298 



LIEUT.-COLONEL S. G. BUEEAED ON THE 



the geodetic azimuths are at present affected by the errors accumulated in the tri- 

 angulation, which have not as yet been determined. Whilst, then, we are endeavouring 

 to discover the influence on the plumb-line of a mountainous mass situated to the north- 

 east, we are limited to observations which give the north and south component only. 



The other difficulties attending plumb-line research are, that our deductions are 

 based upon an assumed figure of the earth and upon an assumed direction of gravity 

 at a station of origin. We have to imagine a mean spheroid, and we then assume 

 that the angle of inclination between the surface of this spheroid and the actual level 

 surface at any place is equal to the deflection of the plumb-line ; we have also to select 

 some station as an origin, and to assume that the surfaces of the spheroid and geoid 

 are there parallel. We have finally to decide from the results accumulated over wide 

 areas, whether the fundamental assumptions on which those results are based the 

 assumptions of spheroid and origin are correct. 



In the publications of the ' Survey of India ' the deflections of the plumb-line have 

 been always based (1) on the mean spheroid of EVEREST, and (2) on the assumption 

 that gravity acts normally at Kalianpur, our geodetic origin. In his paper on 

 ' Geodesy,' published in 1895, General WALKER gave the deflections of the plumb- 

 line in terms of the spheroid of CLARKE. 



EVEREST'S spheroid had agreed closely with BESSEL'S ; but the objection had been 

 raised to both that their values of the ellipticity, 1/300'80 and 1/299'15, differed too 

 seriously from the value 1/289 derived by CLAIRATJT'S theorem from pendulum 

 observations. In 1880, in his work on ' Geodesy,' Colonel CLARKE deduced an 

 ellipticity of 1/293 '4G5 from measures of arcs, and of 1/293 from pendulum results; 

 and his removal of the hiatus gave great weight to his spheroid. Professor 

 HELMERT'S investigations have, however, shown that modern pendulum work has not 

 borne out CLARKE'S result, and that BESSEL'S ellipticity was after all nearer the truth. 



Recent geodetic measurements have tended to confirm the accuracy of CLARKE'S 

 value of the major axis, and to indicate that BESSEL'S value was too small.* Until a 

 new determination of the dimensions of the mean spheroid has been made under the 

 authority of the International Geodetic Association, it is advisable for us to adopt 

 for computations a spheroid that has the major axis of CLARKE and the ellipticity of 

 BESSEL. 



ELEMENTS of Spheroids. 



'United States Coast and Geodetic Survey.' "The Transcontinental Triangulation, 1900 ;" "The 

 Eastern Oblique Arc of the United States," 1901. 



