"Yes, that is the place we're going to, and presently I'll tell you what we're going for; but one thing at a time. You see the course is a little west of south, nearly but not quite southwest. The distance, in an air line is about a hundred and twenty-five miles: that is to say Pensacola is about a hundred and ten miles further south than camp Jackson, and about fifty miles further west."
"That would be a hundred and sixty miles then," said Billy Bowlegs.
"Yes," replied Sam, "it would if we went due south and then due west, taking the base and perpendicular of a right angled triangle, instead of its hypothenuse."
"Whew, what's all them words I wonder," exclaimed Billy.
"Well, I'll try to show you what I mean," said Sam, taking a stick and drawing in the sand a figure like this:
"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.