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, he 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.’