This extension of the surplus labour-time from b c to b' c, from 2 hours to 3 hours, is, however, evidently impossible, without a simultaneous contraction of the necessary labour-time from a b into a b', from 10 hours to 9 hours.
The prolongation of the surplus-labour would correspond to a shortening of the necessary labour; or a portion of the labour-time previously consumed, in reality, for the labourer's own benefit, would be converted into labour-time for the benefit of the capitalist. There would be an alteration, not in the length of the working-day, but in its division into necessary labour-time and surplus labour-time. On the other hand, it is evident that the duration of the surplus-labour is given, when the length of the working-day, and the value of labour-power, are given.
