30 
POPULAR SCIENCE REVIEW. 
known, and the crystalline form of that compound having been 
determined, it was only necessary to determine the quantity of 
the element whose combining number was desired, which was 
capable of replacing an amount of one of the elements in the 
compound represented by the combining number of that element* 
without altering the crystalline form of the compound, in order 
to fix the required number. Thus, the crystalline forms of 
copper sulphate and iron sulphate are similar : the combining 
number of copper is 63*2 ; but the amount of iron which re- 
places this amount of copper without altering crystalline form 
is represented by the number 56. Hence 56 is the combining 
number of iron. 
If the equivalent system of notation were rigidly carried out 
Mitscherlich’s law of isomorphism, as it is termed, remained un- 
explained — a fact by itself without a place in the general theory 
of chemistry. 
The combining numbers obtained from a study of the crystal- 
line forms of compounds are generally the same as those obtained 
from analyses of gaseous compounds, and from specific heat 
determinations. There are, however, many precautions to be 
taken in the practical application of Mitscherlich’s generalization. 
If the elements be arranged in a series, beginning with 
that having the least, and ending with that having the greatest 
combining number, many very remarkable points of connection 
are made manifest between the position of an element in the 
series and the general properties — physical and chemical — of 
that element. I shall point out one or two of these relations. 
If the volumes occupied by masses proportional to the com- 
bining numbers of the elements be arranged in order, beginning 
with that element which has the smallest combining number* 
and if these numbers be compared with the combining numbers 
so arranged, it will be seen that the former numbers increase 
and decrease periodically with the latter. By representing the 
specific volumes — as they are termed — and combining numbers 
graphically by means of a curve, this periodic connection is 
rendered very manifest. Further, a connection is seen to exist 
between the positions of the elements on such a curve, and the 
physical properties of the elements. The more ductile metals 
are situated at the maximum and minimum points of the curve, 
or immediately follow those elements which are situated at 
these points. The more brittle metals are situated on the as- 
cending portions of the curve, at no great distance from the 
points at which the maxima are reached. A relation also holds 
between specific volume, position on the curve, and volatility, 
between the same data and fusibility, & c. &c. Further, a close 
periodic relation is traceable between the combining numbers 
and the chemical properties of the elements. 
