to show you what I mean," said Sam, taking a stick and
drawing in the sand a figure like this:

[Illustration]

"There," said Sam, "that's a right angled triangle, but you may call
it a thingimajig if you like; it doesn't matter about the name.
Suppose we start at the top to go to the left hand lower corner; don't
you see that it would be further to go straight down to the right hand
lower corner and then across to the left hand lower corner, than to go
straight from the top to the left hand lower corner."

"Certainly," replied Billy, "it's just like going cat a cornered
across a field."

"Well," said Sam, pointing with his finger, "if I were to draw a
triangle here on the map beginning at camp Jackson and running due
south to the line of Pensacola, and then due west to Pensacola itself,
with a third line running 'cat a cornered' as you say, from camp
Jackson straight to Pensacola, the line due south would be about a
hundred and ten miles long and the one due west about fifty miles
long, while the 'cat a cornered' line would be about a hundred and
twenty five miles long."

"How do you find out that last,--the cat a cornered line's length?"
asked Tom.

"I can't explain that to you," said Sam, "because you haven't studied
geometry."

"Oh well, tell us anyhow, if we don't understand it," said Sid
Russell, who sat with his mouth open.

"Sid wants to find out how to tell how far it is from his head to his
heels, without having to make the trip when he's tired," said Bob
Sharp, who was always poking fun at Sid's long legs.

"Well," said Sam smiling, "I know the length of that line because I
know that the square described on the hypothenuse of a right angled
triangle is equal to the sum of the squares described on the other two
sides."

"Whew! it fairly takes the breath out of a fellow to hear you rattle
that off," replied Sid.

"Come," resumed Sam, "we aren't getting on with what we undertook. Now
look and listen. Here is the line we would follow if we could go
straight from Camp Jackson to Pensacola. If we could follow it, I
would only have to guess how many miles we march each day, and mark it
down on the map. But we can't go straight, because of swamps and
creeks and canebrakes, so I must keep looking at my compass to find
out what direction we do go; then I mark on the map the route we have
followed each day, and the distance, and each night's camp gives me a
new starting point."

"Yes, but Sam," said T