PRESIDENTIAL ADDRESS. 333 
is left. This is the composition of the mineral prolectite, and the increment, 
Mg,(SiO,), is the composition of the mineral forsterite. 
If the law of valency volumes be correct the equivalence parameters of 
forsterite should be the z and y of the first three minerals, and a value z which 
is the difference between the z values of chondrodite and humite, or of humite 
and clinohumite; further, prolectite should have z and y values identical with 
those of the other four minerals and a z value which is the difference of the 
z values of chondrodite and forsterite. It is thus possible to calculate the 
equivalence parameters of forsterite and prolectite without using data deter- 
mined on these two minerals, and to compare the values so obtained with those 
calculated from the observed axial ratios of forsterite and prolectite. All the 
values referred to are given in Table III., and it will be obvious that the agree- 
ment between the calculated and the observed equivalence parameters is very 
close; as this agreement could not occur without the operation of the law of 
valency volumes, which was deduced from entirely different data, strong con- 
firmation of the accuracy of the law is provided. 
Taste III. 
Minerals WwW Axial Ratios Equivalent Parameters 2/W 
| a i) ec x yY z 
Chondrodite . . 34 | 108630: 1:3-14472| 23367 2-1510 6-7644 | 0-19895 
b 
1 
Humite ‘ : . 48 | 108021: 1 : 4:40334| 2-3343 22-1610 9-5155 | 0-19824 
Clinohumite . . 62 | 1-08028 : 1 : 5-65883) 2-3384 2-1646 12-2491 | 0-19756 
Prolectite : observed 20 | 1-0803 :1:1-8862 | 2-3130 2-1414 4-0385 | 0-19977 
Prolectite : calculated 20 | 1-0818 :1:1-8618 | 2-3365 2-1589 4-0211 | 0-19968 
1:1-1714 | 2:3426 2-1778 2-7442 | 0-19601 
1:1-1741 
Forsterite : observed 14 | 0-:9296 : 
Forsterite : calculated 14 | 0-9240 : 
2-3365 2-1589 2-7433 | 0-19585 
The several illustrations of the operation of the law of valency volumes have 
been quoted in detail for the purpose of showing how difficult it is to avoid the 
conclusion that this deduction represents some physical reality. It may be 
traced in connection with quantitative data of other kinds; during the last 
few years it has been very successfully applied by Le Bas to the interpretation of 
the molecular volumes of liquid substances. 
From what has been already said it will be seen that the great problem as 
to the relation between crystal structure and chemical constitution, of which 
the solution seems imminent, is a stereochemical one; assemblages must be built 
up in accordance with the principle of homogeneity and in some form of close- 
packing, in which each component atom of a chemical molecule is represented 
as the sole occupant of some specific solid area. The properties of these 
assemblages must also be in agreement with the crystallographic measurements 
and the X-ray photographs yielded by the substances represented. 
A brief indication may be given of what has been already effected in this 
connection. The normal paraffin hydrocarbons of the general composition 
Cn Hon +. consist of a chain of the composition (CH,)n, to each end of which 
one hydrogen atom is attached; in accordance with the principles already 
indicated, a close-packed assemblage of the empirical composition CH, can be 
constructed from carbon and hydrogen spheres of the respective volumes 4 and 
1, of such a nature that it can be divided by planes into blocks, each made 
up of strings of the composition (CH,)n, or .CH, .CH,....CH,.CH,. At each 
plane of cleavage of the assemblage hydrogen spheres can be inserted in appro- 
priate numbers so that close-packing is restored when the cleavage faces are 
brought together again; the assemblage will then have the composition 
H . (CH,)n.H, and may be geometrically partitioned into units each representing 
one molecular complex of a normal paraffin. It is noteworthy that these units 
exhibit the configurations indicated by the van ’t Hoff-Le Bel conception for 
the normal paraffins. Other assemblages can be constructed which represent 
in a similar manner the secondary and tertiary paraffins, and all these 
assemblages are of one particular geometrical type, that which corresponds to 
the chemical behaviour characteristic of the paraffins. In these assemblages 
