to work out his sum with a piece of chalk on a smooth stone. He tried it by practice and the unitary method, by multiplication, and by rule-of-three-and-three-quarters. He tried it by decimals and by compound interest. He tried it by square root and by cube root. He tried it by addition, simple and otherwise, and he tried it by mixed examples in vulgar fractions. But it was all of no use. Then he tried to do the sum by algebra, by simple and by quadratic equations, by trigonometry, by logarithms, and by conic sections. But it would not do. He got an answer every time, it is true, but it was always a different one, and he could not feel sure which answer was right.
And just as he was feeling how much more important than anything else it is to be able to do your sums, the Princess came back. And now it was getting dark.
"Why, you've been seven hours over that sum," she said, "and you haven't done it yet. Look here, this is what is written on the tablet of the statue by the lower gate. It has figures in it. Perhaps it is the answer to the sum."
She held out to him a big white magnolia leaf. And she had scratched on it with the pin of her pearl brooch, and it had turned brown where she had scratched it, as magnolia leaves will do. Nigel read:
AFTER NINE DAYS
T ii. 24.
D ii. 27 Ans.
P.S.—And the griffin is artificial. R.
He clapped his hands softly.
"Dear Princess," he said, "I know that's the right answer. It says R too, you see. But I'll just prove it." So he hastily worked the sum backward in decimals and equations and conic sections, and all the rules he could think of. And it came right every time.
"So now we must wait," said he. And they waited.
And every day the Princess came to see Nigel and brought him food cooked by the dragon, and he lived in his cave, and talked to her when she was there, and thought about her when she was not, and they were both as happy as the longest day in summer. Then at last came The Day. Nigel and the Princess laid their plans.
"You're sure he won't hurt you, my only treasure?" said Nigel.
"Quite," said the Princess. "I only wish I were half as sure that he wouldn't hurt you."
"My Princess," he said tenderly, "two great powers are on our side: the power of Love and the power of Arithmetic. Those two are stronger than anything else in the world."
So when the tide began to go down, Nigel and the Princess ran out on to the sands, and there, in full sight of the terrace where the dragon kept watch, Nigel took his Princess in his arms and kissed her. The griffin was busy sweeping the stairs of the Lone Tower, but the dragon saw, and he gave a cry of rage—and it was like twenty engines all letting off steam at the top of their voices inside Cannon Street Station.
And the two lovers stood looking up at the dragon. He was dreadful to look at. His head was white with age—and his beard had grown so long that he caught his claws in it as he walked. His wings were white with the salt that had settled on them from the spray of the sea. His tail was long and thick and jointed and white, and had little legs to it, any number of them—far too many—so that it looked like a very large fat silkworm; and his claws were as long as lessons and as sharp as bayonets.
"Good-bye, love!" cried Nigel, and ran out across the yellow sand toward the sea. He had one end of a cord tied to his arm.
The dragon was clambering down the face of the cliff, and next moment he was crawling and writhing and sprawling and wriggling across the beach after Nigel, making great holes in the sand with his heavy feet—and the very end of his tail, where there were no legs, made, as it dragged, a mark in the sand such as you make when you launch a boat; and he breathed fire till the wet sand hissed again, and the water of the little rock pools got quite frightened, and all went off in steam.
Still Nigel held on and the dragon after him. The Princess could see nothing for the steam, and she stood crying bitterly, but still holding on tight with her right hand to the other end of the cord that Nigel had told her to hold; while with her left she held the ship's chronometer, and looked at it through her tears as he had bidden her look, so as to know when to pull the rope.
On went Nigel over the sand, and on went the dragon after him. And the tide was low, and sleepy little waves lapped the sand's edge.
Now at the lip of the water, Nigel paused and looked back, and the dragon made a bound, beginning a scream of rage that was like all the engines of all the railways in England. But it never uttered the second half of that scream, for now it knew suddenly that it was sleepy—it turned to hurry back to dry land, because sleeping near whirlpools is so unsafe. But before it reached the shore sleep caught it and turned it to stone. Nigel, seeing this, ran shoreward for his life—and the tide began to flow in, and the time of the whirlpools' sleep was nearly over, and he stumbled and he waded and he swam, and the Princess pulled for dear life at the cord in her hand, and pulled him up on to the dry shelf of rock just as the great sea dashed in and made itself once more into the girdle of Nine Whirlpools all around the island.
But the dragon was asleep under the whirlpools, and when he woke up from being asleep he found he was drowned, so there was an end of him.
"Now, there's only the griffin," said Nigel. And the Princess said: "Yes—only—" And she kissed Nigel and went back to sew the last leaf of the last lily on the bosom of her wedding gown. She thought and thought of what was written on the stone about the griffin being artificial—and next day she said to Nigel: "You know a griffin is half a lion and half an eagle, and the other two halves when they've joined make the leo-griff. But I've never seen him. Yet I have an idea."
So they talked it over and arranged everything.
When the griffin fell asleep that afternoon at teatime, Nigel went softly behind him and trod on his tail, and at the same time the Princess cried: "Look out! There's a lion behind you."
And the griffin, waking suddenly from his dreams, twisted his large neck around to look for the lion, saw a lion's flank, and fastened its eagle beak in it. For the griffin had been artificially made by the King-enchanter, and the two halves had never really got used to each other. So now the eagle half of the griffin, who was still rather sleepy, believed that it was fighting a lion, and the lion part, being half asleep, thought it was fighting an eagle, and the whole griffin in its deep drowsiness hadn't the sense to pull itself together and remember what it was made of. So the griffin rolled over and over, one end of it fighting with the other, till the eagle end pecked the lion end to death, and the lion end tore the eagle end with its claws till it died. And so the griffin that was made of a lion and an eagle perished, exactly as if it had been made of Kilkenny cats.
"Poor griffin," said the Princess, "it was very good at the housework. I always liked it better than the dragon: It wasn't so hot-tempered."
At that moment there was a soft, silky rush behind the Princess, and there was her mother, the Queen, who had slipped out of the stone statue at the moment the griffin was dead, and now came hurrying to take her dear daughter in her arms. The witch was clambering slowly off her pedestal. She was a little stiff from standing still so long.
When they had
