209 



1. Take the first digit, and having placed it below the fourth, 

 make the subtraction in the usual way, thus : 



N'=bcde . . .mn 

 a 



2. Take the first digit of N', and having placed it below the 

 fourth, eifect the subtraction, thus : 



W=cde...mn 

 -b 



3. Continue in the same way till you have effected the subtrac- 

 tion upon (ft), and you will have the rule : 



Is N'" " = ... I'm'n' divisible by 7 or 9, or by 7 and 9 at the same 

 time? then is the number N divisible too by 7 or 13, or by 7 and 13 

 at the same time. 



Ex. I. N =71491 



N' = ^ = 1421 



N"= ^1=420=7-60; 

 therefore N is divisible by 7. 



Ex. II. N =246571 



N'= 46] =46371 



N"= 



001 



N "'= _g=325 = 5 2 -13; 

 the number N is divisible by 13. 



Ex. III. N= 1,1 83530803 

 1,825 

 8,243 

 2,350 

 3,4 8 8 

 4,850 

 8,463 

 455 = 57'13; 



the proposed number N is divisible both by 7 and by 13. 



