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to be derived from the Triangulation may
therefore be stated as follows—The
correct exhibition of the relative positions
which detached surveys occupy, with a
view to their combination; the indication
of the accumulated amount of error existing in the same; the infallible detection
of errors, and the precluding their promulgation outside their precincts in
future surveys.

That these important results have been
accomplished is fully exemplified by the
complications of the surveys which have
been effected in this office during the
past two years, and by the fact that our
sectional surveys are now being prosecuted with such a degree of accuracy,
that chained measurements are rejected
as erroneous, when their results, on comparison with the triangulated measures,
exhibit a ratio of error greater than one
link in every ten chains traversed. It
may further be stated that small as the
assigned limit of error may appear to be,
it is nevertheless a fact that the average
rate of error committed in the prosecution of chain surveys, does not amount
to more than one-half of this limit.

Another very important result derived
from the triangulation is the geodetical
deductions of the latitudes and longitudes
of its principal stations, with reference
to an initial point. In co-operation with
J. T. Thompson, Esq., Chief Surveyor of
the Province of Otago, I was occupied
during the years 1870 and 1871 in fixing
astronomically the longitude of my private
observatory at the Hutt. The observations were embodied in our joint report
to the Hon. the Colonial Secretary, dated
November, 1871, in which we stated the
longitude of the Hutt Observatory to be
174° 57' 40.84" East. I also determined
the latitude of the same place by observations on stars with the transit instrument in the prime vertical and with the
following result:—

From these data the geographical position of the Wellington Observatory, considered as the initial point of surveys,
has been computed to be in latitude
41° 16' 46.84" South, and longitude
174° 48' 49.65" East, and on this basis
the geodetical latitudes and longitudes
of the triangulation have been computed.

The true meridian was determined by
astronomical observations at the Hutt
Observatory, and at the base line in the
Opaki Plain. From these data the true
bearings of the sides of the triangulation
were arrived at by computation, the Hutt
meridian being used for the Wellington
and West Coasts Trigs., while the Opaki
meridian was adopted for those of the
Wairarapa and East Coast. The two
determinations of the true meridian were
found to differ by thirty seconds, on
comparing the true bearing from Mount
Matthews Trig. station to Pencarrow
light, as furnished by each determination.
This difference may be said to represent
the accumulated instrumental errors in
the angular measurements of the triangulation between the Hutt and the Opaki,
and assuming that these have been
gradually accumulating errors, the mean
error in the bearings of the sides of the
triangulation would be fifteen seconds, or
equivalent to six inches per mile, which
ratio of error remarkably coincides with
that which I have before stated.

With reference to the cost of this work,
it is necessary, in the first place, to offer
a few explanatory remarks. The area of
Crown land covered by triangulation is
two and a quarter millions of acres. The
main triangles shown on the map are
composed of 150 stations, while the
minor triangles, which the small scale of
the map does not permit of entry thereon,
furnish about 750 more stations, fixed
with almost the same care and accuracy
as the principal ones. As both works
have progressed pari passu, and were
executed by the same officers, I must
summarise the total cost thereof, and
thence infer the probable cost of each
work.

The total cost was £7000, which is in
the ratio of three farthings per acre or
£8 per station. But as some of the
major stations were built in a most substantial manner, (see drawing on map)
thereby entailing considerable extra expense in construction and in furnishing
the means of transport to reach them;
while as the delays occasioned by the
state of the weather, in obtaining observations from them to distant objects,
would also increase the outlay per station
for the main triangulation—I estimate
the increased expenditure to amount to
£18 per station, which would give a ratio
of one farthing per acre for the main
triangles and a half-penny for the minor.

In connection with this report, I desire
to diverge somewhat from its legitimate
purpose in order to allude to and rebut
those expressions of doubt and scepticism
with reference to the value and practical
usefulness of this system of surveying,
which emanated from certain professional
quarters, when on my arrival in New