"Because, if it was merely a question of making up time on the road, all he had to do was to put himself and his bicycle on the train for part of the way. No; I fancy he was staying in a smallish hotel somewhere. Not a large hotel, because there nobody would notice whether he came in or not. And not, I think, in lodgings, or somebody would have mentioned before now that they had had a lodger who went bathing at East Felpham. Either he lives in the neighbourhood, in which case he should be easy to trace, or was staying with friends who have an interest in concealing his movements. Or else—which I think is more likely—he was in a smallish hotel, where he would be missed from the breakfast-table, but where his favourite bathing-place was not matter of common knowledge."
"That seems feasible," said the stout man.
"In any case," went on the first-class passenger, "he must have been staying within easy bicycling distance of East Felpham, so it shouldn't be too hard to trace him. And then there is the car."
"Yes. Where is the car, on your theory?" demanded the prim man, who obviously still had hankerings after the Camorra theory.
"In a garage, waiting to be called for," said the first-class passenger promptly.
"Where?" persisted the prim man.
"Oh! somewhere on the other side of wherever it was the murderer was staying. If you have a particular reason for not wanting it to be known that you were in a certain place at a specified time, it's not a bad idea to come back from the opposite direction. I rather think I should look for the car at West Felpham, and the hotel in the nearest town on the main road beyond where the two roads to East and West Felpham join. When you've found the car, you've found the name of the victim, naturally. As for the murderer, you will have to look for an active man, a good swimmer and ardent bicyclist—probably not very well off, since he cannot afford to have a car—who has been taking a holiday in the neighbourhood of the Felphams, and who has a good reason for disliking the victim, whoever he may be."
"Well, I never," said the elderly woman admiringly. "How beautiful you do put it all together. Like Sherlock Holmes, I do declare."
"It's a very pretty theory," said the prim man, "but, all the same, you'll find it's a secret society. Mark my words. Dear me! We're just running in. Only twenty minutes late. I call that very good for holiday-time. Will you excuse me? My bag is just under your feet."
There was an eighth person in the compartment, who had remained throughout the conversation apparently buried in a newspaper. As the passengers decanted themselves upon the platform, this man touched the first-class passenger upon the arm.