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general equations, which implied that two fundamental integral forms were reciprocals with regard to a quadratic differential form

$\sum \sum g_{m,n}dx_{m}dx_{n}$

which was assumed to be invariant for all transformations of co-ordinates. The coefficients of the quadratic form were regarded as characteristics of the medium supporting the electromagnetic field and of the motion of the medium and its parts. The vanishing of the quadratic form was regarded as the condition that two neighbouring particles should be in positions such that a disturbance starting from one at the associated time should arrive at the other at its associated time^[1].

The idea that the coefficients of the quadratic form might be considered as characteristics of the mind interpreting the phenomena was also entertained^[2], and it was suggested that a correspondence or transformation of co-ordinates might be considered as a crude mathematical symbol for a mind.

The phenomena here considered were those occurring in the brain and body; and although the correspondence by which the universe is reconstructed, so to speak, may be totally different^[3] from the type contemplated here, yet it was thought that some of the general conclusions might still be valid if a transformation of co-ordinates was adopted as a working model of the correspondence. It was thought, for instance, that there was an analogy between the relativity principle that the earth's motion in space cannot be detected from experiments with terrestrial objects: and the interesting fact that we are unaware of the flow of blood and other processes taking place in our own bodies so long as they take place in the normal way. It was thought that the

1. Loc. cit. p. 225. See also Amer. Journ. of Math. vol. xxxiv. p. 340 (1912).
2. Memoirs of the Manchester Literary and Philosophical Society (1910). A full account of my ideas has not yet been published, owing to the difficulty of eliminating vagueness.
3. The term correspondence is used here in a very general sense, and is by no means restricted to the familiar one to one correspondence of entities of the same type, such as points. We should say, for instance, that there is a correspondence between the disturbance running along a telephone-wire and the sound-waves which produce it, because we can pass from one to the other by mathematical equations of a definite type, or rather by solving the equations and the boundary conditions. A correspondence is, moreover, regarded as an entity which may have real existence and be capable of growth and variation.