THE PROBLEM OF CRYSTALLIZATION. 



5i 



we observe that every ball of the pyramid bears the weight only of 

 those balls that are arranged in three lines parallel to upper edges 

 of the pyramid respectively, and meeting in the center of the ball. 

 Thus, in Figs. 15 a and 15 6 are represented in plan the four layers 

 of a pyramid of twenty balls. The ball a, of the lowest layer, can 

 only receive the weights of the balls b t b 1 b x of the second layer, trans- 

 mitted in direction-lines parallel respectively to the three upper edges 

 of the pyramid (Fig. 14), namely, D A, D A , and D A,. The ball a 

 can not receive the weight of any other ball of 

 the pyramid ; it can not receive the weight of 

 the topmost ball, d, inasmuch as the weight of 

 this ball is transmitted only in the lines D A, 

 DA , and DA 3 , the three upper edges of the 

 pyramid ; nor can it receive the weight of the 

 ball C of the third layer, for that is only trans- 

 mitted in three lines, of which two, CA, and 

 CA 3 , can be seen in the figure. By a simple 

 application of the physical principle known as 

 the parallelogram of forces, we arrive at the 

 deduction that all balls equidistant from the 

 vertex of the pyramid are solicited by the same force ; or, in other 

 words, that every ball of the pyramid is repulsed from the vertex with 

 a force proportional to its distance from the vertex, as a direct con- 

 sequence of this stress distribution. At the vertex itself the repul- 

 sion is zero. The weight of the pyramid is uniformly distributed 

 over its base ; a result which can readily be verified by experiment, 

 and is also a verification of the stated force law. Now, an exactly 

 analogous action occurs among the invisibly small particles of a crystal. 

 In the pyramid of balls, it is the pull of the earth upon each ball 

 which is active ; in the crystal it is the mutual attraction of the parti- 



Fig. 14. 



Fig. 15. 



cles. In the pyramid of balls, there are only three stress direction- 

 lines respectively parallel to the upper edges of the pyramid, inasmuch 

 as the pull of the earth acts only vertically downward, hence there 

 is no weight transmission in the three horizontal direction-lines paral- 

 lel to the basal edges respectively ; in the crystal, however, there are 



