"I haven't the faintest idea," he acknowledged gloomily. "I've overdrawn my allowance already several hundreds. The mater is as poor as a church mouse and I simply daren't ask my Uncle Ravenor, though he's as rich as Croesus. He might disinherit me." We reached the house and stole softly up the back stairs to our rooms. Cecil threw himself, dressed as he was, upon the bed. But I was in no humour for sleep, and after a cold bath I dressed and got downstairs in time for breakfast. To my surprise, de Cartienne was in the morning-room, carefully dressed as usual and with no sign in his appearance or manner of having been out all night. He was chatting lightly with Dr. Randall about some trivial matter connected with the meeting which the latter had attended the previous evening. "Cecil is late again," remarked the doctor, with a frown, as we began breakfast. "James, go to Lord Silchester's room and ask him how long he will be." James retired and reappeared in a few minutes with a grave face. "Lord Silchester desires me to beg you to excuse him this morning," was the message which he brought back. "He has a very bad headache and has had no sleep." Dr. Randall, who was one of the kindest-hearted men breathing, looked compassionate. "Dear me!" he said. "I'm very sorry to hear that! Certainly we will excuse him. Will he have anything sent up?" "A cup of tea, sir, only. I have ordered it in the kitchen." "Poor fellow! It's strange how he suffers from these attacks! I'm afraid he can't be very strong," remarked the doctor absently, as he buttered himself a piece of toast. de Cartienne and I exchanged glances, but we said nothing. Directly after breakfast the doctor took us into the study and we began the morning's labours. It happened that, in working out a series of algebraic questions, de Cartienne and I used a great deal of paper, and when the doctor looked for a piece to explain the working of a rather stiff quadratic, the rack was empty. "Have either of you a piece of wastepaper in your pockets?" he asked. "The back of an envelope, or anything will do. I see it is lunch-time, so it is scarcely worth while sending for any." I felt in all my pockets, but they were empty. de Cartienne drew an envelope from his pocket and handed it to the doctor. The moment he had parted with it, however, I saw him give a sudden start and he seemed as though about to make an effort to regain possession of it. But he was too late, for the doctor was already fast covering it with figures. de Cartienne quitted his seat and stood looking over his shoulder, probably hoping that I should do the same. But I remained where I was, taking care to manifest my interest in the problem by asking frequent questions. The moment the doctor had finished his rapid figuring and solved the equation, I stretched out my hand for it eagerly. "May I see it, sir?" I begged. "I fancy you've made a mistake in the values." He handed it across the table at once, with a quiet smile.