[ 334 ] 
c Tke Operation of the Sieve. 
Count all the terms of the ferics following the 
number 3, by threes, and expunge every third 
number. Thus all the multiples of 3 are ex- 
punged. The firft uncancelled number that ap- 
pears in the feries, after 3, is 5. Expunge the 
fquare of 5. Count all the terms of the feries, 
which follow the fquare of 5, by fives, and 
expunge every fifth number, if not expunged 
before. Thus all the multiples of five are expunged, 
which were not at firft expunged, among the mul- 
tiples of 3. The next uncancelled number to 5 
is 7. Expunge the fquare of 7. Count all the 
terms of the ieries following the fquare of 7, by 
fevens, and expunge every feventh number, if not 
expunged before. Thus all the multiples of 7 are 
expunged, which were not before expunged among 
the multiples of 3 or 3. The next uncancelled 
number which is now to be found in the feries, 
after 7, is 1 1. Expunge the fquare of 1 1. Count 
all the terms of the feries, which follow the fquare 
3. 5. 7. jgf. n. 13. xS- 17. 19. p. 23. p. p. 29. 31. 
3T 37. 3#. 41. 43- AS- 47* A, 9 - 8 *- 53- * 8 - 59- 
61. #3 m- 67. 0. 71. 73. p. //. 79. p. 83. p. pi. 
89. 0x. 03. 0g. 97. 00. 101. 103. Xo$. 107. 109. xxx. 1 13. 
XX&. XX 0 . rp. i'p. Xp. 127. rf 0 . 13 1. x$ 3 . X 3 S‘ 
J 37- x 39* K 4 X. X 0 . XA 3 - xjtjf* 149- l S 1 - xg$. 157. 
of 
