substitution on a key text, primarily — is commonly used to make the translation from number to letter difficult: A long message in such a code can be broken by a bit of fiddling, but for short phrases, one must discover the key. If the key is something external, such as the words on a page of a book, decoding a brief message such as the one we were faced with may prove virtually impossible.
In this case the numerals used were not our Arabic ones, but Roman ones, and as they had not been spaced or had their divisions marked, it was sheer guesswork to know whether there were twenty-five separate numbers, or only seven, or some total in between. That is where Holmes and I had left off, as we could make no sense in the number/letter result we had extracted.
I had to make a few basic assumptions in looking at the problem. First of all, I had to assume that she had left it there for us to see and, eventually, understand, that it was not just a means of maddening us with tantalising clues that led nowhere. Second, I had to believe that the key to it lay somewhere in front of me, waiting to be seen. Third,
I assumed that once the key was found, it would unlock the puzzle fairly quickly. If it did not, I would undoubtedly conclude that this was not the correct key and lay it down again. To give an example, it would call for a boneheaded sort of persistence to unravel the Roman numeral series XVIIIXIIIIXXV through all its possible Arabic equivalents into the numbers 18-13-1-25, and then into RMAY, and then finally to unscramble it to MARY, unless the person already knew what she was looking at. No, the key would not give too much difficulty once it was inserted into the lock. Of that I was certain.
If I was right, the key had been found by the still, small daughter of a voice and laid into my dream for me to find. Henry VIII meant nothing to me, but VIII, or base eight, meant a great deal. If human beings had been born with three fingers instead of four opposing their thumbs, we would count by units of eight instead of tens. A one plus a zero would mean eight, 11 would be how we wrote nine, and 20 would be the same as a base ten sixteen. I wrote it out on a piece of paper, the first twenty-six numbers in base eight with the alphabet underneath:
I 2 3 4 5 6 7 10 11 12 13 14 15 16 17 20 21 22 23 24 25 26 27 30 31 32
ABCDEFGHIJKLMNOPQRSTUVWXYZ
I was left with the problem of dividing up the twenty five
Roman numerals into numbers whose letter equivalent said something. Although I knew them by heart now, backwards and forwards, I wrote them out too as a visual aid: xvxvnxxiixi/xxiixx/vxxxi
Twenty-five numerals, ones, fives, and tens. Taken at its most straightforward, these yielded a series of Hs, Es, and As, which would be meaningless. My job was to divide that string up so that the letters made sense.
I began with the first ten numerals, XVXVIIXXII.
That last / might be attached to the following X to make nine, but I should keep that possibility in mind. XVXVI, or 10-5-10-5-1, yielded H-E-H-E-A, which, unless she wanted to show her derisive laughter, made no sense. Taking the first XV as 15 gave me MHEA. X–V-XVII = 10, 5, 17 gave HEO, which was better than the other. Higher numbers gave the greatest variation of the alphabet. I tried using the highest possible numbers I could get from the twenty-five digits, which divided into 15, 17, 22, 12, 22, 24, 31. In base ten this had read OQVLVX. The 31 was a problem because there are only twenty-six letters. However, in base eight that yielded M-O-R-J-R-T-Y. It took me a moment to realise what I was seeing. My pencil reached out by itself and slowly crossed out the figure 12, substituting 11-1, and there it was. MORIARTY.
Moriarty could not have done this. The professor-ofmathematics-turnedcriminal-mastermind had died at the hands of Sherlock Holmes, hurled over a huge falls in Switzerland nearly thirty years before. Why then was his name here? Was our foe telling us that the purpose behind our persecution was revenge for his death? After nearly three decades? Or was there meant to be a parallel between this case and that of Moriarty and Holmes? I do not know how long I sat there in the Bodleian while the light faded outside, but eventually the little daughter of a voice whispered for one last time, and I heard myself, talking to Holmes in my room on the night it all began. 'My maths tutor and I came across some mathematical exercises developed by an old acquaintance of yours, while we were working with problems in base eight theory.' And the whispery voice of Holmes in my ears: 'Professor Moriarty — '
My maths tutor. She was not the owner of the blonde hairs we had found in the cab; her hair was dark and tinged with grey. However, she had laid Professor Moriarty's base eight exercises before me on the very day the bomb appeared at my door and, I knew now, three days later had slashed that string of ciphers with great precision into the seats of our cab. My maths tutor, Patricia Donleavy, who had left because of an unexplained illness beginning that same week. My maths tutor, a strong woman, a mind of great subtlety, one of the teachers I had found to learn from, who had shaped me, whose approval I cherished, with whom I had talked about my life, and about Holmes. 'Another Moriarty,' Holmes had speculated, and she herself had just confirmed it. I pushed the implications from me. My maths tutor.
I looked up blankly to see someone standing beside my desk, a desk openly strewn with photographs, calculations, and the translation. It was one of the old library clerks, looking amused. He had the attitude of someone who has waited to be noticed.
'Sorry, Miss Russell, it's time to close up.'
'Already? Heavens, Mr. Douglas, I had no idea. I'll be with you in a minute.'
'No rush, Miss. I have some tidying to do, but I wanted to let you know before you took root in here. I'll let you out when you come down.'
As I began hastily to insert the pages back into their envelope, a very unpleasant thought came to me. How many other people had glanced onto the desk during the evening? I knew I had been careful to hide the photographs at first, but at what point had I become so engrossed in the mathematical detective work that I had simply not seen who came past? I seemed to remember two first-year men who had been searching for a book, and an old priest who coughed and blew his nose loudly, but who else? I hoped no one.
Mr. Douglas let me out with a cheery 'Night, now' and locked the door behind me. The dark courtyard was deserted but for the statue of Thomas Bodley, and I walked quickly through the entrance arch to the Broad which, conversely, seemed crowded and well-lit, and safe. I walked back to my lodgings, deep in thought. What to do next?
Telephone Holmes, and hope no one was listening in? Send him a coded telegram? I doubted I could devise one quickly, a message Holmes could read and Patricia Donleavy could not. If I went to him, could I do so without alerting my watchers? A sudden movement on my part could endanger Holmes. And where was Miss Donleavy?
How could I find her, and how could we spring a trap on her now?
In the midst of all these whirling thoughts I became aware of some other idea niggling gently at the back of my mind. I stopped dead and tried to encourage it to show itself. What was troubling me? Busy street? No, not even so crowded now. The idea of the telephone? No, wait; back up. Not crowded? The watchers! Where is my watcher? And I saw then that I had not been followed since I left the Bodleian, and I knew immediately what it meant that they had been pulled off me. I clapped my hat to my head and Mr. Thomas looked up startled at the crashing entrance of a breathless undergraduate into his lodge. 'Mr. Thomas, get Holmes on the telephone, I have to talk with him; it's an emergency.' I was grateful that the old man did not pretend he didn't know the name of his unacknowledged employer, merely saw my face and reached for the telephone.
I stood tautly, tapping my fingers on the counter, wanting to scream at the slowness of the thing. Connexions were made, exchanges consulted, and then Mr. Thomas's face became still.
'I see,' he said, and, 'Thank you.' He hung up and looked at me.
'The telephone lines seem to be down on that side of Eastbourne,' he said. 'Some kind of accident on the road, apparently. Can I do anything, Miss?'
'Yes. You can go around the corner and tell the garage to get my motor out. I'll be there in a few minutes.'
With surprising agility Mr. Thomas ducked out the door, leaving his post unattended, and I pounded off up the stairs. I had the key in my hand before I cleared the last stair, reached for the keyhole, and stopped. There, in the middle of the shiny brass knob, was a black, greasy smudge.
'Holmes?' I whispered, 'Holmes?' and flung open the door.
