24.2 REPORT—1905. 
(6,000 feet) can be 24 inches in error, seeing that the largest difference 
between the forward and backward measure of any of its eight sections 
was only ;3, of an inch. 
Taking now the Belfast base as standard, and comparing it through 
various independent circuits with the other bases, we get the following 
results, which are in much better agreement :— 
Diagram No. 1. : 
Comparison of Measured Lengths of Bases with Lengths computed from Belfast 
Base. 
Approx. Approx. Approx, 
Base wat ough Geigth of Tenth of Error of Ratio 
Chain Base Base 
Miles Feet Feet 
Ottoshoop . 6—5 250 57,212 —0:99 1: 57,900 
Kroonstad 7-65 350 64,920 —0°90 1; 72,380 
Wepener : 8—5 500 71,048 —0'16 1 : 434,300 
Natal . ° 4 4—5 300 10,800 0:09 1: 120,600 
Pert Elizabeth - 5 700 17,058 ! +0:27 1: 63,870 
Zwartland . 1-5 1,200 42,819 —0'70 1: 61,160 
a . » |9-54+3 1,250 ” + 0°73 1: 58,690 
Kimberley . 9-5 450 14,760! — 0:22 1: 66,810 
if | 2-5 1,100 és — 0:26 1: 55,680 
1 These refer to the bases prolonged by triangulation; the measured distances 
were 6,000 feet on both bases. 
But besides the discordances of bases when computed through inter- 
vening triangulation from one to another, in order to attain geometrical 
harmony we must also satisfy the condition that the circuits shall close 
harmoniously ; that is to say, the terminal point of any side of any 
triangle in the chain, when computed in any direction through the chain, 
shall be exactly reproduced in latitude and longitude, and the side in length 
and azimuth. 
The discordances are given in the following tables, illustrated by 
Diagram 2, 
Closure on Lines. 
5 | Log. ; 
Circuit Circuit Junction gaa ae | Discordance Ratio 
5 of Side 
Bruintjes-Hooghte- Miles bc 2 ag 
(a) 142 ice 1,100 0000132 | 1in 32,900 
1 { Pt andabare pees | 700 0000084 |1in 51,450 
q { ee ae a ca 650 0000010 | 1 in 434,300 
(0) b+7 | LubisiXuka .. 1,100 ‘0000031 | 1 in 140,000 
(0) 8444647 { cere og BA. \ 1,500 0000029 | 1 in 150,000 
(a) This is equivalent to the closure on Kimberley base through chains 1 +3 and 
2 (Diagram 1). 
(b) Part of the temporarily adjusted chain for the closure on the Natal base. 
(c) The temporarily adjusted chains for closure on Kimberley and Natal bases 
enter into this circuit ; otherwise the equation would be equivalent to the closure on 
the Kimberley base through ehains 2 and 9 (Diagram No. 1). 
