E 
E i 
REPORT OF COMMISSION V GV-21 
X and Z axes. The direction cosines obtained by the method of Least Squares 
for each axis are combined to obtain /xz: 
COS ax COS az + cos fx cos Bz 4- cos yx cos yz = cos Ixz 
G. ECCENTRICITY OF THE VERTICAL CIRCLE, AND INDEX ERROR 
The arcs defined by 21, 22, * - - , z; are computed. Initially, 
COS a COS az, + COS By COS B,, + COS yo COS Y,, = COS p1 
COS a COS az, + COS By COS B2, + COS YO COS Y,, = COS ps 
COS a COS az, + COS By COS B., + cos yo COS yz, — COS p, 
“en 
Then the true arcs generated in a plane normal to the X axis may be computed. 
cos pı — cos Ix cos Io 
COS zz, = —  —— fat 
sin 7x sin /, 
COS p; — cos Zx cos I, 
cos 7/2» = es : 
sin 7x sin 7$ 
COS p, — COS Ix cos Io 
COS Z'Z, 2 ——————————— — 
sin Ix sin I, 
z/z;' is the index error, and the true arcs generated by the vertical circle are 
^23 — Z2, -604-e- 
‘2s — zu, = 0:4d- es — 72 
Uu 
| 
3 
ta 
ta 
t 
ta 
e 
ta 
ta 
). s! S — 
2a — 221 =0, 11 C4 177 92—1 
where the e values are the errors of circle eccentricity. 
CIRCLE ECCENTRICITY 
Circle eccentricity is defined as the situation where the center of a graduated 
circle does not coincide with the mechanical axis of rotation that is normal to 
the plane of the circle. Circle eccentricity causes errors in the observed angle 
that vary as the sine of the angle referred to the line defined by the circle and 
mechanical centers. The mean of double-reading circles cancels out the errors 
caused by circle eccentricity. It may be seen from Figure 9, 
Direct reading Op=n—e 
Reverse reading 07 — 180° = n +e 
Sum 6p 4 05 — 180?22q 
0n = Or — 180° 
Mean - ^ —