between the Atomic Weizhts. 393 
The first I have called the Nine Series, the second the Eight 
Series, &c. Let us examine the doubtful points in each, com- 
mencing with the first. 
The last five members of the Nine Series are connected by 
so many analogies, that they have been invariably grouped to- 
gether in the elementary books. There can be no doubt, there- 
fore, in regard to the propriety of placing them in the same series, 
on the ground of general analogies. Fiuorine, it is trae, presents 
some striking points of difference from the rest. Fluorid of eal- 
citin is almost insoluble in water, while the chlorid, bromid, and 
iodid of calcium are all very soluble. We must, however, remem- 
ber that we have to do with series, and must not therefore expect 
to find close resemblances except between adjacent members. If, 
then, we consider that oxygen is one of the series, and that fluo- 
tine stands but one step removed from oxygen, while it is two 
Steps removed from chlorine, the discrepancy in a measure van- 
ishes, for lime CaO is but slightly soluble in water.- Nevertheless, 
the difficulty does not entirely disappear; for CaF is much less 
soluble than CaO, although it should be more soluble judging 
from the law of the series and the fact that CaCl is so much more 
soluble than CaF. 
The solubility of a series of homologous elements or com- 
pounds in water, may be regarded as a function of one or more 
variables. In the case of the elements there may be but one varia- 
ble, but it is easy to see that in the case of compounds there must 
be several. One of these variables is probably the same which 
determines the common difference of the series to which the ele- 
Ments or compounds belong ; (it will be hereafter shown that the 
atomic weights of the homologous compounds are related in the 
Same way as those of the clements;) the other variables are per- 
haps the atomic forces which determine the hardness, density, 
&c. of the solid. We may, therefore, with justice, compare the 
relative solubilities of a series of homologues to a curve which 
Should be the same function of the same variables, and what 
Mathematics teaches we ought reasonably to expect in the case of 
this curve, we ought to expect also in the variations of solubility 
of these substances. Now every mathematician is familiar with 
the remarkably rapid changes which a curve undergoes that is a 
function of several variables, and we cannot be surprised that 
Similarly rapid changes should be observed in the solubility of 
homologous substances in passing from one to the next in the 
Series. Jn the curve which corresponds to the relative solubility 
of CaO, CaF, CaCy, CaCl, CaBr, and Cal, it would seem that at 
CaF there is a singular point where the curve, after rising for some 
distance above the axis, bends down again towards it. Several 
the other series of compounds of these elements present simi- 
lar anomalies ; for example, KO, KF1, KCy, KCl, KBr, and KL 
