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SCIENCE 



[N. S. Vol. XLIV. No. 1134 



'Introduction of Logarithms into Turkey," by 

 Lieutenant Salih Mourad, of the Turkish navy. 



'A Short Account of the Treatise, 'De Arte Log- 

 istica, ' " by Professor J. E. A. Steggall, Univer- 

 sity of St. Andrews, Dundee. 



'The First Naperian Logarithm Calculated be- 

 fore Napier," by Professor Giovanni Vacca, 

 University of Rome. 



'The Theory of Naperian Logarithms Explained 

 by Pietro Mengoli (1659)," by Professor 

 Vacca. 



'Napier's Rules and Trigonometrically Equiva- 

 lent Polygons," by Professor D. M. Y. Somer- 

 ville, Wellington University, New Zealand. 



'Bibliography of Books Exhibited at the Napier 

 Tercentenary Celebration, July, 1914," by Pro- 

 fessor R. A. Sampson, University of Edinburgh. 



'Fundamental Trigonometrical and Logarithmic 

 Tables," by Professor H. Andoyer, University 

 of Paris. 



'Edward Sang and his Logarithmic Calcula- 

 tions," by Professor C. G. Knott, University of 

 Edinburgh. 



' ' Formulae and Scheme of Calculation for the De- 

 velopment of a Function of two Variables in 

 Spherical Harmonics, ' ' by Professor J. Bausch- 

 inger, University of Strassburg. 



"Numerical Tables and Nomograms," by Pro- 

 fessor M. d'Ocagne, l'Eeole Polytechnique, 

 Paris. 



"On the Origin of Machines of Direct Multiplica- 

 tion," by Professor d'Ocagne. 



"New Table of Natural Sines," by Mrs. E. Gif- 

 ford. 



"The Arrangement of Mathematical Tables," by 

 Dr. J. R. Milne, University of Edinburgh. 



"Note on Critical Tables," by Mr. T. C. Hudson, 

 of the Nautical Almanac staff. 



"On a Possible Economy of Entries in Tables of 

 Logarithmic and Other Functions," by Pro- 

 fessor Steggall. 



"The Graphical Treatment of some Crystallo- 

 graphic Problems," by Dr. A. Hutchinson, Pem- 

 broke College, Cambridge. 



"A Method of Computing Logarithms by Simple 

 Addition," by William Schooling. 



"How to Reduce to a Minimum the Mean Error 

 of Tables," by A. K. Erlang, Copenhagen Uni- 

 versity. 



"Extension of Accuracy of Mathematical Tables 

 by Improvement of Differences," by Dr. W. F. 



'Unpublished Tables Relating to the Probability- 

 Integral," by Dr. Sheppard. 



"A Method of Finding Without the Use of Tables 

 the Number Corresponding to a given Natural 

 Logarithm," by Dr. Artemas Martin, of the U. 

 S. Coast and Geodetic Survey. 



"Approximate Determinations of the Functions 

 of an Angle, and the Converse," by Mr. H. S. 

 Gay, of Shamokin, Pa. 



' ' Life Probabilities ; on a Logarithmic Criterion 

 of Dr. Goldziher and on its Extension," by M. 

 Albert Quiquet, general secretary of the In- 

 stitute of French Actuaries. 



In addition to the above scientific papers the 

 volume includes a record of the proceedings of 

 the congress, with a list of the members, and 

 subject and name indices. 



Of particular interest is the announcement 

 of new tables, prepared or under preparation, 

 made at this congress. Mrs. Gifford has con- 

 structed and published a table to every second 

 of arc of natural sines to eight places of 

 decimals. Such tables will be increasingly in 

 demand since the larger calculating machines 

 are supplanting in many instances logarithms. 

 No little surprise is occasioned by the fact that 

 a mathematician and astronomer of the ability 

 of Professor Andoyer should have devoted sev- 

 eral years to the laborious task of computation 

 of tables. The partial fruit of this effort is 

 the publication of the logarithms of the trigo- 

 nometrical function for every ten seconds of 

 arc to fourteen places of decimals; a large 

 quarto volume of 600 pages, appearing at Paris 

 in 1911. Following this there is in course of 

 publication, evidently delayed by the war, a 

 similar table of the natural functions, to form 

 a quarto volume of about 1,000 pages. Pro- 

 fessor Andoyer contemplates further a 14-place 

 table of logarithms of numbers between 100,- 

 000 and 200,000. Another set of tables which 

 may be published, and which would render un- 

 necessary the last work mentioned, is the 

 tables of logarithms to fifteen places of the 

 natural numbers from 100,000 to 370,000 by 

 Dr. Edward Sang. The computer resided in 

 Edinburgh where he died in 1890. His tables 

 are accurate to fourteen places, and the manu- 

 script was prepared with such care that it 

 would lend itself admirably to reproduction by 

 photographic processes; to include his tables 



