148 SOME APPLICATIONS OF : 
It may thus be not wholly unprofitable to glance briefly at some of 
the arguments which some of the advocates of the several theories 
base on their ideas of the properties of solid bodies. 
Mr. Taylor’s object is to get an equatorial circumference some 10 per 
cent in excess of its present value, so as to account for the lateral com- 
pression at the surface observed in mountain chains. Thus, following 
Prof. Darwin,* he supposes the earth to have once possessed a much 
greater angular velocity than at present, and speaks of a“ consistent 
crust (of some few miles thickness) ” as having formed ‘ when the rota- 
tion of our planet was at four times its present rate” (l.¢., p. 257). The 
equatorial radius would then have been, he says, some 4,359 miles, and 
the polar some 3,291. The change of shape, as the rotation fell off, 
would account, he thinks, for observed phenomena. He considers his 
conclusions opposed by Sir W. Thomson’s theory that the earth solidi- 
fied throughout and retains at least approximately its original eccen- 
tricity. Itis on this point that he refers to the data supplied by Mr. 
Herbert Spencer’s “juster physical insight;” and he adds, apparently 
as his own contribution to the argument, ‘“ the supposition that a granite 
mountain or equatorial protuberance 400 miles high or 100 miles high 
could for a moment support itself, would hardly be entertained by a 
practical engineer ;” and in a foot-note, “the limiting modulus of height 
of a granite pyramid (equalling one side of its square base) is somewhat 
less than 11 miles” (I. ¢., p. 258). I am quite ready to agree with Mr. 
Taylor that if solidification occurred under the conditions he supposes 
the eccentricity must have altered enormously and that in a non-elastic 
way, and I hardly suppose that Sir W. Thompson would oppose this 
view. No one however so far as I know, has propounded the theory 
of an elastic solid spheroidal earth of eccentricity 0.65 rotating com- 
pletely in six hours, so that the investigation of the strains and stresses 
required by such a theory is unnecessary. I can quite imagine that on 
any probable theory of density the magnitude of the strains is hardly 
likely to be consistent with the application of the mathematical theory 
of elasticity. The force of Mr. Taylor’s remarks as to the pyramid I, 
however, fail to see. Such an isolated mass exists under totally differ- 
ent conditions from any portion of a solid sphere or spheroid, and one 
might as well argue as to the impossibility of a liquid interior from the 
fact that an isolated liquid column 100 miles high has not yet been 
observed on the earth’s surface. If Mr. Taylor were however to cal- 
culate the strains and stresses in such a thin shell as he supposes, of 
material showing anything resembling the structure of ordinary rock, 
with arate of rotation such as he mentions, I very much doubt whether 
he would find it in an essentially better position than his imaginary 
pyramid, 
After this criticism Mr. Taylor considers the question of the probable 
degree of rigidity of our planet quite irrelevant, but the “temptation is 
* Phil. Trans. (1879), p. 532. 
