584 Mr. H. Jeffreys on the Compression 



Fizeau's results indicate that average values of e and e 

 are given by 



e = 7 x 10- 6 -hl° C. ; e' = 2*4 x 10- 8 -f-(l o C.) 2 . 



Adopting these numbers, we find that at the surface 



K = -5'68 xlO" 3 ; 



from this the shortening of the circumference of the earth 

 by compression is at once found to be 227 km. 



A rough approximation to the average effect of the 

 compression may be made by adapting the method of 

 Rev. Osmond Fisher. The volume of rock crumpled up 

 is f 87rc( — Kr). dx, taken through the compressed layer. 

 At "the surface K= -r-5'68 x 10" 3 ; at a depth of 79 km. 

 it is zero, as also is ?3K/^A'. 



Hence, with sufficient accuracy for the present purpose 

 we can interpolate for K by the formula 



K= 



5 - 68xl0 " 3 ( 1 -79^IoJ- 



If this crumpled rock were then spread in a uniform 

 layer over the surface of the earth, the depth of it would 

 be 300 metres. 



Next, consider the exponential distribution of radio- 

 active matter. The temperature is in this case given by 



Y = mx + 



(B-^s&t+aC 1 



Put Aja 2 k=a, S_ a = /3 ; 



then a = 746°, /3 = 454°. 



Then 



~^= |€ + 2eWi^ + 6' / SErfg + e' a (l-^ 2a ^)| ^ ^"« 2 



- -^77^ [(e + 6'u)e-^ + e'mht *\2qr q2 + ir* (1 - Erf q) } 

 + e^^-^ 2 Erf^+-^(l~Erfgi/2)| 



~ € ' a ^-(5+y) 2 ~ 7i /7r(l-Erf(g + 7))}] 5 



where y=hat*. Its present value is 7'82, so that the 

 terms depending on it are small enough to be neglected. 



