192 Notices respecting New Boohs. 



graphy might be compiled." A first instalment of his labours took 

 the form of a " List of Writings," which occupied 41 pages of the 

 ' Quarterly Journal of Mathematics ' (vol. xviii. pp. 110-149) : 

 this, as an offprint, was very liberally dispersed and resulted in a 

 supplemental list, of 22 pages, which was printed in the same 

 journal (vol. xxi. pp. 299-320). It is of interest to our readers to 

 note that a by-result was the note on Schweins, entitled " An 

 overlooked discoverer in the Theory of Determinants," which was 

 printed in our Journal [Phil. Mag. vol. xviii. pp. 416-427 (1884)]. 



Dr. Muir's object is twofold. To provide a work of reference 

 to all that has been written on the subject, and " which should be 

 so indexed that any one engaged in research might easily ascertain 

 exactly what had been done on any particular topic, how it 

 had been doue, and what possible developments it foreshadowed." 

 To show clearly to whom every step in advance had been due, 

 furnishing the student with the actual data on which the author's 

 conclusions were based. These tw 7 o matters have been kept well 

 in view, and the result is a work well worthy of taking rank with 

 the recent historical writings of Todhunter and others on mathe- 

 matical subjects. 



The first 100 pages consider what had been done by mathe- 

 maticians in the period 1693-1812. The prime contributors are 

 Bezout, Yandermonde, Laplace, Lagrange, Monge, Binet, and 

 Cauchy. Were the contributions of these worthies left out, 

 " there would be exceedingly little left to anyone else, and even 

 that little would be of minor interest." A glance at these names 

 shows that the writings of French mathematicians were the most 

 important in this period. Accompanying the retrospect (pp. 131 -2) 

 here given is an admirable Table, which enables the reader to run 

 down any particular result, w 7 hich marks this epoch, to its dis- 

 coverer. 



The second period analysed in this volume ranges from 1813- 

 1841. The period of "pioneering" extended to 120 years, 

 this to only 30 years or thereabouts. In the longer period we 

 have 20 papers by 13 writers, in the period before us we have 35 

 papers by 18 writers ; and these have representatives from the 

 following nationalities : — English, Italian, and Polish, in addition 

 to the previous French and German. Some of the English con- 

 tributions saw the light first in our pages : viz. Drinkwater (on 

 Simple Elimination, vol. x. 1831); S3^1vester (on Derivation of 

 Coexistence, vol. xvi. 1839) ; the same (A method of determining 

 by mere inspection the derivatives from two equations of any 

 degree, vol. xvi. 1820). 



Dr. Muir has done his work very thoroughly, and has supplied 

 all necessary aid to the student for the easy reading of a vast mass 

 of results ; and we heartily wish him equal success in the com- 

 pletion of what will possibly be the more difficult, because more 

 crowded with authors and results, period which yet lies before 

 him. It would have added to the utility of the work if the date 

 and author's name of the memoir analysed could have been fur- 

 nished at the top of each page. 



