220 Br. H. Bateman on 



general equations, which [implied that two fundamental 

 integral forms were reciprocals with regard to a quadratic 

 differential form 



X 2 g mt n dx m dm ni 



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 *. 



The idea that the coefficients of the quadratic form might 

 be considered as characteristics of the mind interpreting the 

 phenomena was also entertained t, 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 J 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 



* Loc. cit. p. 225. See also Amer. Journ. of Math. vol. xxxiv. p. 340 

 (1912). 



t 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. 



X 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. 



