A word may be said here on a materialistic-sounding phrase which is very prominent in Schopenhauer's later expositions, and has been remarked on as paradoxical for an idealist. The world as presentation, he often says, is 'in the brain.' This, it must be allowed, is not fully defensible from his own point of view, except with the aid of a later distinction. The brain as we know it is of course only a part of the phenomenon of the subject,--a grouping of possible perceptions. How then, since it is itself only appearance, can it be the bearer of the whole universe as appearance? The answer is that Schopenhauer meant in reality 'the being of the brain,' and not the brain as phenomenon. He had a growing sense of the importance of physiology for the investigation of mind; and his predilection led him to adopt a not quite satisfactory shorthand expression for the correspondence we know scientifically to exist between our mental processes and changes capable of objective investigation in the matter of the brain. In science his distinctive bent was to the borderland between psychology and physiology. Hence came the attraction exercised on him by Goethe's theory of colours. To his own theory, though, unlike his philosophical system, it has always failed to gain the attention he predicted for it, the merit must be allowed of treating the problem as essentially one of psychophysics. What he does is to attempt to ascertain the conditions in the sensibility of the retina that account for our actual colour-sensations. This problem was untouched by the Newtonian theory; but Schopenhauer followed Goethe in the error of trying to overthrow this on its own ground. He had no aptitude for the special inquiries of mathematics and physics, though he had gained a clear insight into their general nature as sciences. On the psycho-physical side there is to-day no fully authorised theory. The problem indeed has become ever more complex. Schopenhauer's attempt, by combination of sensibilities to 'light' and 'darkness,' to explain the phenomena of complementary colours, deserves at least a record in the long series of essays of which the best known are the 'Young-Helmholtz theory' and that of Hering. It marks an indubitable advance on Goethe in the clear distinction drawn between the mixture, in the ordinary sense, that can only result in dilution to different shades of grey, and the kinds of mixture from which, in their view, true colours arise.