"Dringdring!" sounds three times in one paragraph of Proteus as Stephen imagines priests in various churches and chapels performing their sacred rites: "elevating" the consecrated Host (the priest lifts the wafer toward the heavens and then kneels before the altar), "locking it into a pyx" (a pyx is any receptacle holding the consecrated bread), and "taking housel all to his own cheek" (housel is the act of either giving or receiving the Host, so the priest is ingesting the sacred bread). At each of these moments Stephen hears the sound of the small "sacring bell" or "sanctus bell" that marks important moments in Catholic church ritual.
At the elevation of the Host, the sacring bell signals the transubstantiation of the bread of the wafer into the body of Christ. In Stephen's imagination, the fact that bells could be sounding in multiple places at the same time suggests how the medieval theologian William of Occam might have conceived his theory of a single body of Christ incarnated simultaneously in different pieces of bread.
The argument proceeds by analogy with the pairing of musical notes or spoken vowels: "Bringing his host down and kneeling he heard twine with his second bell the first bell in the transept (he is lifting his) and, rising, heard (now I am lifting) their two bells (he is kneeling) twang in diphthong." In other words, bells sound in different parts of a church as celebrants lift their wafers up toward God and kneel before their separate altars, and by their simultaneity the ringing sounds "twine" with one another in the air, or "twang in diphthong." In an analogous way, the distinct wafers both participate in something that is greater than either: the transcendent body of Christ.
The "sound of the sacring bell" appears also in Cyclops, to introduce an absurdly huge procession of churchmen and churchwomen.