‘If you haven’t time yourself, and I don’t expect you will have, employ a private detective. But get a good man who will do the work thoroughly.’ ‘Yes, yes. But what exactly is to be done?’ ‘This. The evidence seems to me overwhelming that Mr Cosgrove missed the 7.15 at King’s Cross on that Wednesday night, and went to Montrose by the 10.30. But what did he do in between?’ Daunt was puzzled. ‘I don’t understand,’ he said. ‘We have the butler’s and Miss Belcher’s evidence to corroborate Cosgrove’s own story there. I don’t see that we can reasonably doubt he did what he said.’ ‘Don’t you? But I do. Probably both these people were interested. Miss Belcher we know was—she was on too friendly terms not to be. And the butler may have been well paid to tell his story. Another thing makes me doubt Miss Belcher. You remember the conversation Mr Tanner overheard between her and Mr Cosgrove in the restaurant? They mentioned an alibi. Mr Tanner thought they were talking about Austin. I don’t believe it. It was Mr Cosgrove’s own alibi they were discussing. What do you think?’ ‘It’s possible, of course,’ Daunt answered slowly, ‘but I question if we can be sure of it.’ He began to think Lois had got an obsession. ‘Well, whether or not is immaterial. What matters is that Mr Cosgrove’s whereabouts after 7.30 has not been proved.’ ‘But you forget Tanner’s time table. Cosgrove wouldn’t have had time to go to Luce Manor between the trains.’ ‘Yes!’ cried Lois excitedly, ‘he would! That’s the point I’ve been coming to. According to Mr Tanner’s calculations he would have had time or almost time, to go to Luce Manor and back, but he wouldn’t have had time to commit the murder. But Mr Tanner assumed he had first driven to his rooms. If he had gone direct from King’s Cross he would have had time for all.’ This was a new idea to Daunt, and he had to admit its possibility. ‘It may be so certainly,’ he answered, ‘but how are we to prove it? That butler won’t give himself away if he has lied.’ ‘I’ve thought of that, too, and there seems to be one way we might get at it. Mr Cosgrove said he took three drives during that time—first, from King’s Cross to Knightsbridge; second, from Knightsbridge to the Empire; and third, from the Follies’, to King’s Cross. Could we not find the cabmen, or at least one of them?’ ‘By Jove, Lois, you should have been a detective,’ Daunt said with half-unwilling admiration. ‘I believe it’s a good notion.’ ‘You see, if we were to search for these men thoroughly and fail to find them, it would greatly strengthen my theory. On the other hand, if we found them we would be sure of what we are up against, for if Mr Cosgrove took any one of the drives, his statement must be true. Will you try to find them, Jimmy? Or’—her eyes brightened eagerly—‘let’s do it together. Would you mind?’ ‘Mind?’ he echoed. ‘Dear girl, what do you take me for? I’m ready to begin now—in collaboration with you, that is.’