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Musgrave Ritual (1893)
Sir Arthur Conan Doyle
(click on names to see more mathematical fiction by the same author)

A tiny bit of mathematics is used by Sherlock Holmes to solve this mystery. In it, he ties together the disappearance of a housemaid, the discovery of the dead body of the chief butler and a strange poem which the head of each generation is required to pass on to his son by family tradition. As it turns out, the poem is the key to finding a hidden treasure that one of the Musgrave anscestors sought to protect and geometry (see note below) is required to work out the location that the tip of a tree's shadow would have occupied at the time the ritual was written.

Contributed by Tom O'Brien

Your description says that Holmes used trigonometry to work out the location of the tip of the shadow. Not so. He used geometry. By measuring the length of the shadow of a known length, he determined what would have been the length of the shadow of a tree that had been lost to a lightning strike. He used the theorem of similar triangles. He never measured or calculated an angle.

Ah, you are right! I stand corrected, as is the comment to which you referred. Thank you, Mr. O'Brien. In fact, to avoid any further confusion, the exact passage in question from the original story is reproduced below for your perusing pleasure:

(quoted from Musgrave Ritual)

"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.

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Works Similar to Musgrave Ritual
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. The One Best Bet by Samuel Hopkins Adams
  2. Adventure of the Final Problem by Sir Arthur Conan Doyle
  3. The Valley of Fear by Sir Arthur Conan Doyle
  4. The Problem of Cell 13 by Jacques Futrelle
  5. The Image in the Mirror by Dorothy Leigh Sayers
  6. The Ingenious Mr. Spinola by Ernest Bramah
  7. Who Killed the Duke of Densmore? by Claude Berge
  8. Death and the Compass (La Muerte y La Brujula) by Jorge Luis Borges
  9. Mirror Image by Isaac Asimov
  10. Conned Again, Watson! Cautionary Tales of Logic, Math and Probability by Colin Bruce
Ratings for Musgrave Ritual:
RatingsHave you seen/read this work of mathematical fiction? Then click here to enter your own votes on its mathematical content and literary quality or send me comments to post on this Webpage.
Mathematical Content:
1.67/5 (3 votes)
Literary Quality:
3.75/5 (4 votes)

MotifSherlock Holmes,
MediumShort Stories, Available Free Online,

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