Flip, having a wonderfully tenacious memory, did not forget the conversation he had overheard between Myles and Miss Penfold; so going to his patron's office, he repeated it in due course to Dowker. The result was that the detective became much exercised in his mind over the whole affair. He could not understand Desmond's refusal to tell the name of the woman he saw on the night of the murder. True, Desmond denied it was Lena Sarschine, but then his denial went for nothing, as he would do so to save himself from suspicion. Mrs. Povy said Lena Sarschine had been there between eleven and twelve, and it was unlikely she would be wrong, seeing how well acquainted she was with the appearance of the dead woman. But then, judging from the drift of Desmond's remarks, his refusal to speak was dictated by a desire to screen the honour of a woman. If so, it could not have been Lena Sarschine, for she had no honour to lose, and his refusal to speak would be a piece of Quixotism, which he, as a man of the world, would be one of the first to recognize. At this moment, a sudden thought flashed across Dowker's mind--could it have been Lady Balscombe herself who had the interview with Desmond? Here, indeed, would be a strong motive for Desmond to keep silence, as the visit of a lady to a bachelor's rooms at night would endanger her reputation. Lady Balscombe had, it is true, flung reputation to the winds, but on Monday night it would not have been too late to save her, so if she had seen Desmond, he might have tried to persuade her to give up the elopement, and failed.

"I think I see it all," said Dowker, musingly. "She was to have met Lord Calliston on that night to go down by the nine train, but went to the ball first to avoid suspicion. He got tired of waiting for her, and went off to The Pink 'Un.' She would have let him know her plans by telegram, and called at his rooms after the ball to explain. He was away and did not get the telegram, so when she arrived at the rooms she found Desmond. He tried to persuade her to go back; she refuses, and after some angry words goes out in a rage, stays all night somewhere, and goes down to Shoreham in the morning, but all this does not explain Lena Sarschine's death. It can't be possible that Lady Balscombe killed her--no, it can't be that--there is no connection between the two."

He ran over in his mind the principal items of the conversation as reported by Flip, and his thoughts took a new turn.

"Lady Balscombe did not leave her house in Park Lane till after midnight, so that would not have given her time to be at Lord Calliston's chambers and have an interview with Desmond, therefore it cannot have been her. I wish I could find out the name of the Woman who saw Desmond, and I'd also like to know the name of the woman who saw Lady Balscombe on that night, and discover what was the exact time Lady Balscombe left the house--let me see."

He took out his note-book, and wrote the following memoranda:

1. To find out name of woman who called at Calliston's chambers on Monday (night of murder) between eleven and twelve.

This could only be proved by Myles Desmond himself, as Mrs. Povy asserted it was Lena Sarschine, and Desmond denied it; therefore there was a dead-lock--affirmation and denial.

Memo.--To see Desmond and find out name of visitor.

2. To ascertain appearance and, if possible, name of woman who visited Lady Balscombe on night of murder, as it might possibly have some bearing on case.

A servant in Lady Balscombe's house could probably furnish this information.

Memo--To try and find out said servant.

3. To discover exact time Lady Balscombe left her house on Tuesday morning, also ascertain subsequent movements. This would also have to be discovered through a servant--as to finding out subsequent movements, discover, if possible, train she left London by, and what she did between time of leaving her house and leaving by train.

Memo.--These discoveries must be left to future developments of case.

4. To find out what has become of missing dagger.

Possibly this might be discovered in Desmond's possession.

Mem.--Search his room--secretly--employ agent--say Flip.

5. To search out early life of Lena Sarschine!

Might be discovered in a small measure from Lydia Fenny, who, being confidential maid, might possibly have gathered information from casual remarks.

Mem.--To see Lydia Fenny.

Having thus arranged his plan of action satisfactorily, Dowker turned his attention to Number four of his memoranda, and proceeded to tell Flip what he wanted him to do.

"You see this?" asked Dowker, showing Flip the dagger he had abstracted from Cleopatra Villa.

Flip intimated by a vigorous nod of his head that he did.

"I've got an idea," explained Dowker smoothly, "that a dagger very similar to this is to be found in the possession of Mr. Myles Desmond, the gentleman you saw to-day, so I want you by some means to get into his rooms and find out if it's there."

Flip screwed his face into a look of profound thought, and then smiled in a satisfied manner.

"I'll do it, Guv'nor," he said, sagaciously.

"How?" asked Dowker, curious to learn how this juvenile detective proposed to deal with the problem.

"I'll doss on his doorstep to-night," said Flip, "and when he comes 'ome do a 'perish'--you knows"--in an explanatory tone--"say I'm dyin' for victuals--'e'll take me inside, and when I gits there you leave me alone, guv'nor, I'm fly!"

"Well, you can manage it as you please," said Dowker. "But don't you prick yourself with it, as it's poisoned, and Flip, if you bring me this dagger without him knowing about it, I'll give you half a sov."

"Done, Guv'nor!" said Flip, joyfully, and bidding adieu to his patron, went off to get something to eat and prepare his plan of action.

It was now about six o'clock and very dark, the sky being overcast with clouds. Soon it began to rain steadily, and the streets became sloppy and dismal. Flip drew his rags round him............