Notices respecting JYeiv Books. 139 



It would be vain to attempt to convey in a cursory notice any 

 adequate idea of the contents of the thin folio of lithographed 

 facsimiles of the fragments on " Graphs," a subject which formed 

 one of Clifford's commuuications to the 'Proceedings' of the British 

 Association in 1875, " On the Graphical Eepresentation of Inva- 

 riants." 



To those who are acquainted with Clifford's mathematical papers, 

 it is needless to remark how invigorating, disciplinary, and sugges- 

 tive the study of them is — and that they are for the most part by 

 no means easy of reading, but, on the contrary, require a good 

 deal of hard work on the part of the reader to cover with shorter 

 steps the long strides with which he gets over his ground. The 

 reader of this collection is deeply beholden to Prof. H. J. S. Smith 

 for the lucid and helpful analysis of the contents with which he has 

 introduced them, and to Professor Cayley for his elucidatory notes 

 to many of the posthumous papers ; also to Mr. Spottiswoode, 

 P.R.S., as well for similar assistance as, we believe, for his liberality 

 in undertaking the cost of Kthographing the Fragments on Graphs. 

 The labour which Mr. Tucker has contributed as editor it is super- 

 fluous to point out; and the circumstances which induced him to 

 undertake so heavy and responsible a charge are explained in the 

 Prefatory Letter. It is the best return we can make an editor 

 for such labour in our behalf, to point out whatever imperfections 

 and errata come under observation, for amendment in the Second 

 Edition, which the interest likely to be taken in this collection may 

 be expected to call for ere long. 



[By the Editors' kindness I have been permitted to see the 

 above Review in " proof," and to append to it the few remarks 

 which follow. "Triangular" symmetry, I need hardly say, is 

 Clifford's own title to his paper, though in line 9 he writes, " I call 



rectangular symmetry." In the Bibliography I state that 



the lower date of publication is given : the Beviewer is no doubt 

 aware that alterations are frequently made by authors in their 

 papers in the interval which elapses between composition and pub- 

 lication : I think, but I am open to correction, that the paper (viii.) 

 was not published in its entirety until 1870. The Reviewer implies, 

 in writing of my remarks on p. 555, that I made the arrangement 

 without consulting any one else ; but I can assure him that these 

 two papers were submitted to the, I believe, careful consideration 

 of one of my four referees ; and it was on his advice that I took the 

 course I adopted and wrote the " very unfortunate " remarks. I 

 am now able to say that my difficulties have been cleared up, or 

 nearly so, by a young mathematician who is working on some of 

 CUfford's lines. Eor a second edition, if such should be called for, 

 the Reviewer's remarks, and any further ones he may be willing to 

 send me, will be most acceptable. — R. Tucker.] 



