“No,” replied the Chairman, “of course not, and that is just where the most interesting part of the operation comes in. I have shown you how to measure the height of your lighthouse in degrees along the edge of a circumference; and now we must find out how to measure the distance of the lighthouse, or the radius of the circle, from the center where we are standing, to the point in the circumference where the lighthouse stands.”
Dick looked up with interest and said, “I don’t see, sir, how that can be done, because we want the distance in miles or yards, and there is nothing to show us the number of miles or yards in a degree.”
“That’s true,” said the Chairman, “but happily for us, some old fellow a long time ago had a bright idea. He knew that, in every circle, the length of the radius is always in the same proportion to the length of the circumference, and so he laid out a line equal in length to the radius along the circumference, and found that it was equal to a little more than 57 degrees. Supposing, then, that you found your lighthouse to be four degrees above the horizon, you could then calculate what fraction of the length of the radius the height of your tower is by finding the number of times that four is contained in 57. Let me see,—that would be about 14 1/4, wouldn’t it?”
“I guess so, sir,” said Dick.
“Now,” continued the Chairman, “if your lighthouse is 300 feet high, this 300 feet will be the same part of the distance as 4 degrees is of 57 degrees. But 4 goes into 57, 14 1/4 times; therefore, the length of the distance will be 300 feet × 14 1/4, which is 4,275 feet, or about four-fifths of a mile.”
“Oh, I see,” cried Dick, “but how do we find out the height of the lighthouse?”
“That’s a good question,” said the Chairman; “we can’t find the distance unless the height is given, and for that reason the heights of lighthouses and other conspicuous objects are usually given on the charts. But, if we knew our distance from the lighthouse, we could easily find its height by similar reasoning.”
Just then the Captain, who had been writing at the cabin table, looked up and said: “I’ll show you the chart, Gray—I don’t just remember the height of ‘Whale’s Back’,” and he reached out for the chart of Portsmouth Harbor, which was rolled up in its place on the cabin bulkhead. When he had unrolled it he showed Dick the figures.
“Thank you, sir,” said Dick. “Mr. Chairman, is there any time when you’d like me to report about this?”
“Come and speak to me, right after ‘colors’,” replied the Chairman.