. The night those
chaps burgled us he said, 'They're up a gum-tree when they should be
under one.' I'm not so sure of the exact words now, but that's the
substance of them anyway."

"But," Cumshaw objected, "he didn't know as much about the Valley then
as we do now."

"Quite so," I said. "I never thought he really meant anything by what he
said, but that remark's been running through my head. It seems to me
that everyone right through has been obsessed by the idea of the tree,
and now that it's disappeared we're at a loose end. Everybody, from your
father and Bradby down to Bryce and ourselves, has taken it for granted
that a tree's vital to the solution."

"Isn't it?" Cumshaw queried quickly.

I shook my head. "Not in the least," I said. "If the tree was absolutely
necessary it'd mean that we'd have to wait until 3rd or 4th of December,
the day on which Bradby buried the treasure, and the only day of the
year on which the sun, the tree and the threshold of the hut would be in
an exact line. Bryce's idea of having to wait three months must have
been conceived in the belief that the 3rd or 4th June would answer
equally well. It might, but I'm not so sure about it. I guess there'd be
a lot of difference in the declination of the sun. But now the tree's
gone we're left without that seemingly necessary leading mark."

"What are we going to do about it?" Cumshaw demanded.

"We can't give up after having gone so far," said Moira.

"We're not," I told her. "There's a way out of it, and the simplest way
on earth. It's so infernally simple that we've all overlooked it. It
narrows down to a simple problem in geometry. Do you remember what the
cypher said?"

"'When the Lone Tree, the hut door and the rising sun are in line
measure seven feet east. Then face direct north, draw another line at
right angles to the previous one, extending for twelve feet. Dig then.'"
He rattled through the directions so rapidly that I knew he must have
had them off by heart.

"That's it," I said, while the others listened in breathless interest.
"Now this is the position to my mind: The line that runs through the
doorway, the tree and the sun must go due east. The sun at that time of
the year would be due east. Well, all we have to do is to cast our east
line, carry it along for seven feet, and then turn so that we are facing
direct north."

"And at right angles to the previous line," Moira reminded me.

"It's the same thing," I said. "D