On New Zealand Surveys.

Transactions and Proceedings of the Royal Society of New Zealand, Volume 8, 1875, Page xxvii

On New Zealand Surveys. By J. S. Connell. [Read before the Otago Institute, May 25, 1875.] It has been thought by some with whom I have lately conversed, that a paper on the above subject might, at the present time, be acceptable to the members of this Institute, and possibly interesting to the public. For a number of years past the feeling has been growing in the public mind, that the surveys, at least in many parts of the Colony, were in an unsatisfactory condition, and the matter was, during the last two sessions of the General Assembly, pretty freely ventilated. During his recent visit to the Colony, Major Palmer, of the Royal Engineers, was requested to examine into the condition of the Survey Departments of the various Provinces, to report thereon to the Colonial Government, and to submit such a scheme as he might deem necessary for the reform and correction of that branch of the public service. His report, together with the recommendations he had to give, has now been made. It discloses a state of affairs in some of the Provinces which, although known pretty generally to the profession to exist, has never before been tabulated and duly recorded. The report is therefore exceedingly valuable, in so far as it contains a correct statement of facts connected with the actual condition of the surveys of the Colony. The remedy, however, proposed by Major Palmer, is open to criticism, and I venture to doubt whether it is indeed the remedy, which under the special circumstances of the case is required. It is of very great importance, in coming to the consideration of any practical subject such as the one now before us, that the mind should be perfectly clear as to the special result desiderated, and should have in full view the entire existing state of surrounding circumstances. To apply this to the concrete and to the subject before us. A system of survey might be admirable, if the special result desiderated were a correct record of the relative position of existing objects, such as buildings, fences, roads, railways, canals, &c., &c., and yet might be quite unsuitable where the problem was to give possession of a portion of the earth's surface not possessing any permanent marks, or bearing upon itself evidences of its boundaries. Or, shortly—It is one thing to survey and record an already existing possession; it is another to create it.

Where the problem is an accurate survey of existing possessions, there can be, I think, little doubt but that the system adopted in England, and recommended by Major Palmer for adoption here, is the best one. It matters little if twenty or even fifty years elapse before its details are completed. The boundaries of estates, the position of which upon the land itself, have been recognised for centuries, are not likely to vanish, nor any question as to the whereabouts of a canal or of St. Paul's Cathedral likely seriously to disturb any one's repose. The surveyor may leisurely proceed with his 36-inch theodolite to measure the various angles of his great triangulation, and may occupy his time in solving the interesting geographical and geodetical problems which meet him in dealing with a large portion of the area of our globe, without a single person feeling the want of his services or being possibly aware of his very existence. It is, however, quite another matter where the surveyor is required to deal with naked portions of the earth's surface, and, with the least possible delay, divide the same into suitable portions for the occupation of the colonist. He is required, first, upon the earth itself, to mark the boundaries of the various properties; and secondly, to construct on paper, on a proportional scale, a faithful record corresponding in every particular with the actual marks upon the ground, and bearing upon it a record of the measurements of every line of his survey. This document is called a plan of the survey. If the work of measuring the various boundaries and lines upon the ground is correctly performed, and the plan is a complete and faithful record, the boundaries can be reproduced at any time upon the ground, from the information furnished by the plan, provided these boundaries are not entirely obliterated; and hence, in every sound system of colonial survey, it is recognised as requisite that the boundaries of properties which, from the nature of the circumstances, can only be marked in a temporary manner, must be connected or tied to some existing marks or objects not likely to be easily destroyed. This has unfortunately been neglected in many of the Provinces of New Zealand, and hence one source of the existing confusion. But not only is it apparent that boundaries should in this manner be connected to permanent recognised marks or stations, but it is further evident that, inasmuch as the power of reproducing lost boundaries correctly is only possessed where the original detail work has been correctly performed, it is absolutely necessary that some means should be available for testing the accuracy of the detail work itself, and this in two directions. Every line on the earth's surface has two qualities, length and direction,

and it is just as necessary that we should have some means of testing the accuracy of the given direction of a line as its length, ere the check can be complete. The only efficient and proper manner in which this can be done involves the necessity of knowing, and that antecedently to any detail survey being made— 1st, The true lengths of the various lines joining the permanent stations to which a detail survey is connected; and 2nd, The inclination of such lines to a uniform standard of direction, and, as a matter of course, to each other. The lines joining the various permanent stations I shall hereafter call Trig lines, and the permanent stations Trig stations. It is quite true that it is possible to dispense with the knowledge of the inclination of each of the Trig lines to a common standard of direction, but it is absolutely necessary that their inclination to each other, and their true length, should be known, to furnish a sufficient means by which the accuracy of detail surveys can be efficiently checked; and the advisibility of having a standard of direction amounts almost to a necessity. The only means by which practically the length and direction of Trig lines can be correctly ascertained I need scarcely say is by triangulation, founded upon a carefully measured base line; and therefore all competent surveyors are perfectly agreed as to the necessity for this work being undertaken. There appears, however, to be some difference of opinion as to whether it is an imperative necessity that triangulation should precede detail survey, or whether it may not be possible to permit the detail surveys to go on with triangulation to follow. Major Palmer adopts the latter view; I, myself, in common I believe with many other colonial surveyors, hold to the former with extreme tenacity. The special system of triangulation, which it is most advisable to initiate and adopt must depend entirely upon the views which may be adopted on this point. Certain geographical and scientific advantages of considerable importance and of great interest are unquestionably obtained as the ultimate result of the system Major Palmer advocates, but with the terrible consequence attached of losing all control and abandoning all check upon the detail survey of the Colony for many years. It is true that Major Palmer recognises that it is advisable that “due exertions should be made to cause the triangulation in all possible cases to precede the detail survey;” but his system not only makes no provision for

its doing so, but renders it impossible that, in the Provinces lying furthest from his bases such as Auckland and Otago, the detail survey should be overtaken by the triangulation for many years. Major Palmer recommends that, in the meantime, the system known as “poling” should be adopted. (See his report, page 25.) This system consists simply of erecting the permanent stations to be used in the triangulation and requiring detail surveys to be tied to them. (I shall hereafter call the system of triangulation recommended by Major Palmer “Standard Triangulation,” to distinguish it from Minor Triangulation.) By this system (viz., that of “poling”) when the standard triangulation is ultimately completed, and the lengths and direction of the trig lines ascertained, it will be easy to discover the errors which have been made in the detail survey, executed many years previously, and affecting titles which have been long issued. This appears to my mind very like making a provision for locking the stable door after the steed is stolen. What is really needed is not a system which will enable us to discover error, but one which will render its occurrence impossible. There are many other serious objections to the adoption of the system known as “poling,” besides the one which appears to me altogether fatal to it of leaving the detail survey utterly unchecked and uncontrolled; but, if the introduction of such a system were seriously contemplated in the face of this objection, others of a smaller magnitude could no doubt also be got over, and it will be unnecessary for me to occupy your time with a consideration of these. Unless, therefore, all settlement is to be brought to a standstill, or the detail surveys to be conducted, as unfortunately they have already been conducted in many of the Provinces, without proper and efficient check, we must adopt a system of triangulation other than that recommended by Major Palmer. The system of survey introduced into this Province by Mr. J. T. Thomson is one which I consider with very slight modification suitable for adoption by the entire Colony. This system is very fairly described in pages 18, 19, and 20 of Major Palmer's report, who, whilst admitting the general reliability of the work performed under it, points out that the great advantage of a triangulation such as he advocates being carried out, will be to gather up and bring the whole together with the various triangulations in such Provinces as Wellington within the grasp of one comprehensive system, referring everything to a single standard of length and a single starting point. I quite agree with Major Palmer as to the very great advantages which would follow the work of a Standard Triangulation, thus gathering up the

various minor triangulations into one consistent whole, and if the Colony can afford to spend the money, no one would more heartily rejoice than myself to see the work initiated; but let us be clear about one thing—viz., that, until it is completed, such a triangulation cannot replace or do away with the necessity for Minor Triangulation or independent bases. Such triangulation must go on if the detail surveys are not to be left utterly unchacked and unreliable. If the execution of Minor Triangulation is carefully attended to, a means is at once furnished for checking detail surveys, and the work can readily be incorporated with and form a part of a Standard Triangulation, whenever it is deemed advisable that such a work should be undertaken. I turn now to the consideration of the practical question. To what an extent is the extreme accuracy, which we might obtain as the result of a Standard Triangulation, in which instruments of large diameter were used. affected by the prosecution of a more imperfect, but an immediately available system, viz., Minor Triangulation, on independent bases, and carried on with portable instruments of five or six inches diameter. In order that I may appear to speak about a matter with which I am thoroughly conversant, I will take as a sample of Minor Triangulation in this Province a portion of work executed by myself and assistants over the country between Ohau and Hawea Lakes. This country was exceedingly mountainous, the stations varying in elevation above sea-level from 1,100 to 5,286 feet. The instruments used were five-inch plain theodolites. Twelve vernier readings in azimuth were taken at six different parts of the lower plate of the instrument. A base was measured three times with standard welded chain, and due corrections made for temperature near the foot of the Ohau Lake, and a base of verification was measured at the south end of the Hawea Lake about fifty miles distant from the initial base. The result of the angular work was that, taking all the triangles, in number above fifty, the average error uncorrected for the minute spherical excess on each angle was only three and two-tenths (3.2) seconds, or upon the whole triangle, nine and seven-tenths (9.7) seconds. That not more than four (4) out of the entire number of triangles, contained in the sum of its three angles, a greater error than twenty seconds. The length of base of verification was, prior to actual measurement, calculated from the triangulation and found to be 37,383.7 links, and the result of actual measurement 37,386.2 links, or about four inches and one-fifth per mile difference. The measurement of this base of verification was completed in the presence of the present Chief Surveyor, Mr. McKerrow, who himself made the requisite corrections for difference of base and hypothenuse on two steep

terrace slopes at each end of the line, and worked out the result. In a large Minor Triangulation I have now in course of execution for the Provincial Government on ninety-four triangles already observed, the average error in closing each triangle on the sum of its three angles is only eight and seven-tenths seconds, or a little under three seconds to each angle. This shows an improvement on the average of one second to each triangle upon the Lake triangulation, which may be partly attributed to the use of a six-inch instrument over part of the work. The work of many other surveyors who have taken part in the Minor Triangulation survey of this Province is, I believe, of an equally reliable, and possibly even more correct character than that of the sample I have referred to, but the time at my disposal has not enabled me to examine and refer specifically to it. I have noticed particularly that the angular work of Mr. William Arthur and Mr. C. W. Adams, which I have frequently had to refer to, is exceptionally good. Work of this character, I think it may be agreed, is sufficiently good for all practical purposes, and nearly the whole Otago Minor Triangulation, extending over 4,200,000 acres is executed within a fair limit of error, a large portion of it being exceptionally good. All the Minor Triangulation being based upon the true meridian of the initial station of each meridional circuit (of survey districts) is consistent, and refers to one standard of direction within the entire circuit, the whole Province being divided for this purpose into six circuits. For detail concerning meridional circuits, see Major Palmer's report, page 19. As soon, therefore, as a standard triangulation is initiated, whether now or twenty years hence, the whole of the work executed in the Otago system is ready for absorption by it, and in the meantime furnishes a complete means, and that available for immediate use, for checking and controlling the detail survey. The only improvements I would suggest in the practical working of the system of triangulation now in use in this Province are— Ist, That the measurement of bases should either be entrusted to one officer only, who may have displayed a special aptitude for the work, or at least that such officer should invariably be present and responsible for the result, 2nd, That the distances between the various bases should in future be increased. (This has, however, in several recent instances been done.) 3nd, That the limit of error permitted in the observation of azimuth angles should be considerably curtailed, and that the errors of observation should be eliminated from the triangles.

4th, That not less than twelve readings at twelve different parts of the lower plate be taken, if 5-inch instruments are used for azimuth angles. These, however, are mere details, calculated to insure a further improvement in the character of the Minor triangulation, which the greater experience and efficiency of the surveyors available make it now possible to carry out. I think it may now be taken for granted that, with due care, the measurement of bases and angular work, of the character I have shown, may readily he obtained by the careful use of instruments of good quality though small diameter, and that without in any way departing from the system of survey now known as the “Otago System,” in use in this Province, a satisfactory knowledge of the true relative distance and directions of the stations, which it is proposed to use to check the detail surveys by, and that without waiting the eight or ten years spoken of by Major Palmer, or, as I should be inclined to estimate it, the fifteen or twenty years necessary for the completion of the standard triangulation. Before leaving the subject of the triangulation, and taking up the one which I conceive is really of more pressing importance viz., the detail survey of the Colony, I would say a few words in connection with the subject of topographical maps. I have no hesitation in saying that no system of triangulation will either be economical (in the vulgar sense of the term) or suitable for this Colony, unless it makes provision for a topographical survey, to be carried on simultaneously with the observation of the smaller triangles. It is imperatively necessary that, for a considerable time before land is really wanted for sale, the Government should be in possession of a good deal of information about the land, such as its quality, adaptability for settlement, general altitude above sea level, and that the chief topographical features should be mapped out, enabling, the Government, with a tolerable amount of accuracy, to determine the areas of large tracts which it is proposed to open for settlement. And inasmuch as the land laws of several parts of the Colony—our own Province amongst the number—admit of and provide for selection of lands prior to actual detail survey, it is evidently advisable further, that maps should be available, showing the position of natural features, such as rivers, creeks, forest, &c., &c., to enable selectors to identify, and the Land Department to understand, which particular portion of land it is proposed to apply for. When the present Otago system was initiated by Mr. J. T. Thomson, this want was felt and at once met, the surveyors who conduct the triangu-

lation being required to carry on with their observation of the triangles a topographical survey of the country by means of the use of the theodolite alone. This survey includes the determination of the altitude of all trigonometrical points, chief mountains, passes, junctions of rivers, etc. I do not gather from Major Palmer's report that he makes any provision for such a survey. It is of course unknown to the English Ordnance Survey, as there was no necessity for it in an old country; but without it, in the Colony, everything beyond the actually surveyed sections would be practically unknown, and the satisfactory disposition of the waste lands would be an impossibility. It is true that Major Palmer proposes to have constructed a topographical map of the Colony, but he does not appear to understand the necessity of pushing this branch of the work ahead of settlement. He says (page 26)— “In the preparation of topographical maps the method to be pursued will vary according to the particular circumstances and the means available in different parts of the country. In some parts there are already accurate materials to hand, in others some revision and addition will be needed to work up existing details. All future section surveys should be so made as to furnish the chief necessary particulars. “Lands already occupied should be first included, early attention being given to those which are now under lease from rough surveys, and the work could be afterwards pushed beyond these limits to the country at large. “It might be desirable to station a small staff in each district specially to prosecute this branch.” It appears therefore from this extract— 1st, That future section surveys are to furnish the chief necessary particulars. 2nd, That lands already occupied are to receive attention first. 3rd, That a separate staff is to be appointed in each district for this branch. In my opinion the chief use of topographical maps is to enable us to settle people on the lands and prior to such settlement to afford us the information I have alluded to above. These maps may at a future time be improved by reductions from section survey, but have them we must, and that before section survey is undertaken. The appointment of a separate staff for topographical work, whilst in harmony with English system, is altogether against the genius of colonial practice.

In England there are hundreds. I had almost said thousands, available for the work, whilst here we count our numbers by twos and threes. Here we cannot afford to send a surveyor to the top of a mountain simply to observe the azimuths of the trig lines which any accomplished observer can do even with twelve readings in about two hours, but we keep him on the same point sometimes for four or five hours more taking observations relating to the topography of the country. In this manner we obtain the complete work at very much less cost than if we had a number of observers all following one another over the same ground as in England. It is true that we require men of more varied ability than under the other system, but it is our pride to train them, and it is also true that the amount of work required from the colonial surveyor is greater than it would be under a different system. I now proceed to say a few words on the uses to which the stations of a triangulation must be put in connection with the detail survey of the Colony, and I think it suitable here again to advert to the distinction between the detail work of such a survey as the Ordnance Survey of England and that of a Colony such as New Zealand. The end to be attained by the former survey being chiefly correct cadastral maps or plans shewing the relative position and size of objects occupying the earth's surface, a system was adopted of breaking down these triangles, measuring the sides with the chain and multiplying the tie lines; in fact, arriving at the knowledge of the position of the various objects almost entirely by a system of chain measurements and offsets, without employing the theodolite at all. Nor, so far as I can gather, was any more thorough test applied to the detail work than to see that it was kept within such a limit of error as would not be apparent in the construction of the cadastral plans. Traverse work with theodolite and chain appears to have been occasionally resorted to in road surveying, with no trace of any other test being applied save the one I have referred to. For the first time for many years, and since the greater portion of the preceding part of this paper was written, I have looked into what may be considered a standard work on surveying. Lieut.-General Frome's work, “An outline of the method of conducting a Trigonometrical Survey, etc.,” revised and enlarged by Captain Warren, fourth edition, published 1873, may, I suppose, be looked upon as one of the best and latest works on the subject now published. Whilst this work contains much interesting and valuable information connected with trigonometrical survey, and contains a chapter on colonial

surveys (General Frome having formerly been Surveyor General of South Australia), I have been a good deal struck by the meagreness of information exhibited when the practical details of survey are under consideration, and the inapplicability of English methods and even General Frome's colonial methods, to the survey of New Zealand. The rude method of measuring lines by “plumbing the chain” is the only one used and recommended in connection with the Ordnance survey, and the probable amount of error in chaining alone is stated by General Frome (page 47) to be 1 in 1000, or 8 links per mile, a greater amount being often allowed when surveying for small scales, according to the nature of the ground passed over. In this Province the total error, including both the angular and linear work, must not exceed eight links per mile, as tested by the direct length between the trig stations to which the work is tied, the traverse being usually one-half and sometimes twice as long as the direct distance between these points. And whilst this error is admitted as an extreme, several of our surveyors do not average more than from one to three links per mile when subjected to the severe test of traverse reduction hereafter referred to. In Otago the detail work is all founded upon long and sometimes intricate traverses, which it is absolutely necessary to have executed within a small limit of error, and subjected to the severest tests to ensure accuracy. Nearly all the distances of boundaries of properties, opposite sides of road lines, areas, etc., are calculated from, and depend upon the accuracy, both angular and linear, of the traverse work, and the whole of the more minute topographical details which accompany the plans of section and traverse work, are obtained chiefly by observation with the theodolite alone from the stations of the traverses, and from points fixed by observation with the theodolite along the various section lines. The surveyor is required to refer the direction of each of the traverse lines as well as all section boundaries, and, indeed, every line of the detail survey to the standard of a single meridian—viz., that of the initial station of the meridional circuit, and one of the chief uses of the triangulation is that it furnishes a means by which this can readily be done. He is further required to furnish tables (called traverse tables), showing the position of each of his pegs (the mark put into the ground at every angle throughout the detail survey) on the meridian and perpendicular of the trig station at which his traverse starts, and further to close every traverse at another trig station. This necessarily involves a large amount of computation; but it enables the Inspector to ascertain the amount of error in the surveyors' work, even without inspection in the field, unless the tables are wilfully falsified. In

such a case field inspection alone can discover the errors. Field inspection may be considered an indispensable part of every sound system of survey, and experience has proved that it is only in very exceptional cases that it can be safely dispensed with. As the relative position of the trig stations, at which any traverse starts and closes, is known, the sum of the reductions of his traverse lines can be at once compared with the single reduction of the trig line, and if absolutely correct, the two will exactly correspond. In so far as it departs from this result, we discover the amount of error in the traverse. The traverses, if of considerable length, should also be checked at intermediate points by using the trig lines as bases, and throwing smaller triangles on to any portion of the work at intermediate points which it is desired to test. It is also exceedingly desirable that frequent observations should be taken from the stations of the traverse to any trig points in view, and to other stations of the traverse, as if this is done it enables a skilful surveyor in a few minutes to discover any mistake in the chain-work, such as ten or twenty links or a chain dropped in any traverse line, and that without going over the work again in the field, though it is always necessary to verify by a re-measurement any line upon which an error is thus discovered. This, then, is, in my opinion, the chief practical use of the triangulation, viz., to furnish a means by which this system of check can be applied to the detail survey; and yet the system recommended by Major Palmer renders, as I have already shewn, the application of such a check impossible in many parts of the Colony for a number of years. No such crucial test of the correctness of the detail work of the English Ordnance Survey was ever, so far as I can learn, applied, as we are in the daily habit of applying to the surveyor's work in this Province, at least, of the Colony by the above method of traverse reduction, and I believe this system is also used in the Province of Wellington. I have met gentlemen in this Colony apparently familiar with methods in use in England, who were palpably ignorant of the way to measure a line correctly on the earth's surface, and who opened their eyes on being informed that there was any other way of checking a detail survey save by seeing whether it would “come in” in the plotting. So far as I can read Major Palmer's report, he does not see the necessity for any more thorough test being applied to detail work in the Colony than that applied in England. Referring to revision of old surveys (Report, page 27), he says, if old surveys are connected to the trigonometrical points and re-plotted in new maps, “It is not unlikely that a good deal will be found to fit in such a manner

as to leave no doubt of its accuracy.” And again, “But nothing must be humoured, and nothing admitted in the new record maps which does not plot correctly.” However sufficiently such a check by construction may have satisfied the requirements of the English Ordnance Survey, it is quite insufficient as a check in the detail work of this Colony, and has long been thrown aside in this Province as of not the slightest value, dependence being alone placed on the calculated traverse reductions, without which it is impossible to verify the accuracy of colonial surveys satisfactorily. The introduction of this complete system of check for detail work over the whole Colony, in connection with a carefully executed Minor Triangulation is, I conceive, the reform which we require. Improvement of Detail Surveys. I would venture to suggest also, that it is desirable to improve the character of the detail survey even in this Province, and to state my opinion that it is quite possible to diminish the allowed error in amount, without affecting the rapidity of execution, or cost of survey. So long as the system of chain measurements is permitted, known as “plumbing the chain,” a comparatively large error may almost with certainty be looked for. Fourteen years ago, I ceased the “plumbing system,” and have ever since persevered in observing the inclination of the surface for each chain in ordinary undulating ground, with the best results. As regards accuracy, I find no difficulty in keeping the average error of traverse work, both chain and theodolite, under two links per mile; and I think, out of some four or five hundred miles of traverse now in the Otago Survey Office, the average error does not exceed from one to one and a half links per mile—the greater portion of the chain measurements having been taken by skilled assistants, trained on this system. I may say also that I find it possible to get through the work more rapidly by following this system than I could ever do before. I would therefore suggest, for the improvement of detail survey, that the limit of error be reduced to four links per mile, and that surveyors be required to observe the surface slopes, and make the necessary reductions. Also, that either the surveyor himself, or an educated and trained cadet, should make all the chain measurements. Particular attention should also be given to the condition and character of all theodolites permitted to be ussed in the survey of the Colony. It is not infrequent, in some parts of the Colony, to observe instruments in use which should have been for some time put on the shelf. Any theodolite constructed in the usual manner, after about twelve months' work, begins to shew signs of “shakiness,” and is really unfit to

render correct work. Lately I have adopted the principle of doing away with the lower tangent screw altogether, and bolting the clamping collar direct to the upper levelling plate. This I find to answer admirably; the perfect rigidity of the lower plate thus obtained being invaluable, especially in trigonometrical work. This alteration in the construction of the instrument renders a system of notation slightly different from that in common use, necessary, but one not in the least inconvenient. I shall be very happy to exhibit and explain this improvement in the theodolite to any practical surveyor, and also to explain the system of notation. An instrument constructed on this principle will last about four times as long in good observing condition as one with a lower tangent screw; and instruments now useless may easily be converted and rendered again workable. In any case, I would attach considerable importance to a thorough periodical inspection of every instrument allowed to be used on the survey of the Colony. Instruments used by the Otago staff are, I am informed, periodically inspected, and every contract surveyor is, by the survey specifications, required to produce and exhibit the instruments to be used in carrying out his contract. Plotting Detail and other work. The methods of construction of maps, where the plotting of traverse work is concerned, pursued in connection with the English survey, I venture to say are very rude and inaccurate; and even in laying down the points of a triangulation, the method used in England, and described by General Frome (pages 131 and 132, “scoring triangulations” and “plotting triangulations,”) are, in my opinion, very far behind those in use in this part of the Colony. Where the scale is not a very large one, and the triangles are at all numerous, the methods recommended will give rise to a constantly increasing and intricate series of errors. By the system in use here of reducing all stations of the triangulation to the meridian and perpendicular of the initial station, the position of each station is laid down independently of every other, and thus the perpetuation of error rendered impossible—the only really difficult problem of the plot being practically to raise the perpendicular accurately to the meridian. The results of the ordinary method of doing so by beam compasses I have found it useful to check and test by measuring with standard brass straightedge for the proportional lengths of sides and hypothenuse of the two right angled triangles, which may be formed by the perpendicular on each side of the meridian.

To obtain as speedily as possible a correct diagram of the triangulation has evidently been felt highly desirable in England as well as here, but the method recommended by General Frome (page 132) can only give a very rough approximation—one indeed so rough that I should be inclined to call it useless. In order to keep the plot of topographical work well forward, I suppose every surveyor engaged in trigonometrical work has felt the necessity for this diagram. The method pursued by myself is to keep a series of separate calculations, which I term “rough solutions and reductions,” some of which I exhibit in connection with a triangulation now in progress. These solutions are made as the triangulation proceeds, most frequently from two observed angles, only no attempt being made to eliminate errors of observation or to obtain mean results. These reductions, however, enable the stations to be accurately laid down on paper at once, leaving the ultimate calculations, with all corrections, mean results, etc., applied, to follow in the rear. In this manner the plot of topographical work is kept almost as far on as the triangulation itself, and that in a manner which, I think, all surveyors will agree, is very far in advance of the methods apparently sanctioned in England. As regards the plotting of detail work, the best method apparently known in England, and recommended by General Frome (note page 50) for plotting traverses is by using a card-board protractor, with the centre cut out; or, for surveys on a large scale, the circular brass protractor, with vernier, is recommended, as being more minutely accurate, each line being added from the plotting of the preceding one. Both these methods have been tried here, and thrown aside many years ago as unsatisfactory, inexpeditious, and incorrect in practice. Sometimes on a detail, or particularly a large topographical survey, there are not less than several thousand bearings to be protracted, and it is of the greatest importance that a method should be used, combining accuracy and expedition. The following is the method in use by myself and most other colonial surveyors, I believe:— The meridian and perpendicular of the initial station being first laid down on the sheet, lines parallel to these are carefully transferred, cutting each other about the centre of the sheet, and a large protraction is laid with a fine needle point on the sheet itself. This may be done with great accuracy by means of a heavy brass ruler, with cylinders of large diameter, and a boxwood scale from the table of natural sines and cosines, using parts of each of the four lines in the direction of the cardinal points alternately as sines and cosines for each arc, differing one degree of the circle.

Taking a radius of ten inches, we have thus a protractor twenty inches in diameter, divided accurately to each degree of the circle, and the degrees may then with the scale be subdivided to thirty or even fifteen minutes, leaving intermediate proportions to be estimated by the eye on applying the brass ruler for the purpose of protracting a bearing. As a fine needle only is used to mark the points, the protraction is scarcely visible, except on close inspection, on the completion of the map, after pencil marks have been rubbed out, and yet it may at any time be resuscitated for the purpose of testing the plotting, if necessary. I exhibit a plot sheet of topographical work in progress, with protraction twenty inches in diameter thus constructed. * For the suggestion of the above method of constructing a protraction, which I find superior to every other I had previously tried, I was indebted to my late assistant, Mr. Begg, who gave promise of being an ornament to the profession, but who is now unfortunately no more. Whilst the use of protractors of large diameter, carefully laid down in the plot sheet itself, enables us to lay down bearings, however numerous, correctly, it must be borne in mind that all traverse points of the detail survey are, under the Otago system, plotted altogether independently of any protraction whatever, directly from the traverse tables, and furnish reliable points from which the various bearings may be accurately protracted by the method I have referred to. I venture to say that it is quite impossible to construct a large map with a good deal of traverse work in it, correctly, by either of the methods recommended by General Frome in the note referred to. Before bringing this paper to a close, by referring shortly to the subject of the revision of old surveys, I think it will be appropriate that I should say a few words as to the reasons which have induced me, in referring to the Otago system, to say little or nothing about the work which had to be done ere it was possible to institute the Minor Triangulation on the satisfactory basis upon which that work was begun in this Province. My reason for so doing has been because I conceive we have to-night amongst us gentlemen who can handle that branch of the subject very much more ably than I could hope to do, gentlemen who initiated and carried on the astronomical and, as we call it, the standard part of the work. I trust these gentlemen will supplement my dry and somewhat commonplace paper on the immediately practical branches of colonial survey, by some account of their more interesting and more scientific labours. I proceed, in conclusion, to consider shortly the subject of proposed revision of surveys already in existence, but pervaded confessedly in some parts of the Colony with many and considerable blunders.

In devising or attempting to devise any remedy, we cannot lose sight of the fact that we have not only to be sound in our principles of measurement, but that we must also be sound in our principles of law. When these two sciences come into positive collision, as they will sometimes be found to do, it is very clear that the law must relax somewhat of its demands. A law can be made or altered, but we cannot alter the properties of a mathematical figure. I feel that, to go at all exhaustively into the subject, would occupy a much greater portion of time than we have at our disposal this evening, but, after a good deal of reflection, I cannot see any practical way out of the difficulty save by the introduction of a special measure into the Legislature dealing with the whole subject. This measure might provide that in any district within which serious errors existed, a majority of the holders of land might, on application to the Surveyor-General, have a re-survey of their properties made and their titles corrected, the expense of the re-survey being defrayed either entirely or partly by the imposition of a special rate. The details of such a measure would require the most careful consideration, and the best authorities in the Colony, both in law and mensuration, ought to be consulted as to its provisions, otherwise it might prove a curse rather than a blessing. I would also, whilst upon the question of old and incorrect surveys, desire to record my opinion that the present system of trying suits involving questions of disputed boundaries by ordinary common or special juries is a very great mistake. In the matter of disputed boundaries, a very wise provision was included in “The Crown Lands Act, 1862,” which reads as follows:— “Section XIV. If in any action, suit, or proceeding, touching or concerning any Crown Lands, or any Grant, Lease, or License relating thereto, any question shall arise as to the limits or extent, or as to the boundary of any land comprised in any Grant, Lease, or License, it shall be competent for the Court before which such action, suit, or proceeding may be pending, to order and direct that such question shall be referred to any person or persons whom the Court shall think fit, subject to such terms and conditions as the Court shall think fit, and the award, order, and determination of such person or persons shall be conclusive in such action, suit, or proceeding as to the matter so referred, and shall be binding on the parties, and may be enforced as a rule of the Court, and the Court may make such rule or order as to it shall seem fit touching such reference or the costs thereof.” So far as I am aware the course of procedure contemplated by this provision has never yet been followed by any of our Courts, and yet I venture to say it would be very much more satisfactory than the opinion of twelve

persons possessing no special training which would lend to their opinion any weight when given as to the boundaries of land, and the provision remains practically a dead letter of the law. Whether this may arise from insufficiency in the wording of the clause, from ignorance of its existence, or from disinclination to act upon it, I am not aware. It is owing, no doubt, very much to errors in survey operations that litigation has been unfortunately so much induced of late, but, until a change is made in the description of land in the Crown Grants, we cannot, I think, expect that even correctness of survey will altogether remove the cause of litigation. Two years ago, I was induced to write on this subject owing to a decision of the Court of Appeal in the celebrated Blue Spur case. As the dispute in that case was concerning the boundaries of auriferous lands of great value, the question was tried at great length and at enormous cost; and as the views I then expressed affect directly the subject of errors in survey, and the best mode of correction of the same, I append to this paper two letters which I addressed to the Daily Times, July 23 and 26, 1873, which any one interested in this phase of the subject may peruse. In conclusion, I would say that I quite agree with Major Palmer as to the necessity for placing the survey of the Colony under the direction of an able Surveyor-General, and removing as far as possible the conduct of his operations from political interference and influence. In no other way, so far as I can see, can that uniformity of system which is so much to be desired, be obtained, and steady prosecution of the work of survey be ensured; but I venture to think, that a uniform system of Minor Triangulation properly carried out, the application of traverse reductions as a check in all cases to detailed surveys, and a steady endeavour to improve the detail survey by every means likely to keep allowed error within the smallest possible limits, is what is really so urgently required at the present time, and that the initiation of a great Standard Triangulation, however desirable on geographical and scientific grounds, is no cure whatever for the evils under which many of the Provinces appear to be now suffering.