“That'll do it!” the Gardener shouted, as he hurled the watering-can across the flower-bed, and produced a handful of keys—one large one, and a number of small ones.

“But look here, Professor dear!” whispered Sylvie. “He needn't open the door for us, at all. We can go out with you.”

“True, dear child!” the Professor thankfully replied, as he replaced the coins in his pocket. “That saves two shillings!” And he took the children's hands, that they might all go out together when the door was opened. This, however, did not seem a very likely event, though the Gardener patiently tried all the small keys, over and over again.

At last the Professor ventured on a gentle suggestion. “Why not try the large one? I have often observed that a door unlocks much more nicely with its own key.”

The very first trial of the large key proved a success: the Gardener opened the door, and held out his hand for the money.

The Professor shook his head. “You are acting by Rule,” he explained, “in opening the door for me. And now it's open, we are going out by Rule—the Rule of Three.”

The Gardener looked puzzled, and let us go out; but, as he locked the door behind us, we heard him singing thoughtfully to himself,

“He thought he saw a Garden-Door
That opened with a key:
He looked again, and found it was
A Double Rule of Three:
'And all its mystery,' he said,
'Is clear as day to me!'”

“I shall now return,” said the Professor, when we had walked a few yards: “you see, it's impossible to read here, for all my books are in the house.”

But the children still kept fast hold of his hands. “Do come with us!” Sylvie entreated with tears in her eyes.