REVIEWS 



Napier Tercentenary Memorial Volume. Edited by Cargill Gilston Knott. 

 [Pp. xii + 441.] (Published for the Royal Society of Edinburgh by 

 Longmans, Green & Co., London and New York, 191 5. Price 21 s. net.) 



This volume is splendidly produced and provided with several fine plates, two of 

 which are in colour, the frontispiece being a reproduction in colour from the 

 portrait of Napier in the possession of the University of Edinburgh. It consists 

 of the Addresses and Essays communicated to the International Congress which 

 met at Edinburgh in July 1914 to celebrate the Tercentenary of the publication of 

 Napier's Description and at the end there is an account of the Congress, list of 

 members, and other matter relating to the Congress, and indexes. 



The first thirteen contributions deal with the life and work of Napier himself, 

 and constitute an exceedingly valuable addition to our knowledge of the history of 

 mathematics ; the remaining sixteen papers deal with subsequent developments 

 of the logarithmic idea, and the common feature of them is progress in methods 

 of calculation. An account of the Congress — the last International Congress held 

 before war broke out— has been given by Dr. Knott in Science Progress for 

 October 191 5, and an account of some of the papers read at the Congress was 

 given there. Here it will only be necessary to give a list of the papers and make 

 a few remarks on them. The Inaugural Address on " The Invention of Logarithms, 

 its Genesis and Growth," by Lord Moulton, is perhaps the most interesting and 

 novel of all the contributions in the volume. Lord Moulton, with his wide ex- 

 perience of inventions gained in his career at the Bar, has given a reconstruction 

 of the gradual evolution of Napier's ideas, which must be taken into account by 

 all future historians of mathematics. Prof. P. Hume Brown writes a biographical 

 paper on "John Napier of Merchiston," and Mr. George Smith writes a descrip- 

 tive article on "Merchiston Castle." The other historical papers are in order; 

 Dr. J. W. L. Glaisher, "Logarithms and Computations"; Prof. D. E. Smith, 

 "The Law of Exponents in the Sixteenth Century"; Prof. F. Cajori, "Algebra 

 in Napier's Day and alleged Prior Inventions of Logarithms"; Prof. G. A. 

 Gibson, " Napier's Logarithms and the change to Briggs's Logarithms " ; Lieut. 

 Salih Mourad, " Introduction of Logarithms into Turkey " ; Prof. J. E. A. Steggall, 

 "A Short Account of the Treatise De Arte Logistica" ; Prof. G. Vacca, "The 

 First Napierian Logarithm calculated .before Napier " ; Prof. G. Vacca, " The 

 Theory of Napierian Logarithms explained by Pietro Mongoli (1650)"; Prof. 

 D. M. Y. Sommerville, " Napier's Rules and Trigonometrically Equivalent 

 Polygons ' ; and Prof. R. A Sampson, " Bibliography of Books Exhibited at the 

 Napier Tercentenary Celebration, July 1914." The papers in the second group 

 are as follows : Prof. H. Andoyer, " Fundamental Trigonometrical and Logarithmic 

 Tables" ; Prof. C. G. Knott, "Edward Sang and his Logarithmic Calculations" ; 

 Prof. J. Bauschinger, " Formulas and Scheme of Calculation for the Development 

 of a Function of Two Variables in Spherical Harmonics"; Prof. M. d'Ocagne, 

 " Numerical Tables and Nomograms " ; Prof. M. d'Ocagne, " On the Origin of 



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