EIIOMBOHEDEAE SYSTEM. 29 number will be six ; and when all three are equal, the number will be two. hkl I kli k I h khl I h k hi k 113. If li be algebraically the greatest, and I the least of three unequal indices h, k, I, the annexed figure will repre sent the arrangement of the poles of the form hkl on the surface of the sphere of pro jection. 114. The form bounded ei ther by all the faces which have tor their symbols the different > , , . arrangements of + h, + k, u \ 1 /*" + I, or by all the faces which ave for their symbols the *——. different arrangements of - /?, _ 11,1 ■n i — ^ ' s 8a *d to be hetnihedral with inclined faces, and ^lll be denoted by the symbol kJiJcI, where hkl is the symbol of any one of its faces. The first and second columns of the table in (112) contain the symbols of the form Mel; the third and fourth columns those of the form Mel. If the surface of the sphere of projection be divided into two parts by the zone-circle through the poles of the form 101, one part will contain the poles of Ml, and the other part the poles of KhJcl, except when the sum of the indices is zero. When the sum of the indices is zero, three alternate arcs, of the six arcs joining the poles of the form 101, contain the poles of Ml ; and the other three alternate arcs the poles of Ml. 115. The form hounded either by all the faces of the form hkl, the indices of which stand in the order hklhk, or by all the faces the indices of which stand in the order Ikhlk, is said to be hemihedral with parallel faces, and will be denoted by the ®y m hol vhkl, where hkl is tho symbol of any one of its faces. Ihe first and third columns of the table in (112) contain the symbols of the faces of irhkl; the second and fourth those of irlkh. II tho surface of the sphere of projection bo divided into twelve^ lunes by zone-cireles through the polos of the forms 111 > 211, 10I, six alternate lunes will contain the poles of nhkl, c 3 hkl Ikh klh k hi I h k h I k EIG. 43. li* i.cn kl/i Ihk* •hlk •010