ON THE PRIMITIVE FORMS OF CRYSTALS. 63 



have explained in another place*, that a single po- 

 larising axis may be the resultant of any number of 

 equal axes of an opposite character. 



When the separate axes lie in the same plane, 

 the single axis may be produced by the joint action 

 of any odd or even number of equal axes, situated 

 symmetrically around it ; and the polarising force 



F of the resultant axis, will be > n being 



the number of axes, and f the force of each axis 

 acting separately. The planes which pass through 

 each axis cut one another at the poles of the resul- 



tant axes, at angles equal to _ - ; but as the real 

 angle of the forces, or the virtual inclination of the 



axes, is double of this angle, or — -f , it follows, that 



n ' 



if A a, B b f C c 9 D d, are the axes, the action of 



A a, and B b, at the pole O of the resultant axes, will 



not be according to the directions AO, BO, but 



according to the directions AO, CO ; for, AOB 



360° 360° 

 == ir: an d AOC, = Hence it appears that 



the virtual directions of the planes passing through 

 each axis are transferred, as it were, to the real di- 

 rections of the plane passing through the next axis ; 

 so that the virtual directions of the axes' A a, B b 9 

 C c, D d, instead of being AO, BO, CO, DO, will 

 be AO, CO, a O, c O, which being all equal and 



* See Phil Trans. 1818, p. 245. 



t Id. p. 239, 240. 



