345 



GEODESY. 



GEODESY. 



310 



Greenwich to Dunkirk. This was undertaken by General Roy, who 

 began his operations by measuring a base of 27,404 feet on Hounslow 

 Heath in the summer of 1784. For the measurement of the angles a 

 large and exquisitely divided theodolite, having a horizontal circle of 

 three feet in diameter, and carrying telescopes of 36 inches focal length 

 an instrument far superior to any that had ever been employed in 

 geodetical observations was constructed by Ramsden. In the summer 

 of 1787, the triangulation was begun by General Roy, assisted by Mr. 

 Dalby, and before the end of the year it was carried to the eastern 

 coast of Kent, and connected with a series of triangles on the opposite 

 coast, which had been extended from Dunkirk to Calais and Boulogne, 

 by Cassini, Mechain, and Legendre. Throughout the whole of this 

 survey the practical operations were conducted with a degree of 

 accuracy and precision, of which, till that time, there had been no 

 example. The methods of calculations were however less excellent ; 

 the sum of the three observed angles of each triangle was made equal 

 to 180" by an arbitrary correction, and the sides computed by plane 

 trigonometry. By reason of the small extent of country surveyed, the 

 neglect of the earth's curvature did not lead to any serious error, but 

 such a method of proceeding would be inadmissible at the present day. 

 A base of verification of 28,535 feet was measured on Romney Marsh 

 with a steel chain, and the difference between the measured length 

 and the length computed from the Hounslow Heath base through the 

 series of triangles was found to be only about 28 inches. So near an 

 agreement might afford a satisfactory proof of the general accuracy of 

 the work, but this has since been submitted to a more decisive test. 

 In 1821 and some of the following years, the angles were remeasured 

 by Colonel Colby and Captain Kater, with the same excellent instru- 

 ment, and the triangles calculated with reference to tha sphericity of 

 the earth. On comparing the results with those of General Roy, the 

 greatest difference was found to be in the distance between the signals 

 at Dover and Calais, and this amounted only to 12J feet, the whole 

 distance being 137,472 feet. (Roy, 'PhiL Trans.' 1790; 'Trigono- 

 metrical Survey of England and Wales,' vol. 1 ; Kater, ' Phil. Trans.,' 

 1828.) 



The operations for establishing a geodetic connection between the 

 observatories of Greenwich and Paris had the effect of suggesting the 

 expediency of a general survey of the British isles. This great national 

 undertaking was commenced in the year 1791. The operations were 

 conducted by Colonel Williams, and Captain (afterwards General) 

 Mudge, of the Royal Engineers, and Mr. Dalby, who had previously 

 assisted General Roy. Their first step was to remeasure the base on 

 Hounslow Heath. This was effected by means of two steel chains, 

 each 100 feet long, which had been carefully constructed for the 

 purpose by Ramsden. The length of the base was found to be 

 27404-24 feet, a result differing only 2J inches from that obtained by 

 General Roy. [Rov, MAJOR-GENERAL, in Bioo. Div.] The terrestrial 

 angles of the survey were measured with two large theodolites by 

 Ramsden, each 3 feet in diameter ; and a smaller theodolite, by the 

 same artist, of 18 inches diameter. In 1801, it reached Clifton in 

 Yorkshire. The length of the arc of the meridian extending from 

 Dunnose in the Isle of Wight to this station was determined in the 

 following year by General Mudge. In 1806 the arc was prolonged to 

 Burleigh Moor, about a degree to the north of Clifton. At the same 

 time the triangulation had extended considerably over other parts of 

 England. In the course of these operations three bases of verification 

 were measured; one on Salisbury Plain (1794), by Lieutenant-Colonel 

 Williams and General Mudge [McooE, GENERAL, in Bioo. Div.] ; one 

 on Misterton Carr, near Clifton (1801), by General Mudge ; and one on 

 Rhuddlan Marsh, in Wales (1806), by the. same officer. These various 

 bases were measured with the same steel chains which were employed 

 in the measurement of the base on Hounslow Heath. The astronomical 

 latitudes of six stations on the arc of the meridian extending from 

 Dunnose to Burleigh Moor, namely, Dunnose, Greenwich, Clifton 

 Beacon, Arbury Hill, Delamere, and Burleigh Moor, were determined 

 . with a zenith sector of 8 feet radius, constructed by Ramsden. The 

 operations of the survey down to 1811 are recorded in a work, the 

 concluding volume of which was published in the year just mentioned. 

 (' An Account of the Operations carried on for accomplishing a Trigo- 

 nometrical Survey of England and Wales, &c. ; by order of the Honour- 

 able Board of Ordnance,' by Captain Mudge, R.A., Mr. Dalby, and 

 Captain Colby, R.E. ; 3 vols., 1799-1811.) 



The triangulation continued without interruption to be extended 

 towards the north. In 1817, a new base of verification was measured 

 on Belhelvie Links, near Aberdeen, by Major-General Colby, with the 

 Msistance of Mr. Gardner. The same instruments of measurement 

 were employed on this as on previous occasions of a similar kind. In 

 .820, upon the death of General Mudge, General (then Captain) Colby 

 was appointed Superintendent of the Ordnance Survey. In 1824, the 

 operations for the survey of Ireland were commenced. A base was 

 inertly afterwards (1827-8) measured on the shores of Lough Foyle, in 

 the county of Londonderry. (' An Account of the Measurement of the 

 Lough Foyle Base, in Ireland, &c.,' by Captain William Yolland, R.E., 

 1847.) The apparatus of measurement differed on this occasion from 

 that employed in ascertaining the lengths of the previous bases, con- 

 sisting of a combination of bars of different metals, so adjusted as, by 

 their unequal exparmion, to obviate the varying effects of temperature. 

 A description of this apparatus, which was devised by Colby, will be 



given presently. The triangulation was rapidly extended over Ireland. 

 The instruments were the same as those which had been used in the 

 survey of England, with the addition of a 2-foot theodolite constructed 

 by Troughton & Simms. The triangulation was connected at several 

 points with the triangles observed in England, Wales, and Scotland. 

 The astronomical latitudes continued to be determined with Ramsden's 

 zenith sector until 1841, when it unfortunately was destroyed in the 

 course of the conflagration which burned a considerable portion of the 

 Tower of London in that year. An account of the operations wvith 

 this fine instrument was published in the following year. (' Astrono- 

 mical Observations with Ramsden's Zenith Sector,' 1842.) The sub- 

 sequent determinations of latitude were effected with a new zenith 

 sector, devised by Mr. Airy, the astronomer-royal, with the view of 

 obviating certain inconveniences which atteuded the use of Ramsden's 

 instrument. Three important principles of a novel character were 

 involved in the construction of Airy's zenith sector. " The first 

 principle was the arrangement for making successive observations in 

 two positions of the instrument, face east and face west, at the same 

 transit. The second was the substitution of a level, or system of levels, 

 for the usual plumb-line. The third principle was the casting in one 

 piece, as far as practicable, of each of the different parts of the instru- 

 ment, in order to avoid the great number of screws and fastenings 

 with which most instruments are hampered, and to secure, if possible, 

 perfect rigidity." An account of the observations with this sector was 

 published in 1852. ('Astronomical Observations with Airy's Zenith 

 Sector, from 1842 to 1850,' by Captain William Yolland, R.E.) 



At the stations of Balta in Shetland, Cowhythe in Aberdeenshire, 

 and Dunnose in the Isle of Wight, the latitudes were determined first 

 with Ramsden's and subsequently with Airy's zenith sector. A com- 

 parison of the results affords satisfactory evidence of the degree of 

 precision attained in such observations. Thus we have 



Station. 

 Dunnose . 

 Balta . 

 Cowhythe 



Airy. 



50'37'6"-98 

 60 45 1 -i, a 

 57 41 D -58 



Ramsden. 

 5<T37'7"-09 

 GO 492 -31 

 57 419 -74 



Difference. 



In 1849 the base on Salisbury Plain was re-measured with Colby's 

 compensation bars. The result, in combination with the Lough Foyle 

 base, has formed the groundwork of all the subsequent computations 

 connected with the triangulation, the other bases having been used 

 merely for purposes of verification. 



Upon the retirement of General Colby in 1847, Colonel Hall was 

 appointed Superintendent of the Ordnance Survey. In 1858 a work 

 was published by Colonel James, who has recently succeeded Colonel 

 Hall as superintendent of the survey, containing a complete account of 

 the observations and calculations relative to the triangulation of the 

 British Isles, with an investigation of the figure, dimensions, and 

 mean density of the earth, as deducible from the results in combination 

 with the data of the same kind which had hitherto been established. 

 (' Ordnance Trigonometrical Survey of Great Britain and Ireland ; ' 

 ' Account of the Observations and Calculations of the Principal Trian- 

 gulation, and of the Figure, Dimensions, and Mean Specific Gravity of 

 the Earth, as derived therefrom,' drawn up by Captain Alexander Ross 

 Clarke, R.E., 4c., under the direction of Lieut.-Colonel H. James, R.E., 

 SLC., Superintendent of the Ordnance Survey, 4to, London, 1858.) The 

 triangulation embraces an arc of the meridian extending from Dunnose 

 in the Isle of Wight to Saxavord, the most northerly of the Shetland 

 Isles. The former of these stations is situate in lat. 50 37' 3"748 ; 

 the latter in lat. 60 49' 41 "'992. The amplitude of the arc is, conse- 

 quently, 10 12' 38"-244. 



It has been stated that the terrastrial distances were computed from 

 the base lines measured on Salisbury Plain (1849), and on the shore 

 of Lough Foyle, in Ireland. The difference between the measured 

 length of each of these bases aud the length computed from the other 

 base was found to amount to 0'4178 feet, or about 5 inches. From 

 this result a mean base has been derived by the theory of probabilities, 

 and this mean base has been used as the immediate groundwork of all 

 the subsequent calculations. The following table exhibits a comparison 

 between the lengths of the bases as measured and reduced to a common 

 standard, and their lengths as determined by the triangulation : 



Length in 

 Triangulation Difference. 



Feet. Feet. 



27400-363 + 0-173 

 36577-656 -f 0-820 

 26343-869 0'191 

 24517-596 + 1-596 

 26517-770 + 0-240 

 41641-1C3 -f 0-216 

 36577-656 0-202 



Many of the sides of the triangles are of great length, especially those 

 which connect the triangulation of Ireland with the stations on the 

 opposite coasts of England, Wales, and Scotland. The following is a 

 statement of the sides which exceed 90 miles ; the names given are 



This was one of two 10 feet bar with which the compensation bars 

 employed in the measurement of the base-lines was compared. 



