We have attempted to link the solution actomyosin ATPase with the mechanical properties of in vitro actin filament sliding over heavy meromyosin. To accomplish this we perturbed the system by altering the substrate with various NTPs and divalent cations, and by altering ionic strength. A wide variety of enzymatic and mechanical measurements were made under very similar solution conditions. Excellent correlations between the mechanical and enzymatic quantities were revealed. Analysis of these correlations based on a force-balance model led us to two fundamental equations, which can be described approximately as follows: the maximum sliding velocity is proportional to square root of V(max)K(m)(A), where K(m)(A) is the actin concentration at which the substrate turnover rate is half of its maximum (V(max)). The active force generated by a cross-bridge under no external load or under a small external load is proportional to square root of V(max)/K(m)(A). The equations successfully accounted for the correlations observed in the present study and observations in other laboratories.