150 FENNELL — PURE CIRCULATING DECIMALS. [Oct. 4, 



B 



D 



C i 



f 3. If an or <p(q) = 10m + 2 and q = 10/9+3 or 10/9 -f 9, 



then 3, 6 occur m + 1 times 

 and the other digits m times 



[ each. 



f 4. Tf a?i or c?(a) = 10m + 4 and g = 10,9 + 1, then 0, 9, 3, 



6 occur m + 1 times each 

 and the other digits m times 

 each. 



5. If an or <p(q) = 10m + 4 and 5 = 10/5 4- 3, then 0, 9, 



3, 6 occur m + 1 times each, 

 and the other six digits m 

 times each. 



6. If, however, q is a multiple 



of 3, then 3, 6 occur m + 2 

 times each, and the other 

 digits m times each. 



7. If an or <p(q) = 10m + 4 and 10/9 + 7 or 10,9 + 9, then 



0, 9 occur m times each, 3, 6 



m — 1 times each and the 



i other digits m + 1 times each. 



: 8. If an or ?(o) = 10»i + 6 and q = 10,9 + 1 or 10/9 + 3, 



or 10,9 + 9, then 0, 9 occur 

 m + 1 times each, 3, 6 m + 2 

 times each and the other 

 digits m times each. 



9. If an ox w(q) = 10m + 6 and 3 = 10/9 + 7, then 0, 9, 



3, 6 occur m times each, and 

 the other digits m + 1 times 

 each. 



10. But if q == 10/9 + 7 = 35 or 



(10* + 3H then 3, 6 occur 

 >?i — 1 times each, and the 

 other digits m + 1 times each. 



11. If an or <p(q) = 10m 6 and 3= 10/5+9 = (10^+3)' 2 , 



then 0, 9, 3, 6 occur m times 

 each, and the other digits 

 m + 1 times each. 



