252 Applications of Physics and Mathematics to Geology. 



have seen, none of the objections apply ; but in his § 10, in 

 order " to know how far the results .... may differ, if the 

 elastic solid be compressible," he supposes that while the 

 rigidity constant is finite the bulk modulus is very small. In 

 other words, he applies mathematical formulae which assume rj 

 nearly equal to —1. Such a value has been here regarded 

 as impossible. It should also be noticed that if tj were equal 

 — 1 then E would vanish, and if 77 be nearly —1 the value of 

 E must be very small. Thus the strains and displacements 

 given by equations (2) to (4) would in the case supposed by 

 Professor Darwin be enormously greater than even those 

 given in Table IV. I do not observe, however, that either in 

 the paper itself or in one supplementary * to it Professor 

 Darwin makes any explicit reference to the terms in the strain 

 independent of the angular coordinates, from which the equa- 

 tions (1) to (4) are derived. I am thus unable to say whether 

 his neglect of the limitations that these terms are here regarded 

 as setting to the application of the mathematical theory is 

 intentional or not. Again, in a recent paper f, "On Sir 

 William Thomson's estimate of the Rigidity of the Earth," 

 Mr. Love has also considered the problem of the earth treated 

 as an isotropic elastic sphere, more especially for the value 

 *25 of tj. In his equations (14) and (18) Mr. Love deter- 

 mines the values of two arbitrary constants which occur in the 

 terms independent of the angular coordinates ; and it is easily 

 seen that the expression he would thence obtain for these 

 terms is identical with minef . After determining the second 

 constant he, however, dismisses the subject with the remark, 

 " This .... gives the mean radial displacement, a matter 

 which need not detain us here." So far as I. can see, Mr. 

 Love makes no reference to any principle such as (0), nor to 

 the possibility of the stress-strain relation ceasing to be linear. 

 I ought also to explain that in my paper (a), directing my 

 attention solely to the theories of rupture, I left out of sight 

 any such limitation as (B) or (0), and treated the case of an 

 earth in which tj = as one in which, according to the greatest- 

 strain theory of rupture, the mathematical theory was ap- 

 plicable. I also failed to notice that the case r} = '0 was 

 sanctioned by the greatest-strain theory as well as by the 

 stress-difference theory. 



[To be continued.] 



* Proceedings of the Royal Society, vol. xxxviii. (1885), pp. 322-8. 

 t Trans. Camb. Phil. Soc. vol. xv.'pp. 107-118. 

 I (a), equation (17), p. 281. 



