726 BELL SYSTEM TECHNICAL JOURNAL 



group. For instance, there are directions in which no h'ght at all is 

 sent by the regular array, though assuredly light would be scattered 

 in those directions by any member of the array if it were solitary. 

 These facts are explained by invoking interference of waves. The 

 wavelets expanding outwards from the various rulings or scattering 

 particles are supposed to arrive in opposite phases at the "dark 

 fringes" of the diffraction-pattern, so that they cancel each other. 

 But one might also say that the beam of light is a stream of corpuscles 

 which are deflected or scattered by the atom-groups or rulings which 

 they happen to strike, and that the law of scattering of the individual 

 atom-group is altered by the marshalling of the scattering elements 

 into a regular pattern, so that in particular the probability of a 

 deflection towards one of the dark fringes is reduced to zero. 



I am not prepared to say that such a compromise is a full alternative 

 for the wave-theory, though modern theoretical physics seems to be 

 tending in that direction. But if we wish to describe with the language 

 of the corpuscle-theory the phenomena of diffraction by a crystal, 

 whether of waves of light or waves of negative electricity: then we 

 must certainly adopt the idea of a probability-of-scattering, of a 

 mean-free-path, which varies with the irregularity of the placing of 

 the atoms. 



The principle is especially simple and especially startling, if we deal 

 with a beam of which the wave-length — considering it as a beam of 

 waves — exceeds the spacing of the lattice. Waves of such a magnitude 

 would not be diffracted at all by scattering particles placed exactly 

 at the points of the lattice. Though any particle singly would scatter 

 them, they flow through the lattice intact. If then we wish to interpret 

 the beam as a stream of corpuscles, the probability of deflection of 

 any corpuscle by any atom must sink to zero when the arrangement is 

 made perfect ; the mean free path must then be considered infinite. 



The resistance of a perfect crystal of an element should then be 

 zero when all the atoms are stationary in their places on the lattice — 

 if they ever are, which apparently they are not; and should increase 

 steadily with increasing temperature, in a way which can be computed 

 if we know two things: the way in which the scattering of waves by 

 particles on a lattice varies with the amplitude of the quiverings of 

 the particles about their lattice-points, and the way in which the 

 amplitudes of the particles vary with the temperature. The second 

 of these questions is the subject of the theory of specific heats of 

 solids, developed principally by Debye. The first has been profoundly 

 studied by Debye and by several other physicists interested chiefly 

 in the scattering of X-rays by crystals. Transferring their results 



