ON MATHEMATICAL TABLES. 



37 



was employed by Gauss early in the century to represent approximately 

 the number of primes inferior to x ; but his researches were not published 

 till 1863.' This integral was also used for the same purpose by 

 Tchebycheff ^ in 1848 and Hargreave ^ in 1849. 



The following table exhibits the amount of deviation between the 

 numbers of primes counted and the values given by Legendre's formula. 



The next table exhibits the deviations between the numbers of primes 

 counted and the values of li x. 



• Gauss, Werhe, t. ii. 



2 Mem de VAcad. de St. Pctcrsbonrg (Sav. Etr.) t. vi. or Lionville, t. xvii. 



• Phil. Mag. July 1849. More detailed references to those papers will be found 

 in Section V. of the Introduction to the FouHh Million, pp. 36, 37. 



