1879.] 



the number of primes betiueen limits. 



803 



headed difference-ratio, exhibits the ratio of the difference between 

 the number of primes counted and the number given by the 

 formula to the former number ; thus for example, to four places of 

 decimals, 



TABLE V. 



It appears from the last column of this table that the differ- 

 ences between the values given by the formula and the numbers 

 of primes counted diminish relatively to the latter as x increases, 

 as should be the case, 



§ 9. Gauss compared the numbers of primes obtained by his 

 enumeration with the values given by Legendre's formula; the 

 deviations he found are as follows: — 



