Hal confessed he was unable to explain.

“It’s too much highbrow for me,” he said.  “And I bet it’s too much highbrow for Cub.”

The latter said nothing.  Evidently he was thinking hard.  He leaned back in his camp chair and hoisted his feet upon the rail again.

“Well, let’s quit the highbrow field and get down to business,” suggested Mr. Perry.  “If we’re able to put this thing through along mathematical lines, I bet you boys will have enough imagination to tell me why mathematics and imagination can put any mystery on earth to rout.”

“I’m goin’ to get busy with the spark gap,” Cub announced suddenly, as he sprang to his feet.

“You’ve got a big thing ahead of you, boys,” announced the owner of the Catwhisker.  “I venture to say there are some big surprises in store for you.  For instance, you’re likely to find the newspapers of the United States and Canada giving considerable space to this affair.”

“How are they going to get hold of it?” asked Bud.

“There’s where you’re short of imagination, my boy.  How many amateurs do you suppose were listening in and got the messages between you and those two radio contestants?”

“I bet there were a hundred if there was one,” declared Hal.

“And were they interested?”

“Were they?” exclaimed Cub.  “Every last one of ’em was wild with curiosity.”

“And did they talk about it to anybody?”

“They didn’t talk about anything else,” Bud opined.

“And didn’t you suppose some of those amateurs know some newspaper reporters?”

“We fellows all know several reporters,” said Cub, with an appreciative grin.

“All right,” said Mr. Perry, significantly.  “Now, all I have to say to you boys is, watch the headlines whenever you get near a news stand.”

The three radio boys now repaired to the cabin, while the owner of the yacht busied himself about matters of nautical interest to him on deck.

“You’ve got to hand it to my father for one thing,” Cub declared as he seated himself near the radio table and hoisted his feet thereupon.  “He sure has some imagination.”

“And some mathematics, too, the way he subtracts mist from mystery every time our brains get lost in a fog,” Hal added, with a self-appreciative “tee-hee.”

Cub and Bud also laughed in spite of Hal’s excusable self-appreciation.

“Do you know, I don’t feel nearly so mystified as I did before that talk with your father began,” Bud announced.

“It’s the mathematics and imagination getting their work in,” Cub explained with a wink.

“It sounds funny, and yet, I can’t help feeling there’s something to it,” Hal remarked.

“Well,” said Cub, bringing his feet down from the table with enough noise to rivet a conclusion; “you may call it addition, or subtraction, or multiplication, or division, or algebra, or geometry, or trigonometry, or calculus—­does that complete the list?—­I’m going to make my imagination leap across the spark gap; so here goes.”