This account of Walter Brooklyn’s movements was quite convincing to Joan and her two listeners; but they had to admit that there was not much in it to persuade others of its truth. According to his own account, he must have been in the neighbourhood of Liskeard House at 11.30 when the ’phone message was supposed to have been sent; and not one of his movements between 10.15 and midnight seemed to be at all easy to confirm by any independent testimony. When Joan had finished her narrative, they all felt that, if Walter Brooklyn’s vindication was to depend on an _alibi_, his chances were not particularly good. Still, if he had not been in the house, the police could after all have very little against him beyond a suspicion. At this point Mary Woodman came into the room to say that Sir Vernon would be very pleased if Mr. Lucas would come and sit with him for a while, and Lucas, promising to obey her order to be very quiet and not to allow the patient to excite himself, was led off to the sick room. “I tell you what, Joan,” said Ellery, who had been sitting still, with a prodigious frown on his face, trying to think the thing over, “we’ve jolly well got to establish that _alibi_. We don’t know what else the police may have; but we’re safe enough if we can prove that he wasn’t here that evening. Unless we can establish positively that he wasn’t there, the circumstantial evidence will go down with a jury.” “But how can we establish it? I only wish we could.” “We’re going to. We’re going to find those people he spoke to, and we’re going to hunt London for people who saw him strolling about. After all, he’s very well known, and lots of people must have seen him. I know we shall be able to prove he’s telling the truth.” “You’re a dear to say so, and I don’t see what we can do but try. How do you propose to set about it?” “First of all, I propose that we make a map of the wanderings of Ulysses—shall we call it?—showing exactly where he went, whom he spoke to and when, and so on. That will help us to see exactly what’s the best way of getting to work.” So Ellery took a sheet of paper, and they sat down side by side at the table. Under Joan’s directions, Ellery made a map of Walter Brooklyn’s journeyings on Tuesday evening. It took an hour to do, and this is what it looked like when it was done, with notes to help them in prosecuting their inquiries. [Illustration: A map of some streets in London, entitled “Walter Brooklyn’s Odyssey.” A dotted line traces a path from Liskeard House to Byron Club that meanders along a dozen streets, including Piccadilly, Charing Cross Road, Jermyn Street, Pall Mall, and Liskeard Street. Nine different points on the path are labelled indicating points where Walter Brooklyn engaged in some activity.] “It isn’t very hopeful, I’m afraid,” said Joan, as they looked together at the finished plan; “but I’m afraid it is all we have to go upon.”