74 ON THE PRIMITIVE FORMS OF CRYSTALS. 



direction of that line, equal in intensity to _+ N f 9 

 (/being the force of each separate axis,) and of the 

 same character with each of the separate axes. As 

 the angle which the axes form with this line in- 

 creases, the intensity of the resultant axis dimi- 

 nishes. At an inclination of 54° 44' 8 /y the angle 

 which the faces of a cube, a regular octohedron, and 

 a rhomboidal dodecahedron, form with the axis of 

 these solids, all the separate axes will be in perfect 

 equilibrium, or will destroy each other, and the force 

 of the resultant will be 0. At a greater inclina- 

 tion, the resultant axis reappears with an opposite 

 character, and gradually increases in intensity, till 

 the angle is 90°, when all the axes are in one plane, 



and the force of the resultant is 3T 



This law may be represented by the following 

 formulae : 



Sin. 2 <p = .6666 + — ^— — , and 



m 



■* T /. 3 Sin. 2 a 



n 



N(l-3^>); 



where N is the number of axes combined, n the 

 number of axes to which the intensity of the re- 

 sultant is equal, and <p the inclination of each axis 

 to the resultant. , The sign + is to be used when 

 n is of an opposite character to N. 



Edinburgh, March 1819* 



