On fixed-interval schedules of reinforcement, subjects are reinforced for the first response which occurs after a fixed time interval has elapsed. Responses occurring before the interval has elapsed are recorded, but have no specified consequences. Fixed-interval schedules produce characteristic response patterns. A period without responses (initial pause) occurs at the start of each interval, and is followed by accelerated responding which reaches a constant high rate that is maintained until reinforcement. The present paper reports the development of a mathematical index for describing characteristics of fixed-interval curves. Examples from behavioral and pharmacological studies will illustrate applications of this index. DERIVATION OF THE INDEX OF CURVATURE'A cumulative-response record drawn to approximate the performance of a pigeon trained on a 10-minute, fixed-interval schedule (FI 10) is presented in Fig. 1.If the response rate were constant throughout the interval, the cumulative-response record could be completely described by the straight line O Y. However, the actual cumulative record departs from a straight line. Insofar as we can indicate the extent and the direction of this departure from a straight line, we indicate the curve characteristic of the cumulative record.The extent to which the cumulative record departs from a straight line can be determined by comparing the area under the cumulative record with the area under the straight line. That is, the difference between the area of the triangle OXY and the area of the figure 0 a'b'c'YX can be used to indicate the curvature of the cumulative record.

Pigeons were required to complete three successive fixed-interval components to obtain food.When the same exteroceptive stimulus was correlated with the three components, responding was positively accelerated between food deliveries. When different exteroceptive stimuli were correlated with each component in a fixed sequence, prolonged pauses developed in the first component; low response rates developed in the second component; and responding was positively accelerated in the second and third components. When different exteroceptive stimuli were correlated with each component in a variable sequence, responding was positively accelerated in each component. Because the response and reinforcement contingencies were the same in all three procedures, the differences in performances must be due to the changes in the sequence of stimuli.In a three-component, chained fixed-interval schedule of reinforcement, the completion of a fixed-interval schedule in the presence of one stimulus produces a second stimulus; the completion of a fixed-interval schedule in the second stimulus produces a third stimulus; and the completion of a fixed-interval schedule in the third stimulus produces food. Of the various functions that a stimulus may have (Skinner, 1938), two are emphasized in chained schedules. First, the presence of a stimulus can control a specific rate and pattern of responding; this is the discriminative function of the stimulus. Of course, the rate of responding and the pattern of responding that occur in the presence of a discriminative stimulus are a function of the schedule of reinforcement that is in effect. Second, a stimulus can reinforce a specific rate and pattern of responding that preceded its appearance; this is the conditioned reinforcing function of the stimulus.

In his analysis of temporal discriminations, Skinner (1938) described an experiment in which the response rates of rats were decreased by reinforcing only interresponse times (IRT's) which exceeded 15 seconds (p. 306). Wilson and Keller (1953) confirmed and extended this finding by demonstrating that the rate of responding is inversely related to the duration of the minimum required IRT. This type of schedule of reinforcement is referred to as the "differential reinforcement of low response rates" (DRL). Recent investigations indicate that DRL schedules engender temporal discriminations which can be analyzed by means of the relativefrequency distribution of IRT's or the distribution of response probabilities (Anger, 1956; Sidman, 1956).On DRL schedules of reinforcement, each response starts the required delay interval. Responses which occur before the delay interval has elapsed not only are unreinforced but they also postpone reinforcement by starting a new delay interval. To the extent that the animal can discriminate the delay interval, these two contingencies should eliminate responding during the delay interval. Wilson and Keller (1953) reported that their rats adapted to the DRL schedule by developing varioua chains of overt behavior which persisted between lever presses and which occupied enough time so that the lever presses following the chains were reinforced.More recent investigations, which include detailed analyses of the temporal response patterns which develop on DRL, have consistently indicated that a large proportion of IRT's occur at about 0-3 seconds (Conrad, Sidman, & Herrnstein, 1958; Sidman, 1955;Sidman, 1956a;Sidman, 1956b). These short IRT's result from frequent "bursts" of responding, and they generate IRT relative-frequency distributions and probability distributions which are bi-modal. One mode occurs in the vicinity of the minimum IRT which is required for reinforcement; the second mode, which is a result of these bursts, occurs at about 0-3 seconds. Sidman presented evidence indicating that the probability of a burst was high near the minimum IRT required for reinforcement. le suggested that "late in the delay period, a single lever press often fails to reset the animal's 'clock,' with the result that several quick responses are emitted" (Sidman, 1956a, p. 472).A very precise control of the rate of responding can be developed by reinforcing only those IRT's which fall within a specified range (Ferster & Skinner, 1957, pp. 498-502); that is, a reinforced IRT must not only be longer than some minimum value (as in DRL) but also shorter than some maximum value. Thus, reinforcements are available for only a limited period of time. This type of schedule is referred to as DRL with a "limited hold" (DRL LH). For example, on DRL 20 LH 3, only responses which are emitted between 20 and 23 seconds after a preceding response will be reinforced; responses emitted at less than 20 seconds or more than 23 seconds after a preceding response start the timing interval again. On DRL LH 91

On an adjusting schedule of reinforcement, a parameter of the schedule is varied as a function of some characteristic of the animal's performance. In Experiment I, the fixed-ratio response requirement was varied as a function of the time that elapsed before the animal started responding in each fixed-ratio (initial pause). When initial pauses were shorter than a specified duration, the response requirement was increased; when they were longer than the specified duration, the response requirement was decreased. Specified durations of 1, 2, 4, 8, and 15 min were studied. The average response requirement maintained by each monkey was directly related to the length of the specified duration of initial pause. In Experiment II, the fixed-ratio response requirement was constant, but reinforcement occurred only when the initial pause was longer than a specified duration. The average durations of initial pauses were directly related to the length of the specified duration and to the response requirement. Meprobamate consistently decreased the average durations of initial pauses.