5 o4 SCIENCE PROGRESS 



excellent comparative chronology (p. 67, cf. pp. 32-3), a bibliography (pp. 68-70), 

 some notes on Indian mathematicians (pp. 35-7), a collection of extracts from 

 texts (pp. 46-50), and notable examples from the texts (pp. 51-66). The 

 amusing example 40 on p. 59 should be compared with that on pp. 148-9 of the 

 fourth edition of Mr. Rouse Ball's Short History of Mathematics. 



Philip E. B. Jourdain. 



Modern Instruments and Methods of Calculation : a Handbook of the Napier 

 Tercentenary Exhibition. Edited by E. M. Horsburgh, M.A., B.Sc, 

 Assoc. M. Inst. C.E., Lecturer in Technical Mathematics in the University 

 of Edinburgh. With the co-operation of the following committee : Herbert 

 Bell, M.A., B.Sc, G. A. Carse, M.A., D.Sc, David Gibb, M.A., B.Sc, 

 J. R. Milne. D.S. Convener: Prof. E. T. Whittaker, Sc.D., F.R.S. 

 Honorary Secretary : Cargill G. Knott, D.Sc. [Pp. viii + 343.] (London : 

 G. Bell & Sons, Ltd., and The Royal Society of Edinburgh, n.d. 6s. net.) 



As Dr. Knott has explained in his article in this quarterly for last October, this 

 Handbook was prepared for the use of those who attended the Napier Tercentenary 

 celebrations at Edinburgh in July 1914. It is only necessary here to give an account 

 of the contents of this splendidly printed volume, which is of permanent value to 

 the mathematician even from other points of view than that of historical interest. 

 "The aim of the Exhibition," we are told in the Preface, " is to do honour to one 

 whose influence on science has been singularly profound ; partly by a display 

 of relics, partly by indicating the scope of his work, but more particularly by 

 tracing what may be considered as the development of his great achievement. 

 The modern mathematical laboratory may look upon Napier as its parent." The 

 first article in the volume is a reprint (pp. 1-16) of Prof. G. A. Gibson's article 

 "Napier and the Invention of Logarithms" from the Proceedings of the Royal 

 Philosophical Society of Glasgow, and is illustrated by portraits of Napier and 

 some admirable views of Merchiston Castle. Other portraits of Napier, Babbage, 

 and Sang are also contained in this volume. The other contents, in order, are as 

 follows, where notes of more general interest are mentioned. First there is a 

 catalogue of a loan collection of objects of antiquarian interest in connection with 

 Napier's life and works, including some early portable sundials (there is a note by 

 John R. Findlay on " Portable Sundials " on pp. 20-2), calculating machines, and 

 various tables. Dr. Knott (pp. 38-47) gives a paper, reprinted from the Proc. Roy. 

 Soc. Edinburgh, on Sang's tables ; Herbert Bell and Dr. J. R. Milne give " A 

 Working List of Mathematical Tables" (pp. 47-60); Dr. W. G. Smith writes a 

 learned and interesting " Note on the Special Development of Calculating 

 Ability" (pp. 60-8); F. J. W. Whipple writes an introduction to the exhibits 

 of calculating machines (pp. 69-75); P. E. Ludgate writes on "Automatic 

 Calculating Machines" (pp. 124-7) » an d T. C. Hudson writes on " H.M. Nautical 

 Almanac Office Anti-Differencing Machine (pp. 127-31). Dr. Knott gives an 

 abridged reprint of his well-known article on the Abacus from the Trafisactions of 

 the Asiatic Society of fapan of 1886 (pp. 136-54) ; Dr. G. D. C. Stokes gives a 

 useful summary about "The Slide Rule" (pp. 155-65), and this paper is followed 

 by descriptions of various exhibits. The subjects of and exhibits of apparatus for 

 integrating, differentiating, harmonic analysis, tide prediction, equation solving, 

 plotting, and so on is dealt with in papers by Charles Tweedie, Dr. G. A. Carse 

 and J. Urquhart, Dr. A. M. Robb, Dr. J. Erskine Murray, Edward Roberts, 

 D. Gibb, and Dr. R. F. Muirhead (pp. 181-277). The Section on ruled papers 



