4. Mr. F——, of Brooklyn, New York, writes: "I was studying algebra, in which I was quite interested, and had an example to do in six unknown quantities. I worked at it in the evening, and after an hour or two gave it up and went to bed. That night I dreamed the way to do it was so-and-so, and arrived at the right answer. On awakening in the morning I tried it before I got up, and, following the way suggested in the dream, got the correct answer."
5. Mrs. B——, of New York city, writes: "In guessing double acrostics, of which I am very fond, I often carry a question on in my mind without giving it any particular attention, until at last the answer suddenly occurs to me."
6. Mr. F——, of Westerly, Rhode Island, writes: "Have worked out many algebraic or geometrical problems during sleep. Have, when some years ago in Worcester Academy, scanned some fifty or seventy-five lines of Virgil, not yet translated, except ten or fifteen, felt tired, went to bed, in sleep accurately translated all of it, and remembered it on waking,"
7. Mrs. B——, of New York city, writes: "In reading a difficult language, I read the text over without attempting to translate, getting as much of the sense as this perusal may give; then I leave it for a few hours and return to it later, to find its difficulties solved—this is not the case when the second follows directly on the first."
8. Dr. S——, of New York city, writes: "I remember, when in college, having been engaged all the evening in working on a geometrical problem and going to bed with it unsolved; having an uneasy sleep, in which I dreamed of geometrical figures and of working with them; and, on awaking in the night, the solution of the problem suggested itself to my mind, which solution I remembered and found correct next day."
9. Mrs. X——, of Paterson, New Jersey, writes: "Have played a game of whist in my sleep and deplored the mistakes I have made while awake; gone over the whole game, replayed it in sleep, with much better results and to my entire satisfaction."
The following cases belong to the same class, and demonstrate that perception in consciousness often occurs long after the perception of the fact has been fully grasped by the individual unconsciously. The discussion of the relations of consciousness to unconsciousness will appear later:
10. Mr. B—— (a Frenchman) writes as follows: "I once received a French letter from Paris, describing a race, and ending with the English words, "O how I am sorry!" I could not decipher the words when awake, but it came to me in sleep as it was written, and I made it out perfectly then."
11. Mrs. D—— writes as follows: "On one occasion, having written a note, I received a note which conveyed to my mind the idea that the writer had entirely misunderstood my communication. I fell asleep