5 2 



THE POPULAR SCIENCE MONTHLY. 



Fig. 16. 



six stress direction-lines, inasmuch as the mutual forces between the 

 ultimate particles of the crystal act in all the directions joining the 

 centers of the particles respectively. That the stress can only be 

 transmitted in six direction-lines is evident from the following consid- 

 eration : In a pyramid of four balls (Fig. 15 b) we have evidently the 



six stress direction-lines 

 joining the centers of the 

 balls respectively. In 

 case of a larger number 

 of particles in contact, it 

 is clear that in an octa- 

 hedral face (Fig. 16) the 

 stress can only be trans- 

 mitted in three direction- 

 lines, A Aj , B B x , and 

 C C t , for there is no con- 

 tact between the parti- 

 cles which would allow 

 the stress to be transmit- 

 ted in any other direc- 

 tion ; in the cubical face 

 (Fig. 17) there are but 

 two stress direction-lines, D D, and E E t , and in the dodecahedral face 

 (Fig. 18) there is but one stress direction-line, F F 1 ; and generally on 

 any particle in the tetrad configuration the stress can only be trans- 

 mitted in six direction-lines, respectively parallel to the six edges of 

 the pyramid. All this applies not only to the first or monometric sys- 

 tem of crystallization, in which 

 the ultimate particles are sym- 

 bolized by the spherical form, 

 but also to the dimetric and tri- 

 metric systems in which the ulti- 

 mate particles are symbolized by 

 an oval form. But this analogy 

 between the pyramid of balls and 

 crystals holds not only for the 

 stress distribution, but extends 

 also to the law of the forces 

 active between the ultimate par- 

 ticles. In order to satisfy the 

 equilibrium condition, the physi- 

 cal doctrine demands a unique 

 law of force for a stated stress distribution, and elsewhere I have 

 shown this law to be Every particle is attracted to the center of 

 the crystal with a force proportional to its distance from the center ; 

 while the law for the ball pyramid is Every particle is repulsed from 



Fig. 17. 



