In this example of stream of consciousness, the third-person narrator blends so completely with Septimus—who's not thinking clearly—that it's as if the passage is delivered by an unreliable narrator:
A sparrow perched on the railing opposite chirped Septimus, Septimus, four or five times over and went on, drawing its notes out, to sing freshly and piercingly in Greek words how there is no crime and, joined by another sparrow, they sang in voices prolonged and piercing in Greek words, from trees in the meadow of life beyond a river where the dead walk, how there is no death [...].
The sparrow doesn't actually say Septimus's name, nor does it join with another sparrow and sing to him in Greek. But the narrator has so thoroughly inhabited Septimus's consciousness that the narration itself can no longer be relied on to accurately report what's happening—except, of course, for what's happening inside Septimus's head. There's a subtle escalation throughout this passage, as Septimus goes from thinking that a sparrow is calling his name to thinking that two sparrows are singing about death (or, rather, the absence of death, which is still a form of thinking about death). This, in turn, is a good indication of his state of mind: he's constantly pondering death, since he has severe trauma from what he experienced as a soldier in World War I. It almost seems inevitable, then, that these sparrows seem to sing to him of such matters. Stream of consciousness enables Woolf to fully immerse herself in Septimus's thoughts, illustrating how he thinks by presenting his wild perceptions as if what he's experiencing is actually happening.