ORIGIN AND PROGRESS OF GEODETIC SURVEY IN SOUTH AFRICA. 241 
In Northern Rhodesia Dr. Rubin’s results, so far, appear to be of like 
accuracy with those obtained by Mr. Simms in Southern Rhodesia. 
But now with regard to the nine crucial tests given in Diagrams 
Nos. 1 and 2, Plate IIT.. 
If it were possible to measure all the angles of a triangulation without 
error, and base lines without error, it is clear that if the length of any one 
base was calculated from any other base as origin through any intervening 
chain of triangles, we should obtain a length of the base by computation 
which would agree precisely with that of its measured length. As all 
human operations are fallible, this agreement never occurs except as a 
matter of chance ; and, as the operation of triangulation is necessarily 
much less accurate than that of base measurement, the discordance 
between bases compared through intervening triangles is generally far 
greater than the probable errors of base measurement. 
On this account it is usual to consider the base lines as free from 
error, and to compute by least squares the corrections applicable to the 
angles of the triangles which are necessary to bring about an agreement 
between the measured and computed lengths of all the base lines. 
Colonel Morris has kindly communicated to me the results of the pre- 
liminary computations made for intercomparing the bases measured in 
Cape Colony, the Transvaal, Orange River Colony, and Natal, with 
the exception of the Limpopo, or Houts River base, the triangulation 
connecting which with the Belfast base is not yet completed. 
Diagram No. 1. 
Comparison of Measured Lengths of Bases with Lengths computed from the Port 
tthzabeth Base (produced). 
Approx. Approx. 
Base rou Tareth of Lenath of Pen she 2 Ratio 
nan Chain Base Tror 0. ase 
Miles Feet Feet 
Zwartland . 1 500 42,819 — 1:37 1 ; 31,250 
Kimberley . 2 400 14,760! —0°50 1 ; 29,750 
s ? 3 600 fe —0°50 1 ; 29,750 
‘s . 7 1+3 1,100 3 —0:94 1 : 15,620 
=) P 9 1,150 “ — 0°45 1 : 32,650 
Natal. - 4 400 10,800 — 0°26 1: 41,770 
Belfast 5 700 62,316 —0°98 1 : 63,870 
Ottoshoop . 6 950 57,212 — 1:88 1 : 30,380 | 
Kroonstad . 7 1,050 64,920 - 1:92 1 : 33,930 
Wepener 8 1,200 71,048 —1:28 1: 55,680 | 
! This refers to the base prolonged by triangulation from 6,000 feet, directly 
measured, 
It is very remarkable that these comparisons agree in showing all the 
other bases are apparently shorter than the Kimberley base, and it seems 
impossible not to conclude that there is some undiscovered source of error 
in the Kimberley base, although it is hardly possible that the base itself 
is really six inches too long, as this comparison would appear to show. It 
is more likely that the error has been produced by a grazing line or lines 
in the extension of the base ; although the residuals in the angles of the 
quadrilateral figures by which the base was prolonged show extremely 
bey Fine for one cannot imagine that the measured part of the base 
1905, R 
