Two experiments examined ordinal numerical knowledge in rhesus macaques (Macaca mulatta). Experiment 1 replicated the finding (E. M. Brannon & H. S. Terrace, 2000) that monkeys trained to respond in descending numerical order (4333231) did not generalize the descending rule to the novel values 5-9 in contrast to monkeys trained to respond in ascending order. Experiment 2 examined whether the failure to generalize a descending rule was due to the direction of the training sequence or to the specific values used in the training sequence. Results implicated 3 factors that characterize a monkey's numerical comparison process: Weber's law, knowledge of ordinal direction, and a comparison of each value in a test pair with the reference point established by the first value of the training sequence.Keywords: Weber's law, ordinal numerical knowledge, visual arrays, numerical representations, animal cognition How animals represent number is an important question that has recently stimulated much research by investigators of animal cognition, cognitive development, cognitive psychology, and cognitive neuroscience. Since the discredited claims that a horse named Clever Hans could count and perform long division, many experiments have carefully documented the actual numerical abilities of many different nonhuman species (for reviews see Brannon & Roitman, 2003;Brannon, 2005). Examples include studies that show that animals can learn the relation between arbitrary symbols and numerosities (e.g., Boysen & Berntson, 1989;Matsuzawa, 1985;Pepperberg, 1987;Washburn & Rumbaugh, 1991;Xia, Siemann, & Delius, 2000), that animals can compare the relative numerosity of visual stimuli (e.g., Brannon & Terrace, 1998Smith, Piel, & Candland, 2003; Judge, Evans, & Vyas, 2005), that animals can perform operations analogous to addition (e.g., Boysen & Berntson, 1989;Olthof, Iden, & Roberts, 1997), that animals may represent number abstractly without regard to the modality in which stimuli are presented (Church & Meck, 1984;Jordan, Brannon, Logothetis, & Ghazanfar, 2005), and that monkeys spontaneously track small numbers of objects by using object file representations (Hauser, Carey, & Hauser, 2000;Hauser & Carey, 2003;Hauser, MacNeilage, & Ware, 1996).Here we focus on the following question: How do rhesus monkeys compare the numerical values of two or more visual arrays?In previous work, we demonstrated that rhesus monkeys have the capacity to represent ordinal relations (Brannon & Terrace, 1998. Two rhesus monkeys, Rosencrantz and Macduff, were first trained to respond in ascending order to exemplars of the numerosities 1-4. They were then tested with all possible pairs of the numerosities 1-9. We hypothesized that if the monkeys had learned an ordinal ascending rule for one set of numerosities (1-2-3-4), they should be able to extrapolate that rule to novel numerical values outside the range in which they were originally trained (i.e., 5-6 -7-8 -9).We took three precautions to ensure that our subjects used a numerical rule to order the stim...