222 PROCEEDINGS OF SECTION A. 
“The advances made in the construction of modern instruments, 
and the employment of modern methods, render the execution of 
such a plan far less troublesome and costly than formerly would 
have been the case. An instrument like the 10-inch Repsold 
theodolite, with its observing hut and observer, can be con- 
veniently transported in a spring-cart with a pair of trotting 
horses, the hooded cart forming a sleeping place for the observer 
when necessary.” 
“Taking from the data, the probable accidental error of a single 
measurement of the difference of zenith distance of a pair of stars 
as + 0”:40, and for the probable error of the tabular declination 
of each star + 0:50 we have for the probable error of latitude, 
determined from the single observation of a single pair of stars. 
V/ (0:40)? + 202)? = 07-54 
Thus from sixteen pairs of stars, observed on a single night, the 
latitude can be determined with a probable error of 
+ 0"-14 
a result which is at least ten times smaller than the probable 
deflection of the plumb-line at each station.” 
“The probable error of azimuth from a single night’s observation, 
derived from all the azimuth determinations made with the 
Repsold theodolite at Port Elizabeth, Hanover, Kimberley, and 
Tygerberg is 
a=07-30 
or if the result from the azimuth determination at Port Elizabeth 
(the first station at which the instrument was used) be excluded, 
the probable error of azimuth from a single night’s determination 
becomes 
sal) k 
and this accuracy is abundantly sufficient.” 
With an instrument and observatory thus easily transported 
and erected (the same instrument being also available for measure- 
ment of horizontal angles) and capable of giving results of all 
requisite precision from the observations of a single evening, the 
construction of a latitude and azimuth hexagon about each longi- 
tude point would be a simple and inexpensive matter compared 
with the labour of and cost involved in the astronomical deter- 
minations of the longitude of the central point, and would give a 
sevenfold value to the geodetic results. 
ASTRONOMICAL AND GEODETIC RESULTS. 
In places where investigations have been made it has, however, 
been found that, notwithstanding such abnormal deflections of the 
vertical as have been referred to, a discussion of the geodetic data 
in connection with the astronomical observations, where these are 
