130 LAMBERT: CONSTITUTION OF THE EARTH 



approximation to an earth of continuously varying density, and 

 sometimes it gives very nearly the same results as the hypothesis 

 of a continuously varying earth. In some problems, particularly 

 in the elasticity of the earth, the hypothesis is about our only 

 resource, since the mathematical treatment is either beyond our 

 powers or excessively complicated. 



To sum up : as far as concerns the density, we know the mean 

 density and the average surface density with some accuracy; 

 the density at a given distance from the center is not known, and 

 the prospect of determining it from its gravitational effects does 

 not seem good. Legendre's law may be taken as, on the whole, 

 the most satisfactory hypothesis, since it has a certain plausibility 

 in its physical aspects and is mathematically convenient. 



The doctrine of the earth's fluidity did not remain uncontested. 

 The idea was put forward, and supported by mathematical rea- 

 soning that the force causing the precession of the equinoxes 

 could produce the observed result only if the earth were solid or 

 at least had a very thick and ver}^ rigid crust over its molten 

 fluid interior. Even Lord Kelvin^- for a while thought the 

 argument sound but changed his view as the result of a talk with 

 Newcomb. He says under date of vSeptember, 1876: "But 

 doubt entered my mind regarding the so-and-so and so-and-so; 

 and I had not completed the night journey to Philadelphia which 

 hurried me away from our unfinished discussion before I had 

 convinced myself that they were grievously wrong. So now I 

 must request as a favor that each one of you on going home will 

 instantly turn up his or her copies of the Transactions of the 

 Royal Society for 1863 and of the first edition (1867) of Thomson 

 and Tait's 'Natural Philosophy,' Vol. i, and draw the pen 

 through," etc., etc., naming the passages to be excised. What 

 Lord Kelvin thought out that night on the train has been worked 

 out in detail and published by Darwin^ l It appears from their 



'- Mathemalical and Physical Papers 3: 320. 



^^ Darwin. On the precession of a viscous spheroid and on the remote history of the 

 earth. Phil. Trans., Part II, 170. 1879. Scientific Papers 2: 36. See also Op- 

 PENHEIM, Uber die rotation und prazession eines flussigen sphdroids. Sitzungsber. 

 Konigl. Akad. Wiss. Wien, Math, naturw. Kl. 92: 528. 1885. 



