Volltext Seite (XML)
EnOMBOIIEDEAL SYSTEM. 31 118. Lot hkk, pqr be any two faces in a zone containing Hi. Then 119. Let ovw be any face in the zone containing oio, Oil. Then 120. Let uvv be any face in a zone containing 111, oil. Then 121. "When h, k, I, p, q, r are connected by the equations, P = — h + 2k + 2l, q = •ah — k + il, r = 2h + 2k — I, the arc joining the poles hkl, pqr, is bisected in the pole ill. Ihe forms h/cl, pqr are, in this case, said to be transverse with respect to.each other. _ In certain crystals belonging to the rhombohcdral system, com binations of pairs of transverse forms occur frequently. Such a combination is called dirhombohedral. It may be denoted by the symbol Ihkl, where hkl is the symbol of either of the two forms. The poles of the form hkl are symmetrically situated with respect to each of the three zone-circles through the poles of the forms in, all. The poles of the dirhombohedral combina tion of forms hkl, pqr are symmetrically situated with respect to each of seven zone-circles through every two of the poles of tho forms in, 21I, 101. 122. The two hcmihedral forms, either with inclined or with parallel faces, derived from the same hololiedral form, are identical in all respects, position excepted; for, if the sphere of projection be made to revolve through two right angles round any two opposite poles of the form 10I, the poles of Mikl come into the places of those of 1Ml, and the poles of irhkl come into the places of the poles of irlkh. The forms uhkl, alkh are essentially different. 123. Let p, a be any two adjacent poles of the forms hkk, 100 respectively, o the ndarest polo of the form 111, po = T, A0 — n, the angular element of a crystal belonging to the rhombohedral system. Then k -~ 1 tan (UZ, ill) h + k + I v q — r . p + q + r tan(2?2T,lll). tan (ocw,OiT) = v W - tan (010,011). v — w tan (mot,oil) = -tan(ill,oil). v tanx = c 4