1865.) On Local Attraction. 37 
=r55 { 1-40-0608, +-0:0085¢, -+-0:0103,--0-0016/ ,4+0:0059¢, 
+ 0:0003¢, + 0:0039¢, + 0:001639¢, }. 
where t, t, ... t, are the eight unknown deviations of the plumb-line 
from the true vertical at the standard stations of the eight arcs arising 
from local attraction. 
These formule for the semiaxes and ellipticity of the mean figure 
of the earth show us, that the effect of local attraction upon the final 
numerical results may be very considerable : for example, a deflection 
of the plumb-line of only 5’ at the standard station (St. Agnes) of the 
Anglo-Gallic are would introduce a correction of about one mile to the 
length of the semi-major-axis, and more than three miles to the semi- 
minor-axis. If the deflection at the standard station (Damargida) of 
the Indian Great Arc be what the mountains and ocean make it 
(without allowing any compensating effect from variations in density 
in the crust below, which no doubt exist, but which are altogether 
unknown) viz. about 17”24, the semiaxes will be subject to a 
correction, arising from this cause alone, of half a mile and two miles. 
This is sufficient to show how great a degree of uncertainty local 
attraction, if not allowed for, introduces into the determination of the 
mean figure. As long as we have no means of ascertaining the 
amount of local attraction at the several standard-stations of the arcs 
employed in the calculation, this uncertainty regarding the mean 
figure, as determined by geodesy, must remain. The effect of our 
ignorance in this case is far more serious than that already noticed in 
mapping a country with minute precision. 
4, The third section of the Paper is occupied in devising means 
for removing this ambiguity. Although it has been necessary to 
assume one step in the argument, I think that the sequel shows that a 
very high degree of probability exists that the process is a correct one. 
Each of the three great arcs—the Anglo-Gallic, the Russian, and 
‘the Indian—is divided into a number of subordinate ares. I therefore 
take each of these three great arcs and apply the method described in 
the last section to find the semiaxes of the ellipse which best 
represents that arc. The expressions for the semiaxes involve one 
/ unknown quantity, viz. the amount of deflection at the standard 
_ station of the arc. In this way I obtain the semiaxes of three ellipses, 
