ON ASTRONOMY. 103 



the plumb line at the two extremities will not meet at 0, the centre 

 of the earth, but at C, some distance below. We may now suppose 

 A B to be an arc of one degree upon the circle whose radius is A 0. 

 That being supposed, we shall readily know the whole circumference, 

 which is 360 times A B ; and knowing the circumference we can 

 read'ly find the radius, A C, which is known as the radii of curvatw^e. 

 And by this is meant that the arc A B will coincide with a circle 

 drawn round C as a centre, and A C as a radius, more nearly than 

 with any other circle which can be drawn. 



Assuming the meridian curve to be an eclipse with two radii of 

 curvature, we can compute the two semi-axes of the figure N and 

 E. The ratio of these two, the polar and equatorial radii, gives the 

 oblateness or ellipticity. 



Professor Airy, some years ago, selected thirteen of the most reliable 

 arcs, and from the combinations, two and two, deduced the probable 

 value of the polar and equatorial diameters, as follows : 



Polar diameter in miles 7899.17 Kadii 3949.58 



Equatorial diameter in miles 7925.65 " 3962.82 



Difference 13.24 



More recently, Bessel, selecting eleven arcs, some of them the same 

 and others different from those of Airy, by widely different methods 

 computed the values, as follows : 



Polar diameter in miles 7899.11 Eadii 3949.55 



Equatorial diameter in miles 7925.60 " 3962.80 



Difference , 13.25 



It is not a little remarkable that results based upon different mea- 

 surements and computed by different methods, and in both cases, as 

 Sir John Hersliel remarks, " the mass of figures to be gone through 

 with being enormous," — I say it is most remarkable that the differ- 

 ence in the length of the earth's radius, as determined in the two 

 cases, should be less than the -j^-^ part of a mile. Any residual 

 error which may affect these results must be extremely small. 



We then have for the figure of the earth a spheroid flattened at the 

 poles to such an extent that the polar radius is 13^ miles shorter than 

 the equatorial. This difference divided by the equatorial radius gives 

 the oblateness or ellipticity. It comes very near to 3 Jy, more exactly 

 jgV. r- This variation from perfect sphericity in a 20-incli globe could 

 scarcely be detected by the most accurate eye^ and yet this oblateness 

 of the earth enters as an essential element into many of the most 

 important and curious probleu>s in astronomy. The equatorial cir- 

 cumference of the earth is 24,886 miles. It is proper to remark, in 



