230 TJic American Geologist. October, isoo 
average observed value of /'^i(ooi) A (oio) The comparison 
can even be carried to the individual cases :/j^' (001) A(oio) 
calculated from// '(001) A (001) with crystal number four 
equals 94° 18', while the observed value is 94" 19'; 
the calculated value with number six is 94° ^ ', 
while the observed value is 94° 7' ; for number seven and num- 
ber twelve the calculated and observed values are identical; 
for number eleven the observed value is 94° 13', while the cal- 
culated value is only half a minute larger. 
Therefore it seems evident that the real value of the an- 
gle/^Xooi) A (010) is actually variable, because the position of 
the plane ^^^lo) is variable; and that its real average value 
in the locality studied is near 94° 16'. We now have the ex- 
planation of the so called "vicinal" planes; they are, in the 
case in hand, representatives of the plane^i(oio) in its varia- 
ble positions. It being once admitted that the position of the 
plane ^'"(010) really varies, it is evident that the only way to ob- 
tain a representative value is to take the average of a large 
number of determinations. 
The importance of this crystallographic measure lies in its 
bearing upon the theory of the continuity of the plagioclase 
feldspars as isomorphous mixtures of albite and anorthite. 
For, according to this theory, all the other triclinic feldspars 
must be strictly intermediate in all their characters, chemical, 
physical, and Optical, between these two end compounds. Now 
the angle /^ '(001) A (010) in albite is 93° 36', while in anorthite 
it is 94° 10'. These values are well established and at the 
present time are called in question by no one. If a labradorite 
occurs with the angle /^Xooi) A (010) greater than 94° 10' it is 
conclusive evidence of the inaccuracy of the theory. Of 
course, that a few exceptional measures of the angle should 
exceed 94° 10' could easily be explained as due to uneven sur- 
faces on _i,'-'(oio), but that a series of twenty-five measures on 
carefully selected material should give an average over 94° 10' 
is not BO easily explained. 
A comparative crystallographic study of labradorite from 
various other localities confirms very clearly the conclusion 
that the position of the face ^'•'(010) is variable, and it shows 
further that the variation is undoubtedly due to very slight 
variations in the chemical composition. 
