68 H. G. Fourcade —On the [April 26,. 
each of the directions B’;,B, observed. The correction to the second. 
angle will therefore be 
Hg = dy cot 2% — dy, cot 2 
In the small spherical triangle 7Z,P, right angled at P, 
d, = ZLLy sin Z2,P 
And in triangle ZVZ, 
therefore 
Beg ae) oN Vee 
dy Cot 2 =2 2 sin—> sin Z2Z,P cot 2. 
T 
But from triangle ZOZ,, in which O = A, and Z = 
7. B 
ZZ,P=5—A Ue 5 
ee 
so that 
dy cotrz;7—=) 22 asin 605 (4 _ 5) cot 2 3 
similarly 
ds cot 2, = 22” sin = cos (4 — =) cot 29, 
and 
am) B , 
Xo = 20" sin — 5 | ( A — — ) cot 2 — cos (4 _ = cot a | 
Similarly, the error in the third angle will be 
M e 2B ‘ 4B 
x3 = 2i sin ae | cos (4 — =) cot 2 — cos (4 a =) cot a | 
and in the zth angle 
mB [ os( 4-7-8) oot 2—cos(A—"5=B oot a | ‘ 
Let 
4B 
S; = sin > cos (4-5) aie Dads (4-5) See 
+ sin ee ee 
Lae 1A) sin - 
ep. Bo ANE 
S; = sin > cos (A—F ) + sin cos (AF at i 
-_ ra— 
+ sin 9 
