264 Prof. Grassmaan on the Theory of Compound Colours. 



the periphery be 1), then the total intensity is « + /3, or^ as the 

 radius is sup])osccl to be 1, (a + /S)OD. The total intensity, 

 according to the supposition, will be equal to the intensity of 

 the colour ja/iw the intensity of the intermixed white; the latter 

 is consequently («H-y8)OD-(a + /S)OC = (a + y(3)CD. The in- 

 tensity of the intermixed white is therefore equal to the distance 

 of the centre of gravity from the periphery, multiplied by the 

 sum of the weights. From this it follows, further, that if the 

 total mass be regarded as united in the centre of gravity, in 

 which case, when furnished with such a weight, it is called the 

 geometrical sum* of the individual points with their attached 

 weights, then every impression of light, according to its three 

 elements, is accurately represented by a point with a certain 

 weight attached to it. The direction in which this point lies 

 with regard to the centre, or the point at which this direction, 

 if followed, strikes the peripheiy, represents the tint ; the 

 weight of the point, the total intensity of the light ; and the 

 distance from the periphery multiplied by this weight, the inten- 

 sity of the intermixed white. If by the depth of the colour 

 of a light we understand the intensity of its colour, divided by 

 the total intensity of the light, the depth of colour is repre- 

 sented by the simple recession of the point from the centre. If, 

 then, two or more colours be represented in this manner, their 

 mixture is completely represented by the geometrical sum of 

 the loaded points denoting the individual colours. It will be 

 seen that this rule, derived by a purely mathematical method 

 from four sufficiently well-founded assumptions, agrees in its 

 essential features with Newton^s empirical rule. Nevertheless, 

 the manner in which Newton distributes the homogeneous colours 

 on the circumference of his discs requires a thorough revision, 

 towards which only the first steps are made by the researches of 

 Helmholtz. Not until sufficient light has been thrown upon 

 this subject can we attempt the solution of the interesting ques- 

 tion with regard to the law by which the vibrations belonging 

 to the various colours combine to produce simple impressions of 

 colour upon the nerves of the sensorium, a question upon the 

 solution of which the idea of the various colours and of colour- 

 less light essentially depends. 



* See my Ausdehnungskhre and Mobius' Barycentrischen Calcul. 



