D —No. 20.

felt as much as possible, it was arranged to permit the claimants of large blocks of land within it to have their boundaries surveyed at the same time, by a system of minor triangulation based on the major triangles, and carried round the boundary lines in single series. The extension of this detail work would give the whole geographical completeness, and the charge made to the land claimants for it of about id. per acre, though far less than has been paid for very inferior work, would fully repay all the additional expense incurred in performing it. From the want of instruments and other causes, this work was not commenced until late in the season, and the Taupo plains were not reached until it was too advanced for work in that elevated and cold country. It was resumed ear]y in the present season, and so great a progress was made that by the end of February the surveys were ready for the adjudication of at least 500,000 acres, of claims which were set down for hearing in the Native Land Courts to be held in Taupo and at Tauranga early in March and April; but unfortunately the irruption of Te Kooti into the district spread such alarm and excitement, and created so much real danger in parts, as necessarily put a stop not only on the surveys but to the sitting of the Courts. By this untoward circumstance a large quantity of work in the Bangitaike Valley has been left unfinished, and at its resumption at a future period the greater part of it will have to be done over again. This interruption necessarily greatly enhances the expense of the work ; nevertheless, I think I am entitled to claim it on the whole as a success. The area included within the whole district covered by the triangulation is 2,000,000 acres, of which 915,000 acres within computed triangles may be considered completed; reconnoisance has been carried a good deal further, and most of the detail work of the boundary surveys of nearly 300,000 acres has also been completed. The positions of the major stations are determined within a limit of error which cannot exceed one foot in a mile, and trustworthy sketch-maps have been prepared of a district previously very imperfectly known, which will, it is believed, servo many useful purposes, and will greatly facilitate a more elaborately accurate survey, if it should ever hereafter be desirable to make one. I do not now propose to enter upon any detailed description of the processes of survey adopted ; these are minutely set out in the instructions, of which a copy was forwarded you, for the survey of the Chatham Islands and elsewhere. I need only say here that the principle is that of minor triangulation, that is the triangles are treated as parts of a plane surface. The angles have all been observed with a 12-inch and an 8-inch theodolite, and precautions have been taken to secure their observation with the utmost accuracy attainable with such instruments. The base was very carefully levelled and measured, under precautions which seem to exclude the possiblity of error to the amount of three inches in a mile. The direction of the prime meridian and the latitude of the starting point were determined with great nicety, and the calculations, from which result the distances on the meridian and perpendicular of each station from the starting point, have all been checked and recomputed in the head office at Auckland, and the computation all duly tabulated. The convergence of meridian and other corrections necessary to reduce the whole to a near approximation to the truth, have also been computed for outlying stations. It is obvious that this system is theoretically inaccurate, but since it furnishes the elements to which approximate corrections for spheroidicity can be readily applied, it is believed that the result will afford as near an approach to the truth as is attainable with instruments of the size and class used; and in the first instance, in entire ignorance of the country and of its roads, it would have been wholly impracticable to have used larger ones, even if we had possessed them, since the only means of carriage of them is on men's backs. The result is certainly quite accurate enough for any practical object connected with the titles of land. Still since the survey will I hope bo used as the centre upon which all the other surveys from Hawke's Bay, from Cook's Strait, from the Thames and Waikato, and ultimately from the West Coast (Aotea and Kawhia) will close, and the standard by which they will be checked, I still retain the hope, at some future period, to retake the angles of a few selected stations with instruments of a superior class, and to close a few large triangles embracing the whole work on a base of verification at Taupo, or at Hawke's Bay, and so to reduce the possible error to a very small quantity indeed. The south end of the survey enters to some distance into the Province of Wellington, and the north-west angle of the Hawko's Bay Province has been reached. If any survey from which geodetic elements could have been deduced had existed in the Province of Hawke's Bay, I could with facility have closed my survey upon it, and so have checked the two reciprocally, and have incorporated them into one work. But only a small part of Hawke's Bay Province has been triangulated, and even that not in a manner to admit of comparison and closure with a general triangulation. It is obvious that the mere taking triangles, even with some degree of accuracy, will not afford geographical information unless the quantities resulting from their computation can be converted into differences of latitude and longitude from a point the position of which is known, and this involves the accurate determination of the prime meridian and the latitude and longitude of the starting point. The Hawke's Bay triangulations have not this character. In my observations on the surveys in the Province of Wellington, I have stated that the triangulation there may well be united with that at Taupo, and be made part of a Colonial work ; but this must be done by first extending it over the greater part of Hawke's Bay Province, a work which will receive no aid from anything that has yet been done there, but which will not be either long or expensive. A triangulation has been completed of the Chatham Islands by_ Mr. P. Smith, under general instructions prepared by me. Mr. Smith has furnished you with a detailed report of his operations, sothat it is unnecessary for me to say more than that the work appears to have been most carefully performed, and that notwithstanding some difficulties met with, especially in finding a suitable base, there can bo no doubt of its thorough accuracy and completeness. Mr. Smith's Field Book is a perfect model of neatness and accuracy, and of lucid arrangement of the different observations and calculations. The only point in the work which I find open to criticism is the method used in the determination of the direction of the true meridian: this has been done by azimuth in altitude of the sun, and occasionally of a star, a few hours before or after their culmination. This method is not susceptible of much accuracy with a theodolite, unless in the case of a star very 3

9

INSPECTOR OE SURVEYS.