ADVEKTISEMENT. 
T HE present volume contains fifty-eight papers (numbered 101, 102,..., 158) 
originally published, all but two of them, in the years 1851 to 1860: 
they are here reproduced nearly but not exactly in chronological order. 
The two excepted papers are 142, Numerical Tables Supplementary to 
Second Memoir on Quantics, now first published (1889); and, 143, Tables 
of the Covariants M to W of the Binary Quintic: from the Second, 
Third, Fourth, Fifth, Eighth, Ninth and Tenth Memoirs on Quantics 
(arranged in the present form, 1889) : the determination of the finite 
number, 23, of the covariants of the quintic was made by Gordan in the 
year 1869, and the calculation of them having been completed in my 
Ninth and Tenth Memoirs, it appeared to me convenient in the present 
republication to unite together the values of all the covariants: viz. those 
of A to L are given in the Second Memoir 141, and the remainder 
M to W in the paper 143. I have added to the Third Memoir 144, in the 
notation thereof, some formulae which on account of a difference of notation 
were omitted from a former paper, 35. 
I remark that the present volume comprises the first six of the ten 
Memoirs on Quantics, viz. these are 139. 141, 144, 155, 156 and 158. 
I have, in the Notes and References, inserted a discussion of some length 
in reference to the paper 121, Note on a Question in the Theory of 
Probabilities: and also some remarks in reference to the theory of Dis 
tance developed in the Sixth Memoir on Quantics, 158. 
c. II. 
b