In addition to the Germanic powers that he associates with his ashplant, and possibly some ancient Celtic ones as well, Stephen thinks of it in Proteus as his "augur's rod of ash," associating it with Roman powers of divination.
Roman augurs were priests who divined the will of the gods by observing the flight of birds. They carried a rod or wand called a lituus, which (like Stephen's ashplant) was curved at one end. With it they ritually consecrated a space in the sky called a templum, and then made observations of the birds that passed through this sector: what kinds, how many, flying in which directions, traveling singly or in groups, making which sounds. Only certain species of birds yielded significations, and the hermeneutics were complex. These observations, called "taking the auspices," served as favorable ("auspicious") or unfavorable omens for important activities like waging battles or erecting buildings.
In the last chapter of A Portrait of the Artist, Stephen stands on the steps of the National Library watching the flight of various birds, counting them, listening to their cries and wingbeats, wondering what kinds they are, noting the direction of their flights. Twice, the narrative calls the space in which the birds are flying "a temple of air," "an airy temple of the tenuous sky." And Stephen thinks, "Why was he gazing upwards from the steps of the porch, hearing their shrill twofold cry, watching their flight? For an augury of good or evil?" In Scylla and Charybdis, standing once again on "The portico" of the library, he remembers, "Here I watched the birds for augury."
Stephen's reference to his ashplant as an augur's rod in a late paragraph of Proteus probably bears some connection to his thoughts about George Berkeley in that paragraph, because Berkeley too advocated the reading of "signs" in the visible universe. Gifford observes that the phrase "Signs on a white field," five sentences later, refers not only to the scraps of verse that Stephen is writing down on a corner of Deasy's letter but also to "birds (as the augur sees them) against the sky." The first mention of "The good bishop" follows two sentences after that.