CONTEMPORARY ADVANCES IN PHYSICS 187 



I refrained from mentioning them earlier. I have used the symbol pt 

 for the quantity p sin 0, for this, as one sees immediately, is the tan- 

 gential component of momentum which the corpuscle acquires at the 

 deflection, not having had any before. The wall containing the slits, 

 or the row of atoms if we consider instead the difi^raction of X-rays by a 

 crystal, receives an equal momentum in the opposite sense. We may 

 therefore say that diffraction occurs in such a way, that the regularly- 

 spaced series of slits or atoms receives a momentum pi given by the 



formula : 



apt = nh. (49) 



But now what is the product apt? It is the product of the mo- 

 mentum of the row of atoms or slits by the distance a between any 

 adjacent two; it is therefore the integral J'pdqoi the general principle 

 (45), evaluated for the range of integration a. Now the general 

 principle is supposed to apply when the range of integration covers a 

 complete cycle of a periodic motion. There is nothing obviously 

 periodic about a steady sidewise sliding of a row of atoms with a 

 constant momentum. But in a sense, there is after all something 

 periodic. For if the row of equally-spaced atoms (or slits) extends to 

 infinity in both directions, then when it has moved sidewise through the 

 distance a each atom lies exactly in the former place of another atom, 

 and the original arrangement is to all appearances restored. The 

 steady onward motion of the regular array is also a cyclic departure and 

 return to a periodically-restored arrangement; and the maxima of the 

 difl^raction-pattern are determined by applying the quantum-condition 

 to this cyclic motion. 



The reader may ask: how about the component of momentum in 

 the direction at right angles to the grating? Without precisely answer- 

 ing that question, I will end the article by applying the corpuscular 

 theory to a case in which all the components of momentum are duly 

 taken into account: diffraction of X-rays or of electrons by a three- 

 dimensional crystal. 



Suppose an "ideal" crystal extending infinitely far in all directions. 

 It is composed of similar and similarly-oriented "atom-groups" — I 

 will use the language and the symbols of the eighteenth article of this 

 series — arranged upon a "space-lattice," of which the three spacings 

 shall be denoted by a, a', a". If we start with one atom-group A, 

 then along one direction from it there is an infinite sequence of such 

 groups at distances a. la, 3a, . . . and also at distances (— a), (— 2a), 

 (— 3a), ... in the opposite sense. Call that the .v-direction. Then 

 along another direction through .1, say the y-direction, there is an 



