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The line extending through the Northern Districts and up the Waitaki to Lindis Peak gives an observed meridional difference of 49’ 22”. The line through the South-Eastern Districts, and up the Clutha and Manuherikia to Lindis Peak gives the meridional difference as 49’ 44”, or a discrepancy of 22” in the extension of a line having upwards of thirty intermediate stations. This error of angular measurement is no doubt distributed over many districts; but supposing it occurred all at one station, it would not cause any very material difficulty to the accuracy of the minor triangulations to follow. The calculated meridional difference lies between the two observed differences, and if the mean of the latter be taken, the observed difference will become 49’ 33”, while the calculated for a spheroid is 49’ 30”, or a difference of 3”.

In reporting on the latitude determined at Observation Point, it was mentioned that the mountain masses surrounding that station were likely to deflect the plummet, and consequently by the same quantity the true position of the zenith point. This source of error, unlike the instrumental and personal errors, is not eliminated by observing stars north and south of zenith, but is actually doubled in the resulting latitude. Since no observations at the station, Observation Point, can detect the amount of correction due to the deflection of the plummet, it only remains to apply the difference (14½’) as a correction to the observed latitude, which will thus become 45° 49’ 09” S. It must also be mentioned, that a period of upwards of two years has elapsed between the taking of observations at the two stations, so that unless the tabulated differences of the stars’ declinations be absolutely correct for the period in question, any error that may be, will affect the observed difference of latitude. To get rid of this source of error, it would be necessary to observe at the one station immediately after completing observations at the other. The latitudes of the other stations are not so likely to be influenced by the deflection of the plummet, because, although situated in mountainous districts, the point of observation is always on the summit and not at the base of the mountain as at Observation Point.

The true meridians of Mount York and Mount Nicholas were determined by equal altitudes and azimuths of stars, the star selected at Mount York being ζ Orionis, while α Hydrae was similarly used at Mount Nicholas. The bearings of the several meridians have been extended and closed on each other, and the meridional differences of bearing observed and noted. These have also been calculated both for a sphere and spheroid. The following table gives a comparative view of the results:

The data from which the above results are deduced are the latitudes of the several meridional stations as recently determined, and the differences of longitude between them as determined by the reconnaissance surveys. The longitudinal differences, although not absolutely correct, are still sufficiently so to test approximately at least the observed meridional differences. By referring to the above table, and comparing Observation Point (the most easterly meridian) with Mount York (the most westerly), it will appear that there is only 1½” of difference between the observed and spherical meridional difference and 25.5” between the observed and spheroidal difference.

In comparing the differences between the calculated and observed meridional differences, it must be borne in mind that as the meridional stations are not visible from each other, the errors of angular measurement in extending the lines of bearing between them are necessarily incorporated in the observed meridional differences. As Observation Point and Lindis Peak are connected by two independent lines of bearing, there is the opportunity of comparing the two, and noting the error of the one on the other.

By comparing the meridional differences now determined, and those obtained from the observations of the reconnaissance survey of the Lake Districts, it will be seen by a reference to the report on that survey that the meridional difference between Mount York and Mount Nicholas is given at 30’, and between Mount Nicholas and Lindis Peak at 44’, thus differing in each case from the geodesical determination by about half a minute of arc. But while thus nearly agreeing in the meridional differences, there was found to be an absolute error of several minutes in bearing on each of the reconnaissance meridians of Lindis Peak, Mount Nicholas, and Mount York, the bearings of each reconnaissance meridian being in excess of the corresponding geodesical meridian. On the Lindis Peak meridian the difference is 8’, and this will have to be applied subtractively to the bearings of Leaning Rock District, triangulated on the reconnaissance meridian of Lindis Peak. And similarly 7’ will have to be applied subtractively to the bearings of the Shotover and Coneburn Districts triangulated on the reconnaissance meridian of Mount Nicholas. In regard to the reconnaissance survey, it may be remarked that the error being on the same side of all the meridians, and nearly constant in quality, it cannot affect the distances, areas, or relative positions of the objects of that survey.*

The latitudes of the reconnaissance may also be compared with those of the geodesical survey, and are as follows:

From the above differences it will appear that the sextant determination are all too much north, by the amount of difference in each case; it is satisfactory, however, that the differences are so nearly uniform.

The reciprocal vertical angles of all the geodesical stations have been carefully observed and recorded in the field-books, so that the altitude of each station may be calculated, as the accurate distances are supplied by the extension of the minor triangulation.

During the past season standard chain lengths have been laid down by means of standard brass scale and beam compass at the Reference Trig. Fern Hill, Te Anau Downs, and at the Survey Office, Queenstown.

I have the honour to be, Sir,

Your most obedient servant,

JAMES M’KERRON, Geodesical Surveyor.

• NOTE.—The reconnaissance survey meridians were determined by afternoon observations of the sun, taken by a four-inch Everest theodolite. The constancy of the error both as to quantity and deviation on the western side of the geodesical meridian in each case plainly points to the vertical arc of the Everest being out of adjustment. If both forenoon and afternoon observations had been obtained, this error would have been at least partly detected. The great altitude of the stations, clouds, and other circumstances, prevented this from being accomplished.