PEEFACE. 
R ATHEK more than a year ago I was requested by the Syndics of the 
University Press to allow my mathematical papers to be reprinted in 
a collected form : I had great pleasure in acceding to a request so com 
plimentary to myself, and I willingly undertook the work of superintending 
the impression of them, and of adding such notes and references as might 
appear to me desirable. 
The present volume contains one hundred papers (numbered 1, 2, 3,...,100) 
originally published in the years 1841 to 1853. They are here reproduced 
nearly, but not exactly, in chronological order : and as nearly as may be 
in their original forms ; but in a few cases where the paper is con 
troversial, or where it is a translation (into French or English) of an 
English or French paper, only the title is given : there are in some few 
cases omissions which are indicated where they occur. The number is 
printed in the upper inside corner of the page ; it is intended that the 
numbers shall run consecutively through all the volumes ; and thus a paper 
can be referred to simply by its number. 
I have of course corrected obvious typographical errors, and in particular 
have freely altered punctuation, but I have not attempted to verify formulae. 
Additions are made in square brackets [ ] ; to avoid confusion with these, 
square brackets occurring in the original papers have in general been 
changed into twisted ones {}, but where they occur in a formula it was 
not always possible to make the alteration. The addition in a square 
bracket is very frequently that of a date : it appears to me that the 
proper reference to a serial work is by the number of the volume, accompanied 
by the date on the title page : the date is always useful, and, in the case 
of two or more series of a Journal or set of Transactions, we avoid the 
necessity of a reference to the series; Liouville t. I. (1850) is better than 
Liouville, Série 2, t. I. I regret that this rule has not been strictly 
followed as regards the titles of some of the earlier papers, see the remark 
at the end of the Contents. 
January 23, 1889. 
A. CAYLEY.