CLASSICAL THEORY OF LIGHT 743 



shape during the operation, the grating is good for nothing. This 

 cannot be foreseen, it is not even known when it happens; to stop the 

 process to see how things are going would be Hke digging up a seed 

 to see how it is sprouting. The chance of such an accident is 

 naturally greater, the more numerous the lines — another obstacle to 

 the successful ruling of many-lined gratings of high resolving power. 



A grating having been completed, it is removed from the engine 

 and examined, to learn not merely whether it has been impaired by 

 deformations of the diamond, but how — assuming it to have escaped 

 that peril — the intensities of the various diffraction-maxima of different 

 orders compare with one another. This is something which, as I have 

 intimated, is controlled by the shape of the groove; this is the feature 

 in which the individual units of the periodic structure manifest their 

 quality. One shaping might obliterate all diffraction-maxima of even 

 order; another might make the maxima on one side of the normal 

 to the grating-surface stand out much more prominently than their 

 companions on the other; still another could concentrate most of the 

 diffracted light into one single beam. The maker of the grating can- 

 not foresee, or can at best foresee only in part, what distribution of 

 intensities he is going to get; for he cannot control the shape of the 

 diamond-point, nor find it out by examination." Having observed the 

 distribution of intensities, however, he can deduce from it some facts 

 about the shape of the grooves. This I suppose would be classified 

 in most cases as useless knowledge; but the problem happens to be 

 very nearly the same as that of determining the finer details of the 

 arrangement of atoms in a crystal from the relative intensities of the 

 various diffraction-beams which it produces when acting on an X-ray 

 beam; and so I will devote a few paragraphs to it. 



We return, then, to the grating of alternate slits and bars, to deter- 

 mine the influence of the ratio of slit-width to bar-width on the 

 diffraction-pattern. Before making any calculations whatever, one 

 striking prediction can be made directly. I have said that diffraction- 

 maxima occur in every direction 0„ for which 



sin dn = n\/c, w = 0, 1, 2, 3, 4 • • •, 



because in every such direction the component vibrations arrive at 

 the focal plane from the various slits with identical phase. But if 

 for any of these directions the component vibrations are themselves 



^ He can control the result to a slight extent by varying the pressure with which 

 the diamond bears upon the plate, ruling "with a light touch" or reversely; if he 

 guesses the force just right, he may approach the condition of grooves separated by 

 unbitten bands of smooth metal as wide as they, which resembles the theoretical 

 case of an alternation of slits and bars of equal width. 



