"You mean problem," reminded Mr. Perry with a smile.

"Well, maybe,--I won't dispute your word since your idea has proved so brilliant thus far--but I can't see the mathematics yet."

"Nor the geography?"

"Well, yes; it took us from Kingston to Port Hope and from there to Edwards College," Cub admitted. "I suppose there's a little geography in that."

"Remember this, that mathematics isn't all figures," said the operator's father. "Keep that in mind, and maybe it'll be worth something to you before we're through with this affair."

"How does the discovery of my cousin come in?" Hal inquired. "Is that geography or mathematics?"

"Do you mean that, Hal?" asked Bud wonderingly. "You don't mean that fellow is really your cousin?"

"I surely do, if he's Alvin Baker. You know my folks used to live in Canada. And don't you remember that my cousin Al visited us three years ago with his father and mother? He wrote to me several times from Edwards College, but I didn't know he had a wireless set, and I suppose he didn't know I had one."

"Well, it makes the hunt more interesting, anyway," said Cub. "But let's not waste any more time. Here goes again."

He called the other Canadian amateur on his list of three and learned from him that many wireless boys had followed the course of the rescue boat with their receiving outfits. From him Cub got the calls of four of these interested boys. Then he called the third on his original list, but all the information the latter was able to give was that a metropolitan morning newspaper carried a column "story" on the front page about the Thousand Island Crusoe and the rescue boat from Oswego.

"You're right again, dad," said Cub, with a grim grin of subdued wonder and eagerness.

"I shouldn't be a bit surprised to find that the a.s.sociated Press has chartered a boat and is following us," declared Mr. Perry.

"Would that be mathematics or geography?" asked Bud.

"It would be imagination," replied Mr. Perry with a keen smile. "But, say, Cub, don't you think you've grabbed off enough glory for yourself?

Give your friends a chance to win some honors."

"Right you are, dad," returned the boy at the key, rising and removing the phones from his ears. "Hal, you call half this list and then let Bud call the rest"

It was well for the sake of a distribution of honors that this course was taken, for a thrilling surprise was in store for them in response to the next call.

CHAPTER IX

The Radio Diagram

As good fortune decreed, Hal found Number One in the new list sitting in and listening for anything interesting in the ether. It required only a few short sentences to acquaint this amateur with the object of the Catwhisker's search.

"I can tell you just how to find those fellows," he replied. "I listened-in to the best line of detective work on that subject you ever heard of. Sherlock Holmes isn't in it there."

"Hooray!" shouted Bud, as he finished jotting down the last sentence.

"There are three amateurs, one in Clayton, N.Y., one in Rockport and one in Gananoque, Ontario, who have radio compa.s.ses and they worked together to locate the fellow on the island," continued the informant with the eagerness of fraternal interest and generosity. "I will give you their calls--"

The message was interrupted by a strong spark, which could not be ignored. Sender Number one stopped sending, and Hal gave ear to the new message.

"I will save you the trouble," read the dots and dashes evidently addressed to the operator he had just "crowded out," "I am at Rockport and am one of the three radio compa.s.s boys referred to. I can supply the dope right now."

Hal threw over the aerial switch and flashed the one word "Shoot!" Then he swung back again and all three boys listened eagerly.

"Have you a good map of the Thousand Island region?" inquired the loop aerial operator.

"Yes," Hal replied.

"Well, take these directions and then draw the line on the map. Draw one line from Clayton, N.Y., northeast, 47-1/2 degrees from perpendicular; another from Rockport, Ontario, southeast, 11 degrees from perpendicular; another from Gananoque, southeast, 76 degrees from perpendicular. The intersection of those lines will indicate the island those messages came from."

"He was on an island, was he?" asked Hal.

"Sure, or on a boat," was the reply. "He could not have been on the mainland. We were careful and could not have been more than a mile off in our reckoning. All three of us. .h.i.t it the same."

"Where was the fellow who tried to head us off?" asked Hal.

"When?"

"At any time."

"We located him at various points along the river. No doubt he was on a boat up to the very last when the two were very near together."

"Where was the island operator when he sent his last message? Did you get the one in which he confessed the affair was a hoax?"

"Yes. But he did not send that message. It was sent by the other fellow."

"How do you know?"

"That was plain. Did you not notice his peculiar manner of sending? All three of us noticed that."

"Did you pick up any more from them since then?"

"Not a dot."

Hal then asked the obliging amateur to indicate as nearly as possible the location of the island from which the messages came. The latter did as requested, and Hal marked the point on the chart of the St. Lawrence River carried by the Catwhisker. This closed the wireless interview. Hal promised to report back to the Rockport amateur any further developments of interest and tapped "goodnight" with his key.

"Well, your two main points have been proved, Mr. Perry," Bud announced as all three boys removed the receivers from their ears.

"What are they?" asked the man thus addressed.

"Mathematics and geography."

Mr. Perry smiled.

"Yes," he said "I could hardly have hoped for so remarkable a demonstration of my theory. You boys have solved the geography of this problem with the aid of some very clever mathematics. But what branch of mathematics is it?"

"We didn't do it ourselves," Hal reminded. "It was those three amateurs with their loop aerials."

"Wasn't it more mechanical than mathematical?" Cub inquired meditatively.