Page:Popular Science Monthly Volume 29.djvu/62

From Wikisource
Jump to: navigation, search
This page has been proofread, but needs to be validated.
52
THE POPULAR SCIENCE MONTHLY.

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

PSM V29 D062 Stress line comparisons between pyramid and crystal structures 1.jpg
Fig. 16.

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 octahedral face (Fig. 16) the stress can only be transmitted in three direction-lines, A A1 , B B1, and C C1, for there is no contact between the particles which would allow the stress to be transmitted in any other direction; in the cubical face (Fig. 17) there are but two stress direction-lines, D D1, and E E1, and in the dodecahedral face (Fig. 18) there is but one stress direction-line, F F1; and generally on any particle in the tetrad configuration the stress can only be transmitted in six direction-lines, respectively parallel to the six edges of the pyramid.

PSM V29 D062 Stress line comparisons between pyramid and crystal structures 2.jpg
Fig. 17.

All this applies not only to the first or monometric system of crystallization, in which the ultimate particles are symbolized by the spherical form, but also to the dimetric and trimetric systems in which the ultimate 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 particles. In order to satisfy the equilibrium condition, the physical 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