There was one short maths lesson first thing on the following morning, but before then George Hannant had done some soul-searching, a little rationalising; so that by the time all the kids were working away and the room was quiet bar the scratching of pens and rustling of papers, he was satisfied that he had the right answer to what had seemed the night before an incident or occur­rence of some moment. Keogh was obviously one of those special people who could get right down to the roots of things, a thinker as opposed to a doer. And a thinker whose thoughts, while they invariably ran con­trary to the general stream, nevertheless ran true.

If you could get him interested in a subject deeply enough to make him want to do something with it, then he'd doubtless do something quite extraordinary. Oh, he would still make errors in simple addition and subtraction - two plus two could still on occasion come out five - but solutions which were invisible to others would be instantly obvious to him. That was why Hannant had seen in the lad a likeness to his own father; James G. Hannant, too, had had that same sort of intuitive knack, had been a natural mathematician. And he too had had little time for formulae.

And equally obvious to Hannant was the fact that he had indeed fanned some spark into flame in Keogh's brain, for it was his pleasure to note that the boy seemed to be working quite hard - or at least he had been, for the first fifteen minutes or so of the period. After that -well, of course, he was daydreaming again. But when Hannant crept up behind him - lo and behold! - the questions he'd set were all answered, and correctly, however insubstantial the working. It would be interesting later in the week, when they got onto basic trigonometry, to see what Keogh would do with that. Now that the circle held little of mystery for him, perhaps he'd take an interest in the triangle.

But there was still something which puzzled George Hannant, and for the answer to that he must now go to Jamieson, the headmaster. Leaving the boys to work alone for a few minutes - with the customary warning about their behaviour in his absence - he went to the head's study.

'Harry Keogh?' Howard Jamieson seemed a little taken aback. 'How did he do in the Technical College examin­ ation?' He took out a slim file from one of his desk drawers, flipped through it, looked up. 'I'm afraid Keogh didn't take the examination,' he said. 'Apparently he was down with hay fever or some such. Yes, here it is: hay fever, three weeks ago; he had two days off school. Unfortunately the exams took place in Hartlepool on the second day of Keogh's absence. But why do you ask, George? Do you think he'd have stood a chance?'

'I think he'd have sailed it,' Hannant answered, frank to the point of being blunt.

Jamieson seemed surprised. 'Bit late in the day, isn't it'

'To worry about it? I suppose it is.'

'No, I meant this interest in Harry Keogh. I didn't know you much approved of him. Wait - ' He took out another file, a thicker one, this time from a cabinet. 'Last year's reports,' he said, checking through the file. And this time he wasn't at all surprised. 'Thought so. Accord­ing to this none of your colleagues here give Keogh a cat in hell's chance at anything - and that includes you, George!'

'Yes,' Hannant's neck reddened a little, 'but that was last year. Also, the Technical College exams are aimed more at basic intelligence than academic knowledge. If you were to give our Harry Keogh an IQ test I think you'd be in for a surprise. Where maths is concerned, anyway. It's all instinct, all intuition - but it's there, sure enough.'

Jamieson nodded. 'Well, it's something when a master takes more than a grudging interest in a Harden boy,' he said. 'And that's not to put anyone down, not even the kids themselves - but they do have a hell of a handicap here, in background and environment, I mean. Do you know how many of our boys got through that exam, by the way? Three! Three out of that age group - which is to say one in sixty-five!'

'Four, if Harry Keogh had taken it.'

'Oh?' Jamieson wasn't convinced. But he was impressed, at least. 'All right,' he said, 'let's assume you're right about the maths side of it. And in fact you are right that the test is a measure of basic intelligence rather than knowledge assimilated parrot-fashion. So what about the other subjects? According to these reports Keogh is a habitual failure in just about any subject you care to mention! Bottom of his class in many of them.'

Hannant sighed, nodded, said: 'Look, I'm sorry I've wasted your time on this one. Anyway, the question hardly arises since he didn't sit the exam in the first place. It's just that I feel it's a shame, that's all. I think the kid has potential.'

'Tell you what,' said Jamieson, coming round his desk and moving towards the door with his hand on Hannant's shoulder. 'Send him to see me during the afternoon. I'll have a word with him, see what I think. No, wait - maybe I can be a little more constructive than that. Instinctive or intuitive mathematician, is he? Very well - '

He returned to his desk, took a pen and quickly scribbled something on a blank sheet of A4. There you go,' he said. 'See what he makes of that. Let him work at it through the lunch break. If he comes up with an answer, then I'll see him and we'll see how we go from there.'

Hannant took the sheet of A4 and went out into the corridor, closing the door behind him. He looked at what the head had written, shook his head in disappointment. He folded the sheet and pocketed it, then took it out again, opened it and stared at it. On the other hand... maybe it was exactly the sort of thing Keogh could handle. Hannant was sure that he could do it - with a bit of thought and a spot of trial and error - but if Keogh could work it out, then they'd be on to something. His case for the boy would be proven. In the event Keogh failed, then Hannant would simply stop worrying about him. There were other kids who were equally deserving of his attention, he was sure...

At 1:30 p.m. sharp Hannant knocked on Jamieson's door, was through it on the instant the head called him in. Jamieson himself was just back from lunch, hardly settled down. He stood up as Hannant crossed the floor of his study, shook out the folds of the A4 and handed it to him.

'I did as you suggested,' Hannant told the head, breath­lessly. 'This is Keogh's solution.'

The headmaster quickly scanned the scribbled text of his original problem:

Magic Square: A square is divided into 16 equal, smaller squares. Each

small square contains a number, 1 to 16 inclusive. Arrange them so that the sum of each of the four lines and each of the four columns, and the diagonals, is one and the same number.

The answer, in pencil - including what looked like a false start - had been drawn beneath the question and was signed Harry Keogh :

Jamieson stared at it, stared harder, opened his mouth to speak but said nothing. Hannant could see him rapidly adding up the columns, lines, diagonals - could almost hear his brain ticking over. 'This is ... very good,' Jamieson finally said.

'It's better than that,' Hannant told him. 'It's perfect!'

The head blinked at him. 'Perfect, George? But all magic squares are perfect. That's the lure of them. That's their magic!'

'Yes,' Hannant agreed, 'but there's perfect and there's perfect. You asked for columns, lines, diagonals all total­ ling the same. He's given you that and far more. The corners total the same. The four squares in the middle total the same. The four blocks of four total the same. Even the opposing middle numbers at the sides come out the same! And if you look closer, that's not the end of it. No, it is perfect.'

Jamieson checked again, frowned for a moment, then smiled delightedly. And finally: 'Where's Keogh now?' 'He's outside. I thought you might like to see him...' Jamieson sighed, sat down at his desk. 'All right, George, let's have your prodigy in, shall we?' Hannant opened the door, called Keogh in. Harry entered nervously, fidgeted where he stood before the head's desk.

'Young Keogh,' said the head, 'Mr. Hannant tells me you've a thing for numbers.' Harry said nothing.

'This magic square, for instance. Now, I've fiddled about with such things - purely for my own amusement, you understand - ever since, oh, since I was about your age. But I don't think I ever came up with a solution as good as this one. It's quite remarkable. Did anyone help you with it?'

Harry looked up, looked straight into Jamieson's eyes. For a moment he looked - scared? Possibly, but in the next moment he went on the defensive. 'No, sir. No one helped me.'

Jamieson nodded. 'I see. So where's your rough work? I mean, one doesn't just guess something as clever as this, does one?'

'No, sir,' said Harry. 'My rough work is there, crossed out.'

Jamieson looked at the paper, scratched his very nearly bald head, glanced at Hannant. Then he stared at Keogh. 'But this is simply a box with the numbers laid in their numerical sequence. I can't see how - '

'Sir,' Harry stopped him, 'it seemed to me that was the logical way to start. When I got that far I could see what needed doing.'

Again the head and the maths teacher exchanged glances.

'Go on, Harry,' said the head, nodding.

'See, sir, if you just write the numbers in, like I did, all the big numbers go to the right and to the bottom. So I asked myself: how can I get half of them over from right to left and half of them from the bottom to the top? And: how can I do both at the same time?'

'That seems... logical' Jamieson scratched his head again. 'So what did you do?'

'Pardon?'

'I said, what - did - you - do, boy!' Jamieson hated having to repeat himself to pupils. They should hang on his every word.

Harry was suddenly pale. He said something but it came out a croak. He coughed and his voice dropped an octave or two. When he spoke again he no longer sounded like a small boy at all. 'It's there in front of you,' he said. 'Can't you see it for yourself?'

Jamieson's eyes bugged and his jaw dropped, but before he could explode Harry added: 'I reversed the diagonals, that's all. It was the obvious answer, the only logical answer. Any other way's a game of chance, trial and error. And hit and miss isn't good enough. Not for me...'

Jamieson stood up, flopped down again, pointed an enraged finger at the door. 'Hannant, get - that - boy -out - of - here! Then come back in and speak to me.'

Hannant grabbed Keogh's arm, dragged him out into the corridor. He had the feeling that if he hadn't physi­cally taken hold of the boy, then Keogh might well have fainted. As it was he propped him up against the wall, hissed 'Wait here!' and left him there looking slightly dazed and sick.

Back inside Jamieson's study, Hannant found the head­ master soaking sweat from his brow with a large sheet of school blotting paper. He was staring fixedly at Harry's solution and muttering to himself. 'Reversed the diag­ onals! Hmm! And so he has!' But as Hannant closed the door behind him Jamieson looked up and grinned somewhat feebly. He had obviously regained his self control and continued to dab away at the sweat on his forehead and neck. 'This bloody heat!' he said, waving a limp hand and indicating that Hannant should take a seat.

Hannant, whose shirt was sticking to his back beneath his jacket, said, 'I know. It's murder, isn't it? The school's like a furnace - and it's just as bad for the kids.' He remained standing.

Jamieson saw his meaning and nodded. 'Yes, well that's no excuse for insolence - or arrogance.'

Hannant knew he should keep quiet but couldn't. ' he was being insolent,' he said. 'Thing is, I believe he was simply stating a fact. It was the same when I crossed him yesterday. It seems that as soon as you crowd him he gets his back up. The lad's brilliant - but he'd like to pretend not to be! He does his damnedest to keep it hidden.'

'But why? Surely that's not normal. Most boys of his age like the chance to show off. Is it simply that he's shy - or does it go deeper than that?'

Hannant shook his head. 'I don't know. Let me tell you about yesterday.'

When he was through, the head said: 'Almost exactly parallel to what we've just seen.'

'That's right.'

Jamieson grew thoughtful. 'If he really is as clever as you seem to think he is - and certainly he seems to have an intuitive knack in some directions - then I'd hate to be the one to deprive him of a chance to get somewhere in life.' He sat back. 'Very well, it's decided. Keogh missed the exams through no fault of his own, so ... I'll speak to Jack Harmon at the Tech., see if we can fix up some

sort of private examination for him. Of course I can't promise anything, but - ' 'It's better than nothing,' Hannant finished it for him.

'Thanks, Howard.'

Tine, fine. I'll let you know how I get on.' Nodding, Hannant went out into the corridor where

Keogh was waiting.

Over the next two days Hannant tried to put Keogh to the back of his mind but it didn't work. In the middle of lessons, or at home during the long autumn evenings, even occasionally in the dead of night, the boy's young-old face would be there, hovering on the periphery of Hannant's awareness. Friday night saw the teacher awake at 3:00 a.m., all his windows open to let in what little breeze there was, prowling the house in his pyjamas. He had come awake with that picture in his mind of Harry Keogh, clutching Jamieson's folded sheet of A4, heading off across the schoolyard of milling boys in the direction of the back gate under the stone archway; then of the boy crossing the dusty summer lane and passing in through the iron gates of the cemetery. And Hannant had believed that he knew where Harry was going. And suddenly, though the night had not grown notice­ably cooler, Hannant had felt chilly in a way he was now becoming used to. It could only be a psychic chill, he suspected, warning him that something was dreadfully wrong. There was something uncanny about Keogh, cer­tainly, but what it was defied conjecture - or rather, challenged it. One thing was certain: George Hannant hoped to God the kid could pass whatever exams Howard Jamieson and Jack Harmon of Hartlepool Tech. cooked up for him. And it was no longer simply that he wanted the boy to realise his full potential. No, it was more basic than that. Frankly, he wanted Keogh out of here, out of the school, away from the other kids. Those perfectly ordinary, normal boys at Harden Secondary Modern.

A bad influence? Hardly that! Who could he possibly influence - in what way? - when the rest of the kids generally considered him a weed? A corruption, then, a taint which might somehow spread - like the proverbial rotten apple at the bottom of the barrel? Perhaps. And yet that simile didn't exactly fit either. Or maybe, in a way, it did. For after all, it makes little difference that an apple can't appreciate its own rottenness: the corruption spreads anyway. Or was that too strong? How could it even be possible that there was something, well, wrong with Harry Keogh, something of which even he was unaware or lacked understanding? Actually the whole thing was becoming distinctly ridiculous! And yet ... what was it about Keogh which so worried Hannant?, What was in him, seeking a way out? And why didHannant feel that when it finally emerged it would be terrible?

It was then that Hannant decided to investigate Keogh's background, discover what he could of the boy's past. Perhaps that was where the trouble lay. And then again, i f maybe there was nothing at all and the whole affair was pi simply something spawned of Hannant's own overactive imagination. It could be the heat, the fact that he was If sleeping badly, the unending, unrewarding, repetitious routine of the school - any or all of these things. It could ! 1 be - but why then did that inner voice keep insisting that Keogh was different? And why on occasion would he find Keogh staring at him with eyes which might well be those of his own dead and buried father...?

Ten days and two Tuesdays later, tragedy struck. It happened when the boys, PTI Graham Lane, and the Misses Dorothy Hartley and Gertrude Gower went off on their end-of-day stone-gathering trek to the beach. 'Sergeant', ostensibly to collect specimens of some rare wild flower, but more likely to impress his lady love, had climbed the beetling cliffs. When he had been more than half-way up the treacherous face of the cliff, projecting stones had given way under his feet, pitching him down to the boulder- and scree-clad beach below. He had tried to cling to the crumbling surface even as he fell, but then his feet had struck a narrow ledge, breaking it away, and he had been set spinning free in air. He had landed on his chest and face, crushing both and killing himself outright.

The affair was made more especially gruesome in light of the fact that 'Sergeant' and Dorothy Hartley, only the night before, had announced their engagement. They were to have been married in the spring. As it was, the following Friday saw 'Sergeant' buried. It would have been better for him, Hannant later remembered thinking, as he watched Lane's coffin being lowered into a fresh plot of earth in the old cemetery, if he'd stayed in the Army and taken his chances there.

Afterwards, there had been sandwiches, cakes and coffee in the staff-room at the school, and a nip of something stronger for those who fancied it. And of course, Dorothy Hartley to console as best she could be consoled. So that none of the teachers had been there to see the grave filled in, or, after the gravedigger was through and the wreaths lay in position, the last lone mourner where he sat on a slab nearby, chin in the palms of his hands and lacklustre eyes staring from behind his spectacles, fastened mournfully - curiously? expectantly? - upon the mound.

Meanwhile, Howard Jamieson had not been remiss in seeking to get Harry Keogh a post-examination place at the Tech. in Hartlepool; or if not an actual place, at least the opportunity to win one for himself. The private examination - in the main an IQ test consisting of questions designed to measure verbal, numerical and spatial perception and aptitude - was to take place at the college in Hartlepool under the direct supervision of John ('Jack') Harmon, the headmaster. Wind of it had got out, however, along the Harden Boys' School grapevine, and Harry had become something of a target for various jibes and japes.

He was no longer simply 'Speccy' for instance but had acquired other nicknames including 'the Favourite' -which meant that Big Stanley had been putting it about that Harry was some sort of teacher's or headmaster's pet. And with the help of a twisted sort of logic, of which Stanley was a past-master - not to mention the threat in his pudgy but hard-knuckled fists - it hadn't taken long to convince even the more liberal-minded lads that there was definitely something fishy about Keogh's belated emergence as someone who was a bit more than just 'ordinary'.

Why, for instance, should Speccy - or 'the Favourite' - why should he alone get this crack at a special Tech. examination? Other kids had been sick that day, too, hadn't they? And were they being given special treat­ ment? No they weren't! It was just because that dreamy little fart got on well with the teachers, that was all. Who was it went digging up stupid, smelly shells for that old bag Miss Gower? Speccy Keogh, that was who - and hadn't old Sergeant always used to stick up for him? Of course he had! And now, since he'd suddenly started being a bit clever at maths and so on, even snotty old Hannant was on his side. Oh, he was 'the Favourite', all right - the four-eyed little fart. But not with Big Stanley Green he wasn't!

It had all sounded very logical; to which add the now sullen voices of the others who, through no fault of their own, had missed the exam, and soon the bully had a fair- sized crowd of like-minded boys on his side. Even Jimmy Collins seemed of the opinion that something 'niffed a bit'.

Then Tuesday came around, one week exactly after the gym-teacher's death, when once more the school trooped down to the beach for what was hopefully to be the last stone-gathering expedition of the season. The idea had been a novelty at first, but now boys and teachers alike were fed up with it; Lane's death had soured it for everyone. Miss Gower was present, as usual, with Jean Tasker of Science (a little older than Gower but much less frumpish) taking the place of Dorothy Hartley who had been given leave of absence. George Hannant was also there, replacing Graham Lane.

As usual, after the stones had been collected and piled up, the boys were allowed to do their own thing for an hour before carrying their booty back to the school. 'Gee-gee' Gower, (as her pupils sometimes called her, referring to her equine aspect as much as her initials) was giving instructions to a bunch of reluctant non-swimmers in a tidal pool; George Hannant and Jean Tasker stood down by the edge of the sea, gathering shells and bright pebbles, chatting and generally passing the time of day. That was when Big Stanley, who could no longer contain his vindictiveness, saw his opportunity to 'teach Keogh a lesson'.

Harry had been off on his own, head down, hands behind his back, beachcombing; but as he returned to the pile of stones he looked up and spotted Green and a large handful of the others waiting for him.

'Well, well!' sneered the bully, pushing his way to the front of the crowd. 'And if it isn't our little teacher's pet - little skinny Speccy Keogh - with a fistful of pretty shells for daft old Gee-gee! How's things then, Speccy? How d'you fancy your chances with this "special" exam they've fixed it for you to take, eh?'

'Reckon you'll pass it, do you then, Speccy?' said another, his voice hard-edged. 'They'll push you through it, will they?'

'Oh, he's "favourite", all right!' said a third. 'What, him? Teacher's pet and all - how can he fail?'

Jimmy Collins, towelling himself dry as he came up the beach, saw the mood of the crowd at once but said nothing. Instead he went to the rear of the group, wrapped a towel round his waist and started to dress.

'Well?' Green prodded Harry in the chest. 'How about it, four-eyes? Are the nice teachers going to let you pass your little exam, then - so you can get away from all us nasty rough boys and go to school in Hartlepool with the rest of the fairies?'

Harry staggered backward from the other's shoving, dropping the shells he'd collected. Big Stanley gave a whoop, jumped forward, crushed them to dust under his shoes and ground them into the sand. Harry swayed, looked sick, began to turn away. His eyes were suddenly misty behind his spectacles; his face, which wasn't tanned like the faces of the rest, turned even paler.

'Shitty little cowardly teacher's pet!' Green crowed maliciously. 'Old Man Jamieson's little "Favourite", eh, Speccy? And is that you crying, then? Tears, is it? Wetting ourself, are we? You four-eyed little - '

'Shut it, shithead!' Harry growled, turning back and facing the bully. 'You're ugly enough without me making it worse!'

'Wha-?' Green couldn't believe his ears. What was that Keogh had said? No, it couldn't have been. Why, it hadn't even sounded like him. He must have a frog in his throat, or he was all choked up with fear.

'Whyn't you leave him alone?' said Jimmy Collins, pushing through the crowd. Three or four of them grabbed him, held him back.

'Stay out of it, Jimmy,' said Harry in his new, gritty voice. 'I'm all right.'

'All right, is it?' cried Big Stanley. I'll say you're not, Speccy my son. I'll say you're - in - the - shit!'-

With his last word he swung his fist for the smaller boy's head. Harry ducked easily, stepped forward, jabbed with a straight arm, fingers straight and stiff. Big Stanley folded in the middle, jack-knifed, his face coming down on Harry's knee - which was coming up! The crack was like a pistol shot. Green straightened up and flew backward, his arms straight out from his shoulders. And down he crashed on the sand.

Harry stepped close. Seconds passed but Green just lay there. Then he sat up, shook his head groggily. His nose was the wrong shape, bleeding profusely; his eyes were glassy behind welling tears of pain. 'You... you... you!' he spat blood.

Harry bent over him, showed him a white, knobbly fist. 'You what?' he growled, the corner of his mouth lifting from his teeth. 'Go on, Bully, say something. Give me a reason to hit you again.'

Green said nothing, reached up a trembling hand to touch his broken nose, his split mouth. Then he started to cry real tears.

But Harry wasn't finished with him. He wanted him to remember. 'Listen, shithead,' he said. 'If ever - if you ever once - call me Speccy or Favourite or any other bloody funny name again - if you even speak to me, I'll hit you so hard you'll be shitting teeth for a month! Have you got that, shithead?'

Big Stanley turned on his side in the sand and cried even harder.

Harry looked up, glared at the rest of them. He took off his spectacles, put them in a pocket, scowled. He didn't squint, didn't look as though he'd needed the glasses at all. His eyes were bright as marbles, full of sparks. 'What I said to this shit goes for the rest of you. Or if any one of you fancies his chances here and now - ?'

Jimmy Collins stepped beside him. 'Or any two of you?' he said. The crowd was silent. As a man, all their mouths were wide, their eyes even wider. Slowly they turned away, began talking, nervously laughing, fooling about as if nothing had happened. It was over - and strangely, they were all glad it was over.

'Harry,' said Jimmy quietly out of the corner of his mouth, 'I never seen anything like that! Not ever. Why, you did it like - like - like a man! Like a grown man! Like old 'Sergeant' when he used to shadow-fight in the gym. Unarmed combat, he called it.' He elbowed his pal in the ribs - but gingerly. 'Hey, you know something?'

'What?' Harry asked, trembling all over, his voice his own again.

'You're weird, you are, Harry Keogh. You're really weird!'

Harry Keogh sat his examination a fortnight later.

The weather had changed in the first week of Sep­tember, since when it had grown progressively worse until the sky seemed permanently filled with rain. It rained on the day of the examination, too, a downpour which washed the windows of the head's study where Harry sat at a huge desk with his papers and pens.

Jack Harmon himself invigilated, seated behind his own desk, reading the minutes of (and adding his com­ments and recommendations to) the observations and notes of the last Staff Meeting. But while he worked, occasionally he would look up, glance at the boy, wonder about him.

Actually, Harmon didn't particularly want Harry Keogh at the Tech. Not for any personal motive - not even because he half felt that he'd been pushed into this unheard-of situation: that of being obliged to test a boy who had, quite simply, already missed his chance - but because it might set an unfortunate precedent. Time was precious enough without extra work of this sort being found or manufactured. Exams were exams: they were held annually and the colliery boys who passed them had the opportunity to finish their final years of schooling here, where perhaps they could go on to better things than their fathers had known. The system was long-established and worked very well. But this new thing -Howard Jamieson pushing the Keogh boy forward like this...

On the other hand, the headmaster at Harden Modern Boys' was a proven friend from the old days, and it was also true that Harmon owed him a favour or two. Even so, when Jamieson had first approached him on the subject, Harmon had been cool about it; but the other had persisted. Finally Harmon's curiosity had been aroused: he'd wanted to see this 'teenage prodigy' for himself. At the same time, however, and as stated, he had not wanted to set any sort of precedent. He had looked for an easy way out and believed he'd found one. He himself had set the questions, choosing only the most difficult problems from the last six years' examination papers. No boy of Keogh's educational background could possibly hope to answer them (not all of them, anyway, and certainly not correctly) but while the examination itself would almost constitute a farce, still Harmon would be able to look at examples of Keogh's work and so satisfy his curiosity. Jamieson, too, would have been mollified, at least in respect of his request that the boy be tested; Keogh's failure would destroy the credibility of any further, like requests in the future. And so Jack Harmon invigilated, keeping an eye on the boy while he worked at the papers.

An hour had been allowed for each subject; there were to be ten-minute breaks between subjects; tea and biscuits would be served right here in the head's study during the breaks, and a staff toilet was right next door. The first paper had been the English exam, following which Keogh had sat quietly drinking his tea, staring pallidly at the rain beyond the windows. Now he was half-way into the maths paper - or should be. That was a moot point.

Harmon had watched him. The boy's pen had seemed barely to scratch the answer paper; or if it had, then it was during those moments when the Tech's headmaster had been busy with his own work. Oh, the boy had been hard enough at it through the first hour, the first test: the English paper had seemed to interest him, he'd done a lot of frowning and pen-chewing and had written and re­written - indeed he'd still been working when Harmon had called time - but the maths paper obviously had him stumped. He made the occasional, sporadic attempt at it, Harmon must give him that much (and there he went again, even now, his pen flying, scratching away) but after only a moment or two he'd sit back, stare out of the windows, go pale and quiet again, almost as if he were exhausted.

Then he would appear to pick up, glance at the next question, scribble away at frantic speed, as if inspired -before pausing again, exhausted - and so on. Harmon could well understand his tension or anxiety or whatever it was: the questions were very difficult. There were six of them, each one of which would normally take at least a quarter of an hour to complete - and only then if the boy's aptitude was well in advance of his years and present level of education at Harden Modern.

What Harmon couldn't understand was why he both­ered at all, why he kept making these furious attacks on the paper, only to sit back each time after a little while, frustrated and tired. Wasn't it obvious to him that he couldn't win? What were his thoughts as he gazed out of the windows? Where was he when his face took on that blank, almost vacant expression?

Maybe Harmon should stop this now, put an end to it. Plainly the lad wasn't getting anywhere...

They were now (the headmaster glanced at his watch) thirty-five minutes into the maths section. As the boy sat back yet again, his arms dangling and his eyes half-closed behind the lenses of his spectacles, so Harmon quietly stood up and approached him from the rear. Outside, the rain was blowing in gusts against the windowpanes; in here, an old clock ticked on the wall, pacing the head's breathing. He glanced over Keogh's shoulder, not really knowing what he expected to see.

His glance became a fixed stare. He blinked, blinked again, and his eyes opened wide. His eyebrows drew together as he craned his neck the better to see. If Keogh heard his gasp of astonishment he made no sign, remained seated, continued to gaze blearily at the rain rivering the windows.

Harmon took a step backwards away from the boy, turned and went back to his desk. He seated himself, slid open a drawer, held his breath and took out the answers to the maths section. Keogh had not only answered the questions, he'd got them right! All of them! That last frenzied burst of work had been him working on the sixth and last. Moreover he'd accomplished it with the very minimum of rough work and hardly any use at all of the familiar and accepted formulae.

Finally the head allowed himself a deep, deep breath, gawped again at the printed answer sheets in his hand - the masses of complicated workings and neatly resolved solutions - then carefully placed them back in the drawer and slid it shut. He could hardly credit it. If he hadn't been sitting here through the entire examination, he'd swear the boy must have cheated. But quite obviously, that was not the case. So ... what did Harmon have here?

'Intuitive,' Howard Jamieson had called the boy, an intuitive mathematician'. Very well, Harmon would see how well (if at all) this intuition of his worked with the next paper. Meanwhile �C

The headmaster rubbed his chin and stared thoughtfully at the back of Keogh's head. He must speak to both Jamieson and young George Hannant (who'd first brought the boy to Jamieson's attention, apparently) at greater length. These were early days, of course, but ... intuition? It seemed to Harmon that there just might be another word for what Keogh was, one which the teachers it Harden simply hadn't thought to apply. Harmon could well understand that, for he too was reluctant. > The word in Harmon's mind was 'genius', and if this was so then certainly there was a place for Keogh at the Tech. Harmon would soon discover if he was right. And of course he was. It was only in his application that he was wrong. Keogh's 'genius' lay in an entirely different direction.

Jack Harmon was short, fat, hirsute and generally apish. He would be quite ugly except that he exuded a friendlin ess and an aura of well-being that cut right through his outer guise to show the man inside for what he really was: one of Nature's truest gentlemen. He also had a quite brilliant mind.

In Harmon's younger days he had known George Hannant's father. That was when J. G. Hannant had been head at Harden and Harmon had taught elementary Maths and Science at a tiny school in Morton, another colliery village. On and off over the intervening years he'd met the younger Hannant and so watched him grow up. It had come as no great surprise to him to learn that George Hannant, too, had finally come into 'the business' - teaching must be as much a part of him as it had been of his father.

'Young Hannant', Harmon had always thought of him. Ridiculous - for of course George had been a teacher now for almost twenty years!

Harmon had called the Maths teacher down from his own school to Hartlepool in order to talk to him about Harry Keogh. It was the Monday following Keogh's 'examination' and they had met at the Tech. Harmon lived close by and had taken the younger man home with him for a lunch of cold meats and pickles. His wife, knowing it was business, served the food then went shopping while the two men ate and talked. Harmon opened with an apology:

'I hope it isn't inconvenient for you, George, to be called away like this? I know Howard keeps you pretty busy up there.'

Hannant nodded. 'No problem at all. "Himself is standing in for me this afternoon. He likes to take a crack at it now and then. Says he "misses" the classroom. I'm sure he'd swap that study of his - and the admin that goes with it - for a classroom full of boys any time!'

'Oh, he would, he would! Wouldn't we all?' Harmon grinned. 'But it's the money, George, it's the money!

And I suppose the prestige has a little to do with it, too. You'll know what I mean when you're a "head" in your 'own right. Now then, tell me about Keogh. You're the one who discovered him, aren't you?'

'I think it's truer to say he discovered himself,' Hannant answered. 'It's as if he's only recently woken up to his town potential. A late starter, so to speak.' 'But one who's all set to overtake the rest of the runners in a flash, eh?'

'Ah!' said Hannant. Since Harmon hadn't yet said : anything about the results of Keogh's tests, he had half-feared that the boy had failed. Being called down here had reassured him a little, and now Harmon's remark about Keogh 'overtaking the rest' had clinched it. 'He passed then?

'Hannant smiled .

'No,' Harmon shook his head. 'He failed - miserably! ' The English paper let him down. He tried hard, I believe, but-'

Hannant's smile faded. His shoulders slumped a little. ' - but I'm taking him anyway,' Harmon finished, grinning again as Hannant's wide eyes came up once more to meet his. 'On the strength of what he did with the other papers.' 'What he did with them?'

Harmon nodded. 'I admit that I gave him the most difficult questions I could find - and he made mincemeat of them! If he has any fault at all, I'd say it was his unorthodox approach - if that in itself is a fault. It's just that he seems to dispense with all the customary ' formulae.'

Hannant nodded, made no comment, thought: / know exactly what you mean! And when he saw that Harmon was waiting, he said out loud, 'Oh, yes - he does that.'

'I thought it might just be Maths,' said the other, 'but it was just the same with the other paper. Call it "IQ"or "spatial" or whatever, it's mainly designed to test the potential of the intellect. I found his answer to one of the questions especially interesting; not the answer itself, you understand, which was absolutely correct anyway, but the way he arrived at it. It concerned a triangle.'

'Oh, yes?' Ah! Trig, Hannant thought, forking a piece of chicken into his mouth. / wondered how he'd do with that.

'Of course, it could have been solved with simple trigonometry,' (Harmon had almost read his mind,) 'or even visually - it was that simple. Indeed it was the only simple question in the batch. Here, let me show you:'

He pushed his plate aside, took out a pen and sketched on a paper napkin:

'Where AD is half AC, and AE is half AB, how much greater is the larger triangle than the smaller?' Hannant dotted the diagram so:

and said: four times greater. Visual, as you said.'

'Right. But Keogh simply wrote down the answer. No dotted lines, just the answer. I stopped him and asked: "How did you do that?" He shrugged and said: "A half times a half is a quarter - the smaller triangle is one quarter as great as the big one.'"

Hannant smiled, shrugged. 'That's typical of Keogh,' he said. 'It's what first attracted me to him. He ignores formulae, jumps gaps in the normal reasoning process, leaps from terminal to terminal.'

Harmon's expression hadn't changed. It was a very serious expression. 'What formulae?' he asked. 'Has he done Trig yet?'

Hannant's smile slipped. He frowned, paused with his fork half-way to his mouth. 'No, we were just starting.'

'So he wouldn't have known this formula anyway?'

'No, that's true,' Hannant's frown deepened.

'But he does now - and so do we!'

'Sorry?' Hannant had been left behind somewhere.

Harmon went on: 'I said to him, "Keogh, that's all very well, but what if it wasn't a right-angled triangle? What if it was like... this?"'

Again he sketched

' And I said to him,' Harmon continued, '"this time AD is half AB, but BE is only a quarter of BC." Well, Keogh just looked at it and said: "One eighth. Quarter times a half.' And then he did this

'What point are you trying to make?' Hannant found himself fascinated by the other's tense expression, if not by his subject. What was Harmon getting at?

'But isn't it obvious? This is a formula, and he'd figured it out for himself. And he'd done it during the examination!'

'It may not be as clever or inexplicable as you think,' Hannant shook his head. 'As I said, we were going to be starting on Trig in the near future. Keogh knew that. He may have done some reading in advance, that's all.'

'Oh?' said Harmon, and now he beamed, reached across the table and punched the other on the shoulder. 'Then do me a favour, George, and send me a copy of the text-book he's been swotting from, will you? I'd very much like to see it. You see, in all my years of teaching, that's a formula I never came across. Archimedes might well have known it, Euclid or Pythagorus, but I certainly didn't!'

'What?' Hannant stared again at the diagram, stared harder. 'But surely I know this? I mean, I understand Keogh's principle. Surely I've seen it before? I must have - Christ, I've been teaching Trig for twenty years!'

'My young friend,' said Harmon, 'so have I, and longer. Listen: I know all about sines, cosines, tangents - I fully understand trigonometrical ratios - I am as familiar with all the common or garden mathematical formulae as you yourself are. Probably more familiar. But I never saw a principle so clearly set forth, so brilliantly logical, so expertly... exposed! Exposed, yes, that's it! You can't say Keogh invented this because he didn't - no more than Newton invented gravity - or "discovered" it, as they say. No, for it's as constant as pi: it has always been there. But it took Keogh to show us it was there!' He shrugged defeatedly. 'How might I explain what I mean?'

'I know what you mean,' said Hannant. 'No need to explain further. It's what I told Jamieson: this thing of Keogh's for seeing right through the trees to the wood! But a formula...?' And suddenly, in the back of his mind:

Formulae? I could give you formulae you haven't even dreamed of...

'...Oh, but it is!' Harmon insisted, cutting in on Hannant's wandering thoughts. For a specific sort of question, certainly, but a formula nevertheless. And I ask myself, where to from here? Are there any more "basic principles" in him - principles we simply never stumbled on before - just waiting for the right stimulus? That's why I want him here at the Tech. So that I can find out.'

'Actually, I'm glad you're taking him,' said Hannant after a moment. He found himself on the verge of mentioning his disquiet concerning Keogh, then changed his mind and deliberately lied: 'I ... don't think he can realise his full potential at Harden.'

'Yes, I see that,' Harmon answered, frowning. And then, a little impatiently: 'But of course we've already made that point. Anyway, you can rest assured that I shall do my utmost to develop his potential here. Indeed I will. But come on now, tell me about the lad himself. What do you know of his background?'

On his way back to Harden, at the wheel of his '67 Ford Cortina, Hannant reflected on what he'd told Harmon of Keogh's origins and upbringing. Most of it he'd had from the boy's aunt and uncle, with whom Keogh lived in Harden. His uncle had a grocery shop in the main street; his aunt was mainly a housewife, but she also helped out in the shop two or three days a week.

Keogh's grandfather had been Irish, moving from Dublin to Scotland in 1918 at the end of the war and working in Glasgow as a builder. His grandmother had been a Russian lady of some note, who fled the Revol­ution in 1920 and took up residence in an Edinburgh house close to the sea. There Sean Keogh met her, and in 1926 they'd been married. Three years later Harry's uncle Michael was born, and in 1931 his mother, Mary.

Sean Keogh had been hard on his son, apparently, bringing him into the building business (which he'd hated) and working him hard from the age of fourteen; but by comparison he had seemed literally to dote on his daughter, for whom nothing had ever been good enough. This had caused some jealousy between brother and sister, which came to an end when Michael was nineteen and ran off south to set himself up in a business of his own. Michael was the uncle Harry Keogh now lived with.

By the time Mary Keogh was twenty-one, however, her father's doting had turned to a fierce possessiveness which totally shut her off from any sort of social life, so that she stayed mainly at home and helped with the housework, or assisted her aristocratic Russian mother in the small psychic circle she had built up, when she would attend and regularly take part in those stances for which Natasha Keogh had become something of a local celebrity.

Then, in the summer of '53, Scan Keogh had been killed when an unsafe wall he was working on fell on him. His wife, who for all that she was not yet fifty was already ailing, had sold the business and gone into semi-retirement, holding the occasional seance to eke out her living, which now mainly derived from the interest on banked money. For Mary, on the other hand, the death of her father had heralded a hitherto undreamed-of freedom; quite literally, a 'coming out'.

For the next two years she enjoyed a social life limited only by her tiny allowance, until by the winter of '55 she had met and married an Edinburgh man twenty-five years her senior, a banker in the city. He was Gerald Snaith, and he and Mary had been very happy for all the gap in their age groups, living in a large house in its own private grounds not far from Bonnyrigg. Unfortunately, by then Mary's mother was rapidly sickening and her doctors had diagnosed cancer; so that Mary lived half of her time at Bonnyrigg, and the rest of it looking after her mother, Natasha, at the seaside house in Edinburgh.

Harry 'Keogh' was therefore born Harry Snaith just nine months after his grandmother died in 1957 - and just a year before his banker father would follow her, dying from a stroke in his office at the bank.

Mary Keogh was a strong girl and still very young. She had already sold the old family house by the sea and now found herself sole beneficiary of her husband's not inconsiderable estate. Deciding to get away from Edin­burgh for a little while, in the spring of '59 she had come down to Harden and hired a house until the end of July, spending a lot of time in becoming reconciled with her brother and in getting to know his new wife. During that time she saw how his business was declining and helped out with sufficient hard cash to tide him over.

It was then, too, that Michael first detected an aura of sadness or hopelessness about his sister. When he asked what was bothering her (other, of course, than the recent death of her husband, which still weighed heavily) she reminded him of their mother's 'sixth sense', her psychic sensitivity. She believed she had inherited something of it; it 'told' her that she would not have a long life. That didn't worry her unduly - what would be would be - but she did worry about little Harry. What would become of him, if anything should happen to her while he was still a child?

It was unlikely that Michael Keogh and his wife, Jenny, would be able to have children of their own. They had known this when they married, but mutually agreed that it was not a matter of overriding importance; their feelings for each other came first. Later, when their small business was better established, there would be time enough to consider adoption. In these circumstances, however, and

if anything should 'happen' to Mary - a prediction which, while her brother himself put little store by it, Mary seemed strongly inclined, indeed resolved, towards - then she would not need to let it concern her. Of course her brother and his wife would bring up little Harry as their own. The 'promise' was made more to put her mind at rest than as a real promise as such.

When Harry was two his mother met and was 'swayed' by a man only two or three years older than herself, one Viktor Shukshin, an assumed dissident who had made his way to the West in pursuit of a political haven, or at least political freedom, such as Mary Keogh's mother had done in 1920. Perhaps Mary's fascination with Shukshin was due to this 'Russian connection', but whichever, she married him late in 1960 and they lived at the house near Bonnyrigg. A linguist, Harry's new stepfather had been giving private lessons in Russian and German in Edin­burgh for the last two years; but now, all financial problems set aside, he and his new wife gave themselves over to a life of leisure and personal interests and incli­nations. He, too, was greatly interested in the 'paranor­mal', encouraging his wife in her psychic pursuits.

Michael Keogh had met Shukshin at his sister's wed­ ding, and again, briefly, while on a touring holiday in Scotland - but after that... only at the inquest. For in the winter of '63 Mary Keogh died, as she had predicted, at only thirty-two years of age. Of Shukshin himself Hannant had only ascertained that the Keoghs hadn't liked the man. There had been that about him which alienated them; probably the same thing which had attracted Michael's sister.

As to Mary's death:

She had been a skater, had loved the ice. A river within view of the house near Bonnyrigg had claimed her, when she had apparently fallen through thin ice while skating and been swept away. Viktor had been with her but had been unable to do anything. Distraught -almost out of his mind with horror - he had gone for help, but...

Beneath the ice, the river had been swollen, rushing, at the time of the accident. Downriver were many little backwaters where Mary's body might have been washed up under the ice, remaining there until the thaw. Lots of mud had been washed down out of the hills, too, and this had doubtless covered her. At any rate, her body was never found.

Within six months Michael had fulfilled his promise; Harry 'Keogh' had gone to live with his uncle and aunt in Harden. This had suited Shukshin; Harry had not been his child, and he was in any case middling with children and did not feel inclined to bring the boy up on his own. Mary's will had made good provision for Harry; the house and the rest of her estate went to the Russian. To Michael Keogh's knowledge, Shukshin lived there yet; he had not re-married but gone back to giving private tuition in German and Russian. He still gave lessons at the house near Bonnyrigg, where he apparently lived alone. Not once over the years had he asked to see Harry, nor even enquired about him.

Dramatic as his family history might seem, still, all in all, Harry Keogh's beginnings had not been very remarkable. The only matter which had made any real impression on Hannant had been Keogh's grandmother's and mother's predilection for the paranormal; but that in itself was not very extraordinary. Or there again... perhaps it was. Mary Shukshin had seemed convinced that Natasha's 'powers' had been passed down to her, and what if she in turn had passed them down to Harry? Now there was a thought! Or there might be one, if Hannant believed at all in such things.

But he did not.

It was an evening some three weeks later, four or five days after Keogh had left Harden Modern Boys' for the Tech., when Hannant stumbled across one final 'oddity' concerning the boy.

Up in Hannant's attic he'd long kept an old trunk of his father's containing one or two books and bundles of old papers, dusty bits of bric-a-brac and various mem­entoes of the old man's years of teaching. Having gone up there to fix a tile loosened in a brief storm off the North Sea, he had seen the trunk and admired it. Stoutly constructed, its dark body and brass hasps and hinges retained an olde-worlde appeal. It would create a very handsome effect beside the bookshelves in Hannant's front room.

Dragging the trunk downstairs, he had started to empty it, glancing again at old photographs unseen for many a year, and putting aside items which might be useful at school (several old text-books, for example) until he'd come across a large leatherbound notebook full of notes and jottings in his father's hand. Something about the pattern and layout of his father's work had held his eye for a moment... until it dawned on him just exactly what it was - or what he thought it was.

In the next moment that awful inexplicable chill had come again to strike Hannant's spine, causing him to tremble where he sat holding the book open in his lap, stiffening his back with shock. Then ... he had snapped the book shut, carried it through to his front room where a coal fire blazed beneath the wide chimney-piece. There, without even glancing at the book again, he thrust it into the flames and let it burn.

That same day Hannant had collected Keogh's old Maths books from the school for forwarding on to Harmon at the Tech. Now, taking the most recent one, he let its pages fall open for one last glance, then closed it with a shudder and let it join his father's old book in the flames.

Prior to Keogh's - awakening? - his work had been scruffy, lacking in order, by no means precise. After­wards, for the last six or seven weeks...

Well, the books were gone now, roared up in a sheet of flame and lost in the chimney, lost to the night.

There was no comparing them now, and that was probably the best way. To consider that there might be any real comparison would be too gross, too grotesque. Now Hannant could put the whole thing out of his mind forever. Thoughts like that had never belonged in any completely sane mind in the first place.