“You won’t do anything of the kind,” I exclaimed.  “I am as keen on plotting them as you are, and, besides, I want to see how it is done.  It seems to be a rather useful accomplishment.”

“It is,” said Thorndyke.  “In our work, the ability to make a rough but reliable sketch survey is often of great value.  Have you ever looked over these notes?”

“No.  I put the book away when I came in and have never looked at it since.”

“It is a quaint document.  You seem to be rich in railway bridges in those parts, and the route was certainly none of the most direct, as you noticed at the time.  However, we will plot it out and then we shall see exactly what it looks like and whither it leads us.”

He retired to the laboratory and presently returned with a T-square, a military protractor, a pair of dividers and a large drawing-board on which was pinned a sheet of cartridge paper.

“Now,” said he, seating himself at the table with the board before him, “as to the method.  You started from a known position and you arrived at a place the position of which is at present unknown.  We shall fix the position of that spot by applying two factors, the distance that you travelled and the direction in which you were moving.  The direction is given by the compass; and, as the horse seems to have kept up a remarkably even pace, we can take time as representing distance.  You seem to have been travelling at about eight miles an hour, that is, roughly, a seventh of a mile in one minute.  So if, on our chart, we take one inch as representing one minute, we shall be working with a scale of about seven inches to the mile.”

“That doesn’t sound very exact as to distance,” I objected.

“It isn’t.  But that doesn’t matter much.  We have certain landmarks, such as these railway arches that you have noted, by which the actual distance can be settled after the route is plotted.  You had better read out the entries, and, opposite each, write a number for reference, so that we need not confuse the chart by writing details on it.  I shall start near the middle of the board, as neither you nor I seem to have the slightest notion what your general direction was.”

I laid the open notebook before me and read out the first entry: 

“’Eight fifty-eight.  West by South.  Start from home.  Horse thirteen hands.’”

“You turned round at once, I understand,” said Thorndyke, “so we draw no line in that direction.  The next is—?”

“‘Eight fifty-eight minutes, thirty seconds, East by North’; and the next is ‘Eight fifty-nine, North-east.’”

“Then you travelled east by north about a fifteenth of a mile and we shall put down half an inch on the chart.  Then you turned north-east.  How long did you go on?”

“Exactly a minute.  The next entry is ‘Nine.  West north-west.’”

“Then you travelled about the seventh of a mile in a north-easterly direction and we draw a line an inch long at an angle of forty-five degrees to the right of the north and south line.  From the end of that we carry a line at an angle of fifty-six and a quarter degrees to the left of the north and south line, and so on.  The method is perfectly simple, you see.”