Throughout his philosophical career Berkeley had a deep and consistent concern with the contemporary development of science, in particular Newton's natural philosophy and mathematics. This paper explores Berkeley's engagement with Newton's mechanics from a new perspective by reference to the question about the status of 'knowledge of relations'. Berkeley's introduction of 'relations' as the third-kind objects of knowledge (besides 'ideas' and 'spirits') in the second edition of the Principles has been neglected in the literature. I will argue, however, that the new mention of 'knowledge of relations' is closely interconnected with Berkeley's engagement with Newton's gravitational system of the world. This line of interpretation is elaborated by showing the hitherto unnoticed link between the introduction of 'knowledge of relations' in the Principles and 'the doctrine of signs' developed in his middle-period work Alciphron. What is remarkable about Berkeley's discussion of 'the doctrine of signs' in Alciphron is his clear recognition of the essential use of symbols in the progress of scientific knowledge. This recognition indicates the development of Berkeley's view of scientific laws. In the first edition of the Principles, he simply equated Newton's law of gravitation with phenomenal similitude, but the Alciphron view takes into account the essential role of 'analysis' in the discovery of gravitational law―how symbols have heuristic significance in the discovery of pervasive 'analogies' which underlie phenomena. I will substantiate this point by drawing attention to Berkeley's mention of the parallelogram of force in his exposition of 'the doctrine of signs'.

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