evidently
addressed to the operator he had just "crowded out," "I am at Rockport
and am one of the three radio compass 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 hit 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 c