Notices respecting New Books. 137 



ticians of the present generation, but whom Hankel characterizes as 

 the true founder of the method of representing a complex geome- 

 trically), Cauchy, and G-rassmann. 



The years 1871, 1872 produced only five short Mathematical 

 Papers, the most considerable being an extension to tridimensional 

 space of a plane theorem of the late Mr. CotteruTs. In the Editorial 

 note to the first of these (p. 234) " nodal conic. " should be " nodal 

 cone" In 1873 appear evidences — from his translation of Niemann's 

 Essay " on the Hypotheses which He at the basis of Geometry," and 

 the " Preliminary Sketch of Biquaternions " — of Clifford's thoughts 

 having been directed to speculation on hyper-dimensional space, 

 a subject reverted to in a succession of papers down to the close 

 of his career — the last being the unfinished " Classification of Loci " 

 (Phil. Trans. 1878). On the whole of this subject Prof. H. J. S. 

 Smith's masterly analysis will be the reader's best guide. To the 

 same year belongs the first of his two contributions to the Phil. 

 Trans., " On Mr. Spottiswoode's Contact Problems." The year 

 1871, though one of great activity in other scientific directions, 

 produced no published mathematical papers ; the abstracts of his 

 communications to the British-Association Meeting showing that 

 Clifford took his part in the Peaucellier " revival " of the period, 

 and in following up the idea of bringing Chemical Equations under 

 a general formula. 



The published mathematical papers of the next three years were 

 contributions to the Mathematical Society's 'Proceedings,' those 

 which attracted most attention being : — (i.) " On the Transforma- 

 tion of Elliptic Enactions " (1875), — suggested by a paper of 

 Dr. Liiroth's in the Mathematische Annalen, Bd. I., — followed by 

 " Notes " thereon (1876), in which Darboux's priority both in 

 matter and method on certain points is acknowledged and the 

 geometric proof of the transformation-formidse is restated and 

 completed ; (ii.) " On the Canonical Eorm and Dissection of a Pde- 

 mann's Surface " — a most characteristic example of Clifford's powers 

 in its kind. But these three years produced many papers left 

 incomplete by the author and now printed as left. Some, which 

 are mere fragments, were apparently the commencements of papers 

 to be offered to the Societies or Mathematical Journals ; others are 

 more probably compilations to form the bases of courses of 

 Lectures planned, but destined never to be carried out. A 

 singular and doubly melancholy contribution to the volume is the 

 late Miss Watson's series of notes of the course of Lectures on 

 Quaternions which, as a student of University College, London, 

 she attended. This was probably the first instance of public 

 instruction in Quaternions offered in England. In Edinburgh it 

 has been for some years a recognized subject in the Mathematical 

 Curriculum, having been introduced by the late Prof. Kelland and 

 by Prof. Tait- — the most skilled adept in the method among 

 English mathematicians, and whose elementary Treatise has been 

 the source whence most of the younger mathematicians who have 



