FRIENDS AND ACQUAINTANCES 41 



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 spheriod 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 also be 

 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 

 which I gradually acquired confidence in my own judgment, 

 so that in dealing with any body of facts bearing upon a 

 question in dispute, if I clearly understood the nature of the 

 facts and gave the necessary attention to them, I would 

 always draw my own inferences from them, even though I 

 had men of far greater and more varied knowledge against 

 me. Thus I have never hesitated to differ from Lyell, 

 Darwin, and even Spencer, and, so far as I can judge, in all 



