Prof. Grassmann on the Theory of Compound Colours. 263 



the centre of gravity then represents the tint ; and when mul- 

 tiplied by the sum of the weights, the intensity also. The 

 identity of this determination with the preceding one is readily 

 seen from the following construction of the centre of gravity 

 pointed out in my Ausdehnungslehre. The centre of gravity of 

 the points A, B, C . . . , to which are respectively attached the 

 weights a, /3, 7 . • . , is ascertained by drawing from any point 

 O the lines OA, OB, OC ; these are multiplied respectively by 

 a, /8, 7 . . . , and changed in the proportion of 1 :«, 1 : /3, 1 : 7 ... 

 without altering their directions ; from the lines thus obtained 

 the geometrical sum is formed, and this divided by a + /S + 7 ... ; 

 the terminal point of the line thus obtained is the desired centre 

 of gravity. 



Lastly, with regard to the intermixture of colourless lightj 

 another assumption is still necessary. The simplest method is 

 to assume — 



" That the total intensity of the mixture is the sum of the 

 intensities of the lights mixed.'^ 



I understand under the term total intensity of light, the 

 sum of the intensity of the colour, expressed as abovCj and 

 the intensity of the intermixed white. The intensity of the 

 white, as also of every single colour, is assumed proportional, 

 not to the square of the amplitude, but to the amplitude itself] 

 so that by the mixture of two white, or similarly coloured lights, 

 the intensity of the mixture is the sum of the intensity of the 

 mixed lights. 



This fourth assumption is not to be regarded as so well 

 founded as the three preceding, although on theoretical grounds 

 it appears to be the most probable. In order to draw the con- 

 clusions from this hypothesis, we will suppose the intensity of 

 the colour represented by the line a to be equal to 1, and assume 

 that the various homogeneous colours, the intensity of which is 

 1, are represented by points on the periphery of a circle, so that, 

 in conformity with what has been stated above, the weight of 

 these points must also be supposed equal to 1. Now let A and 

 B (fig. 6) be two points on the periphery, which consequently 

 represent homogeneous colours of an intensity =1. Let the 

 colours aA and /3B be mixed, i. e. two homogeneous colours, 

 whose intensities are u and/3,and their tintsA and B, then the sum 

 of the intensities is a. + ^. In order now to determine the colour 

 of the mixture, we have, as above described, to find the centre of 

 gravity of the points A and B, furnished with the weights a. 

 and /3. Let this be C, the centre of the circle ; then if the 

 radius of the circle be supposed =1, the intensity of the colour 

 is = (a + fS)OC. Let the point at which OC, if produced, strikes 



