Gabbroid Rocks of Minnesota. — Winchell. 229 
measures (No. 14), was kindly verified by Prof. A. Lacroix, 
who found 94° 31'. The cause of the variations must be 
sought in the mineral itself; an attentative examination shows 
that while the face /(ooi) is usually perfectly plane in the feld- 
spar from Carlton peak, the face g\o\o) is sometimes slightly 
irregular, being composed of two (or, less commonly, even 
more) of the planes such as are often called "vicinal." It is 
further to be noted that these planes vary more or less in the 
angle which they make with /(ooi); in extreme cases this va- 
riation amounts even to one degree. Further, these planes, 
while sometimes about equal in size and lustre, are more com- 
monly unequal, but either one may be the larger and brighter, 
and either one may even entirely obliterate the other, without 
that fact having any visible influence upon its own position. 
Thus we find crystals showing a single image from the face 
g^{o\6) and giving an angle as high at 94° 40', and others show- , 
ing also a single image from ^'(010), and giving an angle as 
low as 93° 40', though both are quite exceptional. This prob- 
ably explains also the wide variations in the measures obtaiwed 
by other observers. 
It may be at once suggested that the same cause has opera- 
ted to produce the remarkable average, ?'. ^. that the "vicinal" 
plane forming the larger angle with /> (001) being accidentally 
more common than the other, the average is therefore consid- 
erably too high. But is this the case? As physical laws are 
so often not mathematically exact, it is conceivable that it 
should occur in rare cases, but it is contrary to reason to sup- 
pose that it could become the general rule in a hundred cases. 
Furthermore, if such a false plane could supplant the true 
cleavage plane in many cases, it could hardly at the same time 
affect the twinning plane which in the nature of the case, 
would remain parallel to the true plane. Now the albite twin- 
ning as noted elsewhere, occasionally furnishes wide lamellae 
by means of which the angle// '(001) A(ooi) can be measured 
with considerable precision. It is evident that the angle 
Pg'^ (001 ) A (010) can be very readily calculated from the angle 
//'(ooi) A (001). Indeed one-half of the latter angle is equal to 
the supplement of the former. The average value obtained 
for//'(ooi) A(ooi) was 171° 25'; the supplement of the half 
of this equals 94° i7>^', which agrees very closely with the 
