A fundamental relationship is presented that relates the variance of the human-machine noise to the mean-square velocity of the human-machine output. This noise-velocity relationship: links McRuer's crossover model, Fitts' Law, and Elkind's human-machine model, and shows that these models are consequences of a fundamental human-machine behavior property; it also shows that the velocity and accuracy of the human-machine movement are inversely related. Theoretical results are then presented concerning information transmission rates in human pursuit tracking using position control. These results derive from the noise-velocity relationship the authors have developed. Good agreement is noted between the theoretical equations for information transmission rate and the empirical results of several investigators.< >