CLASSICAL THEORY OF LIGHT 747 



diffraction-beams one may determine the spacings within the crystal 

 if one knows the wave-length of the waves, or the wave-length if one 

 knows the spacings. From the relative intensities of the beams one 

 may deduce the distribution of the atoms within the groups, or rather 

 the distribution of that which scatters the waves — commonly supposed 

 to be mobile negative electricity, when the scattered waves are light; 

 I do not know whether anyone has yet conjectured what it is that 

 scatters the electron-waves. 



The diffraction-beams proceeding from a crystal large enough to be 

 manageable are very sharp, for the rows of atoms are far more numer- 

 ous than the lines of the largest optical grating which can be made or 

 hoped for. However, there is a limitation on their sharpness set by 

 something to which an artificial grating is quite indifferent — the 

 thermal agitation of the atoms, which has the same effect as though the 

 widths of successive periods were variable and fluctuating. This 

 effect is naturally more pronounced, the higher the temperature of the 

 crystal; but the measurements show — for from the breadth of the 

 diffraction-maxima it is possible to determine the mean amplitude of 

 the temperature-agitation, another service of the crystal grating — - 

 that even at absolute zero it would not disappear, the atoms retaining 

 a certain minimum amount of energy of vibration which apparently 

 can never be taken from them, so long as they remain bound together 

 in a crystal. 



A few words, before leaving the subject of gratings, about the 

 diffraction-pattern of a multitude of gratings oriented at random. 



On an earlier page I said that, in computing the diffraction-pattern 

 of a sequence of slits, we need determine it not for the entire focal 

 plane, but only for a single line thereof — the line for which 7 = 0, 

 which is the line of intersection of the focal plane with the plane 

 running normal to the slits and containing the infinitely-distant point- 

 source of the parallel waves of light. The reason can now be stated. 

 If we work out the expression C^ -j- S" for a single long and narrow 

 rectangular slit with its long sides are parallel to the 2-axis, we find that 

 the brighter parts of the diflfraction-pattern form a long narrow band 

 (criss-crossed with dark lines) with its length parallel to the y-axis 

 and its breadth parallel to the z-axis. If the length of the rectangle 

 grows infinitely long, the breadth of this band shrinks to zero; we 

 have a single line of varying brightness parallel with the y-axis, which 

 is the diffraction-pattern of the infinite slit. If instead of a single slit 

 we have a regular sequence, their diffraction-pattern is still concen- 

 trated upon this line; it is the pattern which has just been computed, 

 a function of the single variable 13, or y, or d; away from the line, the 



