Is that what he wants: to pay for Drago's schooling? Yes. He wants Drago to have a good education, and then, after that, if he holds to his ambition, if the sea is indeed his heart's desire, to qualify as a naval officer. He wants Ljuba and her elder sister to grow up happy too, and have their own hearts' desire. Over the whole brood he wants to extend the shield of his benevolent protection. And he wants to love this excellent woman, their mother. That above all. For which he will pay anything.

'Yes,' he says. 'That is what I am offering.'

She meets his gaze squarely. Though he cannot swear to it, he believes she is blushing. Then, swiftly, she leaves the room. A moment later she is back. The red kerchief is gone, her hair is shaken free. On one arm she has Ljuba, on the other the pink satchel. She is murmuring into the child's ear. The child, thumb in mouth, turns and inspects him curiously.

'We must go,' Marijana says. 'Thank you.' And in a whisk they are gone.

He has done it. He, an old man with knobbly fingers, has confessed his love. But dare he even for a moment hope that this woman, in whom he has without forethought, without hesitation sunk all his hopes, will love him back?

THE NEXT DAY Marijana does not arrive. Nor does she come on Friday. The shadows that he had thought gone for ever return. He telephones the Jokic home, gets a female voice, not Marijana's (whose? the other daughter's?), on an answering machine. 'Paul Rayment here, for Marijana,' he says. 'Could she give me a call?' There is no call.

He sits down to write a letter. Dear Marijana, he writes, I fear you may have misunderstood me. He deletes me and writes my meaning. But what is the meaning she may have misunderstood? When I first met you, he writes, beginning a new paragraph, I was in a shattered state. Which is not true. His knee might have been shattered, and his prospects, but not his state. If he knew the word to describe his state as it was when he met Marijana, he would know his meaning too, as it is today. He deletes shattered. But what to put in its place?

While he is dithering the doorbell rings. His heart gives a leap. Will the troublesome word, and the troublesome letter, not after all be needed?

'Mr Rayment?' says the voice on the entryphone. 'Elizabeth Costello here. May I speak with you?'

Elizabeth Costello, whoever she is, takes her time climbing the stairs. By the time she gets to the door she is panting: a woman in her sixties, he would say, the later rather than the earlier sixties, wearing a floral silk dress cut low behind to reveal unattractively freckled, somewhat fleshy shoulders.

'Bad heart,' she says, fanning herself. 'Nearly as much of an impediment as' (she pauses to catch her breath) 'a bad leg.'

Coming from a stranger the remark strikes him as inappropriate, unseemly.

He invites her in, offers her a seat. She accepts a glass of water.

'I was going to say I was from the State Library,' she says. 'I was going to introduce myself as one of the Library's volunteers, come to assess the scale of your donation, the physical scale, I mean, the dimensions, so that we could plan ahead. Later it would have come out who I actually am.'

'You are not from the Library?'

'No. That would have been a fib.'

'Then you are-?'

She glances around his living-room with what seems to be approval. 'My name is Elizabeth Costello,' she says. 'As I mentioned.'

'Ah, are you that Elizabeth Costello? I am sorry, I was not thinking. Forgive me.'

'No need.' From the depths of the sofa she struggles to her feet. 'Shall we come to the point? This is not something I have done before, Mr Rayment. Will you give me your hand?'

For an instant he is confused. Give her his hand? She reaches out her own right hand and he takes it. For a moment the plump and rather cool feminine hand rests in his own, which he notices with distaste has taken on the livid hue it does when he has been inactive too long.

'So,' she says. 'I am rather a doubting Thomas, as you see.' And when he looks puzzled: 'I mean, wanting to explore for myself what kind of being you are. Wanting to be sure,' she proceeds, and now he is really losing her, 'that our two bodies would not just pass through each other. Naive, of course. We are not ghosts, either of us – why should I have thought so? Shall we proceed?'

Heavily she seats herself again, squares her shoulders, and begins to recite. 'The blow catches him from the right, sharp and surprising and painful, like a bolt of electricity, lifting him up off the bicycle. Relax! he tells himself as he tumbles through the air, and so forth.'

She pauses and inspects his face, as if to measure the effect she is having.

'Do you know what I asked myself when I heard those words for the first time, Mr Rayment? I asked myself, Why do I need this man? Why not let him be, coasting along peacefully on his bicycle, oblivious of Wayne Bright or Blight, let us call him Blight, roaring up from behind to blight his life and land him first in hospital and then back in this flat with its inconvenient stairs? Who is Paul Rayment to me?'

Who is this madwoman I have let into my home? How am I going to rid myself of her?

'And what is the answer to your question?' he replies cautiously. 'Who am I to you?'

'You came to me,' she says. 'In certain respects I am not in command of what comes to me. You came, along with the pallor and the stoop and the crutches and the flat that you hold on to so doggedly and the photograph collection and all the rest. Also along with Miroslav Jokic the Croatian refugee – yes, that is his name, Miroslav, his friends call him Mel – and your inchoate attachment to his wife.'

'It is not inchoate.'

'Yes it is. To whom you blurt out your feelings, instead of keeping them to yourself, though you have no idea and you know you have no idea what the consequences will be. Reflect, Paul. Do you seriously mean to seduce your employee into abandoning her family and coming to live with you? Do you think you will bring her happiness? Her children will be angered and confused; they will stop speaking to her; she will lie in your bed all day, sobbing and inconsolable. How will you enjoy that? Or do you have other plans? Do you plan for Mel to walk into the surf and disappear, leaving his wife and children to you?

'I return to my first question. Who are you, Paul Rayment, and what is so special about your amorous inclinations? Do you think you are the only man who in the autumn of his years, the late autumn, I may say, thinks he has found what he has never known heretofore, true love? Two a penny, Mr Rayment, stories like that are two a penny. You will have to make a stronger case for yourself

Elizabeth Costello: it is coming back to him who she is. He tried once to read a book by her, a novel, but gave up on it, it did not hold his attention. Now and then he has come across articles by her in the press, about ecology or animal rights, which he passes over because the subjects do not interest him. Once upon a time (he is dredging his memory now) she was notorious for something or other, but that seems to have gone away, or perhaps it was just another media storm. Grey-haired; grey-faced too, with, as she says, a bad heart. Breathing fast. And here she is preaching to him, telling him how to run his life!

'What case would you prefer me to make?' he says. 'What story would make me worthy of your attention?'

'How must I know? Think of something.'

Idiot woman! He ought to throw her out.

'Push!' she urges.

Push? Push what? Push! is what you say to a woman in labour.

'Push the mortal envelope,' she says. ' Magill Road, the very portal to the abode of the dead: how did you feel as you tumbled through the air? Did the whole of your life flash before you? How did it seem to you in retrospect, the life you were about to depart?'