FOR THE EARTH'S SURFACE. 305 



Combining these formulae we get 



dG 



where for ( - ) we must put - -j- + -j. 



\ap/ 2 |_rf/i a/a' J 



fnr /^ X ^ , ^'1 



for " " " + ' &c - 



Now if Gr, 6r +1 , &c., have the signification given them in Section I. 

 (see p. 259), each of these quantities is proportional to the differential co- 

 efficient of the one immediately preceding taken with respect to p., also 

 the highest powers of p. in these quantities are respectively n m, n m l, 

 &c., and the coefficients of these highest powers are in every case unity. 



Hence ^ (0;) = (n-m) %, 



^(<^) = (n-m)(n-m-l)6?r, &c. 



Hence if as above we denote by (6r +1 ), (Gr +3 ), &c., the means of the 

 several quantities obtained by substituting p. and p.' for //, in the respective 

 functions, we have 



(n-wi) (n-m- 1) (n-m -2) (n-m- 3) (n-m- 4) . rm+5 , , , 



J2Q \ Mr 4 r 1 / 



&c., &c., 



which is a convenient test formula for examining the values of Gr and 

 G'l by taking their difference. 



A. ii. 39 



