Prof. Grassmauu ua the Tlieury of Comjjuund Colours. 257 



tinuous change of the thit, this will generally be produced by 

 the continuous change of the duration of vibration determining 

 this tint ; with this difference, that the impression of colour of 

 the extreme violet will continuously unite itself to that of the 

 extreme red. In point of fact, the transition from violet to red 

 through purple is just as continuous to the eye as that between 

 any two other colours, although the limit has not yet been fixed 

 by observation at which the same impression of colour is repro- 

 duced by a diftcrent duration of vibration. I will call the trans- 

 ition from red through orange, yellow, green, blue, violet, and 

 purple back to red, the positive, and that in the reverse direction 

 the negative transition. According to this, any coloured light 

 A may continuously pass into another coloured light B in three 

 different ways; namely, by the colour continuously assuming all 

 the tints which lie between A and B in the positive transition, 

 or by its passing through all those in the negative transition, or 

 lastly, by the light becoming colourless once or several times 

 during its transition. The principle of continuous transition 

 which we have just developed must be regarded as perfectly 

 established by experience, as a sudden spring in the plifenomena 

 would be apparent even in the most crude observations, and 

 such a spring has not as yet been discovered. 



From these propositions the following position may be derived 

 with mathematical certainty : — 



" To every colour belongs another homogeneous colour, which, 

 when mixed with it, gives colourless light." 



Proof. Let a be the tint of the given colour. Let it be 

 assumed that there is no homogeneous colour, which, when 

 mixed with this, furnishes colourless light ; let any homogeneous 

 colour whatever be taken possessing the tint of x and the inten- 

 sity y. If now, whilst x remains constant, y be increased from 

 nothing upwards until the intensity of the colour a disappears 

 in comparison, the mixture will continuously change ; and as, ac- 

 cording to the assumption, it can never give colourless light, 

 its tint will also change continuously ; thus, as the mixture at 

 first has the tint a, and finally the tint x, it has continuously 

 passed from a to x. This transition may be either positive 

 or negative ; whether it be the one or the other will depend 

 upcm the tint x. If the tint x be supposed to differ infinitesi- 

 mally from a, but on the side of ])ositive transition, this transition 

 will also be positive. For if it were negative, all tints besides 

 those differing infinitesimally from a must be produced by the 

 elevation of the intensity y, and therefore tints which are 

 quite different from a ; let y be an intensity by which a tint 

 quite different from a is produced. Now it is clear that the 

 colour, the tint of which is a and its intensity y, when mixed 



