[ 334 ] 



The Operation of the Sieve. 



Count all the terms of the feries 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 leries 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 5. The next uncancelled 

 number which is now to be found in the feries, 

 after 7, is 11. Expunge the fquare of 1 1. Count 

 all the terms of the feries, which follow the fquare 



3. 5. 7. 0. 11. 13. xg. 17. 19. fit. 23. $& z/7. 29. 31. 



S3. &. si- 2& 41- 43- &$• 47- *$• && 53- *£- M- 59- 

 61. %& ft. 67. 0£. 71. 73. /& ff. 79. fr. 83. &. %$. 



89- jgfavjgfc. jjg. 97. Sfjgf. 101. 103. ?6$. 107. 109. xtx* 113. 

 fc*£. itfi. Xi$. *p. i'j-3. rfi. 127. rj$. 131. *gs. ts$. 



*27- J 39- *#*• *$• *#$• *#/« i49« ip« r53> "*($* iS7- 



of 



