Mr. J. Brill on " Densities in tJie Earth's Crust." 95 



can be obtained from the above expression by direct integra- 

 tion. A\ r e will not write down the whole series, but only the 

 term obtained by the integration of that containing h n . The 

 other terms can be deduced from this. The value of this 

 term will be 



a d/m d(f> — — j-P n _ 2 K, 

 r n+ 1 



where 



K ={>-('-r'}^{('-^r-('-r>. 



+-+{('-¥r-('-r> 



We will now introduce the following assumptions : — 



{p l —p2)h+ ••• + (Pm-\— pm)km-l+ pmk m =aA l , 



where A 1? A 2 , . . ., A P are constant throughout the entire 

 extent of the crust. The first (p — 2) terms of our series 

 expressing the portion contributed to the value of gravity at 

 P by our solid element, may then be written 



ad / jLdcf>{C 1 + 2C 2 P l + ... +(p-2)C p - 2 ? P -z}, 

 where 



Ci = A x — A 2 -f 3 A 3 , 



C3 = Aj — ^A 3 + A 3 — ^A 4 , 



\jp-2— i^i -j 2 2 1 ^~3 3 ' ' ~t~\ *■) -A p . 



p 



The (p — l)th term of the series may be written in the 

 form 



adfLdQip-VF^G^ + TJ}, 

 where 



