8 GEUEEAL GEOMETRICAL PROPERTIES OE CRTSTALS. a ^Li me f US ° f thl3 e( l uation > having given pq, pr, and the symbols of p, q, r, s, we can find ps ; or, having given pq, pr, ps, the indices u, v, w may be found, by combining it with the S™.cMtr”, + ” “ °’ “ wMch u " k “f 23. If-~ [Q E ] sin pq sin (pr—rs) . . . « [io] sinQR iEiT - ’ m ’ n bcmg Regers, u = me + npt v=mf+nqi w = mgJrnT ' t^s^bofofs mfy V be foundf’ ^ and ^ Symb ° ls of P ’ Q > B > 24. Let tan0 = NMsinQS [ps] [QR]sim>Q ‘ en ’ tan(ps — |pr) = tan| pr tan (as 0 — 0). I? EotT® ei ™ „ 25. Let q, s lie between p and r ; i = [ pa 1 [Qk] , [sr] [pq] ' en ’ C0S(2PR PQ-RS) _ (l_j) cos (pq — us) + i C0S(PQ + BS ) r4 e K.tr g6iie ° , " ! -”-“ a “o 26. To change the axes of a crystal. Let the new axes be parallel to the axes of the zones ofir tu pqr. Let mw be the symbol of any face referred to tlm nVi axes, uvw its symbol when referred to the new axes. Then u — eu + iv 4- g w t tt = h« -f- ki> + bo, x = pu qv rw. j 7 \ ^° 7 , cban S e the parameters of a crystal. Let M/be the symbol of a given face with fhn 11 meters hid' its symbol with the new parameter P T symbol of any other face with tho l Pera > uvw the symbol with the new parameters. Then Paramoters > wV «/ its U ~ h ' klu > v> = vJ = hJ c l’ w right angles withSfother - in ’T' 1 ^ mflk ° perpendicular to the other two- aud ir ^, whlch ° ne is equal angles with each other. In the m u : “u" 8 making axes, and in some of the crystals m'n. ^ , a s Wltb c qmangular crystals with rectangular axes, equal
