lever 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
biggest factor in all mechanics. Bud, I thought from the way you spoke
that you grasped the situation completely. Can't you help Bob and Hal
out? By means of what branch of mathematics was that island of our
Canadian Crusoe located?"

"Geometry," replied Bud confidently.

Cub snapped his finger with an impatient jerk of his long right arm.

"Of course!" he exclaimed in disgust. "Every branch of mathematics I ever
heard of, except geometry, went buzzing through my head. I was trying to
recall something in algebra that would fit this case."

"Oh, Cub," laughed Hal; "algebra is all x's and y's and z's over z's and
y's and x's,"

"I admit I'm a chump," Cub grinned with a shrug of self-commiseration;
"but say, let's draw those geometrical lines on our chart and see if we
get the same result those radio compass fellows got."

Cub produced the chart and a hand-book diagram of a mariner's compass
about three inches in diameter. Fortunately the chart was made of thin,
vellum-like paper, almost transparent, so that when laid over the
diagram, the minute points of the compass, indicated with clear black
lines, could be seen through. First the dot representing the town of
Clayton was placed over the point at the center of the compass, with the
north and south line of the compass exactly coinciding with the meridian
of the town. Then Cub traced on the chart lightly with a pencil the
47-1/2-degree northeast line of the compass. Next he performed a similar
operation with the center of the diagram over Rockport and next with the
center of the diagram over Gananoque, following instructions in each of
these cases with reference to the direction lines to be drawn. The result
was that the intersection of the three lines was at approximately the
point indicated by the Rockport amateur.

"Now we're ready to continue our search," Cub announced.

"That's pretty good progress, I must say," Bud declared; "but here's a
new question to get us into trouble again."

"Oh, for goodness sake, don't," pleaded