760 TRANSACTIONS OF SECTION E. 



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 discrepancies 

 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 pre- 

 cision 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 180° + 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 ex- 

 pressed. 



In our British survey this quantity equals 1*20 second of arc, while in good 

 modern work it does not in general exceed 0'25 second. Making duo allowance 

 for the fact that the network of triangles over our islands is a complicated 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 resurvey would at least halve the final errors. 



Such a resurvey 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 triangula- 

 tion 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 resurvey does not affect the question of the reliability 

 of our Ordnance Survey maps. Any errors which exist in our 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 

 reconstruction would involve a very heavy expenditure, while the cost of the 

 retriangulation suggested would be quite trifling compared with the actual annual 

 expense of our national surveys. 



The result of this inferioritj^ in accuracy of the British survey is that it is 

 useless to co-ordinate it with the continental series for geodetical purposes. This 

 defect is all the more noticeable in tliat the recessary 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; Coldham, 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 1861-63. The observations 

 were of a high order of precision. It would not be necessary to repeat them. 



The importance of the co-ordination is apparent when we inspect a map of 

 Europe with the neighbouring part of Africa, upon which the triangulation lines 

 are entered. We then see that the British part of the work is imperatively 

 required to extend, and in fact to complete at one end in each case, two important 

 geodetic arcs, viz., the meridional arc along the meridian of Greenwich and the 

 longitudinal arc along the latitude of 52° north. Without the British portions 

 these arcs extend from Ain Sefra in Algeria to Gravelines in Fr.ance, an ampli- 

 tude of 18°, and from Orsk in Russia to the same point in France, an amplitude 

 of 67°. W^ith the British section added they would be further extended to 

 Saxavord, the northernmost point of the Shetland Islands, and to Valentia, on 

 the West of Ireland, respectively. Tlie added amplitudes would be 10° and 11J°, 



