402  ~——s«S-<. P. Cooke on the Numerical Relation 
The isomorphism of lithium, sodium, and potassium, is fully 
established ; but [can find no data which prove hydrogen iso- 
morphous either with them or with the metals of the other group. 
The unit of the atomic weights which has been used thins far 
throughout the table, is the double atom of hydrogen; but the 
nucleus of the Three Series is the weight of the single atom, so 
that the unit in this series is one half of the unit of the weights 
in all the other series. This fact must be kept in mind in com- 
paring the atomic weights of this with these of the other series. 
All the weights might have been made uniform by doubling them 
throughout ; but as this would not have changed the relation, and 
would have been departing from the general custom, it was 
thonght best to confine the donbling to the Three Series into 
which alone hydrogen enters. The general symbol of this series 
is 1+3n, where of course the unit is one half of that of the sym- 
bols at the head of the other series. The observed atomic weights 
will be found to correspond very closely with the theoretic 
numbers ; indeed, the two coincide, except in the case of potas- 
sium, where the difference is 0-6. This, however, it must be 
remembered, is 0°6 of the single hydrogen atom. Compared 
with the donble atom, as the weight of potassium is generally 
given, the difference amounts to but 0:3. F 
One of the most remarkable-points of the classification which 
has been now explained, is the affiliation of the series. We fin 
in chemistry, as iu other sciences, that Nature seems to abhor 
abrupt transitions, and shades off her bounding lines. Many of 
the elements, while they manifestly belong to one series, have 
properties which ally them to another. Several examples of this 
have already been noticed. In such cases, we find invariably, 
that there is a similar affiliation of the atomic weight. O all 
the elements chromitm and manganese are the most protean. 
Two atoms of these elements unite with seven atoms of oxygen 
aud form acids analogous to perchloric acid, and, as has already 
been shown, the weight of two atoms of either element falls 1to 
the Nine Series. Moreover, one atom of chromium or of man- 
ganese, unites with three atoms of oxygen, to form chrome or 
manganic acid. Chromic acid isa strong oxydizing agent, an 
resembles closely nitrous acid, and the atomic weight of chroml- 
um falls into the Six Series just below that of nitrogen. Manganle 
id, on the other hand, resembles sulphuric acid, with which it 
is isomorphous, and the atomic weight of manganese would place 
it in the Eight Series. In like manner osmium in many of its 
perties resembles platinum and the other metals with which it 
is associated in nature ; but, unlike them, it forms a very remars- 
able volatile acid, whose insupportable and suffocating odor, a 
well as composition, reminds one of the acids of the Nine Series; 
and its atomic weight seems to justify the apparent analogy- old 
