392 J. P. Cooke on the Numerical Relation 
sent the constitution of these elements, in the same way that the 
symbol (C:H)O:, HO+n(C:H:) represents the composition of 
the volatile acids before mentioned. In the place of (C2H)Os, HO 
we have 8=-O= the weight of one atom of oxygen, and in the 
place of C2H2 we have nine. What it is that weighs nine (for 
it must be remembered that those numbers are weights) we can- 
not at present say, but it is not impossible that this will be here- 
after discovered. In order to bring the general symbol of the 
volatile acids into exact comparison with that of the Nine Series, 
we must reduce the symbols to weights, when the two formule 
ome 
46+n14, where 46=(C2H)Os,HO and 14=C:H:; 
and 8+” 9, where 8=O and 9=2. 
The numbers 46 and 14 are known to represent the weights of 
aggregations of atoms. The number 8 represents the weight of 
one oxygen atom, but we cannot as yet say what the 9 represents. 
After this comparison, it does not seem bold theorizing to suppose 
that the atoms of the members of this series are formed of an 
atom of oxygen as a nucleus, to which have been added one or 
more groups of atoms, the weight of which equals nine, or pet- 
haps one or more single atoms each weighing nine, to which the 
corresponding element has not yet been discovered. As 1t will 
be convenient to have names to denote the two terms of the 
formule which represent the constitution of the different series, 
we will call the first term, in accordance with this theory, the 
nucleus, and the number in the second term multiplied by the 
common difference of the series. 
From what has been said, it will be seen that the idea of the 
classification is that of the organic series. It is in this that the 
classification differs from those which have preceded it. Other 
authors, in grouping together the elements according to the prit- 
ciples of isomorphism, have obtained groups very similar to those 
here presented. Indeed, this could not be otherwise, since, 8S 
has been already said, the members of each series are isomorph- 
ous, while, as a general rule, to which, however, there are many 
exceptions, no isomorphism can be established between membe™ 
of different series. These groups, however, have been merely 
groups of isomorphous elements, and not series of homologues 
These general remarks will suffice to indicate the principles 
to speak of those points which are of special interest, oF pec 
may require explanation, or in regard to which there may © 
doubt. The series I have named from their common differences 
