Of course, when Maigret is simply on a personal visit and a murder is committed, the provincial police would love to enlist the help of the great detective who has appeared in their midst. For his part, Maigret finds himself irresistably drawn to the scene of the crime, even if he is out of his jurisdiction and officially he should remain hovering in the background.

Maigret's appearance in the spa town of Vichy in central France is a case in point. He and Madame Maigret had been having their regular dinner visit to their friends Dr and Madame Pardon in Paris, and the doctor noticed that Maigret was off-colour. Maigret was 53 at the time and, as we regular readers know, is just a couple of years off forced retirement from the Police Judiciaire. He and Louise will leave the apartment in Boulevard Richard-Lenoir and go to live in the country home they have bought at Meung-sur-Loire.

The Detective Chief Inspector works long hours at times, smokes his several pipes a lot and often calls in at bars and cafés to use the phone, invariably ordering some beer, wine or calvados. Pardon tells Maigret he is generally in good shape but needs a rest, and should take the waters at Vichy for 21 days. The therapeutic benefit will be a thorough cleansing of his system. Maigret knows Pardon is right and doesn't argue.

Simenon, over the course of his lifetime from 1903 to 1989, was well-travelled and had 33 homes (further aficionado diligence), but it doesn't seem to have mattered where he was when writing because he could always conjure up his scene with great economy and vividness. In 1968, when "Maigret in Vichy" was first published, he would have been living on the shore of Lake Geneva in Switzerland.

So here we find the Maigrets in the French countryside wellness centre taking their daily walk round the park and the springs under the luxuriant trees, past the sunbathers, and the tennis and boules players. Hundreds of yellow iron chairs face the bandstand where the uniformed musicians will strike up the band at 9pm.

"He wasn't on a case, wasn't following any leads. Nothing was forcing him to watch people to try and discover their inner truth," writes Simenon. But, in a way, Maigret is always playing the detective. "He studied people, as if he couldn't help it, noted the slightest details and classified them by category. ... He tried to guess each person's story, to imagine them in their everyday life ... "

One peron who intrigues him is a woman whom he refers to Madame Maigret as the "lady in lilac", a distinguished figure, dignified and aloof with a very long and narrow face, thin lipped. The Maigrets see her regularly on their daily strolls. Is she a widow, a spinster? She mixes with no one.

Then it happens, almost inevitably. The Maigrets have only been there five or six days – it's hard to keep count when each day is the same – when a body is discovered. And it is the lady in lilac and she has been murdered, strangled, not far from their hotel. It transpires that she was a resident of the town, not a visitor. She owned a house on the Rue du Bourbonnais and rented out furnished rooms. The killer doesn't appear to have taken money, jewellery or anything else. She wasn't raped.

A struggle takes place inside Maigret. The case is nothing to do with him but, out walking, he is drawn off his normal route and to the murder scene like a magnet. At the same time, if he should be asked to advise he would feel guilty about leaving Madame Maigret waiting for him while he helps where he can.

The inspector in charge is Désiré Lecoeur, who was part of Maigret's team at the Quai des Orfevres in Paris 15 years ago and is now chief superintendent heading the Clermont-Ferrand Police Judiciaire. Inevitably, Maigret's fame means his presence in Vichy has been noticed and Lecoeur does indeed seek his help. He still calls Maigret "chief", and Maigret begins to "consult".

The victim was Hélène Lange, 48. Why was she such a secretive person and what were the two- or three-day trips she took to different small cities every month? How did she accumulate such a large amount in her bank account at the Credit Lyonnaise? Every month Lange had deposited 5000 francs or more in the bank, after returning from the trips.

The arrival of the dead woman's sister for the funeral adds an element to the mystery. Francine Lange claims she'd hardly ever had contact with Hélène, who led a solitary life. But Lecoeur and Maigret discover, when Francine abruptly leaves Vichy after receiving a phone call at her hotel, apparently from the killer, that her connection with her sister had been deeper. Maigret sits in on Lecoeur's interrogations and helps discover why Lange was killed. When the suspect is found, the story becomes clear.

"Maigret in Vichy" is told with Simenon's deadpan flatness of prose style and bare-bones vocabulary. At an economical 170 pages it fits his belief that a novel should be devoured in one sitting, like a play. The plot is strong with a neat turn, and when the truth is revealed we encounter another of Maigret's traits, his notion that the victim can sometimes be guiltier than the offender.

Maigret is a man of sympathy and a reluctance to condemn. After he has helped Lecoeur uncover the truth, the book concludes with Maigret telling Madame Maigret that he hopes the murderer will be acquitted.

"Maigret in Vichy" was published as "Maigret a Vichy" in French in 1968. It is number 68 in Penguin Books' one-a-month chronological reissue of the 75 "Maigret" novels in new translations. It was published in a previous translation as "Maigret Takes the Waters".

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