ASTRONOMY OF EIGHTEENTH CENTURY. 247 



curvature of the equatorial region a b coincides with that of the smaller 

 circle^ b g, which has its centre at c.. It is obvious that any given 

 angle in the circle E A B F must be subtended by a greater length of 

 line A B at c than on the smaller at a b to c. Thus the angles A c B 

 and a c b being each 10 degrees, the distance A B is longer than a b 

 in the same proportion that A c is longer than a c. Cassini and his 

 coadjutors would not admit that their determination could be inaccu- 

 rate; and therefore, to settle the matter, France sent out two expedi- 

 tions, one to measure a degree near the equator, the other to do the 

 same in Lapland. The base measured in France by Picard was found 

 to contain a considerable error, which vitiated the conclusions of Cas- 

 sini. The final results fully confirmed the compression of the earth 



\ 



IF 



towards the poles, and from that time mathematicians and astronomers 

 have all agreed in assigning to the earth the form of an oblate spheroid. 

 Arcs of the meridian and degrees of parallels of latitude have since 

 been measured in various other countries, as in 1768 by Beccaria in 

 Piedmont, and by Liesganig in Hungary; in 1800 by Mudge in Eng- 

 land; in 1 80 1 by Suanberg in Lapland. These various determina- 

 tions did not exhibit a satisfactory concordance in their results, so 

 that the exact form and dimensions of the earth were ascertained only 

 within certain limits. It may here be added, that, in more recent 

 times, the pendulum has been used for determining the earth's ellip- 

 ticity, and that arcs have been measured with all possible refinement 

 of instrumental means. In order to complete all that will be said on 

 this subject, the statement of the best recent results may be here laid 

 before the reader. Airey calculates the length of the earth's polar 

 diameter to be 7,899-170 miles, and Bessel makes it 7,899-114 miles. 

 The former assigns for the equatorial diameter 7,925-648 miles, the 

 latter 7,925-604 miles. Thus, if the earth be represented by a globe 

 3 feet in diameter, we must reduce the polar diameter by one-tenth of 

 an inch to bring it to the true oblately spheroidal shape of the earth. 

 The attention of astronomers had been directed from the time of 

 Copernicus to the parallax (page 2 1 5 ) of the fixed stars. It was known 

 that this parallax, if it existed, must be very small ; but it seemed 



