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. 
3. 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 are 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 formule 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 following 
are the results arrived at :— 
a=20928627 + 1057°8¢, + 342:9¢, + 152°3t, + 27°3¢, + 93:6¢, 
+ 8°84, + 63°7t, + 62:9¢, feet. 
b=20849309—3762:6¢, — 334-3¢, —661°3¢, —101-5¢, —372:6¢, 
—14:0t, —249°3t, —249°1t, feet. 
From these we may easily deduce the ellipticity 

