116 Mr Fisher, Densities of the Earth's Crust 



where a = (p 1 — /m) 8 (d — 8) (Cj + c 2 — 8) 



= (pi ~ M)f( 8 ) suppose, 

 and /3 = (<£ 2 - 9O c, (d - d) (d + c 2 - d) 



= (^-^)/( Cl ). 

 Equation (A) gives a quadratic in (8 - c x ) with the result 



2k 1 + k 2 / a -/3 (2/^-f-^) 2 



JjfCi "T" /bj 



± v |^(^+^)+^- 



It is evident that a is positive unless 8 is greater than c x + c 2l 

 that is than the whole thickness of the continental crust, which is 

 out of the question, and /3 is clearly positive. Hence if we adopt 

 the negative sign of the root we have 



c 1 = 8 + Te x + -£ + a^I h(h + h) +-£ ■ 



.•. Cj > 8 + &x + Jc 2 , 



which would make the upper layer of the continental crust greater 

 than the depth of the ocean and the whole thickness of the sub- 

 oceanic crust taken together. If there are to be two layers on the 

 side of the land, the upper layer cannot be so thick as this. Hence 

 we need not regard the negative sign of the root, and then 8 — c x 

 is positive or negative as 



a 7 ,i i s h 2 /2k 1 + k 2 \ 2 

 h (h + k 2 ) + ^>< (— L £- J ) 



k 2 

 ><ki>+ kjc 2 + '' 



4 



a 



or as -x > < 1 ; that is, as 



|i-^/(S)x/( Cl ). 



92-91 



Now 8 being the depth of the ocean varies from place to place, 

 but it is capable of measurement; while c 1} the thickness of the 

 upper layer of the continental crust, may be considered constant, 

 but cannot be measured. It must therefore be estimated with 

 reference to some assumed value of 8. If then we can show that 

 8 — c x is positive, i.e. that c x < 8, for some given value of 8, it will 

 be less than 8 for all larger values of 8, provided they do not 

 nearly approach Cj + Ci, which we have assumed with evident good 

 reason to be greater than 8. 



