'Where was he going?' asks Maud.

'It doesn't matter where he was going.'

'Why was he so fat?' demands Horace. This ad hoc jury seems to believe it may ask questions whenever it likes.

'I don't know. He must have been even greedier than you. In fact, he was so greedy that when the train pulled in, he found he couldn't get through the door of a third-class carriage.' Horace starts tittering at the idea. 'So next he tried a second-class carriage, but he was too fat to get into that as well. So then he tried a first-class carriage-'

'And he was too fat to get into that too!' Horace shouts, as if it were the conclusion to a joke.

'No, members of the jury, he found that this door was indeed wide enough. So he took a seat, and the train set off for – for wherever it was going. After a while the ticket collector came along, examined his ticket, and asked for the difference between the third-class fare and the first-class fare. Monsieur Payelle refused to pay. The railway company sued Payelle. Now, do you see the problem?'

'The problem is he was too fat,' says Horace, and starts giggling again.

'He didn't have enough money to pay,' says Maud. 'Poor man.'

'No, neither of those is the problem. He had money enough to pay, but he refused to. Let me explain. Counsel for Payelle argued that he had fulfilled his legal requirements by buying a ticket, and it was the company's fault if all the train doors were too narrow for him except the first-class ones. The company argued that if he was too fat to get into one kind of compartment, then he should take a ticket for the sort of compartment he could get into. What do you think?'

Horace is quite firm. 'If he went into a first-class compartment, then he has to pay for going into it. It stands to reason. He shouldn't have eaten so much cake. It's not the railway's fault if he's too fat.'

Maud tends to side with the underdog, and decides that a fat Frenchman comes into this category. 'It's not his fault he's fat,' she begins. 'It might be a disease. Or he may have lost his mother and got so sad he ate too much. Or – any reason. It wasn't as if he was making someone get out of their seat and go into a third-class compartment instead.'

'The court was not told the reasons for his size.'

'Then the law is an ass,' says Horace, who has recently learned the phrase.

'Had he ever done it before?' asks Maud.

'Now that's an excellent point,' says George, nodding like a judge. 'It goes to the question of intent. Either he knew from previous experience that he was too fat to enter a third-class compartment and bought a ticket despite this knowledge, or he bought a ticket in the honest belief that he could indeed fit through the door.'

'Well, which is it?' asks Horace, impatiently.

'I don't know. It doesn't say in the report.'

'So what's the answer?'

'Well, the answer here is a divided jury – one for each party. You'll have to argue it out between you.'

'I'm not going to argue with Maud,' says Horace. 'She's a girl. What's the real answer?'

'Oh, the Correctional Court at Lille found for the railway company. Payelle had to reimburse them.'

'I won!' shouts Horace. 'Maud got it wrong.'

'No one got it wrong,' George replies. 'The case could have gone either way. That's why things go to court in the first place.'

'I still won,' says Horace.

George is pleased. He has engaged the interest of his junior jury, and on succeeding Saturday afternoons he presents them with new cases and problems. Do passengers in a full compartment have the right to hold the door closed against those on the platform seeking to enter? Is there any legal difference between finding someone's pocketbook on the seat, and finding a loose coin under the cushion? What should happen if you take the last train home and it fails to stop at your station, thereby obliging you to walk five miles back in the rain?

When he finds his jurors' attention waning, George diverts them with interesting facts and odd cases. He tells them, for instance, about dogs in Belgium. In England the regulations state that dogs have to be muzzled and put in the van; whereas in Belgium a dog may have the status of a passenger so long as it has a ticket. He cites the case of a hunting man who took his retriever on a train and sued when it was ejected from the seat beside him in favour of a human being. The court – to Horace's delight and to Maud's dissatisfaction – found for the plaintiff, a ruling which meant that from now on if five men and their five dogs were to occupy a ten-seated compartment in Belgium, and all ten were the bearers of tickets, that compartment would legally be classified as full.

Horace and Maud are surprised by George. In the schoolroom there is a new authority about him; but also, a kind of lightness, as if he is on the verge of telling a joke, something he has never done to their knowledge. George, in return, finds his jury useful to him. Horace arrives quickly at blunt positions – usually in favour of the railway company – from which he will not be budged. Maud takes longer to make up her mind, asks the more pertinent questions, and sympathizes with every inconvenience that might befall a passenger. Though his siblings hardly amount to a cross-section of the travelling public, they are typical, George thinks, in their almost complete ignorance of their rights.

Arthur

He had brought detectivism up to date. He had rid it of the slow-thinking representatives of the old school, those ordinary mortals who gained applause for deciphering palpable clues laid right across their path. In their place he had put a cool, calculating figure who could see the clue to a murder in a ball of worsted, and certain conviction in a saucer of milk.

Holmes provided Arthur with sudden fame and – something the England captaincy would never have done – money. He bought a decent-sized house in South Norwood, whose deep walled garden had room for a tennis ground. He put his grandfather's bust in the entrance hall and lodged his Arctic trophies on top of a bookcase. He found an office for Wood, who seemed to have attached himself as permanent staff. Lottie had returned from working as a governess in Portugal and Connie, despite being the decorative one, was proving an invaluable hand at the typewriter. He had acquired a machine in Southsea but never managed to manipulate it with success himself. He was more dextrous with the tandem bicycle he pedalled with Touie. When she became pregnant again, he exchanged it for a tricycle, driven by masculine power alone. On fine afternoons he would project them on thirty-mile missions across the Surrey hills.

He became accustomed to success, to being recognized and inspected; also to the various pleasures and embarrassments of the newspaper interview.

'It says you are a happy, genial, homely man.' Touie was smiling back at the magazine. 'Tall, broad-shouldered and with a hand that grips you heartily, and, in its sincerity of welcome, hurts.'

'Who is that?'

'The Strand Magazine.'

'Ah. Mr How, as I recall. Not one of nature's sportsmen, I suspected at the time. The paw of a poodle. What does he say of you, my dear?'

'He says… Oh, I cannot read it.'

'I insist. You know how I love to see you blush.'

'He says… I am "a most charming woman".' And, on cue, she blushed, and hurriedly changed the subject. 'Mr How says, that "Dr Doyle invariably conceives the end of his story first, and writes up to it". You never told me that, Arthur.'

'Did I not? Perhaps because it is as plain as a packstaff. How can you make sense of the beginning unless you know the ending? It's entirely logical when you reflect upon it. What else does our friend have to say for himself?'

'That your ideas come to you at all manner of times – when out walking, cricketing, tricycling, or playing tennis. Is that the case, Arthur? Does that account for your occasional absent-mindedness on the court?'