“Which is as follows,” Bud announced; “to-wit, why have we established our camp on this island, how long are we going to remain here, and what shall we do while here?”

“Now, we’re getting down to business,” said Cub.  “But that’s a composite question.  First, why are we here?”

“We’re here because we’re here,” Hal replied solemnly.

“The chair is willing to accept that as a good and valid reason provided other collateral questions are answered satisfactorily,” Mr. Perry announced.

“Next question, how long are we going to stay here?” Cub continued.

“I should say we will stay here until we find a reason for moving on to the next place,” said Bud.

“Another excellent answer and fully supporting answer number one,” Mr. Perry announced.  “Now, for an answer to question number three—­What shall we do while here?”

“I’ll answer that,” said Cub; “well fish, cook, eat, sleep, explore and keep our eyes peeled.”

“Peeled for what?” asked Hal.

“More mathematical evidence.”

“Good!” exclaimed Bud.  “We mustn’t lose sight of the purpose of this expedition.  If our radio Crusoe is really Hal’s cousin, we’re bound by the ties of friendship to stick to our task till it’s finished.”

“Very well,” said the chair.  “Having settled the question of general policy, let’s get down to some more detail.  What shall we do next?”

“Complete our exploration of the islands,” said Cub.  “There’s no telling what we may find.”

“Now, you’re beginning to look at things the way your father does,” put in Hal shrewdly.

“How’s that?” Cub inquired.

“Why you’re willing to look for a trail.  I’m not saying you were any worse than Bud and I were before we got started on this hunt.  We just stumbled on a trail to begin with, but when we lost it we didn’t know what to do next until your father told us it was up to us to scout around and find it again.”

“Yes, that’s right,” Cub admitted.  “We scouted around in the air and found the trail that brought us here.”

“Moral:  Whenever at a loss, do some broadcasting,” suggested Mr. Perry.

“Right,” declared Bud; “Now the thing for us to do is some physical broadcasting on this island.”

“In other words, we’ll all go in different directions and examine every square foot of this island,” Cub inferred.

“Exactly,” assented Mr. Perry.  “It ought not to take very long.  There are only about five acres here, although the place is pretty well covered with bushes and trees.”

Without further ado they separated toward different points of the compass.  It was indeed a random exploration, well characterized as something of a “broadcast,” but the task was well executed by all.  They had no definite expectation in view, and hence they had to content themselves with examining every physical feature as a naturalist or a topographer, perchance, would look for the feature demands of his specialty, and in about half an hour reconvened in front of their tent.  Hal was the only person present with a look of excitement or eagerness on his face, and consequently the general interest of the others was directed toward him.