502 



NA TURE 



[September 17, 1908 



work of this class, upon terms agreeable to both sides, 

 in a similar manner to that in which cadastral survey 

 is executed by the Indian survey for provincial Govern- 

 ments, and it need hardly be pointed out that the geodetic 

 points fixed by triangulation would in any case be avail- 

 able as a framework for the large-scale map. 



The geographical survey of the British Empire, apart 

 from Africa, will not on this occasion detain us long. I 

 exclude from present consideration the great self-govern- 

 ing colonies — Canada, Australia, and New Zealand — and 

 also the whole country lying within the sphere of the 

 survey of India. Ceylon has an elaborate land survey 

 system ; and though, owing to past mistakes, the geo- 

 graphical mapping of the island is in a most lamentably 

 backward condition, there are good grounds for hope that 

 this state of affairs will be remedied in the near future. 

 The Malay States, where, owing to the fertility of the 

 soil and the ubiquity of rich tin ore, the land values are 

 high, have the basis of an excellent survey system, and 

 possess a backbone of triangulation which will eventually 

 extend southward to Singapore, and possibly northward 

 to join the Indian series in the south of Burma. Hong 

 Kong, including the leased territory on the mainland, is 

 of small area and of no appreciable geographical import- 

 ance. It has been adequately mapped for military pur- 

 poses. Of our insular possessions, Mauritius, St. Helena, 

 and (in the Mediterranean) Cyprus and Malta are 

 thoroughly surveyed. The other islands scattered through- 

 out the ocean which fly the Union Jack, including the 

 West Indies, while their coast lines have naturally been the 

 subject of close attention by the Hydrographic Depart- 

 ment of the Admiralty, are, as regards their internal 

 geographical features, still quite imperfectly known. The 

 large and important territory of British Guiana is entirely 

 unsurve\'ed, and indeed in part almost unexplored. 



You will thus realise that if we are prepared to admit 

 the validity of the premiss that the mapping of its own 

 territory is an imperative duty of a State which aspires 

 to justify itself before the nations as the possessor of a 

 world-wide Empire, there is still plenty of employment 

 for the scientific geographer in the British dominions. 



Having thus far spoken of our duties and obligations, 

 for such they appear to me, which lie abroad in countries 

 remote from our own sliores, let us now turn our eyes 

 inward and see if we cannot discern some similar duties 

 lying close to our hands. 



I take it that tire great majority of us have been brought 

 up in the idea that our own Ordnance Survey is of such 

 a high order of accuracy that a proposal to undertake a 

 revision of the fundamental triangulation of the British 

 Isles must appear strange. Yet this idea will not be a 

 new one to the British Association, for two years ago at 

 the York meeting I brought the subject before this Section 

 in a short note, which gave rise to a useful discussion. 



What I shall say now will be in a large measure a 

 repetition of my previous remarks, a repetition for which 

 I need offer no apology, as it will be apparent to you that 

 had any steps been talven to remove this standing reproach 

 to British geodetical science no recurrence to the subject 

 would be called for. As matters stand, however, I feel 

 impelled to recur to it with increased emphasis, a position 

 in which I am confident of being supported by all those 

 who earnestly care for the scientific repute of our country. 

 Some few years ago, at the request of the International 

 Geodetic Conference, a volume was prepared by General 

 Ferrero, the eminent Italian geodesist, giving a sum- 

 marised account of all the geodetic surveys of the world. 

 If we take this volume and examine the relative degree of 

 precision of the different national surveys there enumerated 

 we shall find that Great Britain stands lowest on the list. 



The popular illusion, for it is really no other, as to the 

 extreme accuracy of the triangulation of the British Isles 

 rests in no small degree upon what must be considered a 

 fortuitous circumstance — namely, the accidental smallness 

 of the closing error. Have we not all been told how at 

 the conclusion of the triangulation, when the observations 

 had been carried from the primary base on the shore of 

 Loch Foyle across part of Ireland and across Wales and 

 England, terminating in two points on Salisbury Plain, 

 the distance between these points was calculated, using 

 as data the measured length of the Loch Foyle base and 

 NO. 2029, VOL. 78] 



the observed angles of the triangles across the country ? 

 i'he distance between the same two points was then 

 measured with every refinement of accuracy, and the 

 measured length compared with the calculated length. The 

 difference between them was found to be twenty inches. 

 If in traversing a large portion of the kingdom the aggre- 

 gate error only amounted to this minute quantity — 

 minute, that is, compared with the distances involved, 

 how can we either expect or demand a better result, even 

 if the work be re-done with the most refined methods that 

 the accumulated experience of the last fifty years can 

 suggest? 



To answer this question we must bear in mind that the 

 closing error of a piece of work such as a triangulation 

 is not the only, nor indeed the best, test of its precision. 

 A small closing error may be due to accident ; larger dis- 

 crepancies may have occurred at intermediate stages 

 which have chanced nearly to cancel themselves at the end. 

 Such undoubtedly did happen in this case. The work was 

 not as accurate as the smallness of the closing error would 

 seem at first sight to imply. We have, however, in such 

 a case an absolute measure of relative precision in the 

 magnitude of the average triangular error, being the 

 quantity by which the sum of the observed angles of a 

 triangle exceeds or falls short of the true value of i8o° + 

 spherical excess. 



From this we can readily deduce the " probable error " 

 of a single observed angle, a form in which the measure 

 of precision of a triangulation is often expressed. 



In our British survey this quantity equals 1-20 second 

 of arc, while in good modern work it docs not in general 

 exceed 0-25 second. Making due allowance for the fact 

 that the network of triangles over our islands is a com- 

 plicated one, and therefore that the ultimate precision is 

 considerably greater than that of a chain of triangles of 

 the same order of individual accuracy, we are probably 

 justified in concluding that a re-survey would at least 

 halve the final errors. 



Such a re-survey is urgently demanded in the interests 

 of international geodesy. 



It will of course be clearly understood that this implies 

 no adverse criticism upon the work of the men who 

 originated and carried out the primary triangulation of 

 the British Isles. For that great achievement we must 

 all have the most sincere admiration. It was pioneer work 

 of the highest order ; it set a standard of accuracy never 

 before attained, and was for long taken as the model for 

 such work in other countries. It was, however, started at 

 the end of the eighteenth century, and was completed in 

 1857. It is therefore hardly surprising that it falls some- 

 what short of the precision of modern observations of the 

 same class. It will also be understood that this re-survey 

 docs not alYect the question of the trustworthiness of our 

 Ordnance Survey maps. Any errors which exist in cur 

 triangulations are important only for geodetic discussions, 

 such as the determination of the exact figure of the earth, 

 and are quite negligible for map-making purposes. There 

 can be no appreciable error from this cause upon the maps 

 of our own country, even those on the largest scales, and 

 no question of reconstructing our maps can arise. This 

 is fortunate from the financial point of view. Such a re- 

 construction would involve a very heavy expenditure, while 

 the cost of the re-triangulation suggested would be quite 

 trifling compared with the actual annual expense of our 

 national surveys. 



The result of this inferiority in accuracy of the British 

 survey is that it is useless to coordinate it with the Con- 

 tinental series' for geodetical purposes. This defect is all 

 the more noticeable in that the necessary observations for 

 joining up the two series were actually made. Three 

 stations on the coast of Kent — St. Peter's Church, between 

 Margate and Ramsgate ; Coldhani, a hill about two miles 

 north of Folkestone ; and Fairlight, a hill about four miles 

 north-east of Hastings — were connected trigonometrically 

 with three stations in France — Montlambert, near 

 Boulogne ; St. Inglevert, over the village of Wissant ; and 

 the Clock Tower at Gravelines. This was done in 1861— 3. 

 The observations were of a high order of precision. It 

 would not be necessary to repeat them. 



The importance of the coordination is apparent when 

 we inspect a map of Europe with the neighbouring part 



