622 Transactions of the Society. 



immediately arrive at the important conclusion that the two waves 

 (or spectra) meet in equal phase, and produce a maximum of 

 brightness in those points of the image which are coDj'ugate to 

 points in the centres of grating slits ; or, in other words, the 

 diffraction-image yields maximum brightness along lines coin- 

 cident with the geometrical images of the centre-lines of the slits. 

 In order to establish the character of the diffraction-image stilt 

 more closely, we have only to remember that in the first spectrum 

 there is a difference of one whole wave-length in the portions or 

 wavelets coming from adjoining slits ; there will therefore be the 

 same range of one whole wave-length in the phase relation 

 through which the two waves pass between two neighbouring- 

 maxima in the image, and there can therefore be no intermediate 

 bright lines. 



The intensity curve of the light, in passing from the centre of 

 one line in the image to the centre of the next, will be somewhat 

 modified according to the relative brightness of the direct and the 

 diffracted light, which in turn we found to depend on the relation 

 between the width of the slits to the spacing of the gnting; but 

 the visual appearance has been often shown to be that of bright 

 lines separated by more or less dark intervals of approximately 

 the same width, the amplitude curve being of the nature of that 

 shown in fig. 96, a. Hence, the image which we get in this simplest 

 case coincides with the ideal geometrical image ; but whatever the 

 real width of the slits may be, they are always represented as 

 equal to half the spacing — really a commendable compromise, as 

 that is the happy mean of all possible widths. 



2. Now let us proceed to the consideration of the image produced 

 when the oblique direct light and two successive diffraction-spectra 

 are admitted. "We saw that the second spectrum is necessarily 

 less bright than either the first spectrum or the direct light, hence 

 its admission cannot reverse, but can only modify the effect pro- 

 duced by the others. The modification largely results from the 

 phase relations, which, for this reason, I discussed at considerable 

 length, and it takes place in this way : — 



(a) When the slits are narrower than the dark interval, the 

 second spectrum also is in phase with the direct light. As the 

 second spectrum passes through two wave-lengths difference of 

 phase from slit to slit, and consequently also from image to image, 

 we shall have resulting from the co-operation of the direct light, 

 and that of the second spectrum, maxima coincident with those 

 treated above, but also intermediate maxima, corresponding to the 

 centre of each dark space in the image, as shown at fig. 96, b. 



In the formation of the image, the amplitudes resulting from 

 both combinations will be added together (this is very approxi- 

 mately true, but not quite strictly, as there are slight differences of 

 phase to be taken into consideration), with the result shown in 



