37 



2* next less than A — 2" — 2*^ — 2 , and so on till there be no 



remainder; and-then 2"+2'"+S*-f2'+ &c. = A. 



In the second series, all the numbers in the general interval 



from 3— 3"~i 3"^! &c. i to 3"+3""'+3'""' + &c. 



+1, including those terms, may be made up by the 



following Rule. 



After 3" for the j^rs^ term put — 3"'"' for 3""' times, then 



cyphers as often, and then + 3°'"' as often. 



For the second term put — 3""" for 3"~ times, then cyphers 



as often, and then +3""^ as often ; this to be continued three 

 times. 



For the tJiird term put — S""" for 3" ' times, then cyphers 



as often, and then 4-3""' as often ; this to be continued nine 

 times. 



For the fourth term put — 3"~ for 3"~ times, then cyphers 



as often, and then +3"~ as often; this to be continued ifz2?en;y- 

 seven times. 



In general, for the r ' term put — 3"""^ for 3"~' times, then 



cyphers as often, and then +3""^ as often ; this to be con- 



r— 1 



tinned 3 times. 



Proceed thus through all the terms, and you will fill up all 



the numbers. 



But besides these two series, there are many others which 



have the same property ; of these, the two first terms must 



