XXVI] FRIENDS AND ACQUAINTANCES 41 



the poor man lived and died in the conviction that astro- 

 nomers were ashamed to confess their error. Now the 

 essential point, rarely explained in popular books, is, that if 

 the earth were of exactly the same shape it is now, but did 

 not turn on its axis, then degrees of latitude at and near the 

 pole would really be shorter than those at and near the 

 equator ; but the bulging out at the equator is caused by 

 the rotation, owing to centrifugal force diminishing the force 

 of gravity there, and causing the true sphere, which gravity 

 would produce in a non-rotating fluid or flexible mass, to be 

 changed into a spheroid of greater diameter at the equator, 

 where the rotating motion is swifter, and therefore the 

 centrifugal force greater. The surface will therefore become 

 a surface of equilibrium, due to the two forces everywhere 

 acting upon it, and the direction of a plumb-line will be also 

 determined by the same two forces, and will necessarily be 

 at right angles to that surface. It follows that as the curva- 

 ture along a meridian is more rapid near the equator than 

 that of a sphere of the mean diameter of the earth, and less 

 rapid or flatter near the poles, therefore two or more plumb- 

 lines near the equator will meet at a point nearer than the 

 geometrical centre of the earth, while those near the poles 

 will meet at a point beyond the geometrical centre, and there- 

 fore the degrees near the latter, being measured on a circle 

 of longer radius, will be longer than those near the equator. 

 It appears, then, that the problem is not a geometrical one, 

 as the mere statement of the fact seems to make it, but one 

 of mechanics and the laws of motion, and what we really 

 measure is the amount of curvature on different parts of the 

 earth's surface, not an equal angle measured from its centre, 

 which is what the term degree " usually and properly 

 means. From this point of view the astronomers are all 

 wrong, since they use the term " degree " of latitude in a 

 technical sense, which is not its geometrical meaning, and 

 they very rarely explain this to their readers. Degrees of 

 latitude are dynamical, not geometrical quantities. 



This rather long digression may be considered to be out 

 of place, but it is given in order to illustrate the steps by 



