THE YARD, PENDULUM, AND METRE. 443 



Axis major = 41,854,800 feet, in long. 38 44' E. from 

 Paris (one end falling about half-way between Mount 

 Kenia and the east coast of Africa, the other in the 

 middle of the Pacific Ocean). 



Axis minor = 41,850,007 feet, in long. 128 44' E. from 

 Paris (one end falling on Waygiou, one of the Molucca 

 Islands, and the other at the mouth of the Amazon 

 River), giving an ellipticity of one 888oth, or about one- 

 thirtieth part of that of the meridians as already stated. 



(26.) The figure of the equator, and its dimensions 

 thus obtained, the exact equatorial diameter correspond- 

 ing to any given longitude is easily calculated. And by 

 comparing this with the polar axis, the precise ellipticity 

 of the meridian for that longitude may be computed. 

 And executing this computation for Paris, M. Schubert 

 finds 5^-5- for the ellipticity of the French meridian. 



(27.) With these data, viz., a Polar axis of 41,708,088 

 feet, and an ellipticity of 2W which certainly may lay 

 claim to greater precision than anything previously 

 obtained, I shall now proceed to calculate the true length 

 of the quadrant of the French meridian, for which pur- 

 pose the following very simple and convenient formula 

 may be used,* viz. : 



Q=2T A (i + 2m + 9** + 3%m 3 ) 



* For the present purpose it is necessary to carry out the cal- 

 culation to the cube of the ellipticity but in cases where the 

 square of that fraction may be neglected, the following simple rule 

 for finding the circumference of an ellipse is worth remembering. 

 On the longer axis of the ellipse describe a circle, and between this 

 and the ellipse, describe a small circle having its centre in the pro- 

 longation of the minor axis, and touching the ellipse externally, and 



