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 compasses 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 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 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 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 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 nobody there, how are we going to know it's the right one?"
This hit 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 anticipating 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 indorsement 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.