Gabbroid Rocks of Minfiesota. — WiiicJicll. 3 79 
curs, it is represented as a positive, instead of negative ab- 
scissa, taking the place in the ferromagnesian triangle of the 
nonfeldspathisable calcium oxide (<:'), which evidently cannot 
exist. 
The "excess of alumina" is determined as follows : The 
potassium oxide is combined with alumina in the feldspars 
according to the formula KAl. This alumina,* which may be 
obtained by multiplying the per cent of K^^O by 1.085 "^ay be 
called Alk; no rocks are known containing less alumina than 
Alk, that is, containing an excess of potassium. The sodium 
oxide is combined with alumina in the feldspars according to 
the formula NaAl, and this alumina, obtained similarly from 
the per cent of sodium oxide by using the multiplier 1.625, 
can be called Aln ; alumina less in amount than Alk -\- Aln is 
known only in acid rocks (e. g., certain syenytes, pantellerytes. 
etc.)t The calcium oxide in the feldspars is combined ac- 
cording to the formula CaAl- ; this alumina, obtained by af- 
fecting the per cent of calcium oxide with 1.825 as a factor, 
may be called Ale ; alumina less in amount than Alk -\- Aln -\- 
Alc is the general rule in all igneous rocks. t and the excess 
of calcium oxide {c') becomes very notable in the basic and 
ultra-basic rocks. The excess of alumina [ci) is found from the 
equation§: ;;zAl:03 — {^Alk + Aln + Ale) =^ a. But as just 
noted this excess is rare ; usually it is necessary instead to de- 
termine the amount of calcium oxide which will saturate the 
alumina after deduction of Alk and Aln. ' This may readily be 
obtained from the equation : (r=^.548[;«Ab03 — {Alk -\- Aln)\ 
Then, evidentlj/ : e' = wCaO — c. To distinguish between 
FeO and Fe^Os Lacroix || proposes to call/' the per cent, of 
FeO, and /that of Fe^Os. The summit of the triangle remains 
at /while/' is indicated by a mark in the negative ordinate. 
*Cf. Lacroix: Le Gabbro du Pallet: Service Carte Geol. Fr. Bull. 
67. 1899, p. 24. 
tin this case the excess of alumina (a) as well as the fcldspathis- 
able calcium oxide (f), inevitably lack; the excess of sodium oxide 
(«) is represented as a negative abscissa, but is laid off from a point 
on the axis y a little above the axis x. 
$The most imj)ortant exception is among the granites. uIkti.' the 
micas frequently cause an excess of alumina. 
§Inverscly the total alumina can evidently be obtained from the 
diagrams from the equation .v Al203=.--i.825r-(-i.625«-(-i.o85/;- -(- <r; a 
usually being zero. 
II A. Lacroix: loc. cit. p. 25. 
