Prof. Miller’s Crystallographic Notices. 327 
or two straight lines K P, K R, and Akl, wvw are the symbols 
of two poles Q, S or of two points Q, S, may be conveniently 
denoted by KP, Q. KR, S (or Q, KP.S, K R), which shows 
how the indices of KP, KR, Q, S are combined in the nume- 
rator. This notation is especially useful when the indices of K P, 
Q, KR, S are not denoted by letters. When they are denoted 
by letters, it suggests efg, hkl. pqr, uv w as a conyenient ab- 
breviation of the preceding expression. 
Let D, B, F, G be four centres of projections of zone-circles, 
no three of which are in one straight line, and of which the 
symbols are known ; T the centre of the projection of any other 
zone-circle, Let H be the intersection of DE, FG. The sym- 
bols of D, E being given, that of DH is known. When the 
symbol of T is given, that of DT may be found, The angle 
GDT is then given by the equation 
sn GDH sin FDT 
ain FDH sm@pr “? DH. 8, Dr. 
In like manner the angle GET is given by the equation 
TL 
sinGEH sin FET 
sin FEH sinGET See ee 6 B 
Hence the position of T is de- 
termined. 
When T is given, the ratios 
of the indices of the zone-circle 
the projection of which has T for = = 
its centre may be found from the preceding equations. 
Having given the symbol of a pole, to find the centres of the 
stereographic projections of any two great circles which intersect 
in its projection Q. 
Let the locus of the centres of the projections of great circles 
passing through Q, meet DE in V, FGin W, and GD in U. 
The symbol of UWis the same as that of the original of Q. 
From this, and the symbols of D, E, F, G, those of H, UG, UW, 
can be obtained. The points V, W are then given by the 
equations HD EV 
ED ay =H UG-E, UW, 
HG FW 
7G uw = 1 UG.F, UW. 
When Q, the projection of any pole, is given, let the straight 
line U W passing through the centres of the projections of any 
two great circles intersecting in Q, meet DE, FG in V, W. 
Then the preceding equations give the ratios of the indices of 
U W, or of the original of Q. 
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