EVALUATING THE ACCURACY OF A GRAVIMETRIC SURVEY 151 



Omitting the laborious calculations, we give the final result: 



Alo = -^go^a^20-5a^ + a^), (19) 



where a is given in fractions of Zq, 



In formula (18), replacing the value of A^q by its mean square value from 

 equation (19), we obtain 



'- P - ^^ (20) 



'10 



goa]/20-5a^+a^ 



We now find the value g^ — which is the average value of gravity for one 

 extreme point. Using the parabolic equation (13), we obtain 



2 



gm = ^j{2x-x^)dx=jgo. (21) 







From formulae (10) and (21) we find 



E'om=-^ = 1.5^. (22) 



gm^ gf. 



From formulae (15) and (21) we find 



Efm=^=Om^a\ (23) 



gm 



For the error in determining the gravity increments there will be two 

 groups of formulae: 



(1) < d < a or on the basis of formula (18) </) < /d^Q. 

 From the equations (11) and (20) 



P' 



=i(-t)- 



From the equations (16) and (20) 



2 



A^=^=fff(i-^y. (25) 



p2 ^ZlJo 



(2) zlio<p<2Zlio. 



From the equations (12) and (20) 



^-^iU*- 



2 A 



3 



P 



(26) 



