Mr. J. W. L. Glaisher on a Class of Definite Integrals. 433 



ing to arguments between and 3 were probably interpolated 

 from Kramp's Table, and the rest calculated from (55). 



A portion* of Legendre's Traitedes Fonctions Elliptiques (Paris, 

 1826) is devoted to the discussion of indefinite integrals of the 



form I (log — J d%. Legendre writes 



T(a,z)=^(\oziy~\te; , ... (61) 



T(a, c-*)=j e~ v v a ~ l dv, 



so that 



(62) 



and therefore 



J. 



from z = Q to ar=-80. This Table 



Two Tables are given (pp. 520 and 521). Table I. contains 2Erf# 



from x = to oc = *50 at intervals of *01, to ten decimal places. The 



results in this Table should be double ofthose in the corresponding 



Table of Kramp's. I have not yet examined if this is the case 



throughout. This Table was calculated from (53) . Table II. gives 



•■ / l\ a_1 



dxi log - J from #= *80 to #=O00 at intervals of '01 ; that 



is, it gives 2 Erf (log-) 



begins about where Table I. ends; so that together they extend 

 from ErfO to about Erf (2*14) . It was calculated by quadra- 

 tures, with the exception of the last five or six values, which were 

 obtained from the continued fraction. 



At the end of the Berliner Astronomisches Jahrbuch for 1834 

 is a paper by Encke, on the method of least squares, to which 



2 



are appended two Tables. Table I. gives—— Erfc a? from x = 



to #=2*00 at intervals of *01, to seven places, with first and 



2 

 second differences. Table II. gives —j— Erfc (pec) from a?=0 to 



V 7T 



# = 3'40 at intervals of -01, and from ,2? = 3 , 40 to # = 5'00 at 

 intervals of *1, to five decimal places, with first difference, p 



2 

 being determined by the equation — — Erfc p = \ 3 so that 



p = -476 9360. The use of this Table is explained by De Morgan 



* Chapter xvii. vol. ii. 

 Phil. Mag. S. 4. Vol. 42. No. 282. Dec. 1871. 2 F 



