304 



Mr Glaisher, On Legendres formula for [Dec. 8, 



These deviations are of course derived from Gauss's values of 

 «/)(cc), which have been quoted in Table I. (§ 3), and on replacing 

 these by the values of {x) used in this paper, i.e. by applying the 

 differences in Table I. as corrections, we obtain the deviations 



X. Deviation. 



500,000 - 6-3 



1,000,000 + 44-2 



1,500,000 + 28-1 



2,000,000 + 43-8 



2,500,000 + 102-1 



3,000,000 + 95-6 



In order to determine more exactly the amount of the devia- 

 tions, the following table was constructed, in which the arguments 

 are the same as in Table V. 



TA.BLE YI. 



There are two slight discrepancies between Gauss's (corrected) 

 deviations and the corresponding deviations in this table, viz, 

 for .r = 1,500,000 Gauss's value is 28-1, and the value in the table 

 is 26"6, and for x = 3,000,000 there is a discrepancy amounting to 

 only 0"1. It should be stated that in the calculation of the fore- 



