Gabbroid Rocks of Minnesota . — Wi?ichell. 385 
from which the co-ordinates of Ca can be found readily to be 
— I. The area between these three points Na, K, and Ca 
(called the horizontal field) is then divided by the rectangular 
axes and by a perpendicular from Ca upon KNa into six tri- 
angles, the coordinates of the included points of which corre- 
spond to the six possible unequal relations between K, Na, and 
Ca. To represent the other four elements of an analysis he 
lays off the values Si. Al, Mg, and Fe, using the metals al- 
ways, on perpendiculars (to the plane of the paper) erected 
upon the point determined by the coordinates n : k, for the 
given analysis. These values are then projected upon a plane, 
called the vertical field, likewise perpendicular to the plane 
of the paper, and containing the median line CaA of the tri- 
angle. To obtain the abscissa for any rock, the foot A of the 
line CaA being considered zero, and the length CaA, unity, 
the relation used is (if a = abscissa required) : 
I Ca 
square root of 2 ' Ca + Na + K 
But a simpler method is to construct the horizontal field, 
as shown in plate XVI, with CaA horizontal, and project the 
points directly.* 
It is seen from the horizontal field that the olivine gabbro 
(1136), the silicoferrolyte, (960), and the troctolyte (514), have 
practically identical proportions of the metals Ca, Na and K, 
while for the diabase (954), olivine diabase (1843), S"<^1 plagio- 
clasyte (336E), the proportions vary only slightly from each 
other, and from the first three. The orthoclase gabbro (1797), 
differs notably, containing relatively more K and Na, but it 
still remains in the triangle characterized by Ca > Na> K. 
On the contrary the quartz gabbro (854G) and cordierite 
noryte (983), are found in the triangle having Na>Ca> K, the 
only notable difference being that the noryte has relatively 
m.ore K. In the vertical field it is seen that as the sodium and 
potassium relatively increase, the silica, in general, also in- 
creases ; the other elements are conspicuously irregular, but in 
general decrease as the silica increases. Iron shows the great- 
est range varying from zero to a maximum exceeding the 
*In the plate the central half only of the line CaA is represented 
as magnified to twice the original length. 
