218 CORRECTED SEMIN VARIANT TABLES FOR THE WEIGHTS 11 AND 12. [926 
this is to be regarded, not as a seminvariant fg — b 3 e 2 (it is hardly necessary to 
remark that, here and elsewhere the — is not a minus sign, but a mere stroke), 
but as a seminvariant c 2 h — b 3 e 2 , viz. c 2 h is a term entering into the seminvariant, 
and which, although it is in AO subsequent, it is in CO precedent, to the terms 
fg, beg and bf 2 . The seminvariant contains the term — 16c 2 h and other terms with 
the letter h, and it is a misnomer to call it fg — b 3 e 2 , a name implying that the 
highest letter thereof is g. Instead of the stroke, it would perhaps be better to 
write oo, for instance c 2 h oo b 3 e 2 , Avhere of course go would be used as a mere con 
ventional symbol. 
For greater clearness, I give here the express definition of counter order, (CO), 
viz. whereas in AO we begin with the lowest letters, in CO we begin contrariwise 
with the highest letters. A term containing a higher letter or higher power of such 
letter precedes a term containing a lower letter or lower power of the same letter— 
or in the easiest form, the counter order is the alphabetical order corresponding to 
the reversed arrangement z, y, e, d, c, b of the letters. 
A symbol, as c 2 h — b 3 e 2 above, may be regarded as referring to a set of terms 
c 2 h, b 3 e~ and all the terms which are in CO subsequent to c 2 h and in AO precedent 
to b 3 e 2 : as by supposition the terms are arranged in A 0, the set includes no term 
lower than b 3 e 2 , or say the bottom term b 3 e 2 is also the final term of the set, but 
it does include terms fg, beg and bf 2 higher than c 2 h, and thus the top term fg is 
not, but c 2 h is, the initial term of the set. It should be remarked that a seminvariant 
ch — b 3 e 2 need not include all the terms of the set as just defined: there may very 
well be terms with a coefficient zero, or say accidental zeros; an instance presents 
itself, weight 10, where in the column eg — bd 3 we have Oce 2 , no term in ce 2 . 
The changes actually required are very slight, viz. 
Weight 11, instead of 
fg — b 3 e 2 , we require c 2 h — b 3 e 2 , old fg — b 3 e 2 , new named, 
c 2 h — b 3 d 2 , „ fg — b 3 d 2 , linear combination (fg — b 3 e 2 ) + 8 (c 2 h — b 3 d 2 ), 
de 2 — b 5 d 2 , „ c 3 f — b s d 2 , old de 2 — b 5 d 2 , new named, 
c 3 f — b 3 c\ „ de 2 — b 3 c 4 , linear combination (de 2 — b 5 d 2 ) + 6 (c 3 /— 6 3 c 4 ). 
Weight 12, instead of 
cf 2 — bed 3 , we require d 2 g — bed 3 , old cf 2 — bed 3 , new named, 
d 2 g — c 3 d 2 , „ cf 2 — c 3 d 2 , linear combination (cf 2 — bed 3 ) — 5 (d 2 g — c 3 d 2 ); 
but I have thought it desirable to give the complete tables for the weights in 
question, 11 and 12; and I have also rearranged the entire columns of the two 
tables so as to present in each of them the finals in AO. This is the case with 
the existing tables, except that there is a single transposition in the table weight 10.