266 



Archdeacon Pratt on the effect of 



a = 20928627+1057'8f,+342-9^2+152-3^3+27-3^^+93-6^g+8-8#e 



+ 637^,+ 62-9^8, 

 5 = 20849309-3762-6^,— 334-3^2-661-3^3--101'5^4-372-6^s 

 -14-0^6- 249-3#,-249-U8. 

 From these we may easily deduce the ellipticity 



e=2g|:^{l+0-0608^, + 0-0085^2+0-0103#3+0-0016^4+0-0059^5 

 + 0-0003^6 + 0-0039^, + 0'001639#8}. 



These formulse 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-GaUic arc 

 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 de- 

 flection at the standard station (Damargida) of the Indian Great Arc be 

 what the mountains and ocean make it (without allowing any compensating 

 efi^ect 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 cal- 

 culation, this uncertainty regarding the mean figure, as determined by 

 geodesy, must remain. 



§ 3. Comparison of the Anfflo- Gallic, Russian, and Indian Arcs, with a 

 view to deduce the Mean Figure of the Earth. 



9. The first three of the eight arcs which have been used in the calcula- 

 tion, viz. the Anglo-Gallic, Russian, and Indian, are of considerable length ; 

 and as the a priori probability appears to be that the earth nowhere departs 

 much from its mean form, it seems not unlikely that by the following de- 

 vice we may overcome the difficulty pointed out in the last paragraph. I 

 will deduce expressions for the sem.iaxes of the mean figure of each of 

 these three arcs by the method there given. If reasonable values can be 

 assigned to the expressions for the deflection of the plumb-line from the 

 normals to these three ellipses such as will make the axes the same, we 

 shall have a very strong argument in favour of those being the actual de- 

 flections in nature, and of the figure thus deduced, as common to the three 

 arcs, being in fact the mean figure of the earth. 



10. In the previous calculation t has represented the angle which the 

 plumb-line makes, in the plane of the meridian, with the normal to the 

 mean elhpse of the earth. I shall now use T as the angle which the plumb- 

 line makes, in the plane of the meridian, with the normal to the mean 



