Abstract During the process of shortening against a load a muscle liberates extra energy as work and as heat. The methods used in measuring the extra heat due to shortening have been critically examined and are described in some detail. The constant α of the heat of shortening depends on P, the load lifted, according to an average linear relation for frog sartorii at 0 °C, α/P0 = 0·16( ± 0.015) + 0·18( ± 0·027) P/P0P0 is the maximum force developed at constant length. The constant α of the heat of shortening can no longer be regarded as the same quantity as the constant α of the characteristic equation (P+a)v = b(P0-P), relating velocity (v) of shortening to load; but α/P0 and a/P0, being always of the same order of size, are almost certainly connected in some way. The original (Hill 1938) conclusion that α and a were the same was probably due to a persistent error in the measurement of α, making it about 30% too great. In the original (Hill 1938) hypothesis the rate of extra energy liberation (P+α)v during shortening was taken to be proportional to (P0-P), i. e. to the gap between the maximum force a muscle could exert and the actual load it had to lift. In its simple form this idea must be abandoned; but a modification is suggested which still provides the characteristic equation and supplies a connexion between α and a. The assumptions made in calculating the heat of shortening are examined; to regard it simply as a change, produced by shortening, in the maintenance heat would make little difference. Further advances in the chemistry of contraction may allow the facts to be expressed in more concrete terms.