It read like a love affair, an assignation, though when and where were a blank. The constable replaced it in the card-case and returned it with the other things to the pockets of the Burberry. Then, as nothing more suggested itself, I walked back to my house for breakfast, having first arranged that the base of the cliffs should be thoroughly searched.

Stackhurst was round in an hour or two to tell me that the body had been removed to The Gables, where the inquest would be held. He brought with him some serious and definite news. As I expected, nothing had been found in the small caves below the cliff, but he had examined the papers in McPherson’s desk, and there were several which showed an intimate correspondence with a certain Miss Maud Bellamy, of Fulworth. We had then established the identity of the writer of the note.

“The police have the letters,” he explained. “I could not bring them. But there is no doubt that it was a serious love affair. I see no reason, however, to connect it with that horrible happening save, indeed, that the lady had made an appointment with him.”

“But hardly at a bathing-pool which all of you were in the habit of using,” I remarked.

“It is mere chance,” said he, “that several of the students were not with McPherson.”

“Was it mere chance?”

Stackhurst knit his brows in thought.

“Ian Murdoch held them back,” said he. “He would insist upon some algebraic demonstration before breakfast. Poor chap, he is dreadfully cut up about it all.”

“And yet I gather that they were not friends.”

“At one time they were not. But for a year or more Murdoch has been as near to McPherson as he ever could be to anyone. He is not of a very sympathetic disposition by nature.”

“So I understand. I seem to remember your telling me once about a quarrel over the ill-usage of a dog.”

“That blew over all right.”

“But left some vindictive feeling, perhaps.”

“No, no, I am sure they were real friends.”

“Well, then, we must explore the matter of the girl. Do you know her?”

“Everyone knows her. She is the beauty of the neighbourhood - a real beauty, Holmes, who would draw attention everywhere. I knew that McPherson was attracted by her, but I had no notion that it had gone so far as these letters would seem to indicate.”

“But who is she?”

“She is the daughter of old Tom Bellamy, who owns all the boats and bathing-cots at Fulworth. He was a fisherman to start with, but is now a man of some substance. He and his son William run the business.”

“Shall we walk into Fulworth and see them?”

“On what pretext?”

“Oh, we can easily find a pretext. After all, this poor man did not ill-use himself in this outrageous way. Some human hand was on the handle of that scourge, if indeed it was a scourge which inflicted the injuries. His circle of acquaintances in this lonely place was surely limited. Let us follow it up in every direction and we can hardly fail to come upon the motive, which in turn should lead us to the criminal.”

It would have been a pleasant walk across the thyme-scented downs had our minds not been poisoned by the tragedy we had witnessed. The village of Fulworth lies in a hollow curving in a semicircle round the bay. Behind the old-fashioned hamlet several modern houses have been built upon the rising ground. It was to one of these that Stackhurst guided me.

“That’s The Haven, as Bellamy called it. The one with the corner tower and slate roof. Not bad for a man who started with nothing but- - By Jove, look at that!”

The garden gate of The Haven had opened and a man had emerged. There was no mistaking that tall, angular, straggling figure. It was Ian Murdoch, the mathematician. A moment later we confronted him upon the road.