326 BUFORD JOHNSON 



Two alternative rules, based on the formulae, are given by 

 Dunlap. In cases where all of the original terms employed are 

 either positive or negative in sign, either of these two rules may 

 be used. The second is a simpler one for operation on the 

 machine. However, there are cases in which some of the terms 

 averaged are positive and some are negative, the average being 

 based on the algebraic sum of the terms. In these cases there 

 may be difficulty in the application of rules (1) and (2), A third 

 rule should be added which makes the procedure in such a case 

 unmistakable. The procedure indicated in this third rule will 

 avoid all danger of errors which may otherwise be serious. 



The three rules which satisfy all the cases arising are as follows : 



1. Add together the terms greater than the average; from the 

 sum subtract the product of the number of terms (P) so added, 

 multiplied by the average (M) ; and divide the remainder by half 

 the total number of terms in the series (1/2 N). 



2. Add together the terms which are less than the average: 

 subtract the sum from the product of the number of terms (R) 

 so added, multiplied by the average (M)] and divide the re- 

 mainder by half the number of terms in the total series (1/2 N). 



3. In cases where the average is based on the algebraic sum of 

 positive and negative terms, if this average is positive, compute 

 the mean variation in accordance with Rule (1) from the positive 

 terms which are numerically greater than the average. If the 

 average is negative in sign, compute the mean variation in ac- 

 cordance with Rule (2) from the negative terms which are 

 numerically greater than the average. 



