“Don’t you? Well, just think it over for a bit. What is the job of a constable who is told off to give somebody or other house police protection? Obviously to watch any suspicious person who may appear outside the house, or who may approach somebody. But it isn’t to watch the behaviour of that somebody himself, is it? Nor is it part of his job to see what goes on in the house. There’s a very considerable difference. And I’ll tell you another thing, Frant. The average crook is apt to have a healthy respect for a plainclothes detective, but very little for the uniformed officer. He thinks of him as an ornament in the streets, just something to control traffic and arrest pickpockets, and so on. If Du Pine thinks he is being protected by ordinary flat-footed coppers he’ll be much more likely to give himself away than if he’s afraid he has a detective on his heels—that is if he has anything to give away.”

“Certainly he hasn’t done anything to give himself away yet,” Frant remarked.

“Perhaps he wasn’t quite satisfied in his mind about the ‘suspicious characters’,” said Mallett with a grin. “Now I’ve something else to tell you.”

He briefly told the sergeant of what he had seen on the dancing-floor of the Riviera Hotel.

“Odd, very odd,” said Frant, when he had done. “And the oddest part of it, if I may say so, is not that he should have been frightened at seeing you——”

“Thanks,” said Mallett.

“I mean he would naturally connect you with the murder, which must have been a horrible shock to him——”

“He seemed pretty cool about it when I saw him. That was one of the things that struck me at the time. But you were going to say——”

“What really seems strange is that all of a sudden he could afford to be in a place like that. Do you know what they charge you for dinner there?”

“I do not,” said Mallett with relish. “I didn’t have to pay the bill, thank goodness.”

“Well, believe me, sir, it’s something terrific. How could he possibly run to it, I want to know?”

“What do we know about Harper’s position, anyway?” Mallett asked.

“Quite a lot sir,” answered Frant, eager to prove his own industry. “We have his address, you know, down Ealing way. I got into touch with the police there, and I find he lives alone with his mother—most respectable, but as poor as the devil. A tiny house, a servant who comes in twice a week—you know the sort of thing. It doesn’t go with posh hotels at Brighton at all.”