ATTRACTION IN THE CASE OF THE ENGLISH ARC. 
33 
Similar expressions for a may be obtained by comparing- all the five arcs two and two ; 
and hence 
1 ( ^ 
mean ellipticity=:j-j::2 — ? 
10 VEi-Ej- 
4. The following Table exhibits the values of E and A for the several arcs (see 
Appendix) : — 
Values of E. 
Values of A. 
] st arc 
0-18569 
0-00985473 
2r)d arc 
0-15446 
0-00984850 
3rd arc 
01 3545 
0-00987184 
4th arc 
0-09455 
0-00987324 
5th arc 
0-03571 
0-00986587 
From this, taking the arcs two and two, we obtain the following results (see 
Appendix).: — 
Arcs compared. 
Ellipticity deduced therefrom. 
1st and 2nd . 
.... +0*0202690 
1st and 3i-d . 
.... —0*0344944 
1st and 4th . 
.... —0*0205622 
1st and 5th . 
.... —0*0075277 
2nd and 3i-d . 
.... —0*1244090 
2nd and 4th . 
.... —0*0418294 
2nd and 5th . 
.... —0*0148295 
3rd and 4th . 
.... —0*05968*22 
3rd and 5th . 
.... +0*0607577 
4th and 5th . 
.... +0*0125964 
Mean value 
= —0-0209711 = — 
47-6846 
5. This mean value differs widely from the mean ellipticity of the whole earth, 
which is about The discrepancy must arise, either from the English arc being 
curved very differently to the mean meridian of the earth and belonging to an ellipse 
of which the polar axis is greater than the equatorial in the ratio of 48*6846 : 47*6846, 
or from the amplitudes being incorrectly determined. In this i assume that the arcs 
themselves are measured with such exactness as to preclude the possibility of error 
in the ellipticity from this source. (An error of 100 feet would not make an error of 
1" in the amplitude.) 
It is evident that the latter is the true cause of the ellipticity coming out so differ- 
ent to the mean ellipticity of the earth ; for the ellipticities deduced from the com- 
parison of the several subdivisions of the arc, two and two, would not vary among 
themselves, as the last Table shows they do, if the whole arc were elliptic. It may 
MDCCCLVI. F 
