134 



MEMOIRS NATIONAL ACADEMY OF SCIENCES. 



[Vol. XIV. 



Logarithmic. 



Table XXXVIII. 



Unit= 1 radian. 



=IwSriPr)'Qf'Ci cos Arg. +(0-Oo)IwSTjP7j'qftC„ sin Arg. +{0 -Ooyiw^riPq'QJ'td cos Arg. 

 where C^, (\, C^, represent the respective coefficients. 



COMPARISON OF TABLES. 



Table XXX. — With the aid of the manuscriiJt the source of all the discrepancies indicated 

 by brackets has been traced. Coefficients in parentheses are functions of coefficients in paren- 

 theses in Table XXVII. 



Table XXXI. — The function was computed by the fii'st of Z 81, eqs. (137), which is more 

 rigid than the one following it, which v. Zeipel used. Aside from the addition of omitted terms, 

 the bracketed coefficients are more accurate by reason of the errors in v. Zeipel's Table XVIII. 



Table XXXII. — The computation was performed according to Z 82, eqs. (139) and (140), 

 in place of eq. (141) which is less rigid. Besides the discrepancies due to the addition of omitted 

 terms, four bracketed coefficients are of opposite sign. These discrepancies may be due either 



