Survey of Northeast Greenland. 223 
partly because this operation, in circumstances like those in Green- 
land, must occur rather frequently. 
Given are the sides a and b. Further in P г 
the angles a and В have been measured. И we AN: 
knew the angles р and 4, all the pieces of the two SINE 
triangles might be directly determined. That which Een. 
is given is, however, sufficient to determine p and 
q, which may be done most easily by finding half 
of their sum and difference. We have: 
a 8 + (+20) + (+9 = 360°, "2 (p+-q) = 180° +: (a +847 +0) 
Fig. 30. 
sin sin sin b sin a 
Further шт = а - PA = ; 1. — Pen —— 
sin & sin?’ sing a sin В 
Now the auxiliary angle u is introduced as determined by tan u 
__ asinf 
bsina' 
sin 1 Sin p + sin 1—tanu 
gee ence: ee = Or 
sin q tan u sin p +- sing 1— tanu 
2sin!s(p-g)eos!k(p+g) _ tan k(p+Q) _ fans? =") 
2sin1/2(p+q)cos'i2(p+q) tan "2 (p + q) 
tan 1 (р + 9) = tan "2 (p + q) tan (45° - и). 
sinq 
sin p 
The correct computation of p and q is controlled by tan u — 
After all the angles of the triangles have been determined, the 
sides c, d and m are computed by means of the sinus formula. The 
side m is obtained with control, as it enters into both triangles. 
In the latter part of the subsequent table an angle and its oppo- 
site side are designated together; thus pm indicates angle p as well 
as the subtending side. 
Computation table for the station pointing. 
A OME et un lo STARTER EE а 
(7) ER ee — tan (45° м)... 45° —-u...... 
at+tftyto..... — tan 1/5 (p + q).. AIDER 
(a + В +7— 0). — tan!» (p + q).. TEN) ea eee 
РЕ 9)... DR 
DEREN: 
angles log sinus log side 
осо TEE А оС 
Ее ПО Е 
Ме еее ее log (a : sin a).... 
FAC SR re de KS Me PASS ht EN SU U seas a abo lac hare 
ETE SKG Soret OMR chk AORN Ey Alt le ate Ae 
EDER re pe cP OYE EN FREE er LE PAR log (b : sin f).... 
XLVI. 15 
