136 Notices respecting New Books. 



The absence of any kind of arrangement of these Papers with 

 reference either to subject or date is much to be regretted — " tan- 

 tum series juncturaque pollet." For the absence of chronological 

 order an apology is offered in the Preface ; and some amends 

 are made by a chronological Table therein drawn up, which 

 rather serves to show that the apology might have been rendered 

 needless, as far as any difficulty in assigning, with at least approxi- 

 mate accuracy, their dates to the few doubtful papers. At all 

 events, the chronological order of the greater part is clear of doubt ; 

 and had this order been followed, the effect, on a reader able to fol- 

 low intelligently and appreciatively the matter of the Papers, would 

 have been a sense of harmonious development of an almost unique 

 genius among the English mathematicians of his generation. 



Thus, in the earliest papers (contributed to the three leading ma- 

 thematical serials of this country, and covering the period from 

 1863 to the completion of his undergraduate career, with the next 

 year or two) reference is made to the higher geometrical text-books 

 only, which occupy the attention of the candidate for a good place 

 on the Tripos : they contain no strikingly new results, but x'ather re- 

 produce, with extensions and novelties of algorithm, results already 

 known. These papers are of an exclusively geometrical character. 



During the three or four years intervening between taking his 

 degree and his removal to London (1871) his mathematical commu- 

 nications were made to the Cambridge University Philosophical, and 

 London Mathematical Societies, or to Section A of the annual British 

 Association Meeting — the one exception being a geometrical paper 

 commenced in the ' Messenger,' October 1869 (erroneously assigned 

 to 1870 in the chronological list), in which he urges the greater 

 cultivation of the methods of Synthetic, or Organic, Geometry; 

 and, drolly enough, makes a reference (no doubt second-hand) to 

 St. Thomas Aquinas, of all authorities on a geometrical question ! 

 Among these papers occur two purely analytical : — the " Proof 

 that every Eational Equation has a root " (which attracted much 

 attention at the time), and the closely connected (though separated 

 by some 140 pages in the reprint) " Case of Evaporation in the 

 Order of a Resultant." In both these papers the subjects are treated 

 with a masterly conciseness. The "Lecture Notes," drawn up, as 

 we are informed, for tutorial lectures at Trinity College, Cambridge, 

 in 1870, show a gradually extended course of reading. They com- 

 mence with the emphatic words "Geometry is a physical science" 

 (probably adopted from Mill, 'Logic,' ch. xxiv.) ; and in them 

 Eiernann is for the first time quoted — a mathematician whose 

 short but brilliant career of Professor Extraordinary at Gottingen 

 had terminated in 1866, after a few years of struggle against the 

 disease which was sapping his life, as, a few years later, it was to 

 lay Clifford in his grave. There is pervading these "Notes" a 

 strong flavour of Hankel's Vorlesungen uber die complexen ZaMen 

 (1867), which probably accounts for the references to Eiemann, 

 Gauss, Argand (otherwise a name almost unknown to mathema- 



