And why had not the prince approached him and spoken to him

The prince rang the bell, and asked for Nastasia Philipovna. The lady of the house came out, and stated that Nastasia had gone to stay with Daria Alexeyevna at Pavlofsk, and might be there some days.
Madame Filisoff was a little woman of forty, with a cunning face, and crafty, piercing eyes. When, with an air of mystery, she asked her visitor's name, he refused at first to answer, but in a moment he changed his mind, and left strict instructions that it should be given to Nastasia Philipovna. The urgency of his request seemed to impress Madame Filisoff, and she put on a knowing expression, as if to say, "You need not be afraid, I quite understand." The prince's name evidently was a great surprise to her. He stood and looked absently at her for a moment, then turned, and took the road back to his hotel. But he went away not as he came. A great change had suddenly come over him. He went blindly forward; his knees shook under him; he was tormented by "ideas"; his lips were blue, and trembled with a feeble, meaningless smile. His demon was upon him once more.
What had happened to him? Why was his brow clammy with drops of moisture, his knees shaking beneath him, and his soul oppressed with a cold gloom? Was it because he had just seen these dreadful eyes again? Why, he had left the Summer Garden on purpose to see them; that had been his "idea." He had wished to assure himself that he would see them once more at that house. Then why was he so overwhelmed now, having seen them as he expected? just as though he had not expected to see them! Yes, they were the very same eyes; and no doubt about it. The same that he had seen in the crowd that morning at the station, the same that he had surprised in Rogojin's rooms some hours later, when the latter had replied to his inquiry with a sneering laugh, "Well, whose eyes were they?" Then for the third time they had appeared just as he was getting into the train on his way to see Aglaya. He had had a strong impulse to rush up to Rogojin, and repeat his words of the morning "Whose eyes are they?" Instead he had fled from the station, and knew nothing more, until he found himself gazing into the window of a cutler's shop, and wondering if a knife with a staghorn handle would cost more than sixty copecks. And as the prince sat dreaming in the Summer Garden under a lime-tree, a wicked demon had come and whispered in his car: "Rogojin has been spying upon you and watching you all the morning in a frenzy of desperation. When he finds you have not gone to Pavlofsk--a terrible discovery for him--he will surely go at once to that house in Petersburg Side, and watch for you there, although only this morning you gave your word of honour not to see HER, and swore that you had not come to Petersburg for that purpose." And thereupon the prince had hastened off to that house, and what was there in the fact that he had met Rogojin there? He had only seen a wretched, suffering creature, whose state of mind was gloomy and miserable, but most comprehensible. In the morning Rogojin had seemed to be trying to keep out of the way; but at the station this afternoon he had stood out, he had concealed himself, indeed, less than the prince himself; at the house, now, he had stood fifty yards off on the other side of the road, with folded hands, watching, plainly in view and apparently desirous of being seen. He had stood there like an accuser, like a judge, not like a--a what?
And why had not the prince approached him and spoken to him, instead of turning away and pretending he had seen nothing, although their eyes met? (Yes, their eyes had met, and they had looked at each other.) Why, he had himself wished to take Rogojin by the hand and go in together, he had himself determined to go to him on the morrow and tell him that he had seen her, he had repudiated the demon as he walked to the house, and his heart had been full of joy.
Was there something in the whole aspect of the man, today, sufficient to justify the prince's terror, and the awful suspicions of his demon? Something seen, but indescribable, which filled him with dreadful presentiments? Yes, he was convinced of it--convinced of what? (Oh, how mean and hideous of him to feel this conviction, this presentiment! How he blamed himself for it!) "Speak if you dare, and tell me, what is the presentiment?" he repeated to himself, over and over again. "Put it into words, speak out clearly and distinctly. Oh, miserable coward that I am!" The prince flushed with shame for his own baseness. "How shall I ever look this man in the face again? My God, what a day! And what a nightmare, what a nightmare!"
There was a moment, during this long, wretched walk back from the Petersburg Side, when the prince felt an irresistible desire to go straight to Rogojin's, wait for him, embrace him with tears of shame and contrition, and tell him of his distrust, and finish with it--once for all.
How often during the day he had thought of this hotel with loathing--its corridor, its rooms, its stairs. How he had dreaded coming back to it, for some reason.
"What a regular old woman I am today," he had said to himself each time, with annoyance. "I believe in every foolish presentiment that comes into my head."
He stopped for a moment at the door; a great flush of shame came over him. "I am a coward, a wretched coward," he said, and moved forward again; but once more he paused.