352 Tlw Aiiicricaii Geologist. June, isw 
I'ut if we have 
/ Group II Group 
Differences i va a n<7 m>n 
independent - 
and inverse ) ^h 7. b x<7. 
If, in passing from one group to the other the cpiantity of 
the bod\' (7 increases in proportion as the quantity /; diminishes, 
ihis relation is sufficient to estabh'sh the independence of two 
magmas. 
To make this clear: 
If b is a function of a, b may equal f {a) and especiall)' a 
decreasing- function (that is. varying in a direction contrary to 
the variable). The author considers this relation as sufficient 
to establish a chemically independent type of magma. But 
when /; is an increasing function (that is varying in the same 
direction as the variable ) /; equals p{a), this relation, which 
he calls parallel or correlative, as employed by the author 
for the sub-divisions. The choice is arbitrary. 
Starting with these ideas the author constructs curves. (See 
first, Table III at the end of the book, and especially a portion 
of this table carrying a Roman numeral II. There is a singu- 
lar disorder in these tables and in the references.) 
In order to construct these curves the author places upon 
an axis of x's the molecular proportions of SiO^ (i. e., the num- 
bers obtained from analyses in the manner of 0.828 above for 
the diabase of Assa ) and on an axis of y's the molecular propor- 
tions of the different oxides whether grouped as in the curves 
II or separately as in the other curves. The aspect of these 
curves suggests to him conclusions which are enumerated be- 
low. It is necessary to remark, here, that on the square-ruled 
paper employed one side of a square corresponds, on the axis 
of the x's to 0.0 1 of SiO- expressed in molecular proportions, 
and that o.i of the SiO- in molecular proportion corresponds to 
6. of SiO- as expressed in the chemical analyses. 
CouclusioNS (derived from tJic Curves II. 
I , The curves are fragments of right lines, with angular 
points. They differ from those of Iddings in that they express 
always the quantities of oxides and of SiO-: expressed in molec- 
ular proportions, and not the percentages of the analyses. Then 
