[Illustration:  Fig. 17.]

Now let us return to our slit, and, for the sake of simplicity, we will first consider the case of monochromatic light.  Conceive a series of waves of ether advancing from the first slit towards the second, and finally filling the second slit.  When each wave passes through the latter it not only pursues its direct course to the retina, but diverges right and left, tending to throw into motion the entire mass of the ether behind the slit.  In fact, as already explained, every point of the wave which fills the slit is itself a centre of a new wave system which is transmitted in all directions through the ether behind the slit.  This is the celebrated principle of Huyghens:  we have now to examine how these secondary waves act upon each other.

[Illustration:  Fig. 18.]

Let us first regard the central band of the series.  Let AP (fig. 18) be the width of the aperture held before the eye, grossly exaggerated of course, and let the dots across the aperture represent ether particles, all in the same phase of vibration.  Let E T represent a portion of the retina.  From O, in the centre of the slit, let a perpendicular O R be imagined drawn upon the retina.  The motion communicated to the point R will then be the sum of all the motions emanating in this direction from the ether particles in the slit.  Considering the extreme narrowness of the aperture, we may, without sensible error, regard all points of the wave A P as equally distant from R. No one of the partial waves lags sensibly behind the others:  hence, at R, and in its immediate neighbourhood, we have no sensible reduction of the light by interference.  This undiminished light produces the brilliant central band of the series.

Let us now consider those waves which diverge laterally behind the second slit.  In this case the waves from the two sides of the slit have, in order to converge upon the retina, to pass over unequal distances.  Let A P (fig. 19) represent, as before, the width of the second slit.  We have now to consider the action of the various parts of the wave A P upon a point R’ of the retina, not situated in the line joining the two slits.

[Illustration:  Fig. 19.]

Let us take the particular case in which the difference of path from the two marginal points A, P, to the retina is a whole wave-length of the red light; how must this difference affect the final illumination of the retina?

Let us fix our attention upon the particular oblique line that passes through the centre O of the slit to the retina at R’.  The difference of path between the waves which pass along this line and those from the two margins is, in the case here supposed, half a wavelength.  Make e R’ equal to P R’, join P and e, and draw O d parallel to P e.  A e is then the length of a wave of light, while A d is half a wave-length.  Now the least reflection will make it clear that not