52 



Mr Glaisher, Account of an Enumeration [Mar, 12, 

 Third Million. 



In my previous paper (p. 20) I remarked that tlie numbers 

 given in the "primes counted" column of my Table in the British 

 Association Report for 1872 were completely verified for the ninth 

 million by the subsequent examination of that million: but I find 

 that there are several errors in the numbers in the "primes 

 counted" column for the second million which appear in the same 

 Table : they are as follows : — 



and the total number of primes in the million is 70,433 instead of 

 70,420. 



There are two papers by Hargreave in the Philosophical Maga- 

 zine for 1849 and 1854 that relate to the distribution of primes, 

 viz. "Analytical researches concerning numbers" (Vol. xxxv., 

 pp, 36 — 53) and "On the law of prime numbers" (Ser. 4, vol. viii., 

 pp. 114 — 122). It does not appear that Hargreave made an enu- 

 meration of the whole of the first million, though he seems to have 

 counted the primes in some portions of it: the number of primes 

 for the whole million is taken from Legendre. In the second 

 paper he states that he has found, by counting, the number of 

 primes between 2,000,000 and 3,000,000 to be 67,751, and he also 



