ON THE ERRORS WITH WHICH LOGARITHMIC 

 COMPUTATIONS ARE AFFECTED.* 



By Gael Bremiker, Ph. D. 



INTKODUCTION". 



The original of the following dissertation on the errors of 

 logarithmic computation api>earecl in 1852 as an introduction 

 to the first edition of Bremiker's six place* tables. The great 

 excellence of the paper has led many students of mathematics 

 to read it, in spite of the fact that the edition of Bremiker's 

 tables which contains it is quite inaccessible, and although the 

 difiiculties are further increased because the original is in Latin. 



Mr. P. E. Doudiia wrote out a translation of the paper in 

 1894-95, at which time lie was holding a fellowship in applied 

 mathematics in the University of Wisconsin. Mr. Doudna's 

 failing health required him to remove to Colorado, where he 

 died in February, 1900. Mr. E. F. Chandler, who was fellow 

 in applied mathematics in the University of Wisconsin in 

 1898-99, wrote out, at my suggestion, an independent transla- 

 tion of the paper. lie was furnished with a copy of Mr. Doud- 

 na's translation in order to verify his work. We deeply regret 

 that Mr. Doudna was not able to go over the present translation 

 before its publication, as his judgment would have been of 

 great value. It has seemed right, however, that the translation 

 should appear under their joint names. 



♦Translated by P. E. Doudna A. M., late Asst. Professor of Mathematics in Colorado 

 College, and E. F. Chandler, A. M., Instructor in Mathematics in the University of North 

 Dakota. 



1' 1 •"> "' \ 



