What hindered Goethe in this field was his limited insight into the nature of the two distinct kinds of forces which, as we have noted in the course of our own inquiries, correspond to his concepts of Licht and Finsternis.
With the aid of this distinction - which we have indeed established through a consistent application of Goethe's method - we shall now be able to develop precisely that insight into the coming-into-being of the spectral colours which Goethe sought.2
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Dynamically, the process of the formation of the spectrum by light that passes through a prism divides into two clearly distinguishable parts. The first consists in the influence which the light undergoes inside the prism as a result of the latter's special shape, the other, in what happens outside the prism at the boundary between the Light-space - influenced by the shape of the prism - and the surrounding Dark-space. Accordingly, we shall study these two parts of the process separately.
As an aid to distinguishing clearly one process from the other, we shall suppose the prism experiment to be so arranged that the light area is larger than the width of the prism, which will then lie completely within it. We shall further suppose the dimensions of the whole to be such that the part observable on the screen represents only a portion of the total light-realm situated between the boundaries of the prism. The result is that the screen depicts a light-phenomenon in which there is no trace of colour. For normal eyesight, the phenomenon on the screen differs in no way from what it would be if no prism intervened in the path of the light.
These two seemingly identical light-phenomena reveal at once their inner dynamic difference if we narrow the field of light from either side by introducing into it an object capable of casting shadow. If there is no prism we see simply a black shadow move into the illumined area on the screen, no matter from which side the narrowing comes. If, however, the light has come through a prism (arranged as described above) certain colours appear on the boundary between the regions of light and shadow, and these differ according to the side from which the darkening is effected. The same part of the light area may thus be made to display either the colours of the blue pole of the colour-scale, or those of the yellow pole. This shows that the inner dynamic condition of the light-realm is altered in some way by being exposed to an optically resistant medium of prismatic shape. If we are to find the cause and nature of this alteration we must revert to the prism itself, and inquire what effect it has on light in the part of space occupied by it. By proceeding in this way we follow Goethe's model: first, to keep the two border-phenomena separate, and, secondly, not to ascribe to the light itself what is in fact due to certain boundary conditions.
In order to realize what happens to the light in passing through the prism, let us remember that it is a characteristic of an ordinary light-beam to direct itself through space in a straight line if not interfered with, and to illuminate equally any cross-section of the area it fills. Both these features are altered when the light is exposed to a transparent medium of prismatic shape - that is, to an optically resistant medium so shaped that the length of the light's passage through it changes from one side of the beam to the other, being least at the so-called refracting edge of the prism, greatest at the base opposite to that. The dimming effect of the medium, therefore, has a different magnitude at each point of the width of the beam. Obviously, the ratio between levity and gravity inside such a light-realm, instead of being constant, varies from one side to the other. The result is a transverse dynamic impulse which acts from that part of the light-realm where the weakening influence of the prism is least towards the part where it is strongest (see long arrow in Plate C, Fig. i).3 This impulse manifests in the deflection of the light from its original course. Apart from this, nothing is noticeable in the light itself when caught by an observation screen, the reason being that the transverse impulse now immanent in the light-realm has no effect on the reflecting surface.
The situation changes when the light-realm is narrowed down from one side or the other - in other words, when an abrupt change of the field-conditions, that is, a sudden leap from light to dark or from dark to light, is introduced within this realm. In this case, clearly, the effect of the transverse field-gradient on such a leap will be different, depending on the relation between the directions of the two (see small arrows in Fig. i). Our eyes witness to this difference by seeing the colours of the blue pole of the colour-scale appear when the field-gradient is directed towards the leap (a), and the colours of the yellow pole when the gradient is directed away from it (b).
For our further investigation it is very important to observe how the colours spread when they emerge at the edge of the shadow-casting object thus introduced into the light-realm from the one side or the other. Figs, ii and iii on Plate C show, closely enough for our purpose, the position of the colour-bearing areas in each case, with the dotted line indicating the direction which the light would have at the place of origin of the colours if there were no object interfering with its free expansion.4 We observe a distinct difference in the widening out of the two colour-areas on both sides of the original direction of the light: in each case the angle which the boundary of the colour-area forms with this direction is smaller on the side of the colours nearest the light-realm (blue and yellow respectively) than on the opposite side (violet and red).
Remembering what we have learnt about the dynamic characteristics of the two colour-poles, we are now in a position to state the following. When a light-area subject to a lateral gradient is narrowed down, so that the gradient is directed towards the narrowing object, colours arise in which the interaction between the two polarically opposite forms of density is such that positive density makes for lightness, and negative density for darkness. Whereas, when the border is so situated that the gradient is directed away from it, the interaction is such that positive density makes for darkness, and negative density for lightness. Further, the fact that on both occasions the darkness element in the colour-band increases in the outward direction tells us that in this direction there is on the blue-violet side a gradual decrease in positive, and increase in negative, density, while on the opposite side we find just the reverse. We note again that both processes occupy a considerable part of the space originally outside the boundaries of the light-area - that is, at the violet end the part towards which the light-beam is deflected, and at the red end the part from which it turns away.