( 131 ) 



Now one places on the horizontal OO the valncs of li ^ and //. 

 which correspond to the secant-planes, the |)oles of wliich li(> in the 

 cnrve ( TA), as ordinate downward, in the way as lias been done 

 on V\. II for the points F (cf. /J and H (cf. 1^^). From the points 

 (/) and (A) resnlt the curves ilK) and (/>JA), indicating the mode 

 of change of the angles //., and li■^, when the |)ole of S{cf,ö) moves 

 along the cnrve ( TA). As //, remains <^0, and //, > 0, and conse- 

 qnently the cnrves {IK) are drawn doited, the cnrxes (/.,!/) in fnll, 

 one finds in the diagrams the value <i =r h.^ - ll■^, bv providing with 

 a negative sign the sum of the absolute values of the ordinates of 

 • the jioints on {IK) and {L^f) that correspond to a definite abscis. 



In PI. I, II the value « = — i01°45' is easily found from {IK) 

 and {LM). If now one draws // to the curve {LAI) a curve {NO) 

 each point of which with an etiual abscis has an ordinate surjiassing 

 that of the correspondent i)oint on {LM) by i3°50', and one con- 

 structs further with the help of the //-diagram for I^=46°35'J5" 

 the curve (A'J') that indicates the mode of change of the extinction- 

 angle with regard to the trace S : T, if the |)ole of the secant-plane 

 S moves along the curve {TL), then the ijitersection {D) of the 

 curves {NO) and {XY) satisfies the condition 



{AB) — {AC) = h^ — h, = a=z — 101°45' 

 {AD) - {AC) — // - h, =- ,'i — 18°50'. 



The point that on the cnrve (TA) answers to {D) is consequently 

 the requii-ed pole of the secant-plane *S' ((/,«). 



It apj)ears now, that the cnrves {NO) and (A')") cut each other 

 only in 3 octants, i.e. in I, III, and VI. These |)oles of the secant- 

 planes are given according to the figure by the coordinates 



P: 305°30' 57° 



Q: i23°40' 42°10' 



R: 206°45' — 45°30' 

 If one calculates, for the sake of control, from these coordinates 

 with the hel|> of the relations (1), (2) and (3) the values //,,//., and // 

 again, then one Iinds 



/ij Aj A., — Aj error // y — k^ error 



Given: - — _101°45' — — 13°5()' — 



p 5i°57' — 49°15' — 101°J2' —33' 65°42' 13°45' -5' 

 Q 6()°49' — 40°o6' — l()l°4o' - 74°4J' J3°.52' +2' 

 R 42°32' — 59°48' — 102°2()' +35' 56°13' 13°41' —9' 



Consequently the result of the graphical solution may bu called 

 satisfactory. If one constructs, with the help of a relation formerly 



