AT THE PHYSICO-TECHNICAL INSTITUTE 397 



/ Psych, u. PhysioL, the other, ' Shortest Lines in the Colour 

 System/ communicated to the Academy on December 17, 1891), 

 Helmholtz returns to the conclusions laid down by himself 

 and Riemann, that all the characteristics of our particular form 

 of space can be derived from the fact that the value of the 

 distance between two adjacent points may be expressed by 

 the corresponding increment of the co-ordinates, and accord- 

 ingly requires that the interval between any two points of 

 a rigid body should be completely given by the position of 

 its terminal points, and remains the same in all possible dis- 

 placements and rotations of the rigid body. Starting from 

 the fact that each special colour may be represented by the 

 combination of the corresponding measured quantity of three 

 appropriately selected fundamental colours, which take the 

 place of the co-ordinates, he finds in the sharpness of the 

 distinction between any two nearly related colours, a quantity 

 which is analogous to the distance between points in space, 

 and proposes a very simple analytical expression which he 

 hopes will play the same part in the region of colour-sensation 

 as the formula for the length of linear elements in geometry. 



This expression gives the degree of clear distinction between 

 any two colours, which are at the same time different in the 

 fundamental colours that blend in their composition, that is, 

 which differ both in brightness and in quality. In analogy 

 with the shortest line between two points in space, he defines 

 as the shortest colour-series, those series of transitional colours 

 between two given terminal colours of different quality and 

 quantity for which the sum of the perceptible differences is 

 a minimal. 



Helmholtz next applied these results to the solution of 

 a weighty but very difficult problem. Newton's Law of Colour- 

 Mixture referred the entire complex of possible colour-sensa- 

 tions to three co-existent modes of exciting the nervous 

 apparatus of the eye, but left undecided which colour-sensa- 

 tions correspond with these three elementary excitations. 

 Helmholtz once more attacks the question of determining 

 which are the three physiologically simple colour-sensations. 

 The investigation yielded the following results, with some 

 degree of probability, for the three fundamental colours : 

 spectral red is a whitish, slightly yellow modification of a 





