How Sherlock Holmes solved the Musgrave Ritual

That's an English elm.

Sherlock Holmes suspects a missing persons case involves a mysterious ritual passed on from father to son for centuries. But though a document with the ritual still exists, its meaning has been lost.

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from "The Musgrave Ritual"
by Sir Arthur Conan Doyle

Warning: Text in public domain, but crappy transcription.
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[Lord Musgrave] "handed me the very paper which I have here, Watson, and this is the strange catechism to which each Musgrave had to submit when he came to man's estate. I will read you the questions and answers as they stand.

"'Whose was it?'

"'His who is gone.'

"'Who shall have it?'

"'He who will come.'

"'Where was the sun?'

"'Over the oak.'

"'Where was the shadow?'

"'Under the elm.'

"How was it stepped?'

"'North by ten and by ten, east by five and by five, south by two and by two, west by one and by one, and so under.'

"'What shall we give for it?'

"'All that is ours.'

"'Why should we give it?'

"'For the sake of the trust.'

"'The original has no date, but is in the spelling of the middle of the seventeenth century,' remarked Musgrave. 'I am afraid, however, that it can be of little help to you in solving this mystery.'

. . .

"I was already firmly convinced, Watson, that there were not three separate mysteries here, but one only, and that if I could read the Musgrave Ritual aright I should hold in my hand the clue which would lead me to the truth concerning both the butler Brunton and the maid Howells. To that then I turned all my energies. Why should this servant be so anxious to master this old formula? Evidently because he saw something in it which had escaped all those generations of country squires, and from which he expected some personal advantage. What was it then, and how had it affected his fate?

"It was perfectly obvious to me, on reading the ritual, that the measurements must refer to some spot to which the rest of the document alluded, and that if we could find that spot, we should be in a fair way towards finding what the secret was which the old Musgraves had thought it necessary to embalm in so curious a fashion. There were two guides given us to start with, an oak and an elm. As to the oak there could be no question at all. Right in front of the house, upon the left-hand side of the drive, there stood a patriarch among oaks, one of the most magnificent trees that I have ever seen.

"'That was there when your ritual was drawn up,' said I, as we drove past it.

"'It was there at the Norman Conquest in all probability,' he answered. 'It has a girth of twenty-three feet.'

"'Have you any old elms?' I asked.

"'There used to be a very old one over yonder but it was struck by lightning ten years ago, and we cut down the stump.'

"'You can see where it used to be?'

"'Oh, yes.'

"'There are no other elms?'

"'No old ones, but plenty of beeches.'

"'I should like to see where it grew.'

"We had driven up in a dogcart, and my client led me away at once, without our entering the house, to the scar on the lawn where the elm had stood. It was nearly midway between the oak and the house. My investigation seemed to be progressing.

"'I suppose it is impossible to find out how high the elm was?' I asked.

"'I can give you it at once. It was sixty-four feet.'

"'How do you come to know it?' I asked, in surprise.

"'When my old tutor used to give me an exercise in trigonometry, it always took the shape of measuring heights. When I was a lad I worked out every tree and building in the estate.'

"This was an unexpected piece of luck. My data were coming more quickly than I could have reasonably hoped.

"'Tell me,' I asked, 'did your butler ever ask you such a question?'

"Reginald Musgrave looked at me in astonishment. 'Now that you call it to my mind,' he answered, 'Brunton did ask me about the height of the tree some months ago, in connection with some little argument with the groom.'

"This was excellent news, Watson, for it showed me that I was on the right road. I looked up at the sun. It was low in the heavens, and I calculated that in less than an hour it would lie just above the topmost branches of the old oak. One condition mentioned in the Ritual would then be fulfilled. And the shadow of the elm must mean the farther end of the shadow, otherwise the trunk would have been chosen as the guide. I had, then, to find where the far end of the shadow would fall when the sun was just clear of the oak."

"That must have been difficult, Holmes, when the elm was no longer there."

"Well, at least I knew that if Brunton could do it, I could also. Besides, there was no real difficulty. I went with Musgrave to his study and whittled myself this peg, to which I tied this long string with a knot at each yard. Then I took two lengths of a fishing-rod, which came to just six feet, and I went back with my client to where the elm had been. The sun was just grazing the top of the oak. I fastened the rod on end, marked out the direction of the shadow, and measured it. It was nine feet in length.

"Of course the calculation now was a simple one. If a rod of six feet threw a shadow of nine, a tree of sixty-four feet would throw one of ninety-six, and the line of the one would of course be the line of the other. I measured out the distance, which brought me almost to the wall of the house, and I thrust a peg into the spot. You can imagine my exultation, Watson, when within two inches of my peg I saw a conical depression in the ground. I knew that it was the mark made by Brunton in his measurements, and that I was still upon his trail."