404 STUDIES IN SPECIAL SENSE PHYSIOLOGY 



circumscribed by the lines joining their representative points in a 

 plane, e.g. : 



FIG. 6. 



This is our first assumption, and is little more than a generalisa- 

 tion of experimental facts. 



Thus far, we have merely asserted that any stimulus, R', say, 

 can be expressed by the equation R' = z.R + y.G + 2.V, where 

 x, y, z are positive real quantities. But, our only measure of stimu- 

 lation equality being corresponding sensation equality, we imply 

 (and this is our second and most important assumption) that there 

 is a definite relationship between the physiological excitatory pro- 

 cesses which lead up, somehow, to sensations, and the stimulus 

 magnitudes. 



This assumption is justified if we can show that it leads to the 

 formulation of a satisfactory working hypothesis, and if we assume 

 the simplest relationship consistent with the experimental facts. 

 What, then, is the simplest relation we can suppose to subsist 

 between the stimulatory and excitatory processes ? Clearly that, 

 just as stimuli may be reduced to terms of three independent 

 variables, excitatory processes are represented by three inde- 

 pendent variables. Thus, taking our previous example, any 

 stimulus, R' = x.R + y.G + z.V, then A = / a (x, y, z), B = / 2 (x, y, z), 

 C = / 3 (x, y, z), and conversely, x = Y l (A, B, C), y = F (A, B, C), 

 z = F 3 (A, B, C). 



These latter expressions may be taken as " elements " or unit 

 excitatory processes, or any linear functions of them may be so 

 taken. 1 



1 The proof of this statement, although simple, requires some knowledge ot 

 analytical notation, and cannot therefore be reproduced here. See Helmholtz, 

 Handb. d. Phys. Opt., 2nd edition, pp. 342-3. 





