940 REPORT—1905. 
measurement of the angles of the triangles has been computed from the 
formula 
. yA? 
6745, /3Np 
where 2 \? is the sum of the squares of the triangulation errors, and N 
is the number of triangles. 
For the geodetic survey of the Cape Colony and Natal the preceding 
table exhibits the limits of error of the triangles in excess or defect of 
180° +<«. 
The probable error of a single triangle in Bosman’s triangulation is as 
follows :— 
Section I. + 1/41 Very flat, arid country, sides 3 to 8 miles. 
Si es CaO eb th cod Ef ria 3 rather longer sides. 
mG Ee ee oF 
TyoR ce 043} Rolling country, longer sides. 
In Mr. Alston’s connections of the eastern and western extremities 
of Bosman’s are with the geodetic survey the probable error of an angle 
wasi— ; 
For the Eastern connection = 0:58 
» 99 Western - a hte 
In the are through Damaraland the distribution of triangular errors 
is as follows :— 
Limiting Values of Errors of Triangles 
” ” ae ar ” 
| | 
0'0 O5 | 1:0 15 2:0 2'5 3'0 35 4£'0 
| to to | to to to to to | to to 
| 0°5 10 | 16 20 2°5 80 | 35 40 45 
ee eee ee | 
| No. of Triangles| 52.| 48 | 34 | 19 | 18 | aati) “Eek selaie pa 
1 
From the original errors of closure of the 194 separate triangles the 
probable error of an angle was found to be +0'':59, 
In the Transvaal, Orange River Colony, and Rhodesia, so far as the 
results are before me, the triangular errors and probable errors of a single 
angle are as follows :— 
Abstract of Triangular Errors. 
| Limit of Errors of Triangles 
ih 
3 —— Probable 
P ‘ : piesa " @ ” " "| Error of 
3 Portion of Chains dics ni oe a ae Pine re 
5 to to to to to Angle 
06 1'0 15 20 2°5 
| G. | Belfast-Natal . rl 28 15 8 4 — 2 +0133 
G. | Belfast-Ottoshoop . ol 28 14 9 2 2 1 + 0/35 
S. | Pretoria-Cwecweni eGo 25 26 10 2 ae +0'30 
G. | Natal-Kroonstad . Pa fe pet (0) 6 4 [°— — — +0'"19 
G. | Kroonstad-Kimberley .j 18 10 7 1 — _ + 0'23 
L. | Kimberley—Ottoshoop .| 57 19 18 12 T i + 0''33 
\ pee EE en pee es pee ee 
205 | 89 | 72 | 29 | iL | 4 | £0733 
§.=Mr. Alex. Simms. G. = Captain Gordon, R.E. L.=Captain Leys, R.E. 
