e 2 







r, 2 becomes -. 

 a 



Therefore 



Results of the Contraction of a Solid Globe. 13 



dx put - = s. Then dx = adz; and when x becomes 



C € - X idx = a{ a e~ s2 d2 



which, if z > 4, = 0* 



The equation may then be written 



e " 



•{^<-^}=^-*+ !>• 



Divide by r, and neglect terms in — 2 an( l -& 



1 x , a 2 Irx A qqp a # 



2~r + 27-3^ =0886 r-^ 



3aVl 0'886a , a 



?-• 



/l_ 0-886a a*\ 

 \2 r 2rV" 



If we make a the unit, as before, and neglect the very small 



term^— r, this gives 



^ 6 ^=0-0279; 



whereas the value obtained by the fuller method was 

 x= 0*0280, which shows that this is a close approximation. 



Hence, generally, the depth of the level of no strain varies 

 nearly as a 2 , that is as the time t, more nearly as mt—nfi. 



II. 



Let z be the value of z, and x of x, at the 

 level of no strain at any time t. Then at that 

 time the shells above Z are being compressed, 



and the coefficient of linear contraction may be x f 



applied to them in the horizontal and vertical 

 dimensions separately. But we cannot so apply 

 the coefficient to the shells below Z , where the 

 shells are undergoing what Mr. Reade aptly 

 calls "compressive extension." 



From what has already been proved, it appears 



that the position of the level of no strain does 



not depend upon the numerical value of the 



coefficient of contraction; and that, if we neglect 



x 2 



-s, its distance from the centre is O 



a 2 ' 



_ 



