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.
"Those radio compasses make me think of a surveyor's instrument."

"Oh, pshaw, my boy, don't spoil everything," pleaded the last speaker's
father. "I'm afraid you've missed the big point. Mathematics is the