PHYSICS AND MATHEMATICS TO GEOLOGY. 137 
It is obvious from Table 1 that to equal increments in 7 there corre- 
spond nearly equal increments in E; thus the numbers given above 
will enable a sufficiently close approximation to the value of E for any 
other value of 7) to be immediately written down. 
For the sake of comparison with the values found for E in some of 
the commoner materials under ordinary conditions I append the follow- 
ing data, taken from Sir W. Thomson’s article on Elasticity in the 
Encyclopedia Britannica. The units are the same as above. 
DABEE UI 
Values of E/10°. 
| 
asa Copper. Slate. Zine. uooE| Lead. 
| | 
| Highest value ..-. 2953 | 1254 1120 | 955 | 350 | 199 
| Lowest value ..... 984 | 1052 910 CRIN Bae ane | 51 
| 
This table will give a general idea of the limits within which EK may 
reasonably be expected to lie, though some of the data refer to mate- 
rial which is hardly likely to have been isotropic. It shows thatif the 
influence of the gravitational forces on the eccentricity were negligi- 
ble,—which however is not the case,—the earth, though perfectly solid 
and elastic, might reasonably be expected to display not a smaller, but 
aconsiderably greater eccentricity than 1t actually does. 
The question next arises whether the strains and stresses produced 
by the rotation are such as are consistent with the principles on which 
the application of the mathematical theory rests. In the actual case 
of the earth this question is of importance only in exceptional cireum- 
stances, owing to the preponderating influence of the gravitational 
forces; still it possesses sufficient interest to claim separate considera- 
tion. The following table gives a sufficiently close approximation to 
the numerical results obtained for the rotating body treated above, 
when for E are substituted the values which answer to the production 
by rotation alone of an eccentricity equal to that of the earth. 
TABLE III.* 
— 0 25 | 9) 
Maximum stress-difference in tons weight | 
DEW ROUALS ANG Nemes actani- occ coe oes 323 324 32 
| 
EMER DOSUSLEAIN se eetnmtainc ces cle ucaaclens 00040 | 00029 00018 
Longitudinal stress in tons per square 
inch which would produce «a strain 
equal to the greatest strain............. 26 | 23 16 
i 
*See (c) Tables 111, vil, and Ix. 
