Reduction of the Triangulation. 279 
collection to eitliei of these angles will be small. Instead, therefore, of this equation, we 
shall take the equation 
AB AC AE AD 
AC AE AD AB 1 
which contains the ratio of the sines of ADB, ABD. 
Take next the point F: this point is fixed by the bearings from A and E, and the 
observed angle at F gives the condition 
o = A + E + F— 180 0 - s 6 
But F also observes and is observed from B and D ; this gives four equations of condition, 
two of which are 
o = A + B + F — 18o c — e, 
o = A + D + F— 180 0 — e 8 
and the other two 
AB AF AD 
AF AD AB ~ 1 
AD AF AE 
AF AE AD " 1 
Next take the point G: it is fixed by bearings from E and F, and the observed angle at G 
gives the equation 
o=E+F+G— 180 0 - e g 
The reciprocal observation of B at G and G at B gives these two equations 
o=B+F+G— 180 0 — s I0 
and the side equation 
FB FG FE _ 
FG FE FB 
But there is also a bearing to G observed at D, which affords the equation 
GD GE GF _ 
GE GF GD 
Taking now the point H, it may be considered fixed by the bearings from F and G, and the 
observed angle at H gives the equation 
o = F + G + II — 180 0 — e n