﻿762 Dr. A. C. Crehore on the Construction of 



acceleration of the electron. When the planes of the two 

 atoms are parallel these moments of force evidently vanish; 

 and when the two axes of rotation are not parallel there is a 

 moment of force to restore them to the parallel condition, the 

 moment being a function of the angle between the axes of 

 revolution. In fig. 5 the two adjacent atoms in a horizontal 

 row on either side of a given atom with axis downward each 

 tend to tarn the given atom upward, if slightly displaced, 

 while the adjacent pair above and below tend to turn it 

 downward. The sum of the turning moments before dis- 

 placement is zero; but, unless the two sets of moments after 

 displacement show a restoring moment, there is no stable 

 equilibrium. In fig. 5 it is not evident without calculation 

 that the moments after displacement show stability in the 

 plane, since different formulae apply and the distances are 

 different. The calculation has not been made. 



Another arrangement having all axes and atoms in the 

 same plane is shown in fig. 6. This is based upon the formulae 



IT 



where «= 77. Here there is an arrangement of perfect 



squares, the same formulae applying to all adjacent atoms in 

 both rows and columns. The diagonal atoms have axes in 

 the same straight line alternating in direction, anda = 7r. 

 Adjacent atoms along the diagonals have equal and opposite 

 translational effect on the central atom. The moment of the 

 forces to turn the axis by an adjacent horizontal pair of atoms 

 is exactly counterbalanced by an adjacent vertical pair of 

 atoms, the one pair turning clockwise and the other counter- 

 clockwise by an equal amount. If the axis of any atom is 

 displaced in the plane of the paper so as to bring it more 

 nearly into the direction of the adjacent vertical pair, the 

 turning moment due to this pair is decreased. At the same 

 time the turning moment of the adjacent horizontal pair is 

 increased, and the sum of the moment is, therefore, in a 

 direction opposite to the displacement, thus proving that the 

 equilibrium is stable for moments. 



The adjacent diagonal atoms, however, all four tend to 

 turn the central atom in the same direction as the displace- 

 ment; but the rate of change of the moment is of the second 

 order of smallness because the axes are nearly parallel, 

 whereas, the rate for adjacent horizontal pairs is a maximum, 

 their axes being at right angles. The total equilibrium for 

 therefore, stable. 



