66 H. x. Fourcade——On the [ April 26,. 
Il. ROST’S OBSERVATIONS. 
Ill. RHEIMER’S OBSERVATIONS. 
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Towards the end of 1890, I had occasion to carry a small secondary © 
triangulation, over portions cf the districts of George and Kuysna, to- 
connect a few detached surveys and serve asa basis for subsequent 
work. The only instrument available for the purpose (a six-inch: 
Everest theodolite by Troughton & Simms, read by two verniers to 
20 seconds), although excellent for ordinary work, gave results that 
were not altogether satisfactory in a triangulation with sides averaging” 
five or six miles. The method of repetition was then tried experi-- 
mentally, but it was soon found that the instrument showed, to a 
curious degree, the peculiarities which ordinarily vitiate results: 
obtained by repetition: There was an error in the angles, constant 
for a definite origin, but varying with the origin from a positive to- 
a negative value; there was, in addition, a periodic error, which, 
although it was to a great extent masked by the large mean error 
of each reading, seemed to vary with the number of the repetitions ;: 
the direction of rotation had also a marked influence upon the 
resulting value. 
These discrepancies could not be attributed in any way to the 
‘ back lash ”’ of the tangent screws which was entirely taken up by 
unusually strong flatsprings of German silver, and their increase’ 
with the difference in altitude of the stations observed appeared. 
to point to the inclination between the upper and lower vertical. 
axes (a conspicuous defect of some theodolites) as being the chief 
eause of their occurrence in the observations. 
In an angle obtained by repetition, the error due to imperfect 
