Predictions of P. R. Killeen's (1994) mathematical principles of reinforcement were tested for responding on ratio reinforcement schedules. The type of response key, the number of sessions per condition, and first vs. second half of a session had negligible effects on responding. Longer reinforcer durations and larger grain types engeridered more responding, affecting primarily the parameter a (specific activation). Key pecking was faster than treadle pressing, affecting primarily the parameter δ (response time). Longer intertrial intervals led to higher overall response rates and shorter postreinforcement pauses and higher running rates, and ruled out some competing explanations. The treadle data required a distinction between the energetic requirements and rate-limiting properties of extended responses. The theory was extended to predict pause durations and run rates on ratio schedules. Killeen (1994) developed a set of principles concerning reinforcement: that incentives excite an organism and elicit responses, there are ceilings on response rates, and organisms are biased toward the particular locations and types of responses that occurred just prior to the incentive. Each of these principles was given substance by providing simple mathematical representations of them. For instance, models of the frst two principles-arousal and constraint-when combined, yield Equation 1: (1) The dependent variable is B, response rate, the dimensions of which are responses per second. The parameter a is the amount of behavior that is evoked by the incentive under the current deprivation conditions. It is called the specific activation, it varies as a function of motivation (Killeen, 1995, in press), and its dimensions are seconds per reinforcer. The variable R is the rate of reinforcement; its dimensions are reinforcers per second. Delta (δ) measures the response time-the time that it takes for an animal to execute a response-and typically takes values between 0.25 and 0.4 s for both pigeon's key pecks and rat's lever presses. It is not the same as the time the key or lever is depressed, as it also includes the time to initiate and terminate the entire action pattern (DeCasper & Zeiler, 1977). Its dimensions are seconds per response. Equation 1 has the same form as Herrnstein's hyperbola (1970, 1974), but Herrnstein interpreted 1/a as the rate of reinforcement for other (competing) behaviors in the organism's environment. The same form was derived from still other principles by Staddon (1977). It is a robust description of response rates on variable-interval (VI) schedules, but if we take δ literally as response duration, it predicts response rates that are much too high, and it makes incorrect predictions when extended to other schedules (e.g., Pear, 1975). The formulation is incomplete.