30 IKON ORES OF IRON SPRINGS DISTRICT, UTAH. 
constituents. In practice a comparison of size of circles gives the 
gains or losses of any constituent against any other constituent, 
without elaborate calculation. 
Where several circles are of nearly the same size, this means that 
the constituents represented have maintained their mutual propor- 
tions during the alteration, and such maintenance of mutual propor- 
tions becomes presumptive evidence that the group has remained 
essentially constant during the alteration and that the change in 
composition has been effected by gain or loss of other constituents. 
It may be sufficient, therefore, instead of regarding each of the con- 
stituents as possible constants, to consider only those whose ratio 
circles lie near together. Thus in the present illustration the close 
grouping of the circles representing silica, alumina, and iron sug- 
gests that the constant is to be looked for in this group, and the 
conclusions then drawn as to the transfers of materials are probably 
on safer ground than they would be from assumption of constancy of 
one constituent, without taking into account the additional evidence 
afforded by the persistence of mutual relations within certain groups. 
The diagrams have been found also to have unlooked-for value in 
the recording and comparisons of long series of analyses, affording 
means for comparison of composites of series of similar alterations, 
which would involve tedious calculations by ordinary mathematics. 
To avoid confusion, it may be stated that the diagrams represent 
weight alone, and that the gains and losses of weights mean nothing 
as to change in volume, unless the density is taken into account, as 
it may be on the same diagrams by a simple graphic device. 
The attempt has been made to make the above explanation fairly 
brief and nontechnical, and not to emphasize the mathematical 
steps of the process, in order to bring to the reader the real simplicity 
and usefulness of the diagrams. They are easily grasped and under- 
stood by the student when explained empirically, but when the 
various steps in the construction of the diagrams are mathematically 
demonstrated the explanation becomes formidable to the non- 
mathematical reader. For the sake of those requiring more tech- 
nical explanation the following supplementary account is given: 
On the base figure constructed as stated above the percentage 
composition of any two rocks may be readily represented. For 
example, in PL IX, B, if the area of the whole circle be taken to 
represent a 100-unit mass of the altered rock (analysis H), then the 
proportional masses or percentages of the several constituents are 
shown by the areas of the variously colored sectors. Since the area 
of any sector varies as the arc which subtends it, the size of the sec- 
tor of any constituent is readily ascertained by laying off an arc 
proportionate to the percentage of that constituent. The propor- 
tional masses or percentages of the several constituents in a 100-unit 
