300 



Mr Glaisher, On Leg endre's formula for [Dec. 8, 



It will be observed that tlie values of A here found diminish 

 much less rapidly than Gauss's: in the second column the largest 

 value of A is 1'08d, the least is 1'076, and the range is 0"009 ; in 

 the third column the largest value of A is 1"090, the least is 1"072, 

 and the range is O'OIS. 



§ 4. It seemed desirable to examine whether, assuming Gauss's 

 values of {x), his values of A were correctly deduced, and I 

 accordingly recalculated the values of A to which Gauss's values of 

 ^ {x) lead and found them to be, to seven places, 



1-0904065 



1-0768193 



1-0759953 



1-0752906 



1-0717934 



1-0729731 

 It thus appears that the value for 1,500,000 should be 1-07600 

 instead of 1-07582 ; this only changes the difference from 478 to 

 460. It seems not improbable that Gauss's value was l"07o99, 

 and that in writing to Encke he inadvertently copied 82 from the 

 figures in the line above instead of 99. 



§ 5. In order to exhibit more clearly the gradual diminution 

 of ^, I have calculated the values of A corresponding to each 

 quarter-million in the first four millions. These values are given 

 in the following table. 



