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By the time she was dressed and ready to go downstairs, Inspector Tarrant had arrived from Brittlesea. The large police car, she noticed from the staircase window, was standing in the gravel circle by the Headmaster’s terrace, with a plainclothes constable at the wheel. She entered the sitting room and found Dr. and Mrs. Brooke and Inspector Tarrant in grave consultation, with a sergeant taking notes.

“Dr. Brooke,” rapped out Miss Phipps sharply. “Is there a room available which does not look onto your terrace? Your study? Then please let us go there.”

The Headmaster colored a little at being thus ordered about in his own school, but said politely, “This way,” and led the party along a corridor.

“Meanwhile, John,” said Miss Phipps to Inspector Tarrant, “oblige me by summoning your constable indoors on some pretext.”

Inspector Tarrant raised his eyebrows.

“Have you some idea about this troubling affair?” he said.

“Yes. It may be wrong, but if it’s right, it will be much better for your constable to come in here for a few moments,” said Miss Phipps firmly.

Tarrant sent the sergeant on the errand.

“Now,” said Miss Phipps when they were all assembled, “as I said just now, my solution to this problem may be completely wrong. But it is worth trying. I write detective stories. One of my methods is to invent a series of strange incidents — at first sight, inexplicable — and then try to think out a set of circumstances which will explain them. That is what I have done here. I set myself to invent something or somebody that will explain every strange incident that has happened at Star Isle College.”

“And you have succeeded?” inquired the Headmaster, obvious irony in his tone.

“Yes,” said Miss Phipps with quiet confidence. “Here is the solution I have deduced. The thefts of food and money are easily explained by the presence of somebody on the College premises who is without resources. He is hiding here. He needs food. He needs money for later on — after he has escaped from the island. He needs a watch, so as to know when he may expect the various classrooms to be empty. He is a man, I think, belonging to a lower income bracket, for he is unaccustomed to refrigerators, he cannot drive a car or manage a boat. He likes the lighter forms of literature to read. He climbs in and out of the masters’ common-room, opening the window and upsetting poor old Mr. Pryce’s reports, on the chance that the masters have left some coffee over from their elevenses — something to drink during the day,” said Miss Phipps thoughtfully, “and even something to drink from, may well have been one of his most serious problems.”

“Why did he pick up the baby’s rattle?” said his wife.

“And why does he stay here?” said the Headmaster.

“How do you know he can’t drive a car?” said Tarrant.

“He is a small man,” continued Miss Phipps, “and Star Isle is an island.”

“For heavens’ sake, Miss Phipps!” exclaimed the Headmaster. “Please explain yourself.”

“The channel of water between Star Isle and the mainland,” said Miss Phipps, “is too deep to wade and too wide for any ordinary man to swim. Moreover, it has dangerous currents, and quicksands near the mainland shore. As I said, it must be postulated that this man cannot manage a boat. So how is he to get off the island?

“How did he get on it in the first place?” asked Tarrant grimly.

“My dear John,” said Miss Phipps, delighted. “From the tone of your question I gather that my deductions are not totally wide of the mark. Am I not right?”

“Possibly,” said Tarrant. “But please answer my question. How did this man get on the island in the first place?”

“In the luggage compartment of a car, of course,” said Miss Phipps triumphantly. “He was a criminal, you see — a prisoner escaping from the County Gaol — and being hard-pressed by his pursuers he climbed into the trunk compartment of a temporarily unoccupied car. The car then moved off and came to this island. Imagine the poor little man’s horror when he cautiously peeped out, perhaps, and found himself on the ferry! The car brings him to the College. So here he is, with plenty of food in the kitchens, and money to steal for his needs to come — but in moderation, for he doesn’t want to excite suspicion while he’s here by taking too obviously or too much. Clothes from a heap of old wicker baskets would seem to him unlikely to be missed. He has a handy cave to hide in when it’s low tide, and the extensive College buildings to roam in at night. When the tide is high in the daytime, life isn’t quite so easy for him; it’s dark and damp and eerie in that inner cave, so he has to risk coming ashore in daylight. Naturally he’s anxious to get off the island and rejoin his friends. But how is he to get off the island? If he tries the ferryboat, there will be the ticket collectors to face, perhaps even the police. His best chance is to get off the same way he came on. So he is continually on the lookout for cars.”

“But all this doesn’t explain the baby’s rattle!” cried Mrs. Brooke.

“Yes, it does, my dear. The Bishop of Southshire preached here that morning, you said.”

“Yes, yes.”

“He came over in a car — a large car?”

“Yes!”

“He drove himself?”

“No — his young chaplain drove him.”

“Same thing from our point of view,” said Miss Phipps. “The chaplain attended the service in your Chapel, of course. The car stood unattended in the circle of gravel by your front door. The criminal approached. And then your baby dropped his rattle and began to cry. Now what happens when a baby cries?”

“One goes to the baby, of course,” said Mrs. Brooke.

“Exactly. So the criminal puts the rattle back in the pram to stop the baby crying — for crying is bound to bring someone to the pram, and he will be seen. But unfortunately — from his point of view — he is too late! You are already running down the stairs to your baby. The criminal quickly hides himself — it is touch and go, a matter of split seconds — so he has no time to open the trunk compartment.”

“Ah!” said Mrs. Brooke with another shudder. “To think of that odious little man being so near to the baby!”

“My dear,” said the Headmaster, “remember, this is all mere supposition. And how,” he added, turning to Miss Phipps, “does your theory explain the disappearance of poor Crawford?”

Miss Phipps shook her head gravely. “I’m afraid poor Crawford saw the criminal. You see, the Sanatorium has been empty save for the staff, hasn’t it? There have been no previous cases this term, you said, Headmaster. The criminal has been accustomed to regard the Sanatoium sickrooms as safe. Crawford saw him there.”

“The criminal ran off to the cave,” suggested the Headmaster, interested now in spite of himself.

“And young Mr. Crawford followed him,” put in Tarrant. “The tide would be at halfway.”

“The criminal knocked Crawford out and tied him up there.”

“But he knows he has to make a getaway before the next low tide, when Crawford, having recovered consciousness meanwhile, will come back and reveal the criminal’s presence.”

“So the escaped prisoner may make an attempt in your car, now that it’s unobserved,” warned Miss Phipps.

“Surely not in a police car,” objected Tarrant.

“None of you is in uniform,” said Miss Phipps. “He may not notice the small blue police sign. And besides, he is now desperately anxious to get off the island.”

“So all we have to do,” said Tarrant, smiling, “is to arrest Simthwaite in the trunk compartment of my own car—”

“Simthwaite!” exclaimed the Headmaster. “Who’s Simthwaite?”