﻿no Strain within a Solid Earth, 135 



following equation : — 



(r-x)(2(r-x)x-?>) + Ze x2 \ e~*dx = Q. 



If we make x zero, the first side of this becomes negative. 



If we give x such a value as will make the first te rm 

 vanish, it becomes positive. This value is \{r— v^V — 6), or 

 to our present unit is 0*028. Hence the value of x which 

 gives the level of no strain lies between and 0*028, so that 

 ? is small, and x z and higher powers may be neglected. 

 We may therefore put 



J€~ x dx — I e~ x dx— \ e~ x dx, 

 Jo Jo 



n/ 7T 



The equation then becomes 



(7.-o:)(2(r-^>-3)+3(l + ^)(^-^) = 0; 



whence, neglecting # 2 />' 2 > 



_3 1_3n/tT 9_ 

 •- 2 r 4r 2 + 8r r 



Or, restoring the unit V^tct, 



_3 (s/4M _ s/^F (±Kt)$ 3 (±Kt) 2 \ 

 X ~2\ r 2 r* + 4 r z )' 



This differs from the expression when sphericity is not 

 considered, in the small terms. With the values 1/51° F. per 

 foot for the gradient at the surface, and 7000° F. for the 

 temperature of solidification, the depth of the level of no 

 strain was found to be 11,252 feet*. But the depth when 

 sphericity is taken account of in the cooling will be 11,071 

 feet ; so that the level of no strain is brought nearer to the 

 surface by 181 feet by this consideration. The resulting 

 difference, however, comes out so small as amply to justify 

 sphericity being neglected, as was done by Professor Darwin 

 and myself. 



It is obvious that the corrugations formed by compression 



♦ t 



Physics &c.,' 2nd edit. p. 98. 



