Can anybody tell me in what sense the word partial is used here? Then I am not certain if I understand the sentences in bold text correctly. Do they mean, "Even now I see no reaon why it should not have worked the way I hoped(1) and I forgot about it completely(2)?

The answer was certainly not obvious. I mulled it over in my mind for a good while, but in the end came back to the only real idea I had, which was to wait a while, see more plainly what was going on, and try to persuade Julian to let me examine his work. Once I reached that point I counted on being able to see the flaw in it—the reason why it wouldn’t do what he claimed. I never doubted that such a flaw existed. Perhaps I might be able to break him of this delusion at once, but if not, the entering wedge would have been driven. He had suggested that he’d achieved some partial success. (How partial they both were, I thought— Julian with his invention, Mrs Walters with her contact in the “other” world.) Very well, then. I would persuade Julian to demonstrate to me how far he had got. He would have to talk to me as one scientist to another. That in itself would help. He would be reminded of his own innate standards and see that he was being false to them.
The plan was naive, of course. I see that now. But it might have worked. Even now I can’t say positively that it wouldn’t have done what I hoped(1). But there was never an opportunity to test it. And when Julian unwittingly gave us a demonstration of what he had accomplished, I did not know it for what it was(2).

William Sloane, Edge of Running Water.

Thank you very much.