746 BELL SYSTEM TECHNICAL JOURNAL 



the width of the period (slit plus bar) of the grating, the first of its 

 black fringes falls square upon the second-order principal maximum 

 of the grating spectrum, which is obliterated. This is a new way of 

 expressing the fact already mentioned, that when the slits are as wide 

 as the bars the diffraction-maxima of even order are absent. 



More generally, the intensity at any of the principal maxima is 

 proportional to the value of (C^ + S^) appropriate to that direction — 

 proportional to the intensity, in that direction, of the diffraction- 

 pattern of the single slit; and from this we can understand how, from 

 the relative intensities of the maxima of various orders, it is possible 

 to deduce the breadth of the slit or something about the shape of the 

 groove. If we had only a single slit, and could send through it light 

 of known wave-length sufficiently intense to form a measurable 

 diffraction-pattern, we could trace the curve representing observed 

 relation between diffracted intensity and angle 0, and compare it with 

 the predicted curves for various values of slit-breadth; the actual 

 width of the slit would be the value for which the agreement was 

 perfect. If instead we had a multitude of such slits equally spaced, 

 the observed intensities of the diffraction-maxima would supply us, 

 not indeed with the entire continuous curve of intensity-versus-angle 

 for the single slit, but with as many points upon that curve as there 

 were principal maxima within our range of observation ; and these — if 

 we had two or more — would be sufficient for the comparison with the 

 theoretical curve for the single slit, out of which the width would be 

 deduced. From this aspect, the function of the grating is to enhance 

 the intensity, at certain discrete points, of the diffraction-pattern for 

 the single slit. Of course, when we are interested in the breadth of 

 the single slit or the shape of the single groove, we should prefer to 

 observe the entire continuous diffraction-pattern produced by one 

 alone. But it may be impossible to separate one from the rest; or 

 if we could isolate one, it might be too small to transmit or scatter any 

 perceptible amount of light. Such is the case with atoms. 



The natural gratings which atoms form in crystals are three- 

 dimensional, and to them the reasonings which are valid for plane 

 gratings cannot be applied without some change; but the resemblance 

 is very close. A beam of X-rays or electron-waves falling upon a 

 crystal is spread out into a diffraction-pattern with strong maxima, 

 of which the relative intensities depend upon the qualities of the 

 individual diffracting units, the atoms or the groups of atoms which 

 are repeated over and over again to form the crystal; while their 

 directions depend upon the spacings between these identical groups, 

 the periodicity of the crystal. From the directions of the principal 



