"Forty-five minutes would be better."

  "Right. I'll call for a cab."

  We had a pleasant dinner, Dorothy found a friend to flirt with, and we went to the recital. It was an informal affair, mostly Bach, which has the beauty and cadence of a well-balanced mathematical formula, particularly when played on the harpsichord. The symmetry and nobility of the master's music, together with a glass of the champagne served afterwards, calmed my nerves, and I found myself in bed before midnight, a rare occurrence in the past few months.

  It was, I think, about three in the morning when I jerked up in my bed, my pulse thudding thickly in my ears, my breath coming as fast as if I had sprinted upstairs. I had been dreaming, not the Dream, but a confusing mixture of things real and imagined. A shadowy face had leered at me from the bookshelf in the corner, half-hidden by blonde hair, and held out a clay pipe in a twisted hand. "You know nothing!" the figure cackled in a voice both male and female, and laughed horribly. His/her gnarled fist tightened over the pipe, which I knew to be one of Holmes', and then opened.

  Shards bounced slowly about the floor. I stared despairingly at the shattered pipe and knelt down to retrieve the pieces, in hopes of glueing it together again. Some of the larger bits had rolled underneath the bookshelf, and I had to lie down to reach them. As I felt around, my hand was suddenly seized, and I shot upright in terror with a fading image of the bookshelf in my mind's eye. It had been a section of history, the titles all on Henry VIII.

  I groped for a light and my spectacles and lay back until my cold sweat dried and my heart no longer pounded in my chest. I knew that I could never get back to sleep after that, so I reached for my dressing gown and went to make myself a cup of tea.

  In a few minutes I was sitting, inhaling the comforting steam, and thinking about the nightmare. It was very rare for me to be aware of dreams, other than the Dream, and I could not remember having another nightmare since my family had died. What was the purpose behind this one?

  Some of its elements were obvious, but some were not. Why, for example, was the hidden blonde both male and female, when I invariably thought of my adversary as female?

  The smashed pipe was an easily understood image of my intense, nearing frantic anxiety about Holmes, and bookshelves were such a part of my life that I could hardly imagine any part of me, even a dream, omitting them. But why were the books on history? I held no great passion for recent history, and due to my erratic schooling English history was a relative stranger. What was King Henry doing in front of my eyes? That obscene, gout-ridden old man with his numerous wives, all of them sacrificed to his desire for sons, as if it were their fault and not that of his own syphilitic self. What would Freud make of that dream, I wondered, with Holmes falling beneath the misogynist king, to the echoes of a man/woman's laughter? It was the sort of thing that would have made Dr. Leah Ginzberg lean forward in her chair with a Germanic "Ja, and then?" I sighed into the silent room and reached for my books. If I had to be up at three o'clock in the morning, I might as well make some use of it, Henry VIII or no. I settled myself to work, but all morning the dream kept intruding, and I would find myself staring blankly at the wall in front of me, seeing the spines of those books. Henry VIII. What did that mean?

  I worked on, and in the afternoon I went out to take coffee in the covered market before an afternoon lecture, and I ended up ordering a large meal I had not known I wanted until I had walked into the tantalising smell of frying bacon. Two meals, actually, and pudding — more food than I had taken at one sitting at any time since Mrs. Hudson had been feeding me.

  Somewhat bloated, I left the market stalls and walked up Turl Street for the afternoon lecture, only to find my steps slowing as I approached the Broad. I stopped. Henry VIII. When in ignorance, consult a library. With few qualms I abandoned the enquiry into Second Dynasty Burial Texts and turned right instead of left. (The familiar loitering and overaged undergraduate behind me emerged from a shop entrance and followed me up Broad Street and past the Sheldonian, but not through the doors of the library.)

  I called up several books on the period, but they bore no resemblance to my dream image, and leafing slowly through them caused no bells to go off in my mind. Knowing it was hopeless, I retrieved the photographs, laid them out on the desk in front of me, and it was then that the voice spoke to me, and I knew.

  Holmes and I had discussed the possibility that the series was based on a number/letter substitution code, in which, for example, I might be read as A, 2 as B, and 3 1–2 translates as CAB. Extreme complexity — basing the 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.

  SEVENTEEN: Forces joined

  The enterprise is hopeful, but full of hardship and danger, it would seem to have been conceived by some sovereign intelligence, that was able to divine most of our desires.

  "It's a good thing there wasn't another bomb here, Russell. There wouldn't be much left of you." It was the old priest from the library, sitting in my chair and peering at me with disapproval over his spectacles.

  "Oh, God, Holmes, it is good to see you." To this day he swears that I thrust his head between my breasts, but I am quite certain that he was on his feet by the time I reached him. I was reassured that his musculature had not suffered during his weeks of confinement and enforced sloth, and in fact felt distinctly bruised about the rib cage from the force of his arms. He of course denies this.

  "Holmes, Holmes, we can talk again, it's over, I know who she is, but I thought she had you, my watchers disappeared and your telephone line is out, and I was coming up here to get the revolver and drive down to Sussex, but you're here, and — "

  Fortunately Holmes interrupted this drivel.

  "Very well, Russell, I am flattered that you seem relieved to see me alive, but could you be a bit clearer please, particularly concerning the telephone line and the watchers?"

  He reached up to reattach his beard, and I stooped to pick up an eyebrow from the floor and absently handed it to him. "I've been working in Bodley this afternoon — "

  "Oh for God's sake, Russell, don't be completely daft. Or has my absence softened your brain?"

  "Oh, of course, you were there. Why didn't you make yourself known then?"

  "And have a scene like this in the midst of those hallowed halls? I thought you might wish to work there again in the future, so I came here to wait for you. I could also see you were on the edge of something and didn't want to risk knocking it out of your head. I did blow my nose loudly in your ear, if you remember, but when that failed to get your attention I took the hint and left. What did you find? I could see that you were working on the Roman numerals theory, but without peering too closely I couldn't see where your thoughts were taking you."

  "Yes, Holmes, it was a code. Roman numerals in a base eight, not base ten. It spelt Moriarty. And do you know who had me working on base eight three days before the bombs were set?"

  "I do remember, yes, your maths tutor. But how does — "

  "Yes, and she even told me of Moriarty's exercises, though not directly, of course, just mentioned offhand that she had seen some problems in a book and — "

  "Ah, I see now. Yes, of course."

  "Of course what?"

  "Your maths tutor is a woman. I might have known."

  "Didn't you know? I thought I told you. But she's not blonde, you see, so — "

  "And where is she now? Kindly quit blithering, Russell.

  I should greatly enjoy catching this woman if she is so kind as to walk into our trap, so I shouldn't have to spend the rest of my life dodging bombs and pretending to detest the very mention of your name." "Oh. Yes. But she is. I mean, she withdrew my watchers today while I was in the library. She may have guessed what I was doing, or she may have just decided to go ahead, but the telephone lines to the village are down, so I thought — "

  "Right you were, Russell, and that means we must fly. Can you put on some more sensible clothing? There may be rough work ahead of us."

  I plunged into the next room and into my young man's mufti in two minutes flat, and in another thirty seconds had my boots on and the gun and a handful of bullets in my pocket.

  The two of us created quite a sensation clattering down the stairs. The hypochondriac down the hall had just come out of the bathroom when we came running towards her. She screamed and clutched her dressing gown to her chest as we flew past.

  "Men! Two men in the hall!"

  "Oh, for God's sake, Di, it's me," I shouted ungrammatically.

  She leant over the stairwell with several others to watch our descent. "Mary? But who's that with you?"

  "An old friend of the family!"

  "But it's a man!"

  "So I noticed."

  "But men aren't allowed in here!" Their protests faded above us.

  "Russell, I must use Mr. Thomas's telephone — Ah, here he is. Pardon me, Thomas."

  "I beg your pardon, reverend sir, may I help you? Miss

  Russell, who is this? Please, sir, what do you want? Sir, the telephone is not for public use. Sir — "

  "Mr. Thomas, is my car ready?" I interrupted while Holmes awaited connexion.

  "What? Ah, yes, Miss, they said they would bring it out for you. Miss, who is this gentleman?" "A friend of the family, Mr. Thomas. Dear me, I hear

  Dianne at the top of the stairs. Do you think you should perhaps see what she wants? You know how highly strung she is. No, Mr. Thomas, you go help her; I'll show this friend of mine out. Yes, friend of the family. Very old. Yes.

  Good-bye, Mr. Thomas, I'll not be back in tonight."

  "Or tomorrow night," shouted Holmes. "Come, Russell!"

  The car was warmed up and running at the kerb, and the garage man quickly got out when he saw us coming, then paused with his hand on the door.