This paper discusses the development of variable-interval (VI) schedules where the probability of reinforcement (P(rf)) remains constant over time since the last reinforcement. In traditional VI schedules derived from arithmetic or geometric progressions, P(rf) increases with time since the last reinforcement. The authors propose a new method to generate VI schedules where P(rf) remains constant as a function of time since the last reinforcement. The key idea is to use a probability distribution function that ensures P(rf) remains constant. This function is given by: $$ P_d(t) = -(1 - p)^t \log_e(1 - p) \text{ for } 0 < t < \infty $$ where $ P_d(t) $ is the probability distribution of the interval length t, and p is the fixed probability of reinforcement within a unit interval. To create a schedule that satisfies this condition, the number of intervals must be infinite. However, this is not feasible with typical programming equipment, which has a limited number of intervals. Instead, the authors propose a progression of intervals that approximates the ideal distribution. The progression of means is given by: $$ \overline{t}_n = [-\log_e(1 - p)]^{-1} [\log_e N + (N - n)\log_e(N - n) - (N - n + 1)\log_e(N - n + 1)] $$ where $ \overline{t}_n $ is the nth term of the progression, N is the total number of terms, and p is the fixed probability of reinforcement within a unit interval. The mean of the theoretical distribution is $ [-\log_e(1 - p)]^{-1} $, which is also the mean of the progression. This value can be replaced by the desired mean of the VI schedule. The authors demonstrate that by using this progression, the probability of reinforcement can be made constant over time since the last reinforcement, even though the intervals are not infinite. This is possible because the probability distribution of the intervals approximates the theoretical distribution when the number of intervals is large enough.This paper discusses the development of variable-interval (VI) schedules where the probability of reinforcement (P(rf)) remains constant over time since the last reinforcement. In traditional VI schedules derived from arithmetic or geometric progressions, P(rf) increases with time since the last reinforcement. The authors propose a new method to generate VI schedules where P(rf) remains constant as a function of time since the last reinforcement. The key idea is to use a probability distribution function that ensures P(rf) remains constant. This function is given by: $$ P_d(t) = -(1 - p)^t \log_e(1 - p) \text{ for } 0 < t < \infty $$ where $ P_d(t) $ is the probability distribution of the interval length t, and p is the fixed probability of reinforcement within a unit interval. To create a schedule that satisfies this condition, the number of intervals must be infinite. However, this is not feasible with typical programming equipment, which has a limited number of intervals. Instead, the authors propose a progression of intervals that approximates the ideal distribution. The progression of means is given by: $$ \overline{t}_n = [-\log_e(1 - p)]^{-1} [\log_e N + (N - n)\log_e(N - n) - (N - n + 1)\log_e(N - n + 1)] $$ where $ \overline{t}_n $ is the nth term of the progression, N is the total number of terms, and p is the fixed probability of reinforcement within a unit interval. The mean of the theoretical distribution is $ [-\log_e(1 - p)]^{-1} $, which is also the mean of the progression. This value can be replaced by the desired mean of the VI schedule. The authors demonstrate that by using this progression, the probability of reinforcement can be made constant over time since the last reinforcement, even though the intervals are not infinite. This is possible because the probability distribution of the intervals approximates the theoretical distribution when the number of intervals is large enough.