'The homework questions? I've done them.'
'What, here?' Hannant was surprised; and yet thinking about it, it seemed entirely fitting.
'It's quiet here,' Harry answered.
'Would you like to show me?'
Harry shrugged. 'If you like.' He passed over the work book.
Hannant checked it, was doubly surprised. The work was very neat, almost immaculate. There were two answers, both correct if his memory served him right. Of course the working would be equally important, but he didn't check that just yet.' Where's the third question?'
Harry frowned. 'Is that the one with the grease-gun, where — ?' he began.
But Hannant impatiently cut him off: 'Let's not piss about, Harry Keogh. There are only three questions.out of the ten which could possibly qualify. The rest concern themselves with boxes, not circles, not cylinders. Or am I being unjust? The book's a new one to me, too. Give it here.'
Harry lowered his head a little, bit his lip, passed the book over. Hannant flipped pages. 'The grease-gun,' he said. 'Yes, this one,' and he stabbed at the page with a forefinger. It showed this diagram:
the measurements were internal; barrel and nozzle were cylindrical, full of grease; squeezed dry, how long would th e line of grease be?
' Harry looked at it. 'Didn't think it qualified,' he said. " Hannant felt angry. Two out of three wasn't good Enough. Three wrong answers would almost be better than this crap. 'Why don't you just say it was too difficult?' he tried not to bark. 'I've had all I can take of bluff for one day. Why not simply admit you can't do it?'; Suddenly the boy looked sick. His face shone with sweat and his eyes seemed a little glazed through the lenses of his spectacles. 'I can do it,' he slowly answered; then, more quickly, with acid precision: 'An idiot could do it! I didn't think it qualified, that's all.'
Hannant believed his ears must be deceiving him, that he'd misunderstood the boy's answer. 'What about the formula?' he rasped.
'Not required,' said the other.
'Shit, Harry! It's pi times the radius squared times length equals contents. That's all you need to know. Look — ' and he quickly scribbled in the workbook:
Contents of Barrel:
3.14159 x.75 x.75 x 4.5
3.14159 x.25 x.25
Contents of Nozzle: 3.14159 x.25 x.25 x 1.5
3.14159 x.25 x.25
He gave Harry the pencil back, said: 'There. After that most of it just cancels itself out. The divisor is of course the surface area of a cross-section of the line of grease.'
'A waste of time,' said Harry in such a way that Hannant knew it wasn't just rank insubordination, indeed in a voice which hardly seemed like Harry Keogh's voice at all. There was authority in it. For a moment… Hannant almost felt intimidated! What was going on behind the kid's glasses, inside his skull? What was the meaning in his not-altogether-there eyes?
'Explain yourself,' Hannant demanded. 'And make it good!'
Harry glanced at the diagram, not at the teacher's suggested solution. 'The answer is three and a half feet,' he said. And again there was the same authority in his voice.
As Hannant had said, the text-book was new to him; he hadn't properly worked through it himself yet. But just looking at Keogh he'd be willing to bet the kid was right. Which could only mean -
'You went back to the classroom with Collins after the beach,' he accused. Td told him to lock up, but before he did you opened my desk, looked up the answers in the answer book there. I wouldn't have believed it of you, Keogh, but — '
'You're wrong,' Harry cut him short in that same flat, emotionless, precise voice. Now he stabbed at the diagram with his finger. 'Look at it for yourself. The first two questions required formulas, yes, but not this one. Given a diameter to four decimals, what's the surface area? That requires a formula. Given a surface area to four decimals, what's the radius? That requires almost the same formula in reverse. But this? Listen:
The barrel's diameter is three times greater than the nozzle's. The circle's area is therefore nine times greater. The barrel's length is three times greater. Three times nine is twenty-seven. The barrel contains twenty-seven times as much grease as the nozzle. Barrel and nozzle together therefore contain twenty-eight nozzles' worth. The nozzle is one and a half inches long. Twenty-eight times one and a half equals forty-two. And forty-two inches equals three and a half feet, sir…'
Hannant stared at the boy's expressionless, almost vacant face. He stared at the diagram in the book. His mind whirled and it seemed that a cold wind blew on his spine, causing him to shiver. What the hell — ? For Christ's sake, he was the maths teacher, wasn't he? But there was no fighting Keogh's logic. The question hadn't needed formulae, hadn't needed maths at all! It was mental arithmetic — to someone who understood circles. To someone who could see past the trees to the wood. And of course his answer was, must be, right! If Hannant threw his formulae away, he would have been able to do it too — with a little thought. But Keogh's application had been instantaneous. His scorn had been real!
And now Hannant knew that if he didn't play this right, he'd probably lose this boy right here and now. He also knew that if that happened, he wasn't the only one who would lose. There was a mind in there, and it had… hell, potential! Whatever Hannant's confusion, h e forced a grin, said: 'Very good! Except I wasn't just checking out your IQ, Harry Keogh. It was to see whether or not you knew your formulae. But now you've really puzzled me. Seeing as how you're so smart, how come your classwork has always been so lousy?'
Harry stood up. His movements were stiff, automatic almost. 'Can I go now, sir?'
Hannant stood up too, shrugged and stepped aside. 'Your free time's your own,' he said. 'But when you get five minutes, you might still bone up on your formulae.'
Harry walked off, his back straight, movements stiff. A few paces away he turned and looked back. A beam of sunlight striking through the trees caught his glasses, turning his eyes to stars. 'Formulae?' he said in that new, strange voice. 'I could give you formulae you haven't even dreamed of.'
And as the cold chill struck at his spine once more, Hannant somehow knew for a certainty that Keogh wasn't just bragging.
Then… the maths master wanted to shout at the boy, run at him, even strike him. But his feet seemed rooted to the spot. All of the energy had gone out of him. He'd lost this round — completely. Trembling, he sat down again on the slab, leaning back weakly against the headstone as Harry Keogh walked away. He leaned there for a moment — then jerked forward, started upright, threw himself away from the grave. He tripped and sprawled on the close-cropped grass. Keogh was disappearing, lost among the markers.
The evening was warm — no, it was damned hot, even now — but George Hannant felt cold as death. It was in the air, in his heart, freezing him. Here, in this place, of all places. And it came to him now just exactly where and when he had heard someone speak like Harry Keogh before, with his authority, his precision and logic. Thirty long years ago, almost, when Hannant had been little more than a lad himself. And the man had been more than his peer. He had been his hero, almost his god.
Still trembling he got to his feet, picked up Keogh's books and put them in his briefcase, then backed carefully away from the grave.
Cut into the headstone, lichened over in parts, the legend was simple and George knew it by heart: JAMES GORDON HANNANT
13 June 1875 — 11 Sept. 1944
Master at Harden Boys' School
for Thirty Years, Headmaster
for Ten, now he Numbers
among the Hosts
of Heaven.
The epitaph had been the Old Man's idea of a joke. His principal subject, like that of his son after him, had been maths. But he had been far better at it than George would ever be.
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.