338 MR. L. F. RICHARDSON: APPROXIMATE ARITHMETICAL SOLUTION 



The sum of these four 

 functions of position is given ^ 

 on the lower boundary of |( 

 Table X. Its lake and 

 point-force components have 

 been checked by plotting 

 curves and recalculating any 

 number which did not lie 

 smoothly in the series. In 

 this way an error of I'O 

 could be detected, and 

 therefore probably does not 

 exist. The multiplications 

 were made with a 20-inch 

 slide rule. Altogether I ex- 

 pect the " standard devia- 

 tion" of the errors in the 

 lower boundary values is 

 0'15 or less. 



The initial body values 

 assumed may theoretically 

 be arbitrary, but of course 

 the approximation process 

 need not be so long if they 

 are near to the correct inte- 

 gral. In this case the initial 

 body values were made equal 

 to the sum of the four 

 functions 6i// 3 , 3474i// 2 , the 

 linear function of (iii.) above, 

 and -^2 3 in the region below 

 2=0. The numbers were 

 read from graphs in a very 

 rough way. Above 2 = 

 the initial body values were 

 simply guesses. 



The preliminary stages of - H ' 

 approximation wei*e full of H 

 experimental processes which 

 did not completely succeed M 

 and are not worth describing, 



