"Those radio compa.s.ses 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 compa.s.s fellows got."
Cub produced the chart and a hand-book diagram of a mariner"s compa.s.s 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 compa.s.s, 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 compa.s.s, with the north and south line of the compa.s.s 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 compa.s.s. 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 Cub. "You"ve had your example of what my mathematical dad can do with such foolish creatures."
"Let him express his doubt," suggested Mr. Perry with a smile; "for, if a man must doubt, he"d better shout than smother his ideas in a skeptic pout."
"Yes, get it off your chest, Bud, and then take your medicine,"
advised Hal.
"Well, suppose we find the island and n.o.body there, how are we going to know it"s the right one?"
This. .h.i.t the other two boys pretty hard. The possibility of such a situation had not occurred to either of them. However, Cub preferred to take it in lighter vein, for he replied:
"By his footprints on the sandy beach. You mustn"t have a Crusoe Island without some footprints, you know."
"The trouble is you"re antic.i.p.ating too rapidly, Bud," Mr. Perry advised.
"Columbus would never have discovered America in that frame of mind."
"All right, I"ll change the frame," said Bud. "We"ll just go ahead and see what we shall see."
"We"ve got to go ahead if Hal"s cousin is in peril," declared Cub.
"Do you really believe the Crusoe boy is your cousin, Hal?" asked Bud.
"Of course that"s hard to believe, but the evidence points in that direction," Hal replied.
"At least if he is your cousin, we know now that he wasn"t making monkeys out of us, as that last message, supposed to come from him, made it appear he was doing," Cub admitted.
"Yes," put in Mr. Perry; "it looks now as if he was telling a straight story all along."
"If that"s true, then he"s probably in serious trouble right now," said Hal.
"Probably a prisoner in the hands of robbers, if not worse," Bud supplemented.
"Let"s go to bed at once and get a good night"s rest so that we will be in condition to put forth our best efforts to find him and rescue him in the morning," proposed Mr. Perry.
This proposal met with indors.e.m.e.nt from all, and in a short time they were in their berths, employing their best skill to induce sleep under condition of much mental excitement.
CHAPTER X
The Island-Surrounded Island
Early next morning the Catwhisker left its mooring under the tamarack and started on the new search for the "Canadian Crusoe"s" island.
Guided by the "mathematical chart" prepared with the directions given by the radio-compa.s.s amateur, the crew of the motor boat had little difficulty in finding the approximate location of the island prison; but when arrived there, they realized that considerable work was still before them, for they were in the midst of a veritable sea of islands, varying in size from a few car-loads of stone and earth to several acres in extent.
"Well, how are we goin" to begin?" asked Hal as Cub stopped the engine in a pond-like expanse, surrounded by a more or less regular rim of islands.
"The first thing to do, I should say is to make the best possible reckoning of our bearings and then try to fix the point of intersection of those three lines indicated by the radio compa.s.ses," said Mr. Perry.
"That"s right," Cub agreed. "We mustn"t forget our mathematics."
"It seems to me that we ought to be able to pick this place on the chart," Bud suggested.
"Yes, especially if we keep in mind the location of some other landmarks, or watermarks, that we pa.s.sed in the last half or three-quarters of an hour in getting here," said Hal.
Cub produced the chart, and the study of locations and island arrangements began. As indicated by expectations in the course of their discussion, they were able to locate a few of the larger islands and with these as bases for further reckoning, they at last picked out what seemed to be the point of intersection of the three pencil lines on the chart.
This necessitated a little more cruising about, but within an hour after their first stop they completed their reckoning.
"There"s the island that seems to come nearest to the intersection,"
said Mr. Perry, pointing toward an abrupt elevation, a hundred yards long and half as wide and covered with bushes and a few small trees; "but it doesn"t seem to answer the description very well. No other islands near it."
"I don"t see how anybody could be marooned on that place with boats pa.s.sing back and forth near it every hour of the day," Hal commented skeptically.
"Neither do I," Bud agreed.
"Well, let"s do our work thoroughly anyway," Mr. Perry suggested.
"Shall we go ash.o.r.e and look that place over?" asked Hal.
"Sure."
"But what do you expect to find?" Cub inquired.
"I don"t expect to find anything. I had no expectation when I suggested that you boys canva.s.s the radio field for information to clear up what you chose to call a mystery. I had no idea what might turn up as a result of such canva.s.s, but I know it was about the only thing for you to do to start a move in the desired direction."
"And something sure did move," Hal remarked appreciatively.