TABLES OF THE COVARIANTS M TO W OF THE BINARY QUIN- 
TIC : FROM THE SECOND, THIRD, FIFTH, EIGHTH, NINTH 
AND TENTH MEMOIRS ON QUANTICS. 
[Arranged in the present form, 1889.] 
The binary quintic has in all (including the quintic itself and the invariants) 
23 covariants, which I have represented by the capital letters, A, B, C, ... W (alternative 
forms of two of these are denoted by Q' and S'). The covariants A, ... L, and also 
Q, Q' were given in my Second Memoir on Quantics, and except Q and Q' are 
reproduced in the present reprint thereof, 141 ; in all these I gave not only the 
literal terms actually presenting themselves, but also the terms with zero coefficients ; 
in the other covariants however, or in most of them, the terms with zero coefficients 
were omitted. It is very desirable to have in every case the complete series of literal 
terms, and in the covariants as here printed they are accordingly inserted : the number 
of terms is in each case known beforehand by the foregoing «/-table, 142, and any 
omission is thus precluded ; by means of this «/-table we have the numbers of terms 
as shown in the following list. 
I have throughout (as was done in the Ninth and Tenth Memoirs) expressed the 
literal terms in a slightly different form from that employed in the Second Memoir : 
this is done in order to show at a glance in each column the set of terms which 
contain a given power of «, and in each such set the terms which contain a given 
power of b. 
The numerical verifications are also given not only for the entire column but for 
each set of terms containing the same power of «; viz. in most cases, but not always, 
the positive and negative coefficients of a set have equal sums, which are shown by