“Good!” exclaimed Hal, eager to defend his belief in things mysterious, and Bud signified his approval in similar manner.

“Yes, that isn’t bad at all,” admitted Mr. Perry, glad to have stimulated his son’s mind into action.  “But if we can’t explain this affair with mathematics, maybe we can explain it by some other element of human education.”

“What, for instance?” asked Cub.  “Not by readin’, ‘ritin’, or ’rithmetic.”

“No, we’ll exclude the three R’s for the present, although all of them may figure in our work before it is finished.”

“Well,” mused Cub; “the others are history, geography, spelling—­”

“Why didn’t you stop with geography?” asked his father.

“Geography!” exclaimed Bud.  “How can you use that to explain a mystery?”

“It depends on whether geography is involved,” Mr. Perry replied.  “In this case it seems to me that geography is a very important element.  We may have to know considerably more about the geography of the Thousand Islands in order to solve this so-called mystery.  Now, mind you, I don’t mean to say that we’re going to get at the bottom of this affair, but I do want to suggest that if it is to be solved by any systematic process, the first elements to be employed in the process are a little geography and a little arithmetic.  With this in view, I would suggest that you get busy with your wireless outfit and see what you can find out.”

The three boys gazed curiously at Cub’s father and then at one another in a puzzled manner.

“Haven’t I given you enough hint?” asked Mr. Perry.  “I don’t want to do the work myself—­in fact, I couldn’t if I wished to, for I can’t send a wireless message; but if I could, I know exactly what I’d do.”

“We might send a broadcast to all other amateurs and find out if any of them can help us,” Hal suggested.

“How could they help us?” asked Bud skeptically.

“I’m sure I can’t tell you,” replied Mr. Perry.  “But you have a dandy field to work on.  All you need is a little imagination; then begin to do a little head-work, and before you know it you’ll have a lead to work on.  And let me add something more.  There are two things in this world, which, working together, can knock a mystery into a cocked hat more successfully than anything else in the world that I know of.”

“I bet I know what they are,” Cub volunteered, eagerly.

“Mathematics and imagination,” almost shouted Hal in a wild scramble of mind to beat Cub with the answer.

The latter cast a wrathful glance at the saucy youth who had broken in ahead of him.

“Tee-hee!” laughed Bud with fitting imitation of Hal’s characteristic vocal merriment.

As for Tee-hee, that worthy individual preserved his dignity for the nonce.

“Well,” laughed Mr. Perry; “You’ve hit the nail on the head, but I venture to say you can’t explain why mathematics and imagination can put a mystery to rout.”