32 IRON ORES OF IRON SPRINGS DISTRICT, UTAH. 
available 3.7 units of magnesia. Therefore, 3.7—0.95 = 2.7 repre- 
sents the number of units of magnesia lost during the alteration, 
9 7 
if silica has remained unchanged, and -^ = 0.75, or 75 per cent, 
the ratio of loss. The number of necessary operations in this 
calculation may be reduced by using in the place of 3.7 the equiva- 
lent expression 0.59X6.3. Then the formula for the ratio of loss 
, (0.59X6.3) -(0.15X6.3) r • ... , , 
becomes — ^— ' , or, eliminating common factors, 
O.o J X o.o 
0.59-0.15 ^044 rQ75sbefore 
0.59 0.59' 
Now, by construction, the diagram gives the numbers 59 and 15, 
44 
which by substraction gives 44; then ^ gives 0.75 as above; or, con- 
verting this decimal fraction into percentage gives 75 per cent as the 
loss of magnesia during the alteration. 
From the above the following rule is derived: To determine the 
percentage gain or loss of any constituent during alteration, any 
other constituent being assumed as constant, read on the radial scale 
the difference between the ratios expressed by the constant-con- 
stituent circle and the variable-constituent circle, and divide this by 
the ratio expressed by the variable-constituent circle. The result 
will be the percentage gain or loss of the variable constituent. Evi- 
dently gains will be shown by ratios greater than unity and losses 
by ratios less than unity. 
We may take up now the specific inferences which may be drawn 
from the diagrams under discussion. 
If calcium has remained constant there has been a great increase 
of all the other constituents and an increase of weight of the rock. 
If potassa be assumed constant there has been a considerable gain 
of all other constituents, except lime, in analyses I and J, and a gain 
of all other constituents, except magnesia and lime, in analysis H. 
If magnesia has remained constant there has been a loss in potassa 
and lime and a gain in other constituents in I and J, and a gain of all 
constituents except lime in H. 
If silica and alumina remain constant this has involved a loss of all 
constituents except soda. The silica and alumina constants are 
nearly the same throughout. Soda is the only substance which, 
considered constant, shows a loss of all other constituents. 
Of these various assumptions the constancy of alumina and silica 
seems to be the most probable. The conspicuous feature in the alter- 
ation is the relative increase of silica and alumina at the expense of 
calcium carbonate. This means either (1) that silica and alumina 
have been introduced from without to replace the calcite, in which 
case there may not have been any considerable change in the volume 
