36 On Local Attraction. [No. 1, 



deflection of the plumb-line at that station. This, in the Indian 

 Great Arc, will not exceed (supposing my reasoning as described 

 below is accepted) one-thirteenth of a mile at any of the stations 

 where the latitude has been observed. It appears also from these 

 calculations, that, except in places evidently situated in most dis- 

 advantageous positions, the local attraction is rarely of any consider- 

 able amount. 



8. In the second section of the Paper I proceed to ascertain the 

 degree of uncertainty introduced, by our ignorance of the amount of 

 local attraction, into the great problem of the Mean Figure of the 

 Earth. 



Bessel was the inventor of the method now in use for solving this 

 problem. His method enables us to bring all the arcs which have 

 been measured in any part of the world to bear simultaneously upon 

 the solution. He made use of arcs measured in eight parts of the 

 earth's surface ; called the Anglo- Gallic, Russian, Indian II, (or Great 

 Arc), Indian I, Prussian, Peruvian, Hanoverian, and Danish Arcs, 

 the first three of which are very long. For each of these arcs he 

 made use of an algebraical symbol to represent the unknown error of 

 the precise position of the arc on the meridian. In his method he 

 treats these eight quantities as independent variables ; which is 

 tantamount to ignoring local attraction altogether. The calculations, 

 therefore, of the Mean Figure of the Earth hitherto made have left 

 this most important element out of consideration. To remedy this 

 has been my object. By a change, I venture to call it a correction, 

 of Bessel's method I have succeeded in obtaining formulae for the 

 semiaxes and ellipticity of the Mean Figure, which involve expressions 

 for the unknown local deflections of the plumb-line at the standard or 

 reference-stations of the several arcs. 



If a and b represent the semiaxes and e the ellipticity, the folloAving 

 are the results arrived at : — 



a=20928627 -f 1057-8*, -f 342-9* (2 -fl52-3* 3 + 27-3* 4 -f 93-6* s 

 + 8-8* 6 -f 63-7* 7 + 62-9* 8 feet. 



6=20849309— 3762-6^— 334-3*,— 661-3*3— 101-5^— 372'6* 5 

 — 14-0* 6 — 249-3*, — 249-l* 8 feet. 

 From these we may easily deduce the ellipticity 



