417 B. Some striking cases in which, during sleep, complex inferences have been drawn, from data presumably present to the waking mind, with more than waking intelligence, were recorded by Professor W. Romaine Newbold, of the University of Pennsylvania, in a paper entitled "Sub-conscious Reasoning," in the Proceedings S.P.R., vol. xii. pp. n-20, from which I give the following extracts: -

The first case (says Professor Newbold) was given me by my friend and colleague, William A. Lamberton, Professor of Greek in the University of Pennsylvania, and I transcribe his own written statement.

"I went to the Lehigh University in the fall of 1869 as instructor in Latin and Greek. My spare time, however, partly as the result of old leanings of my undergraduate days, partly in consequence of a somewhat intimate companionship that sprang up between me and the instructor in mathematics, after a few months came to be given almost entirely to mathematics. I then made acquaintance for the first time with the pleasures of descriptive geometry; I may say here that this branch of mathematics has a more direct tendency towards quickening the power of mentally picturing bodies and lines in space than any other part of mathematics that can be called elementary. I mention this here because it may have some bearing upon the experience now to be related.

"Outside of this study of descriptive geometry, my mathematical work was entirely algebraic and analytic. I soon began to try my hand at certain problems. Somewhere in the spring, I think it was, of 1870, I attacked this problem: Given an ellipse, to find the locus of the foot of the perpendicular let fall from either focus upon a tangent to this ellipse at any point. I endeavoured to solve this analytically, starting from the well-known equations of the tangent to an ellipse, and of a perpendicular to a given line from a given point. No thought of attempting a geometrical solution ever entered my head. After battling with these equations for a considerable time - it was over a week and may have been two weeks - I came to the natural conclusion that I was bogged, and that all my efforts, if continued, would only sink me deeper in the bog; the proper thing to do was to call a halt, dismissing the problem as far as possible from my thoughts, and after some time, when my mind had got completely free from it, to return to it afresh, when, I had no doubt, a few minutes would put me in possession of the solution. This I did absolutely and with success.

After about a week, I woke one morning and found myself in possession of the desired solution under circumstances to me strange and interesting, so much so that the impression of them has never died away, or even, so far as 1 can say, become dim or altered in any way. First: the solution was entirely geometrical, whereas I had been labouring for it analytically without ever drawing or attempting to draw a single figure. Second: it presented itself by means of a figure objectively pictured at a considerable distance from me on the opposite wall. Now, although I have been able, and have been so for years, to picture to myself a geometrical figure - even moderately complicated - and use it for solution of a geometrical problem without external lines being drawn, such figures have sensationally for me a distinct location in myself, viz., in the eye itself; they are never, so far as I know, externally presented. This, however, was distinctly external. The room that I occupied had once been a recitation room. It was a long room, running east and west, with two windows on the south side, one in the south-east corner. The north wall had once been partially occupied by a long blackboard, set in the wall and surrounded by a moulding.

The blackboard surface was simply a blackened - possibly slated - portion of the wall itself. This had been painted over, but the black showed through the white paint and the moulding was still there; so that, apart from the tradition, with which I was familiar, the fact of a blackboard having been there was perfectly clear and evident. My bed was so placed between the windows on the south and the north wall, that on opening my eyes in the morning the first thing I would be likely to see was the blackboard surface. On opening my eyes on the morning in question, I saw projected upon this blackboard surface a complete figure, containing not only the lines given by the problem, but also a number of auxiliary lines, and just such lines as without further thought solved the problem at once. Both foci were joined with the point of contact of the tangent: the perpendicular was prolonged beyond its point of intersection with the tangent till it met the line from the other focus through the point of contact with the ellipse; a line was drawn from the centre of the ellipse to the foot of the perpendicular, and, lastly, the locus, a circle on the major axis of the ellipse as diameter, was drawn.

I sprang from bed and drew the figure on paper; needless to say, perhaps, that the geometrical solution being thus given, only a few minutes were needed to get the analytical one.

"W. A. Lamberton".

Professor Newbold continues: -

Professor Lamberton has showed me his note-book containing the statement of the problem and the analytical solution. He is unable to find the contemporary drawing above mentioned, and no contemporary account is forthcoming. It is possible that some of the details of the phenomenon have become obscured in the lapse of twenty-five years, but the essential points seem to me to be indubitable, - that Professor Lamberton saw that morning an externalised hallucinatory figure, and that, whatever its precise character, it suggested to him the solution which he had sought in vain by the analytical method. There is no clue to the time at which the reasoning processes necessary to attain the result were carried out, but from general considerations it seems to me most probable that they formed part of some forgotten dream and were not going on "sub-consciously" during waking life. Professor Lamberton is of Scotch-Irish descent, is a man of the most robust physical and mental health, and is of a temperament precisely the opposite of that in which traces of true "sub-conscious " processes are usually found. The function of the disused blackboard, as apparently providing a point de repère for the hallucination, is of interest and will suggest many analogies.

This is Professor Lamberton's only hallucinatory experience. He informs me further that his colour memory is bad, although his memory for line and form is excellent. He visualises little, and it was not until some time after the above experience that he learned that it was within the power of some persons voluntarily to externalise their visual memories.