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Considering the above circumstances and the nature of the country to be submitted to survey, which possessed in every direction prominent features or natural survey stations in the numerous peaks of the hills and mountains; considering also the fact that the requirements of the Board did not demand absolute minuteness as a foundation to their measures above stated, it appeared to me that the system so much had recourse to in Nautical Survey, viz., the ascertaining of differences of latitude for the basis, and the observation of converging angles for the details, was admirably suited to compass the objects in view, by its rapidity of execution and correctness of principle.

In carrying out a series of triangles over a country, correctness demands the careful measurement of a base, and the erection of stations in every direction as minute points of observation; for were this not done, as the operations proceed from small to greater, every incidental error would increase with the progress. This is not the case with the other system; for the basis being founded on the distance between two objects at the extremes of the operations, any errors incidental to the same decrease as the operations contract from greater to smaller. Hence the propriety of adopting less defined natural objects instead of minute artificial stations, in this species of survey.

Having fixed upon the system of survey to be adopted, I proceeded to Campbelltown, in the vicinity of which is situated the well-known prominent object called the Bluff, this being chosen as the southern extreme of the survey operations. Here I carefully ascertained the latitude of the Custom House of Campbelltown, as noted below.

22nd Jan.—Mean of 18 circum-meridional altitudes............ 46 deg. 35 m. 58.8 s.
23rd Jan.—Mean of 16 do. do. 46 35 53.8

Mean latitude of Custom House 46 35 56.3 S.

I also obtained observations for the true meridian, by which and local measurement, I ascertained that the summit of the Bluff was in latitude 46 deg. 36 min. 55.1 sec. South, and that the Dome Mountain, (the other proposed end of the basis of survey), bore from thence 7 deg. 47 min. East.

From the summit of the Bluff I took bearings to all prominent objects having sufficiently defined aspects to be used as stations, after which I proceeded with the general operations of the survey. These I will hereafter shortly describe.

From Campbelltown I returned to Invercargill, and having procured a pack-horse, proceeded over the Waipai and Waimea Plains, diverging in every direction for observations, till I arrived at the foot of the Dome Mountain on the 15th February. From the top of this prominent and commanding object, having the Bluff summit as Zero, I obtained bearings of all the principal objects that I had observed from the latter position, besides other natural features eligible as stations. Near the base of the same mountain, I ascertained the latitude of Observation Bush to be as follows:—

17th Feb.—Mean of 5 circum-meridional altitudes............ 45 34 51
„ Mean of 3 do. do. 45 34 45.6

Mean latitude of Observation Bush 45 34 48.3 S.

These and the preceding observations for latitude were taken by an excellent Sextant of Troughton’s manufacture, and a Mercurial Horizon, accompanied by registers of the Thermometer and Barometer. The distance of Observation Bush on the meridian from the Bluff summit will thus be found to be 1 deg. 02 min. 06.8 sec., or 71.486 English miles.

With this as the basis of the survey, and the knowledge of the true bearing of the Station at Observation Bush from the Bluff summit, which is by calculation 4 deg. 28 min. 30 sec. East, the application of the rules of Plane Trigonometry fixes the position of the Dome Mountain, and thence all other main stations in the survey, where and to which therequisite angles were observed.

Regarding the degree of accuracy that may be attained to by the system of circum-meridional altitudes, while I may state that at prior periods I have had much greater agreement in sets of observations, yet it will be observed that the greatest difference in this instance is 5.4 sec., or as measured on the ground, 547 feet. But considering that this error is halved, by taking the mean of two sets, and that any error of instrument will not affect the length of the base, all the sets of observations being taken with the same instrument, on the same side of the Zenith, the real error may be assumed at considerably less than the maximum above stated.

Assuming the error at the maximum...