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triangulated sides by carefully measured bases, a symmetrical network of triangles — which will presently be proved to have harmonised inter se with remarkable precision — was thrown over those portions of the Province which were immediately under sectional Surveys.

The entire system of the Triangulation therefore rests upon eight measured bases. It will be needless here to detail the manner in which these bases were measured, beyond stating that the printed instructions for the guidance of the Survey Staff on this subject, were strictly adhered to; that every care was bestowed to ensure concordant results in the several measurements of each base line; and that the unit of measure employed was a new standard chain of 66 feet, by Troughton and Simms.

I will now proceed to exhibit in the following table the amount of precision attained in the execution of the work, premising that the severest test Triangulation can be submitted to, is that of comparing the computed length of a verification base line with its measurement.

From such consistent agreements repeatedly occurring between the computed length of a side of the triangulation and its measurement, the ratio of error existing in the work may be inferred with a close approximation to truth; and, founding upon this assumption, I estimate that the mean error of the triangulation is 0.81 links or 6 3/8 inches per mile, which is equal to a ratio of 1/7748. This minute degree of error I attribute to the care which was bestowed on the angular observations; every angle of a triangle entering into the computations having been read off at least eight times on different parts of the limb of the theodolite, and to the system adopted of computing the triangles combined in a series of polygonal figures, so that discrepant results in the common sides of each series (if found to be within the probable errors of observations) became susceptible of elimination on differential principles, before operating on the succeeding ones.

By reference to the map, your Honor will perceive that the connections between Wellington and the East and West Coasts respectively, are not as yet satisfactory, that between Wellington and the East Coast being merely the apex of two adjacent triangles, whilst the West Coast connection is formed with very inefficient and imperfect triangles between Kapiti and the Manawatu River. In order, therefore, to obtain a rigid connection, and simultaneously to explore and prepare for settlement a very large area of the Province, a series of triangles of sides, varying from twelve to twenty-five miles, has been planned, as indicated on the map by dot lines joining the selected stations over which the angular measurements are now being taken.

The perfect symmetry and large dimensions of these triangles, while forming the desired connections in a rigid manner, are proofs that the character of the work should rank in the first order of Trigonometrical operations. But the means at our disposal will not permit the attainment of the precision usually expected to result from such undertakings, where the greatest refinement is observed. If, therefore, a precision is attained equal to, and to confirm the estimate of error I have above stated as existing in the perfected triangulations, I unhesitatingly aver that this will be more exact than is required for the ordinary purposes of surveying, and will preclude the necessity of future similar operations, excepting for the furtherance of scientific researches.

In order to illustrate the practical results accruing from the Trigonometrical survey, I must now glance retrospectively at the conditions of the sectional surveys prior to the execution of this work. They consisted of numberless detached works, dependent solely on chain measurements. The errors arising from direct linear measurements over hilly and broken ground, were unavoidably great, and those, when added to the other errors emanating from a diversity of meridians, equally unavoidable in bush country, would have resulted in such a degree of inaccuracy as to render these surveys incapable of combination. Moreover, apart from these inevitable errors, there were others resulting from the incompetency and carelessness of some of the surveyors. The most important results