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Volume 33, 1900
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Art. LXI.—Survey: Practical and Precise.

[Read before the Wellington Philosophical Society, 12th March, 1901.]

The survey of new lands contains more elements of interest than that of older countries; in the former case the points and lines determined mainly concern the creation of new holdings and new homes, whereas in the latter they only serve to record old ones. In these colonies especially the proportion of land occupiers and owners is so large that most of us are directly or indirectly interested in “section pegs,” “trigs,” and such-like, while at Home the expression of this interest is practically limited to the impersonal “beating the bounds of the parish.” The subject being one of much interest and importance, I propose to consider, from my point of

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view, the merits and defects of our New Zealand surveys as now practically applied.

Among the noticeable defects I give first place to the want of an absolute unit of measure for the colony. The second defect, and a more serious source of confusion, is the want of any provision to ascertain and eliminate the aggregation of errors, which, though not excessive within any given square mile, may become markedly so by accumulation. To these and other points I now ask attention.

The survey system first applied by Mr. J. T. Thomson to Otago, and afterwards to the colony—a system of occupation survey under check by triangulation—was mathematically sound, and, even under the conditions of its application, has resulted in our country occupations being determined with probably as high a degree of accuracy as obtains in any other country, and with a much higher accuracy than has been attempted in most. Theoretically, a primary triangulation with sides ranging from twenty to fifty miles, and, say, a limit of error not exceeding 1in. per mile, should have been carried over the colony; and this should have been broken down to a secondary triangulation with sides of, say, eight to twelve miles, the points of this breakdown governing the working or minor triangulation, which, with sides from two to four miles, would in turn have limited and checked the errors of the occupation surveys.

In the early days of the native troubles, and when the sea-beaches and river-beds were the only available roads, the difficulties in the way of a scientific primary survey were almost prohibitive, and, apart from that, would have required much time to effect, while the demands for occupation surveys were of pressing urgency. To meet the circumstances Mr. Thomson devised a plan of local meridian circuits, with a probable error not exceeding 2 links a mile, and with a locally measured base (being, in fact, a minor triangulation without check), but which would, however, serve for the time to fairly control the occupation surveys, it being an essential part of his scheme that subsequently the rigid primary work should be undertaken, by means of which these meridian circuits would then be brought into harmony and exactitude.

We closed page “one” in 1895–96, when the Surveyor-General reported (page xi.), “We have now a chain of triangles from the North Cape to Stewart Island,” and page “two” still remains unopened. It will be easily understood that in the sixties, when Gunter's chain was used, and when the limit of error of chainage allowed was 4 to 10 links per mile according to the character of the country, a triangulation with a supposed limit of 2 links was a sufficient check.

In the last March number of the New Zealand Surveyor,

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page 184, I wrote, “When it was made, the triangulation met the requirements of the day, for its limit of error was mostly well below that introduced by the old Gunter's chain. Of late years this position has been reversed by the use of the steel band, with the result that ordinary traverse surveys often now possess a higher degree of accuracy than the triangulation which is supposed to govern them. Where close settlement has spread, and on level land, many trig. stations have become useless owing to buildings and plantations, and they require to be supplemented by standard marks at reasonable intervals, which would cost a trifle compared to the tax which the want of them now levies on the public.” I may emphasize this by stating that many trig. stations have disappeared entirely, and that the number missing is on the increase, through neglect to protect or to renew the original marks.

In addition to the “chain of triangles” already quoted, standard bearings have been carried from one end of the colony to the other, from principal stations ten to twenty miles apart; so that our triangulation “bearings” are fairly good, while our “distances” are unreliable. Any so called major triangulation we possess is but an overriding set of large triangles, the sides of which have been calculated from our faulty minor triangulation, and which necessarily contain its cumulative error.

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The accuracy of lineal measurement with the steel band when used with care, but without any attempts at high exactitude, is well within 2 links per mile; that of angular measurements is not so close, but “bearing” and “distance” combined keep our field surveys to about a 2-link limit, while the accuracy of our triangulation is certainly no greater, on the average, than that of our ordinary field-work. As all careful surveyors check their work in itself, the chief use of the present triangulation is to supply the true bearing and a nominal “position value” to which to refer the work. In speaking of “accuracy of lineal measurement,” I mean its approach to coincidence with the official standard chain of the district. These standard chains were laid down by the several provincial authorities with such rude appliances as were then available, and apparently on the abolition of the provinces they were not compared with each other, but were assumed to be similar. Recently it came to my knowledge that differences existed, and as a result of comparison between them and with Sydney I find that Wellington and one other are about 1/10in. short of Sydney standard, the eight other standards being nearly 2/10in. longer than Sydney. In other words, the difference between our longest and shortest official standard amounts to about 3 links per mile—no two of our standards agree—and the Sydney

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standard is a mean between our extremes. As all our standards disagree, it is obvious that nine out of the ten must be wrong, and that probably all ten are; also that these discrepancies must introduce a constant error through all work based upon them, apart from the inherent error of the work itself.

I have recently brought this matter under the notice of the Government, which will, I have no doubt, take steps to lay down a standard chain-length for the colony with the highest degree of accuracy obtainable; and, once a standard is determined, its exact duplication by means of instruments of precision is comparatively simple. The best appliances we possess are two Imperial-standard-yard measures, which do not agree with each other; but, even if they had been reliable, we have not the requisite apparatus to enable us to utilise them. It is clearly necessary to lay down a correct standard for the colony, and, as New South Wales and Victoria each possess a standard chain laid down with extreme care, I should propose to compare one with the other, and, if the coincidences warranted it, to establish our standard of length from theirs. The crypt below the new parliamentary library would be very suitable for its permanent resting-place.

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The Brisbane standard chain (1890), which was laid down with a 10ft. octagonal steel bar floating in mercury, has been tested with that of Sydney (1899) and with the United States American standard (1891 and 1899), the coincidences being within 1/720in.

The next step should be to bring our triangulations into harmony with the standard, and, consequently, with each other. Official objection is sure to be raised to thus eliminating error, on the ground of confusion, but such an objection will not hold water—the confusion exists, and the differences arising through its removal should not exceed the official allowance of error, and can in no way interfere with or affect title.

Having overcome the difficulty of determining a unit of absolute length, the question would arise how best to bring all important measurements into terms with it, and to do this within fine limits of error the only certain and economical plan is to give further effect to our survey system (already described) and carry out the long-postponed primary triangulation. This can be done with marvellous precision, and yet at a smaller cost than would have been possible a few years ago. Many things contribute to this result, but chiefly the modern methods of measuring base-lines and the fact that the country is now opened and its topography completed.

Looking to the necessity for a primary triangulation for our own purposes, and also to the wider interests of science, I should like to see it carried out as a geodetic work of refinement and applied to the measurement of an are of meridian.

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An interesting article on geodetic measurement appears in the October number of Nature, and shows that at the present time great activity is displayed and much interest shown in endeavouring to arrive at a more accurate solution of the great problem involved in determining the figure of the earth.

The Swedes and Russians (jointly) are measuring an arc of meridian in Spitzbergen, the field-work of which is now all but completed; and a well-equipped army of French experts leave shortly for the equator to measure and to lengthen the Peruvian arc.

Lacaille's arc at the Cape, first measured some hundred and fifty years ago, since corrected (in 1840), and still later largely extended, is as yet the only measurement effected in the Southern Hemisphere, the exact form of which, from want of more complete data, is largely arrived at by inference. Sir David Gill, however, proposes to carry a chain of triangulation from the Cape to Cairo, and thence by the coast of the Levant and through the isles of Greece to connect with the existing European systems. This grand conception, if given effect to, would mean an unbroken chain of geodetic measurement from the Cape to the Shetland Islands. At present the Cape triangulation extends from about 28° S. to 35°, the southern limit of Cape Colony, which is nearly on the same parallel as the northernmost point of this Island, Cape Agulhas being in 34° 50′ S. and North Cape in 34° 22′ S.

This colony covers 13° of arc, including the 45th parallel, to which (in the Northern Hemisphere) so much importance was attached when the Formentara arc was measured; and it is also exceptionally situated in this respect: that the curvature of the earth in this hemisphere cannot elsewhere be ascertained in such high latitudes, excepting in South America.

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The cost of a geodetic survey is not now prohibitive, though it necessarily increases with the degree of accuracy demanded, but up to 1/10in. error per mile of base and ½in. error per mile of the triangulation the cost is moderate.

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The elaborate apparatus formerly used in the measurement of primary bases by means of short rods or bars is now discarded in favour of steel bands ranging from 80ft. to 500ft. in length (the most favoured length being 300ft.), and, by means of these, results varying from a probable error of 1 in 1,000,000 to 1 in 1,500,000 (or, say, 1 in. error in twenty miles) can be obtained. I have averaged the results of probable error in five separate bases measured by the United States Coast and Geodetical Survey in 1885 with a steel band of 300ft., and it amounts to 1 in 840,000, or about 1/13in. per mile. Such exactitude is only possible with a measure of absolute length, the modulus of elasticity and coefficient of

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expansion of which have been ascertained, and with the work carried on under the best atmospheric conditions.

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The two base-lines of the Spitzbergen arc were measured by a method introduced by Professor E. Jäderin, of Stockholm, in 1885. It differs, however, but little from that employed by the United States Geodetical Survey, except in respect of the length of band or wires used (Jäderin, 25 metres; United States Coast and Geodetical Survey, 300 ft.), and both processes give almost identical results, or about 1 in 1,000,000, or a probable error of, say, 1 in. in sixteen miles. This accuracy constitutes a forcible protest against our present chain-standard differences, with their mean probable error of 15/100 in. per chain, or 12 in. per mile.

The modern bases used for primary triangulation average about six miles, and do not exceed four hundred miles apart; for secondary, three miles base, one hundred miles apart; and, for tertiary (commonly called minor triangulation), one mile and a half base, and thirty, miles apart. The cost of measuring these bases varies from, probably, not less than £400 per mile for ½0 in. per mile error to £30 per mile for ½ in. per mile probable error.

These detail matters, however interesting, are perhaps out of place when dealing with the main question; so also the magnetic observations now undertaken by the New Zealand Survey Department; and in the same category come tidal measurements, which are necessary to geodetic accuracy, and here as yet are inadequate. Wellington, Westport, and Greymouth represent the South at present, while it requires tide-gauges at the Bluff and Akaroa to complete the surround and establish the necessary reference to “mean sea-level” for the South Island; and the North Island would require similar attention.

The time has now arrived when the perfecting of our survey system has become necessary, and as we can, at small additional cost, largely advance the interests of science while doing so, we should endeavour to compass the two aims in one operation. Looking to what has been effected, to what is now being undertaken, and to what is in contemplation, it seems scarcely open to question that long before the middle of this century is reached all the pathways in the Southern Hemisphere available to geodesy will have been trodden, that the New Zealand arc will probably by then have been merged in a great Australasian arc extending from Cape York (11° S.) to Stewart Island (47° S.), and that the Commonwealth will also have contributed an arc of parallel from Perth to Sydney. The question now is, Is New Zealand, which takes “honours” in most subjects, prepared to seize the opportunity and step into the front rank of science.

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Since writing the above I have perused quite a number of papers and reports on the question of a primary survey for New Zealand, of date 1875 or earlier, and chiefly to be found in vols. viii. and ix. of the “Transactions of the New Zealand Institute,” and in the Appendices to the Journals of the House of Representatives down to and including vol. ii., 1875. All the writers agreed as to the necessity of an accurate governing triangulation, but some of them questioned the advisability of undertaking the work at that date—viz., twenty-six years ago. The two objections raised were—(1) The delays that would be caused if settlement surveys had to wait on primary surveys; and (2) the cost. The first objection has entirely disappeared, and the second is now largely modified. Mr. J. T. Thomson estimated the cost of a complete scheme of survey at £303,000; but he spoke of the work lasting seventy-five years, of the use of a 36 in. theodolite, requiring twenty-seven men for its transport, and other expensive methods, all of which have been rendered obsolete by the use of modern appliances. In 1875 Major Palmer (then late of the Ordnance Survey of Great Britain, and who came to the colony in charge of the Transit of Venus Expedition) estimated the cost at £100,000. With the scientific advances made in the last quarter of a century in the instruments required, our greatly improved means of access, our topography practically complete, and our principal points mapped, it is obvious that even the latter estimate of cost would now be deemed excessive, and also that the cost of a precise survey for New Zealand cannot be appreciably reduced by any further delay. In 1875, the date of Major Palmer's report, our uncontrolled triangulations were only in progress. They have since been carried all over the colony, thereby widely extending the area of our unascertained errors, and consequently intensifying the value of Major Palmer's advice and warnings. I cannot do better than conclude by quoting, from this high authority, his summary of our triangulations*: “The work of the triangulations has been done piecemeal, and each piece in a different way. It rests on a multiplicity of bases and standards, and on separate determinations of true meridian and geographical position. You have disjointed details of good enough quality in themselves, but as yet no means of piecing them together. To put them to their full uses it will be necessary to bring the whole within the grasp of one exact and comprehensive system, and to refer them to a single standard of length and a single starting-point.”

[Footnote] * App. Jrnl. House of Representatives, 1875, vol. ii., H.-1, p. 24.