The relation between force and speed in muscular contraction

IN a recent paper Hill [1938b] has shown that the rate at which energy is liberated by a tetanized muscle increases linearly as the external force is reduced below the isometric tension. If a muscle shortens against a force P, which is smaller than the isometric tension PO, work is done by the muscle, and in addition heat is liberated, in excess of the isometric, at a rate proportional to the speed of shortening v. The rate of total energy production exceeds the isometric heat rate by an amount proportional to the reduction of external tension PO-P. These findings were expressed by the equation v(P+a)=b (PO-P), ...... (1) where a [g.] and b [cm./sec.] are constants (a g.cm. being the " extra heat" for 1 cm. shortening, b g.cm./sec. the increase of the rate of energy production for 1 g. tension loss). This formula relates two variables, the speed of shortening v and the external force P, which can be determined without any heat measurements. According to this formula, which can also be written as